![Foreword
The long-range goal of molecular approaches to biology is to describe living systems in
terms of chemistry and physics. Over the last 70 years great progress has been made in
applying the quantum mechanical equations representing the underlying physical laws to
chemical problems involving the structures and reactions of small molecules. This work
was recognized in the awarding of the Nobel Prize in Chemistry to Walter Kohn and John
Pople in 1998. Computational studies of mesoscopic systems of biological interest have
been attempted only more recently. Classical mechanics is adequate for describing most
of the properties of these systems, and the molecular dynamics simulation method is the
most important theoretical approach used in such studies. The first molecular dynamics
simulation of a protein, the bovine pancreatic trypsin inhibitor (BPTI), was published
more than 20 years ago [1]. Although the simulation was ‘‘crude’’ by present standards,
it was important because it introduced an important conceptual change in our view of
biomolecules. The classic view of biopolymers, like proteins and nucleic acids, had been
static in character. The remarkable detail evident in the protein crystal structures available
at that time led to an image of ‘‘rigid’’ biomolecules with every atom fixed in place [2].
The molecular dynamics simulation of BPTI was instrumental in changing the static view
of the structure of biomolecules to a dynamic picture. It is now recognized that the atoms
of which biopolymers are composed are in a state of constant motion at ordinary tempera-
tures. The X-ray structure of a protein provides the average atomic positions, but the atoms
exhibit fluidlike motions of sizable amplitudes about these averages. The new understand-
ing of protein dynamics subsumed the static picture in that the average positions are still
useful for the discussion of many aspects of biomolecule function in the language of
structural chemistry. The recognition of the importance of fluctuations opened the way
for more sophisticated and accurate interpretations of functional properties.
In the intervening years, molecular dynamics simulations of biomolecules have un-
dergone an explosive development and been applied to a wide range of problems [3,4].
Two attributes of molecular dynamics simulations have played an essential role in their
increasing use. The first is that simulations provide individual particle motions as a func-
tion of time so they can answer detailed questions about the properties of a system, often
more easily than experiments. For many aspects of biomolecule function, it is these details
iii](https://image.slidesharecdn.com/82511-250722051256-fcc71c99/85/Computational-biochemistry-and-biophysics-1st-Edition-Oren-M-Becker-9-320.jpg)
![iv Foreword
that are of interest (e.g., by what pathways does oxygen get into and exit the heme pocket
in myoglobin? How does the conformational change that triggers activity of ras p21 take
place?). The second attribute is that, although the potential used in the simulations is
approximate, it is completely under the user’s control, so that by removing or altering
specific contributions to the potential, their role in determining a given property can be
examined. This is most graphically demonstrated in the calculation of free energy differ-
ences by ‘‘computer alchemy’’ in which the potential is transmuted reversibly from that
representing one system to another during a simulation [5].
There are three types of applications of molecular dynamics simulation methods in
the study of macromolecules of biological interest, as in other areas that use such simula-
tions. The first uses the simulation simply as a means of sampling configuration space.
This is involved in the utilization of molecular dynamics, often with simulated annealing
protocols, to determine or refine structures with data obtained from experiments, such as
X-ray diffraction. The second uses simulations to determine equilibrium averages, includ-
ing structural and motional properties (e.g., atomic mean-square fluctuation amplitudes)
and the thermodynamics of the system. For such applications, it is necessary that the
simulations adequately sample configuration space, as in the first application, with the
additional condition that each point be weighted by the appropriate Boltzmann factor. The
third area employs simulations to examine the actual dynamics. Here not only is adequate
sampling of configuration space with appropriate Boltzmann weighting required, but it
must be done so as to properly represent the time development of the system. For the first
two areas, Monte Carlo simulations, as well as molecular dynamics, can be utilized. By
contrast, in the third area where the motions and their development are of interest, only
molecular dynamics can provide the necessary information. The three types of applica-
tions, all of which are considered in the present volume, make increasing demands on the
simulation methodology in terms of the accuracy that is required.
In the early years of molecular dynamics simulations of biomolecules, almost all
scientists working in the field received specialized training (as graduate students and/or
postdoctoral fellows) that provided a detailed understanding of the power and limitations
of the approach. Now that the methodology is becoming more accessible (in terms of
ease of application of generally distributed programs and the availability of the required
computational resources) and better validated (in terms of published results), many people
are beginning to use simulation technology without training in the area. Molecular dynam-
ics simulations are becoming part of the ‘‘tool kit’’ used by everyone, even experimental-
ists, who wish to obtain an understanding of the structure and function of biomolecules.
To be able to do this effectively, a person must have access to sources from which he or
she can obtain the background required for meaningful applications of the simulation
methodology. This volume has an important role to play in the transition of the field
from one limited to specialists (although they will continue to be needed to improve the
methodology and extend its applicability) to the mainstream of molecular biology. The
emphasis on an in-depth description of the computational methodology will make the
volume useful as an introduction to the field for many people who are doing simulations
for the first time. They will find it helpful also to look at two earlier volumes on macro-
molecular simulations [3,4], as well as the classic general text on molecular dynamics
[6]. Equally important in the volume is the connection made with X-ray, neutron scatter-
ing, and nuclear magnetic resonance experiments, areas in which molecular dynamics
simulations are playing an essential role. A number of well-chosen ‘‘special topics’’ in-
volving applications of simulation methods are described. Also, several chapters broaden](https://image.slidesharecdn.com/82511-250722051256-fcc71c99/85/Computational-biochemistry-and-biophysics-1st-Edition-Oren-M-Becker-10-320.jpg)
![1
Introduction
Oren M. Becker
Tel Aviv University, Tel Aviv, Israel
Alexander D. MacKerell, Jr.
University of Maryland, Baltimore, Maryland
Benoı̂t Roux
Weill Medical College of Cornell University, New York, New York
Masakatsu Watanabe*
Moldyn, Inc., Cambridge, Massachusetts
I. INTRODUCTION
The first hints of the chemical basis of life were noted approximately 150 years ago.
Leading up to this initial awareness were a series of insights that living organisms comprise
a hierarchy of structures: organs, which are composed of individual cells, which are them-
selves formed of organelles of different chemical compositions, and so on. From this
realization and the observation that nonviable extracts from organisms such as yeast could
by themselves catalyze chemical reactions, it became clear that life itself was the result
of a complex combination of individual chemicals and chemical reactions. These advances
stimulated investigations into the nature of the molecules responsible for biochemical
reactions, culminating in the discovery of the genetic code and the molecular structure of
deoxyribonucleic acid (DNA) in the early 1950s by Watson and Crick [1]. One of the
most fascinating aspects of their discovery was that an understanding of the mechanism
by which the genetic code functioned could not be achieved until knowledge of the three-
dimensional (3D) structure of DNA was attained. The discovery of the structure of DNA
and its relationship to DNA function had a tremendous impact on all subsequent biochemi-
cal investigations, basically defining the paradigm of modern biochemistry and molecular
biology. This established the primary importance of molecular structure for an understand-
ing of the function of biological molecules and the need to investigate the relationship
between structure and function in order to advance our understanding of the fundamental
processes of life.
As the molecular structure of DNA was being elucidated, scientists made significant
contributions to revealing the structures of proteins and enzymes. Sanger [2] resolved the
* Current affiliation: Wavefunction, Inc., Irvine, California.
1](https://image.slidesharecdn.com/82511-250722051256-fcc71c99/85/Computational-biochemistry-and-biophysics-1st-Edition-Oren-M-Becker-19-320.jpg)
![2 Becker et al.
primary sequence of insulin in 1953, followed by that of an enzyme, ribonuclease A, 10
years later. The late 1950s saw the first high resolution 3D structures of proteins, myoglo-
bin and hemoglobin, as determined by Kendrew et al. [3] and Perutz et al. [4], respectively,
followed by the first 3D structure of an enzyme, lysozyme, by Phillips and coworkers [5]
in 1965. Since then, the structures of a very large number of proteins and other biological
molecules have been determined. There are currently over 10,000 3D structures of proteins
available [6] along with several hundred DNA and RNA structures [7] and a number of
protein–nucleic acid complexes.
Prior to the elucidation of the 3D structure of proteins via experimental methods,
theoretical approaches made significant inroads toward understanding protein structure. One
of the most significant contributions was made by Pauling and Corey [8] in 1951, when
they predicted the existence of the main elements of secondary structure in proteins, the
α-helix and β-sheet. Their prediction was soon confirmed by Perutz [9], who made the
first glimpse of the secondary structure at low resolution. This landmark work by Pauling
and Corey marked the dawn of theoretical studies of biomolecules. It was followed by
prediction of the allowed conformations of amino acids, the basic building block of proteins,
in 1963 by Ramachandran et al. [10]. This work, which was based on simple hard-sphere
models, indicated the potential of computational approaches as tools for understanding the
atomic details of biomolecules. Energy minimization algorithms with an explicit potential
energy function followed readily to assist in the refinement of model structures of peptides
by Scheraga [11] and of crystal structures of proteins by Levitt and Lifson [12].
The availability of the first protein structures determined by X-ray crystallography
led to the initial view that these molecules were very rigid, an idea consistent with the
lock-and-key model of enzyme catalysis. Detailed analysis of protein structures, however,
indicated that proteins had to be flexible in order to perform their biological functions.
For example, in the case of myoglobin and hemoglobin, there is no path for the escape
of O2 from the heme-binding pocket in the crystal structure; the protein must change
structure in order for the O2 to be released. This and other realizations lead to a rethinking
of the properties of proteins, which resulted in a more dynamic picture of protein structure.
Experimental methods have been developed to investigate the dynamic properties of pro-
teins; however, the information content from these studies is generally isotropic in nature,
affording little insight into the atomic details of these fluctuations [13]. Atomic resolution
information on the dynamics of proteins as well as other biomolecules and the relationship
of dynamics to function is an area where computational studies can extend our knowledge
beyond what is accessible to experimentalists.
The first detailed microscopic view of atomic motions in a protein was provided in
1977 via a molecular dynamics (MD) simulation of bovine pancreatic trypsin inhibitor
by McCammon et al. [14]. This work, marking the beginning of modern computational
biochemistry and biophysics, has been followed by a large number of theoretical investiga-
tions of many complex biomolecular systems. It is this large body of work, including the
numerous methodological advances in computational studies of biomolecules over the last
decade, that largely motivated the production of the present book.
II. OVERVIEW OF COMPUTATIONAL BIOCHEMISTRY
AND BIOPHYSICS
Although the dynamic nature of biological molecules has been well accepted for over
20 years, the extent of that flexibility, as manifested in the large structural changes that](https://image.slidesharecdn.com/82511-250722051256-fcc71c99/85/Computational-biochemistry-and-biophysics-1st-Edition-Oren-M-Becker-20-320.jpg)
![Introduction 3
biomolecules can undergo, has recently become clearer due to the availability of experi-
mentally determined structures of the same biological molecules in different environments.
For example, the enzyme triosephosphate isomerase contains an 11 amino acid residue
loop that moves by more than 7 Å following the binding of substrate, leading to a catalyti-
cally competent structure [15,16]. In the enzyme cytosine-5-methyltransferase, a loop con-
taining one of the catalytically essential residues undergoes a large conformational change
upon formation of the DNA–coenzyme–protein complex, leading to some residues chang-
ing position by over 20 Å [17]. DNA, typically envisioned in the canonical B form [18],
has been shown to undergo significant distortions upon binding to proteins. Bending of
90° has been seen in the CAP–DNA complex [19], and binding of the TATA box binding
protein to the TATAAAA consensus sequence leads to the DNA assuming a unique con-
formation referred to as the TA form [20]. Even though experimental studies can reveal
the end points associated with these conformational transitions, these methods typically
cannot access structural details of the pathway between the end points. Such information
is directly accessible via computational approaches.
Computational approaches can be used to investigate the energetics associated with
changes in both conformation and chemical structure. An example is afforded by the
conformational transitions discussed in the preceding paragraph. Conformational free en-
ergy differences and barriers can be calculated and then directly compared with experimen-
tal results. Overviews of these methods are included in Chapters 9 and 10. Recent advances
in techniques that combine quantum mechanical (QM) approaches with molecular me-
chanics (MM) now allow for a detailed understanding of processes involving bond break-
ing and bond making and how enzymes can accelerate those reactions. Chapter 11 gives
a detailed overview of the implementation and current status of QM/MM methods. The
ability of computational biochemistry to reveal the microscopic events controlling reaction
rates and equilibrium at the atomic level is one of its greatest strengths.
Biological membranes provide the essential barrier between cells and the organelles
of which cells are composed. Cellular membranes are complicated extensive biomolecular
sheetlike structures, mostly formed by lipid molecules held together by cooperative nonco-
valent interactions. A membrane is not a static structure, but rather a complex dynamical
two-dimensional liquid crystalline fluid mosaic of oriented proteins and lipids. A number
of experimental approaches can be used to investigate and characterize biological mem-
branes. However, the complexity of membranes is such that experimental data remain
very difficult to interpret at the microscopic level. In recent years, computational studies
of membranes based on detailed atomic models, as summarized in Chapter 21, have greatly
increased the ability to interpret experimental data, yielding a much-improved picture of
the structure and dynamics of lipid bilayers and the relationship of those properties to
membrane function [21].
Computational approaches are now being used to facilitate the experimental determi-
nation of macromolecular structures by aiding in structural refinement based on either
nuclear magnetic resonance (NMR) or X-ray data. The current status of the application
of computational methods to the determination of biomolecular structure and dynamics
is presented in Chapters 12 and 13. Computational approaches can also be applied in
situations where experimentally determined structures are not available. With the rapid
advances in gene technology, including the human genome project, the ability of computa-
tional approaches to accurately predict 3D structures based on primary sequence represents
an area that is expected to have a significant impact. Prediction of the 3D structures of
proteins can be performed via homology modeling or threading methods; various ap-
proaches to this problem are presented in Chapters 14 and 15. Related to this is the area](https://image.slidesharecdn.com/82511-250722051256-fcc71c99/85/Computational-biochemistry-and-biophysics-1st-Edition-Oren-M-Becker-21-320.jpg)
![4 Becker et al.
of protein folding. As has been known since the seminal experimental refolding studies
of ribonuclease A in the 1950s, the primary structure of many proteins dictates their 3D
structure [22]. Accordingly, it should be possible ‘‘in principle’’ to compute the 3D struc-
ture of many proteins based on knowledge of just their primary sequences. Although this
has yet to be achieved on a wide scale, considerable efforts are being made to attain this
goal, as overviewed in Chapter 17.
Drug design and development is another area of research where computational bio-
chemistry and biophysics are having an ever-increasing impact. Computational approaches
can be used to aid in the refinement of drug candidates, systematically changing a drug’s
structure to improve its pharmacological properties, as well as in the identification of novel
lead compounds. The latter can be performed via the identification of compounds with a
high potential for activity from available databases of chemical compounds or via de novo
drug design approaches, which build totally novel ligands into the binding sites of target
molecules. Techniques used for these types of studies are presented in Chapter 16. In
addition to aiding in the design of compounds that target specific molecules, computational
approaches offer the possibility of being able to improve the ability of drugs to access their
targets in the body. These gains will be made through an understanding of the energetics
associated with the crossing of lipid membranes and using the information to rationally
enhance drug absorption rates. As evidenced by the recent contribution of computational
approaches in the development of inhibitors of the HIV protease, many of which are
currently on the market, it can be expected that these methods will continue to have an
increasing role in drug design and development.
Clearly, computational and theoretical studies of biological molecules have ad-
vanced significantly in recent years and will progress rapidly in the future. These advances
have been partially fueled by the ever-increasing number of available structures of pro-
teins, nucleic acids, and carbohydrates, but at the same time significant methodological
improvements have been made in the area of physics relevant to biological molecules.
These advances have allowed for computational studies of biochemical processes to be
performed with greater accuracy and under conditions that allow for direct comparison
with experimental studies. Examples include improved force fields, treatment of long-
range atom–atom interactions, and a variety of algorithmic advances, as covered in Chap-
ters 2 through 8. The combination of these advances with the exponential increases in
computational resources has greatly extended and will continue to expand the applicability
of computational approaches to biomolecules.
III. SCOPE OF THE BOOK
The overall scope of this book is the implementation and application of available theoreti-
cal and computational methods toward understanding the structure, dynamics, and function
of biological molecules, namely proteins, nucleic acids, carbohydrates, and membranes.
The large number of computational tools already available in computational chemistry
preclude covering all topics, as Schleyer et al. are doing in The Encyclopedia of Computa-
tional Chemistry [23]. Instead, we have attempted to create a book that covers currently
available theoretical methods applicable to biomolecular research along with the appro-
priate computational applications. We have designed it to focus on the area of biomolecu-
lar computations with emphasis on the special requirements associated with the treatment
of macromolecules.](https://image.slidesharecdn.com/82511-250722051256-fcc71c99/85/Computational-biochemistry-and-biophysics-1st-Edition-Oren-M-Becker-22-320.jpg)
![Introduction 5
Part I provides an introduction to the field of computational biochemistry and bio-
physics for nonspecialists, with the later chapters in Part I presenting more advanced
techniques that will be of interest to both the nonspecialist and the more advanced reader.
Part II presents approaches to extract information from computational studies for the inter-
pretation of experimental data. Part III focuses on methods for modeling and designing
molecules. Chapters 14 and 15 are devoted to the determination and modeling of protein
structures based on limited available experimental information such as primary sequence.
Chapter 16 discusses the recent developments in computer-aided drug designs. The algo-
rithms presented in Part III will see expanding use as the fields of genomics and bioinfor-
matics continue to evolve. The final section, Part IV, presents a collection of overviews
of various state-of-the-art theoretical methods and applications in specific areas relevant
to biomolecules: protein folding (Chapter 17), protein simulation (Chapter 18), chemical
process in solution (Chapter 19), nucleic acids simulation (Chapter 20), and membrane
simulation (Chapter 21).
In combination, the book should serve as a useful reference for both theoreticians
and experimentalists in all areas of biophysical and biochemical research. Its content repre-
sents progress made over the last decade in the area of computational biochemistry and
biophysics. Books by Brooks et al. [24] and McCammon and Harvey [25] are recom-
mended for an overview of earlier developments in the field. Although efforts have been
made to include the most recent advances in the field along with the underlying fundamen-
tal concepts, it is to be expected that further advances will be made even as this book is
being published. To help the reader keep abreast of these advances, we present a list of
useful WWW sites in the Appendix.
IV. TOWARD A NEW ERA
The 1998 Nobel Prize in Chemistry was given to John A. Pople and Walter Kohn for
their work in the area of quantum chemistry, signifying the widespread acceptance of
computation as a valid tool for investigating chemical phenomena. With its extension to
bimolecular systems, the range of possible applications of computational chemistry was
greatly expanded. Though still a relatively young field, computational biochemistry and
biophysics is now pervasive in all aspects of the biological sciences. These methods have
aided in the interpretation of experimental data, and will continue to do so, allowing for
the more rational design of new experiments, thereby facilitating investigations in the
biological sciences. Computational methods will also allow access to information beyond
that obtainable via experimental techniques. Indeed, computer-based approaches for the
study of virtually any chemical or biological phenomena may represent the most powerful
tool now available to scientists, allowing for studies at an unprecedented level of detail.
It is our hope that the present book will help expand the accessibility of computational
approaches to the vast community of scientists investigating biological systems.
REFERENCES
1. JD Watson, FHC Crick. Nature 171:737, 1953.
2. F Sanger. Annu Rev Biochem 57:1, 1988.](https://image.slidesharecdn.com/82511-250722051256-fcc71c99/85/Computational-biochemistry-and-biophysics-1st-Edition-Oren-M-Becker-23-320.jpg)
![2
Atomistic Models and Force Fields
Alexander D. MacKerell, Jr.
University of Maryland, Baltimore, Maryland
I. INTRODUCTION
Central to the success of any computational approach to the study of chemical systems
is the quality of the mathematical model used to calculate the energy of the system as a
function of its structure. For smaller chemical systems studied in the gas phase, quantum
mechanical (QM) approaches are appropriate. The success of these methods was empha-
sized by the selection of John A. Pople and Walter Kohn as winners of the 1998 Nobel
prize in chemistry. These methods, however, are typically limited to systems of approxi-
mately 100 atoms or less, although approaches to treat large systems are under develop-
ment [1]. Systems of biochemical or biophysical interest typically involve macromolecules
that contain 1000–5000 or more atoms plus their condensed phase environment. This can
lead to biochemical systems containing 20,000 atoms or more. In addition, the inherent
dynamical nature of biochemicals and the mobility of their environments [2,3] require
that large number of conformations, generated via various methods (see Chapters 3, 4, 6,
and 10), be subjected to energy calculations. Thus, an energy function is required that
allows for 106
or more energy calculations on systems containing on the order of 105
atoms.
Empirical energy functions can fulfill the demands required by computational stud-
ies of biochemical and biophysical systems. The mathematical equations in empirical en-
ergy functions include relatively simple terms to describe the physical interactions that
dictate the structure and dynamic properties of biological molecules. In addition, empirical
force fields use atomistic models, in which atoms are the smallest particles in the system
rather than the electrons and nuclei used in quantum mechanics. These two simplifications
allow for the computational speed required to perform the required number of energy
calculations on biomolecules in their environments to be attained, and, more important,
via the use of properly optimized parameters in the mathematical models the required
chemical accuracy can be achieved. The use of empirical energy functions was initially
applied to small organic molecules, where it was referred to as molecular mechanics [4],
and more recently to biological systems [2,3].
7](https://image.slidesharecdn.com/82511-250722051256-fcc71c99/85/Computational-biochemistry-and-biophysics-1st-Edition-Oren-M-Becker-25-320.jpg)
Computational biochemistry and biophysics 1st Edition Oren M. Becker
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- 5. Computational biochemistry and biophysics 1st Edition Oren M. Becker Digital Instant Download Author(s): Oren M. Becker, Alexander D. MacKerell Jr., Benoit Roux, Masakatsu Watanabe ISBN(s): 9780824704551, 082470455X Edition: 1st File Details: PDF, 5.33 MB Year: 2001 Language: english
- 8. ISBN: 0-8247-0455-X This book is printed on acid-free paper. Headquarters Marcel Dekker, Inc. 270 Madison Avenue, New York, NY 10016 tel: 212-696-9000; fax: 212-685-4540 Eastern Hemisphere Distribution Marcel Dekker AG Hutgasse 4, Postfach 812, CH-4001 Basel, Switzerland tel: 41-61-261-8482; fax: 41-61-261-8896 World Wide Web http://www.dekker.com The publisher offers discounts on this book when ordered in bulk quantities. For more information, write to Special Sales/Professional Marketing at the headquarters address above. Copyright 2001 by Marcel Dekker, Inc. All Rights Reserved. Neither this book nor any part may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, microfilming, and recording, or by any informa- tion storage and retrieval system, without permission in writing from the publisher. Current printing (last digit): 10 9 8 7 6 5 4 3 2 1 PRINTED IN THE UNITED STATES OF AMERICA
- 9. Foreword The long-range goal of molecular approaches to biology is to describe living systems in terms of chemistry and physics. Over the last 70 years great progress has been made in applying the quantum mechanical equations representing the underlying physical laws to chemical problems involving the structures and reactions of small molecules. This work was recognized in the awarding of the Nobel Prize in Chemistry to Walter Kohn and John Pople in 1998. Computational studies of mesoscopic systems of biological interest have been attempted only more recently. Classical mechanics is adequate for describing most of the properties of these systems, and the molecular dynamics simulation method is the most important theoretical approach used in such studies. The first molecular dynamics simulation of a protein, the bovine pancreatic trypsin inhibitor (BPTI), was published more than 20 years ago [1]. Although the simulation was ‘‘crude’’ by present standards, it was important because it introduced an important conceptual change in our view of biomolecules. The classic view of biopolymers, like proteins and nucleic acids, had been static in character. The remarkable detail evident in the protein crystal structures available at that time led to an image of ‘‘rigid’’ biomolecules with every atom fixed in place [2]. The molecular dynamics simulation of BPTI was instrumental in changing the static view of the structure of biomolecules to a dynamic picture. It is now recognized that the atoms of which biopolymers are composed are in a state of constant motion at ordinary tempera- tures. The X-ray structure of a protein provides the average atomic positions, but the atoms exhibit fluidlike motions of sizable amplitudes about these averages. The new understand- ing of protein dynamics subsumed the static picture in that the average positions are still useful for the discussion of many aspects of biomolecule function in the language of structural chemistry. The recognition of the importance of fluctuations opened the way for more sophisticated and accurate interpretations of functional properties. In the intervening years, molecular dynamics simulations of biomolecules have un- dergone an explosive development and been applied to a wide range of problems [3,4]. Two attributes of molecular dynamics simulations have played an essential role in their increasing use. The first is that simulations provide individual particle motions as a func- tion of time so they can answer detailed questions about the properties of a system, often more easily than experiments. For many aspects of biomolecule function, it is these details iii
- 10. iv Foreword that are of interest (e.g., by what pathways does oxygen get into and exit the heme pocket in myoglobin? How does the conformational change that triggers activity of ras p21 take place?). The second attribute is that, although the potential used in the simulations is approximate, it is completely under the user’s control, so that by removing or altering specific contributions to the potential, their role in determining a given property can be examined. This is most graphically demonstrated in the calculation of free energy differ- ences by ‘‘computer alchemy’’ in which the potential is transmuted reversibly from that representing one system to another during a simulation [5]. There are three types of applications of molecular dynamics simulation methods in the study of macromolecules of biological interest, as in other areas that use such simula- tions. The first uses the simulation simply as a means of sampling configuration space. This is involved in the utilization of molecular dynamics, often with simulated annealing protocols, to determine or refine structures with data obtained from experiments, such as X-ray diffraction. The second uses simulations to determine equilibrium averages, includ- ing structural and motional properties (e.g., atomic mean-square fluctuation amplitudes) and the thermodynamics of the system. For such applications, it is necessary that the simulations adequately sample configuration space, as in the first application, with the additional condition that each point be weighted by the appropriate Boltzmann factor. The third area employs simulations to examine the actual dynamics. Here not only is adequate sampling of configuration space with appropriate Boltzmann weighting required, but it must be done so as to properly represent the time development of the system. For the first two areas, Monte Carlo simulations, as well as molecular dynamics, can be utilized. By contrast, in the third area where the motions and their development are of interest, only molecular dynamics can provide the necessary information. The three types of applica- tions, all of which are considered in the present volume, make increasing demands on the simulation methodology in terms of the accuracy that is required. In the early years of molecular dynamics simulations of biomolecules, almost all scientists working in the field received specialized training (as graduate students and/or postdoctoral fellows) that provided a detailed understanding of the power and limitations of the approach. Now that the methodology is becoming more accessible (in terms of ease of application of generally distributed programs and the availability of the required computational resources) and better validated (in terms of published results), many people are beginning to use simulation technology without training in the area. Molecular dynam- ics simulations are becoming part of the ‘‘tool kit’’ used by everyone, even experimental- ists, who wish to obtain an understanding of the structure and function of biomolecules. To be able to do this effectively, a person must have access to sources from which he or she can obtain the background required for meaningful applications of the simulation methodology. This volume has an important role to play in the transition of the field from one limited to specialists (although they will continue to be needed to improve the methodology and extend its applicability) to the mainstream of molecular biology. The emphasis on an in-depth description of the computational methodology will make the volume useful as an introduction to the field for many people who are doing simulations for the first time. They will find it helpful also to look at two earlier volumes on macro- molecular simulations [3,4], as well as the classic general text on molecular dynamics [6]. Equally important in the volume is the connection made with X-ray, neutron scatter- ing, and nuclear magnetic resonance experiments, areas in which molecular dynamics simulations are playing an essential role. A number of well-chosen ‘‘special topics’’ in- volving applications of simulation methods are described. Also, several chapters broaden
- 11. Foreword v the perspective of the book by introducing approaches other than molecular dynamics for modeling proteins and their interactions. They make the connection with what many peo- ple regard—mistakenly, in my view—as ‘‘computational biology.’’ Certainly with the announced completion of a description of the human genome in a coarse-grained sense, the part of computational biology concerned with the prediction of the structure and func- tion of gene products from a knowledge of the polypeptide sequence is an important endeavor. However, equally important, and probably more so in the long run, is the bio- physical aspect of computational biology. The first set of Investigators in Computational Biology chosen this year demonstrates that the Howard Hughes Foundation recognized the importance of such biophysical studies to which this volume serves as an excellent introduction. I am very pleased to have been given the opportunity to contribute a Foreword to this very useful book. It is a particular pleasure for me to do so because all the editors and fifteen of the authors are alumni of my research group at Harvard, where molecular dynamics simulations of biomolecules originated. REFERENCES 1. JA McCammon, BR Gelin, and M Karplus. Nature 267:585, 1977. 2. DC Phillips. In: RH Sarma, ed. Biomolecular Stereodynamics, II. Guilderland, New York: Ade- nine Press, 1981, p 497. 3. JA McCammon and S Harvey. Dynamics of Proteins and Nucleic Acids. Cambridge: Cambridge University Press, 1987. 4. CL Brooks III, M Karplus, and BM Pettitt. Proteins: A Theoretical Perspective of Dynamics, Structure, and Thermodynamics. New York: John Wiley & Sons, 1988. 5. For an early example, see J Gao, K Kuczera, B Tidor, and M Karplus. Science 244:1069–1072, 1989. 6. MP Allen and DJ Tildesley. Computer Simulations of Liquids. Oxford: Clarendon Press, 1987. Martin Karplus Laboratoire de chimie Biophysique, ISIS Université Louis Pasteur Strasbourg, France and Department of Chemistry and Chemical Biology Harvard University Cambridge, Massachusetts
- 13. Preface The first dynamical simulation of a protein based on a detailed atomic model was reported in 1977. Since then, the uses of various theoretical and computational approaches have contributed tremendously to our understanding of complex biomolecular systems such as proteins, nucleic acids, and bilayer membranes. By providing detailed information on biomolecular systems that is often experimentally inaccessible, computational approaches based on detailed atomic models can help in the current efforts to understand the relation- ship of the structure of biomolecules to their function. For that reason, they are now considered to be an integrated and essential component of research in modern biology, biochemistry, and biophysics. A number of books and journal articles reviewing computational methods relevant to biophysical problems have been published in the last decade. Two of the most popular texts, however, were published more than ten years ago: those of McCammon and Harvey in 1987 and Brooks, Karplus, and Pettitt in 1988. There has been significant progress in theoretical and computational methodologies since the publication of these books. There- fore, we feel that there is a need for an updated, comprehensive text including the most recent developments and applications in the field. In recent years the significant increase in computer power along with the implemen- tation of a wide range of theoretical methods into sophisticated simulation programs have greatly expanded the applicability of computational approaches to biological systems. The expansion is such that interesting applications to important and complex biomolecular systems are now often carried out by researchers with no special training in computational methodologies. To successfully apply computational approaches to their systems of inter- est, these ‘‘nonspecialists’’ must make several important choices about the proper methods and techniques for the particular question that they are trying to address. We believe that a good understanding of the theory behind the myriad of computational methods and techniques can help in this process. Therefore, one of this book’s aims is to provide readers with the required background to properly design and implement computational investiga- tions of biomolecular systems. In addition, the book provides the needed information for calculating and interpreting experimentally observed properties on the basis of the results generated by computer simulations. vii
- 14. viii Preface This book is organized so that nonspecialists as well as more advanced users can benefit. It can serve as both an introductory text to computational biology, making it useful for students, and a reference source for active researchers in the field. We have tried to compile a comprehensive but reasonably concise review of relevant theoretical and computational methods that is self-contained. Therefore, the chapters, particularly in Part I, are ordered so that the reader can easily follow from one topic to the next and be systematically introduced to the theoretical methods used in computational studies of bio- molecular systems. The remainder of the book is designed so that the individual parts as well as their chapters can be read independently. Additional technical details can be found in the references listed in each chapter. Thus the book may also serve as a useful reference for both theoreticians and experimentalists in all areas of biophysics and biochemical research. This volume thus presents a current and comprehensive account of computational methods and their application to biological macromolecules. We hope that it will serve as a useful tool to guide future investigations of proteins, nucleic acids, and biological membranes, so that the mysteries of biological molecules can continue to be revealed. We are grateful to the many colleagues we have worked with, collaborated with, and grown with over the course of our research careers. The multidimensionality of those interactions has allowed us to grow in many facets of our lives. Special thanks to Professor Martin Karplus for contributing the Foreword of this book and, most important, for supply- ing the insights, knowledge, and environment that laid the foundation for our scientific pursuits in computational biochemistry and biophysics and led directly to the creation of this book. Finally, we wish to acknowledge the support of all our friends and family. Oren M. Becker Alexander D. MacKerell, Jr. Benoı̂t Roux Masakatsu Watanabe
- 15. Contents Foreword Martin Karplus iii Preface vii Contributors xi Part I Computational Methods 1. Introduction 1 Oren M. Becker, Alexander D. MacKerell, Jr., Benoı̂t Roux, and Masakatsu Watanabe 2. Atomistic Models and Force Fields 7 Alexander D. MacKerell, Jr. 3. Dynamics Methods 39 Oren M. Becker and Masakatsu Watanabe 4. Conformational Analysis 69 Oren M. Becker 5. Treatment of Long-Range Forces and Potential 91 Thomas A. Darden 6. Internal Coordinate Simulation Method 115 Alexey K. Mazur 7. Implicit Solvent Models 133 Benoı̂t Roux 8. Normal Mode Analysis of Biological Molecules 153 Steven Hayward 9. Free Energy Calculations 169 Thomas Simonson ix
- 16. x Contents 10. Reaction Rates and Transition Pathways 199 John E. Straub 11. Computer Simulation of Biochemical Reactions with QM–MM Methods 221 Paul D. Lyne and Owen A. Walsh Part II Experimental Data Analysis 12. X-Ray and Neutron Scattering as Probes of the Dynamics of Biological Molecules 237 Jeremy C. Smith 13. Applications of Molecular Modeling in NMR Structure Determination 253 Michael Nilges Part III Modeling and Design 14. Comparative Protein Structure Modeling 275 András Fiser, Roberto Sánchez, Francisco Melo, and Andrej Šali 15. Bayesian Statistics in Molecular and Structural Biology 313 Roland L. Dunbrack, Jr. 16. Computer Aided Drug Design 351 Alexander Tropsha and Weifan Zheng Part IV Advanced Applications 17. Protein Folding: Computational Approaches 371 Oren M. Becker 18. Simulations of Electron Transfer Proteins 393 Toshiko Ichiye 19. The RISM-SCF/MCSCF Approach for Chemical Processes in Solutions 417 Fumio Hirata, Hirofumi Sato, Seiichiro Ten-no, and Shigeki Kato 20. Nucleic Acid Simulations 441 Alexander D. MacKerell, Jr. and Lennart Nilsson 21. Membrane Simulations 465 Douglas J. Tobias Appendix: Useful Internet Resources 497 Index 503
- 17. Contributors Oren M. Becker Department of Chemical Physics, School of Chemistry, Tel Aviv Uni- versity, Tel Aviv, Israel Thomas A. Darden Laboratory of Structural Biology, National Institute of Environ- mental Health Sciences, National Institutes of Health, Research Triangle Park, North Carolina Roland L. Dunbrack, Jr. Institute for Cancer Research, Fox Chase Cancer Center, Philadelphia, Pennsylvania András Fiser Laboratories of Molecular Biophysics, The Rockefeller University, New York, New York Steven Hayward School of Information Systems, University of East Anglia, Norwich, England Fumio Hirata Department of Theoretical Study, Institute for Molecular Science, Oka- zaki National Research Institutes, Okazaki, Japan Toshiko Ichiye School of Molecular Biosciences, Washington State University, Pull- man, Washington Shigeki Kato Department of Chemistry, Kyoto University, Kyoto, Japan Paul D. Lyne Computer Aided Drug Design, Biogen, Inc., Cambridge, Massachusetts Alexander D. MacKerell, Jr. School of Pharmacy, University of Maryland, Baltimore, Maryland Alexey K. Mazur Institut de Biologie Physico-Chimique, CNRS, Paris, France xi
- 18. xii Contributors Francisco Melo Laboratories of Molecular Biophysics, The Rockefeller University, New York, New York Michael Nilges Structural and Computational Biology Program, European Molecular Biology Laboratory, Heidelberg, Germany Lennart Nilsson Department of Biosciences at NOVUM, Karolinska Institutet, Hud- dinge, Sweden Benoı̂t Roux Department of Biochemistry and Structural Biology, Weill Medical Col- lege of Cornell University, New York, New York Andrej Šali Laboratories of Molecular Biophysics, The Rockefeller University, New York, New York Roberto Sánchez Laboratories of Molecular Biophysics, The Rockefeller University, New York, New York Hirofumi Sato Department of Theoretical Study, Institute for Molecular Science, Oka- zaki National Research Institutes, Okazaki, Japan Thomas Simonson Laboratory for Structural Biology and Genomics, Centre National de la Recherche Scientifique, Strasbourg, France Jeremy C. Smith Lehrstuhl für Biocomputing, Interdisziplinäres Zentrum für Wissen- schaftliches Rechnen der Universität Heidelberg, Heidelberg, Germany John E. Straub Department of Chemistry, Boston University, Boston, Massachusetts Seiichiro Ten-no Graduate School of Information Science, Nagoya University, Nagoya, Japan Douglas J. Tobias Department of Chemistry, University of California at Irvine, Irvine, California Alexander Tropsha Laboratory for Molecular Modeling, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina Owen A. Walsh Physical and Theoretical Chemistry Laboratory, Oxford University, Oxford, England Masakatsu Watanabe* Moldyn, Inc., Cambridge, Massachusetts Weifan Zheng Laboratory for Molecular Modeling, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina * Current affiliation: Wavefunction, Inc., Irvine, California.
- 19. 1 Introduction Oren M. Becker Tel Aviv University, Tel Aviv, Israel Alexander D. MacKerell, Jr. University of Maryland, Baltimore, Maryland Benoı̂t Roux Weill Medical College of Cornell University, New York, New York Masakatsu Watanabe* Moldyn, Inc., Cambridge, Massachusetts I. INTRODUCTION The first hints of the chemical basis of life were noted approximately 150 years ago. Leading up to this initial awareness were a series of insights that living organisms comprise a hierarchy of structures: organs, which are composed of individual cells, which are them- selves formed of organelles of different chemical compositions, and so on. From this realization and the observation that nonviable extracts from organisms such as yeast could by themselves catalyze chemical reactions, it became clear that life itself was the result of a complex combination of individual chemicals and chemical reactions. These advances stimulated investigations into the nature of the molecules responsible for biochemical reactions, culminating in the discovery of the genetic code and the molecular structure of deoxyribonucleic acid (DNA) in the early 1950s by Watson and Crick [1]. One of the most fascinating aspects of their discovery was that an understanding of the mechanism by which the genetic code functioned could not be achieved until knowledge of the three- dimensional (3D) structure of DNA was attained. The discovery of the structure of DNA and its relationship to DNA function had a tremendous impact on all subsequent biochemi- cal investigations, basically defining the paradigm of modern biochemistry and molecular biology. This established the primary importance of molecular structure for an understand- ing of the function of biological molecules and the need to investigate the relationship between structure and function in order to advance our understanding of the fundamental processes of life. As the molecular structure of DNA was being elucidated, scientists made significant contributions to revealing the structures of proteins and enzymes. Sanger [2] resolved the * Current affiliation: Wavefunction, Inc., Irvine, California. 1
- 20. 2 Becker et al. primary sequence of insulin in 1953, followed by that of an enzyme, ribonuclease A, 10 years later. The late 1950s saw the first high resolution 3D structures of proteins, myoglo- bin and hemoglobin, as determined by Kendrew et al. [3] and Perutz et al. [4], respectively, followed by the first 3D structure of an enzyme, lysozyme, by Phillips and coworkers [5] in 1965. Since then, the structures of a very large number of proteins and other biological molecules have been determined. There are currently over 10,000 3D structures of proteins available [6] along with several hundred DNA and RNA structures [7] and a number of protein–nucleic acid complexes. Prior to the elucidation of the 3D structure of proteins via experimental methods, theoretical approaches made significant inroads toward understanding protein structure. One of the most significant contributions was made by Pauling and Corey [8] in 1951, when they predicted the existence of the main elements of secondary structure in proteins, the α-helix and β-sheet. Their prediction was soon confirmed by Perutz [9], who made the first glimpse of the secondary structure at low resolution. This landmark work by Pauling and Corey marked the dawn of theoretical studies of biomolecules. It was followed by prediction of the allowed conformations of amino acids, the basic building block of proteins, in 1963 by Ramachandran et al. [10]. This work, which was based on simple hard-sphere models, indicated the potential of computational approaches as tools for understanding the atomic details of biomolecules. Energy minimization algorithms with an explicit potential energy function followed readily to assist in the refinement of model structures of peptides by Scheraga [11] and of crystal structures of proteins by Levitt and Lifson [12]. The availability of the first protein structures determined by X-ray crystallography led to the initial view that these molecules were very rigid, an idea consistent with the lock-and-key model of enzyme catalysis. Detailed analysis of protein structures, however, indicated that proteins had to be flexible in order to perform their biological functions. For example, in the case of myoglobin and hemoglobin, there is no path for the escape of O2 from the heme-binding pocket in the crystal structure; the protein must change structure in order for the O2 to be released. This and other realizations lead to a rethinking of the properties of proteins, which resulted in a more dynamic picture of protein structure. Experimental methods have been developed to investigate the dynamic properties of pro- teins; however, the information content from these studies is generally isotropic in nature, affording little insight into the atomic details of these fluctuations [13]. Atomic resolution information on the dynamics of proteins as well as other biomolecules and the relationship of dynamics to function is an area where computational studies can extend our knowledge beyond what is accessible to experimentalists. The first detailed microscopic view of atomic motions in a protein was provided in 1977 via a molecular dynamics (MD) simulation of bovine pancreatic trypsin inhibitor by McCammon et al. [14]. This work, marking the beginning of modern computational biochemistry and biophysics, has been followed by a large number of theoretical investiga- tions of many complex biomolecular systems. It is this large body of work, including the numerous methodological advances in computational studies of biomolecules over the last decade, that largely motivated the production of the present book. II. OVERVIEW OF COMPUTATIONAL BIOCHEMISTRY AND BIOPHYSICS Although the dynamic nature of biological molecules has been well accepted for over 20 years, the extent of that flexibility, as manifested in the large structural changes that
- 21. Introduction 3 biomolecules can undergo, has recently become clearer due to the availability of experi- mentally determined structures of the same biological molecules in different environments. For example, the enzyme triosephosphate isomerase contains an 11 amino acid residue loop that moves by more than 7 Å following the binding of substrate, leading to a catalyti- cally competent structure [15,16]. In the enzyme cytosine-5-methyltransferase, a loop con- taining one of the catalytically essential residues undergoes a large conformational change upon formation of the DNA–coenzyme–protein complex, leading to some residues chang- ing position by over 20 Å [17]. DNA, typically envisioned in the canonical B form [18], has been shown to undergo significant distortions upon binding to proteins. Bending of 90° has been seen in the CAP–DNA complex [19], and binding of the TATA box binding protein to the TATAAAA consensus sequence leads to the DNA assuming a unique con- formation referred to as the TA form [20]. Even though experimental studies can reveal the end points associated with these conformational transitions, these methods typically cannot access structural details of the pathway between the end points. Such information is directly accessible via computational approaches. Computational approaches can be used to investigate the energetics associated with changes in both conformation and chemical structure. An example is afforded by the conformational transitions discussed in the preceding paragraph. Conformational free en- ergy differences and barriers can be calculated and then directly compared with experimen- tal results. Overviews of these methods are included in Chapters 9 and 10. Recent advances in techniques that combine quantum mechanical (QM) approaches with molecular me- chanics (MM) now allow for a detailed understanding of processes involving bond break- ing and bond making and how enzymes can accelerate those reactions. Chapter 11 gives a detailed overview of the implementation and current status of QM/MM methods. The ability of computational biochemistry to reveal the microscopic events controlling reaction rates and equilibrium at the atomic level is one of its greatest strengths. Biological membranes provide the essential barrier between cells and the organelles of which cells are composed. Cellular membranes are complicated extensive biomolecular sheetlike structures, mostly formed by lipid molecules held together by cooperative nonco- valent interactions. A membrane is not a static structure, but rather a complex dynamical two-dimensional liquid crystalline fluid mosaic of oriented proteins and lipids. A number of experimental approaches can be used to investigate and characterize biological mem- branes. However, the complexity of membranes is such that experimental data remain very difficult to interpret at the microscopic level. In recent years, computational studies of membranes based on detailed atomic models, as summarized in Chapter 21, have greatly increased the ability to interpret experimental data, yielding a much-improved picture of the structure and dynamics of lipid bilayers and the relationship of those properties to membrane function [21]. Computational approaches are now being used to facilitate the experimental determi- nation of macromolecular structures by aiding in structural refinement based on either nuclear magnetic resonance (NMR) or X-ray data. The current status of the application of computational methods to the determination of biomolecular structure and dynamics is presented in Chapters 12 and 13. Computational approaches can also be applied in situations where experimentally determined structures are not available. With the rapid advances in gene technology, including the human genome project, the ability of computa- tional approaches to accurately predict 3D structures based on primary sequence represents an area that is expected to have a significant impact. Prediction of the 3D structures of proteins can be performed via homology modeling or threading methods; various ap- proaches to this problem are presented in Chapters 14 and 15. Related to this is the area
- 22. 4 Becker et al. of protein folding. As has been known since the seminal experimental refolding studies of ribonuclease A in the 1950s, the primary structure of many proteins dictates their 3D structure [22]. Accordingly, it should be possible ‘‘in principle’’ to compute the 3D struc- ture of many proteins based on knowledge of just their primary sequences. Although this has yet to be achieved on a wide scale, considerable efforts are being made to attain this goal, as overviewed in Chapter 17. Drug design and development is another area of research where computational bio- chemistry and biophysics are having an ever-increasing impact. Computational approaches can be used to aid in the refinement of drug candidates, systematically changing a drug’s structure to improve its pharmacological properties, as well as in the identification of novel lead compounds. The latter can be performed via the identification of compounds with a high potential for activity from available databases of chemical compounds or via de novo drug design approaches, which build totally novel ligands into the binding sites of target molecules. Techniques used for these types of studies are presented in Chapter 16. In addition to aiding in the design of compounds that target specific molecules, computational approaches offer the possibility of being able to improve the ability of drugs to access their targets in the body. These gains will be made through an understanding of the energetics associated with the crossing of lipid membranes and using the information to rationally enhance drug absorption rates. As evidenced by the recent contribution of computational approaches in the development of inhibitors of the HIV protease, many of which are currently on the market, it can be expected that these methods will continue to have an increasing role in drug design and development. Clearly, computational and theoretical studies of biological molecules have ad- vanced significantly in recent years and will progress rapidly in the future. These advances have been partially fueled by the ever-increasing number of available structures of pro- teins, nucleic acids, and carbohydrates, but at the same time significant methodological improvements have been made in the area of physics relevant to biological molecules. These advances have allowed for computational studies of biochemical processes to be performed with greater accuracy and under conditions that allow for direct comparison with experimental studies. Examples include improved force fields, treatment of long- range atom–atom interactions, and a variety of algorithmic advances, as covered in Chap- ters 2 through 8. The combination of these advances with the exponential increases in computational resources has greatly extended and will continue to expand the applicability of computational approaches to biomolecules. III. SCOPE OF THE BOOK The overall scope of this book is the implementation and application of available theoreti- cal and computational methods toward understanding the structure, dynamics, and function of biological molecules, namely proteins, nucleic acids, carbohydrates, and membranes. The large number of computational tools already available in computational chemistry preclude covering all topics, as Schleyer et al. are doing in The Encyclopedia of Computa- tional Chemistry [23]. Instead, we have attempted to create a book that covers currently available theoretical methods applicable to biomolecular research along with the appro- priate computational applications. We have designed it to focus on the area of biomolecu- lar computations with emphasis on the special requirements associated with the treatment of macromolecules.
- 23. Introduction 5 Part I provides an introduction to the field of computational biochemistry and bio- physics for nonspecialists, with the later chapters in Part I presenting more advanced techniques that will be of interest to both the nonspecialist and the more advanced reader. Part II presents approaches to extract information from computational studies for the inter- pretation of experimental data. Part III focuses on methods for modeling and designing molecules. Chapters 14 and 15 are devoted to the determination and modeling of protein structures based on limited available experimental information such as primary sequence. Chapter 16 discusses the recent developments in computer-aided drug designs. The algo- rithms presented in Part III will see expanding use as the fields of genomics and bioinfor- matics continue to evolve. The final section, Part IV, presents a collection of overviews of various state-of-the-art theoretical methods and applications in specific areas relevant to biomolecules: protein folding (Chapter 17), protein simulation (Chapter 18), chemical process in solution (Chapter 19), nucleic acids simulation (Chapter 20), and membrane simulation (Chapter 21). In combination, the book should serve as a useful reference for both theoreticians and experimentalists in all areas of biophysical and biochemical research. Its content repre- sents progress made over the last decade in the area of computational biochemistry and biophysics. Books by Brooks et al. [24] and McCammon and Harvey [25] are recom- mended for an overview of earlier developments in the field. Although efforts have been made to include the most recent advances in the field along with the underlying fundamen- tal concepts, it is to be expected that further advances will be made even as this book is being published. To help the reader keep abreast of these advances, we present a list of useful WWW sites in the Appendix. IV. TOWARD A NEW ERA The 1998 Nobel Prize in Chemistry was given to John A. Pople and Walter Kohn for their work in the area of quantum chemistry, signifying the widespread acceptance of computation as a valid tool for investigating chemical phenomena. With its extension to bimolecular systems, the range of possible applications of computational chemistry was greatly expanded. Though still a relatively young field, computational biochemistry and biophysics is now pervasive in all aspects of the biological sciences. These methods have aided in the interpretation of experimental data, and will continue to do so, allowing for the more rational design of new experiments, thereby facilitating investigations in the biological sciences. Computational methods will also allow access to information beyond that obtainable via experimental techniques. Indeed, computer-based approaches for the study of virtually any chemical or biological phenomena may represent the most powerful tool now available to scientists, allowing for studies at an unprecedented level of detail. It is our hope that the present book will help expand the accessibility of computational approaches to the vast community of scientists investigating biological systems. REFERENCES 1. JD Watson, FHC Crick. Nature 171:737, 1953. 2. F Sanger. Annu Rev Biochem 57:1, 1988.
- 24. 6 Becker et al. 3. JC Kendrew, G Bodo, MH Dintzis, RG Parrish, H Wyckoff, DC Phillips. Nature 181:622, 1958. 4. MF Perutz, MG Rossmann, AF Cullis, H Muirhead, G Will, ACT North. Nature 185:416, 1960. 5. CCF Blake, DF Koenig, GA Mair, ACT North, DC Phillips, VR Sarma. Nature 206:757, 1965. 6. FC Bernstein, TF Koetzle, GJB Williams, DF Meyer Jr, MD Brice, JR Rodgers, O Kennard, T Shimanouchi, M Tasumi. J Mol Biol 112:535, 1977. 7. HM Berman, WK Olson, DL Beveridge, J Westbrook, A Gelbin, T Demeny, S-H Hsieh, AR Srinivasan, B Schneider. Biophys J 63:751, 1992. 8. L Pauling, RB Corey. Proc Roy Soc Lond B141:10, 1953. 9. MF Perutz. Nature 167:1053, 1951. 10. GN Ramachandran, C Ramakrishana, V Sasisekharan. J Mol Biol 7:95, 1963. 11. HA Scheraga. Adv Phys Org Chem 6:103, 1968. 12. M Levitt, S Lifson. J Mol Biol 46:269, 1969. 13. M Karplus, GA Petsko. Nature 347:631, 1990. 14. JA McCammon, BR Gelin, M Karplus. Nature 267:585, 1977. 15. D Joseph, GA Petsko, M Karplus. Science 249:1425, 1990. 16. DL Pompliano, A Peyman, JR Knowles. Biochemistry 29:3186, 1990. 17. S Klimasauskas, S Kumar, RJ Roberts, X Cheng. Cell 76:357, 1994. 18. W Saenger. Principles of Nucleic Acid Structure. New York: Springer-Verlag, 1984. 19. SC Schultz, GC Shields, TA Steitz. Science 253:1001, 1991. 20. G Guzikevich-Guerstein, Z Shakked. Nature Struct Biol 3:32, 1996. 21. KM Merz Jr, B Roux, eds. Biological Membranes: A Molecular Perspective from Computation and Experiment. Boston: Birkhauser, 1996. 22. CB Anfinsen. Science 181:223, 1973. 23. PvR Schleyer, NL Allinger, T Clark, J Gasteiger, PA Kollman, HF Schaefer III, PR Schreiner, eds. The Encyclopedia of Computational Chemistry. Chichester: Wiley, 1998. 24. CL Brooks III, M Karplus, BM Pettitt. Proteins, A Theoretical Perspective: Dynamics, Struc- ture, and Thermodynamics, Vol 71. New York: Wiley, 1988. 25. JA McCammon, SC Harvey. Dynamics of Proteins and Nucleic Acids. New York: Cambridge University Press, 1987.
- 25. 2 Atomistic Models and Force Fields Alexander D. MacKerell, Jr. University of Maryland, Baltimore, Maryland I. INTRODUCTION Central to the success of any computational approach to the study of chemical systems is the quality of the mathematical model used to calculate the energy of the system as a function of its structure. For smaller chemical systems studied in the gas phase, quantum mechanical (QM) approaches are appropriate. The success of these methods was empha- sized by the selection of John A. Pople and Walter Kohn as winners of the 1998 Nobel prize in chemistry. These methods, however, are typically limited to systems of approxi- mately 100 atoms or less, although approaches to treat large systems are under develop- ment [1]. Systems of biochemical or biophysical interest typically involve macromolecules that contain 1000–5000 or more atoms plus their condensed phase environment. This can lead to biochemical systems containing 20,000 atoms or more. In addition, the inherent dynamical nature of biochemicals and the mobility of their environments [2,3] require that large number of conformations, generated via various methods (see Chapters 3, 4, 6, and 10), be subjected to energy calculations. Thus, an energy function is required that allows for 106 or more energy calculations on systems containing on the order of 105 atoms. Empirical energy functions can fulfill the demands required by computational stud- ies of biochemical and biophysical systems. The mathematical equations in empirical en- ergy functions include relatively simple terms to describe the physical interactions that dictate the structure and dynamic properties of biological molecules. In addition, empirical force fields use atomistic models, in which atoms are the smallest particles in the system rather than the electrons and nuclei used in quantum mechanics. These two simplifications allow for the computational speed required to perform the required number of energy calculations on biomolecules in their environments to be attained, and, more important, via the use of properly optimized parameters in the mathematical models the required chemical accuracy can be achieved. The use of empirical energy functions was initially applied to small organic molecules, where it was referred to as molecular mechanics [4], and more recently to biological systems [2,3]. 7
- 26. Other documents randomly have different content
- 27. and then the motion of her lips. His heart beat wildly; they formed the refrain of a popular song,— “Adios, my dearest love!” Pepé reached the court quite dizzy. Ashley Ward and Captain Ruiz were both waiting for him. His excitement had reached a crisis. He seized Ruiz by the arm. “If you would please her,” he hissed in his ear, “find Ramirez, and let him, and not Gonzales, lead the troops.” “You are drunk!” answered Ruiz; yet he clutched the youth by the arm, and led him into his room. Pepé came to his senses with the shock as he sank upon a stone bench against the cold, hard wall. Presently he gave a brief account of Chinita’s desires and reasons. Ruiz listened without a smile. Childish and unprincipled as they were, they were not more so than scores he had heard discussed in the course of the years of anarchy in which he had entered upon manhood. Find Ramirez, pledge him to the Liberal cause, leave it to him to gain such an ascendency over the troops that they would themselves proclaim him their leader! It was an easy task. It set him thinking, and Pepé slunk away to hope, to doubt, to despair, to hope again. “Adios, my dearest love!”— just the refrain of a song, yet it pursued and bewildered him. For less, stronger men than Pepé the ranchero have committed unimaginable crimes. The next morning when they met in the court, Captain Ruiz stopped Pepé. “Tell her her wishes are law to me!” he said. “If she but love me, I—” “Caramba!” cried Pepé, savagely. “Am I an old woman or a priest that I should carry your messages? She love you! she would needs have been born to lead apes, to love you.” And Pepé flung himself off in a rage, while the astounded Ruiz gazed after him in open- mouthed amazement.
- 28. “By my life, he loves her himself!” he muttered vacantly. “Señor Don ’Guardo, heard you ever such presumption? The bare-skin beggar loves the favorite—what shall we say?—niece of Doña Isabel!” “Let us say you are both fools!” said Don ’Guardo in good round English and with a sudden rage, the motive of which was to himself inexplicable; and the discomfited captain bowed, not doubting that his own expression of disgust had been echoed. “Caramba! a woman so beautiful gazed at by every beggar, like an image of the Virgin of Remedios carried in procession! I swear I will not forget thee, Pepito, and will keep a close eye on thee, now I know thou hast been tampered with!” continued Ruiz, hotly. “A word to the General Gonzales will be enough if he is of my mind!” That day, in spite of Doña Isabel’s diligence, a pink note found its way to Chinita. “Good!” she said after reading it, “My General Ramirez will have the men; the Señor Gonzales will be helped, and Doña Isabel will do a double good. This is not so bad a subject,—this Ruiz; and his eyes are as black and large as those of Ramirez himself. All is well. All things will come right at last. Ah, if only what Don Rafael told Feliz one night should come true, and the convents are opened, then—” She paused. It seemed too utterly impossible even to dream of. She looked again at her first love-letter; a twinge of remorse seized her as she thought of Rosario. She laughed, but she tore the paper into infinitesimal shreds. What was the writer thinking? “Onward! I have gone too far to turn back even at the word of Chinita. A promise will gain her love, but the essential thing is the good-will of Doña Isabel. ‘A pearl is all the better for a golden setting!’ No treaties then with Ramirez. Though he is my godfather, I need not his patronage. Doña Isabel, a straight path, and Juarez! Forward! Ruiz, fortune favors you!”
- 29. XXX. A few days later the troops had left Tres Hermanos, and Ashley Ward stood in the silent graveyard on the mountain side, pushing back with his foot the loose sand his tread had disturbed, as it threatened again and again to cover the rude wooden cross upon which his eyes were fixed. It bore the name of his murdered cousin, faint yet distinct, preserved by the sand, for the wind had soon prostrated it after Chinita’s shallow replanting. The words seemed to Ashley to call to him aloud from the dust of his kinsman; in the hot sunshine their spell was as potent as though a ghostly voice had spoken at midnight. For the first time, something more intense than the desire to satisfy conscience by proving that he wronged no rightful heir in entering upon property which would have been John Ashley’s had he lived, arose in his mind. The absolute reality of his cousin’s death for the first time seemed to become an overwhelming conviction; and with it came memories of the young and daring man whom he had in childhood held in wondering admiration. And as he stood within sight of the spot where the brilliant young life had ended in a bloody tragedy, a deep wave of sorrow surged over his soul, and from its depths, as from the loose sands of the wind- levelled grave, appeared to rise a cry for vengeance. Though not till now had Chinita’s charge that he be taken to the American’s grave been carried out, the message from Doña Isabel, which Pepé had not failed to deliver, had reached him some days before, and had been supplemented by a visit from Don Rafael. Although a certain fascination had inclined Ashley to linger still at Tres Hermanos, he had so little hope of adding to the information he had already gained of his cousin’s life,—there seemed so little
- 30. possibility that the marriage which John Ashley had intimated had taken place, could ever have been more than a mere sentimental dedication of the lovers one to the other, in which they deemed themselves man and wife in the sight of God, but which in the sight of man was a mere illicit connection, to be condemned or ignored,— that he had not dared to present himself before the haughty mother of the one Herlinda whom he suspected to have been the object of his cousin’s passion, and to insult her with questions or insinuations that would cast a doubt upon her daughter’s purity and a stain upon the fame of the house of Garcia, which even the blood of John Ashley and his own added thereto would be insufficient to wash away. The young man had decided then to accept the order of dismissal, so delicately conveyed in the intimation that by accepting the escort of the troops as far as they might proceed toward Guanapila, he would not only reach a point whence in all probability he might in safety proceed to that city, but that he would thus render a favor to Doña Isabel, who was minded by the same opportunity to withdraw from the hacienda,—her presence there being liable to act as a lure to either party, who might after seizing her person levy a ransom upon the family which even their large resources would be severely strained to meet. Although the fiction was maintained that her assistance of the Liberal cause was involuntary, it was readily surmised that Doña Isabel Garcia was in reality seeking to avoid the vengeance of the Conservatives, while their forces were so demoralized and scattered that she might hope to reach Guanapila, which was then occupied by a patriot guard, before the tide of the war should turn and bring the army of the Church again to the fore en masse,—collected by the clarion cry of fanaticism, and lavishly rewarded from the hoards of silver and gold drawn from the vaults into which for generations had been drained the prosperity and the very life-blood of the peasantry. Ashley Ward had been struck with admiration of the woman who thus dared the dangers of the road,—to which she had been no stranger. He had felt something of the chivalrous enthusiasm of a
- 31. knight of old, as he joined the irregular band which by daylight had gathered upon the sandy plain before the straggling village. The soldiers had fallen into march with something like order, with Ruiz at their head,—for once with an anxious face, for he felt that the die was cast, and that he had raised up for himself an enemy whom it would be mad temerity to face, and hopeless to attempt to conciliate. The baggage-mules were driven by the leathern-clad muleteers, who even thus early had begun their profane adjurations to the nimble-footed beasts, that listened with quivering ears thrown back in obstinate surprise at every unwonted silence. The women who had come from other villages had laughed and chided their unruly infants, as they arranged and rearranged their baskets of maize and vegetables upon the panniers of their donkeys, if they were fortunate enough to possess any, or upon their own shoulders if they were to walk; and those who were for the first time leaving their birthplace to follow the fortunes of husband or sweetheart, had burst into loud lamentations. Ashley had been glad to find these changed to laughter, however, before they were well past the broken wall of the reduction-works; which they skirted, entering upon the bridle-path which led across the hill, where the rough heaps of sand showed through the scattered cacti, and where, by the rude wooden crosses, he now for the first time learned lay the village graveyard. Pepé had ridden sullenly by his side. He had been sent back with a sharp reprimand from the station he had taken among the mounted servants who surrounded the carriage of Doña Isabel, Ruiz in petty tyranny refusing him so honorable a place. A glance from Chinita had been the deepest reproof of all; and as he pondered upon it, certain words which she had uttered, and which he had hitherto forgotten, had come into his mind. As they neared the graveyard his eye caught Ward’s, and suddenly laying his hand upon the bridle of the American’s horse, he had muttered,— “Señor, she thinks I have forgotten all her wishes; but there is not even one so foolish that I scorn it. Turn aside but for a moment, Señor,—here where the adobe has fallen, your horse can scramble through the wall. Follow me, they will not miss us before we can reach our places again. Caramba! Don Fernando watches me as a
- 32. cat watches a mouse. Here, Señor,—never mind the women. Stupids! how they herd their donkeys together, when they might have the whole hillside to pick their own paths on! Patience! Let us wait a little, Señor! Ah,” he reflected, as they remained silent and motionless, “there is the spot. I have never forgotten it since I followed her through the rushes down there by the stream, and scratched my face in the tuñas, darting behind them that she should not see me. I was not half so tired as Chinita was though, when she sat down to rub sand upon her smarting hands, and fell asleep with the sun beating upon her head. I wonder if she ever thought it was I who covered her face with her ragged reboso,—she wears one of silk now, as clean and soft as a dove’s breast,—or that I lay behind the big pipes of the flowering organ-plant as she turned over the fallen cross which her hand struck against, and read the name and age of the American who had been murdered years before? Who ever would have thought—for I hated her then if I did follow her, as she maddens me now with her soft eyes and her mocking smile— that I should be bringing here the man who perhaps is just the handsome, woman-maddening demon they say that other was, and at her will too? Ave Maria Purissima! what God wills the very saints themselves may not say No to,—much less a poor peasant like Pepé Ortiz.” These thoughts, perhaps scarcely in the order in which they are set down, passed through the mind of Pepé, as lingering until the straggling procession had passed, he emerged from the shade of such an organ-plant as had once sheltered him years ago, and taking his bearings with unerring eyes, beckoned to Ashley,—who had waited within touch of his hand, and whose heart had begun to beat suffocatingly, though he knew that it was utterly improbable that anything more important than the mound that covered the body of his cousin would meet his eye,—and led the way to the most wind-swept and desolate portion of that paupers’ acre, and presently stooping where the ground was sunken rather than heaped, turned with some effort the half-buried cross, and exposed to Ashley’s view the name from which his own had been derived.
- 33. The young man gazed at it in a sort of fascination, actually spelling the letters over and over. He felt as if a part of himself must be buried there. His eyes burned; the glaring sunshine leaped and quivered above the ill-carved letters, distorting and confounding them. His heart beat violently; every sense but that of hearing seemed to fail him, and every sound upon the air became a weird, mysterious voice,—blood crying unto its kindred blood. This deep emotion fixed the indifferent and wandering eye of Pepé, who, holding the bridles of the horses, stood near, impatient to be gone, yet intending to watch out of sight the last stragglers; for it was with a double purpose he had turned aside to point out the grave of the American,—first, perhaps, to gratify the seemingly jesting wish of Chinita; and then to seize the opportunity to turn his fleet steed into the narrow bridle-path which led to mountain villages, where he shrewdly suspected Pedro might be found, or at least be heard of. He had promised to carry the message of Chinita to Pedro, and would have set forth upon the very night she had charged him with it, but until mounted by Ruiz’s command had found it impossible to provide himself with a horse, without which it was hopeless for him to attempt his quest. To escape the discipline of the ranks, he had induced Ashley to retain him as his servant, feeling no scruple at his intended abandonment. As his eye rested upon the pale and excited countenance of Ashley, Chinita’s words, with which she had bade him taunt him, flashed into his mind; yet he forbore to utter them, saying presently in a tone of concern,— “Let us go now, Señor, it is growing hot. It is almost noon, and you are faint. Let us ride on, and I will point out the way that you must take when we have crossed the face of the hill. Then comes a slight descent, Señor, and upon the little plain that lies between that and the cañon of the Water-pots will the troop stop for the nooning. This has been a rapid march. Doña Isabel will feel all the safer when she is once on the highway. But as for us, Señor, we must part company. You will find a better servant; I should but ill serve your grace. You know yourself I am but a stupid fellow, and it is only the patience of your grace that has been equal to my ignorance.”
- 34. Ashley heard neither the excuses of Pepé nor his own praises, but with a gesture at once commanding and entreating the servant to leave him, said: “Pepé, I had forgotten. There is something which will keep me still at Tres Hermanos. The Señora Doña Isabel must pardon me. Go! go to your duty, as I must to mine. God! how could I have forgotten it? Oh John, John! does time and distance make men so unnatural? Is it possible I could leave the place where you were so foully murdered, without knowing why or by whom? Who killed him, and why was the deadly and secret blow struck? Ah, that involves the question of the very mystery I came here to fathom, and which I was turning my back upon; for I am convinced that it is here, and not by following Doña Isabel Garcia, that it may be solved. She is too resolute, too astute; nothing is to be forced or beguiled from her lips! But now that the spell of her presence is removed, I may learn everything from these people, who with all their cunning and clannish devotion can surely be influenced by reasons such as I can give.” “Who would have guessed the sight of a grave would so stir the blood?” soliloquized Pepé. “Can it be that Chinita—But no, she was more in jest than earnest; she always laughed at the niña Chata for her sorrow for the foreigner.—Well, all must die!” he said aloud. “Believe me, Señor, after all these years a knife-thrust is a little matter to inquire into. Caramba! Chinita herself would tell you that to turn back on a journey because of the dead is an omen of evil; ’twas not for that she would have me show you the grave of your countryman,—God rest him!” Ashley looked at him keenly. “Ah,” he said, “it is then no accident that you have brought me here? God! what a mystery! Pepé, tell Chinita I know her thoughts, and that I never will rest till I prove them right or wrong. She is a strange creature, and likely to prove an enigma to more men than myself. Poor lad, she is not for you to dream of.” “I will not see her again till I can tell her that which shall please her,” said Pepé. “Look you, Señor, she is one who will have the world turn to suit her.”
- 35. “A wilful girl,” thought Ashley, with judicial disapproval. “She has all the craftiness and deceit of the Indian and the pride and passion of a Spaniard; yet what if I should follow her? No, no! mere circumstance and conjecture shall not turn me!—Adios, Pepé,” he said aloud, “and beware! It is Doña Isabel you serve, and not the young girl who has bewitched you.” Pepé smiled vaguely; his glance roved over the landscape. “Her heart is virgin honey in a cup of alabaster!” he murmured. Ashley was becoming accustomed to the poetic expressions of these unlettered rancheros, and with some impatience took in his own hand the bridle-rein of his horse, and reminding Pepé that it was nearly noon, and that he would be missed should he longer delay, bade him mount and hasten with messages of excuse to Doña Isabel for his own sudden return to Tres Hermanos. With the customary apparent submission of a peasant, Pepé prepared to obey. He was in fact anxious to set forth as soon as he could be certain that no straggler was near to mark his movements. The troops and their followers had disappeared. “The Señor Don ’Guardo should leave this solitary spot on the instant,” he said with genuine concern; “in these days of revolution, one can never say what dangerous people may be wandering abroad.” “I have nothing to fear from them,” answered Ashley, “unless it should be that they might attempt to rob me of the horse Doña Isabel has lent me. Well, for its sake, I will be prudent; though in truth the sight of a ghost in this desolate spot of sunken graves would seem more probable than that any living being should pass here. Now, then, good-by, Pepé.” “Until our next meeting, Señor!” replied Pepé, gravely lifting his hat. He had attached himself to Ashley, and it seemed to him an evil omen that they should part at a grave, and he thus attempted to console himself by the pretence that it was but for a little while. “For a short time Señor, and God keep you!” Ashley shook his hand warmly. The ranchero drew his hat over his eyes, adjusted his serape so that his face was almost hidden, and dropping into that utterly ungraceful posture into which the skilled horseman of Mexico relapses when he suffers his steed to take his
- 36. own way and pace across a wearisome stretch of country, he turned his horse’s head toward the bridle-path they had left, and slowly receded from Ashley’s gaze. Once however beyond the crest of the hill, the rider’s eye brightened, his figure straightened; a distant sound of voices reached his keen ear,—it was so remote that but for the rarity of the atmosphere it would have failed to reach him. Bending his head, he listened intently for a moment; then raising it he gazed searchingly on every hand, rode for a short distance to the right, guided his nimble-footed beast down the cleft sides of a deep ravine and along the dry bottom of a rock-strewn path, which rapid floods had in some past time cut in their fierce descent from the steep sides of the frowning mountains, and so gradually gained the dark and solitary defiles that led directly to those eyries of bandit mountaineers, who under the guise of shepherds, charcoal-burners, and goat-herds had been, as Pepé well knew, the chosen comrades of Pedro Gomez and his mates in the boyhood days of that Don Leon whose wild deeds were still the theme of many a tale, and like the story of his death became more mythical with every repetition. Pepé rode steadily on for hours, picturing to himself his meeting with Pedro should he find him, or the quiet exultation of Chinita when she should hear that he had deserted the troops, or of the return of Don ’Guardo to the hacienda. In his heart he was not displeased that the American should be separated from Chinita, though it left her the more completely to the gallant care of Ruiz. He had comprehended instantly the emotion which had seized upon Ashley at his kinsman’s grave,—the instinct for revenge. He said to himself that those Americans, after all, were people of sensibility, and he felt a certain satisfaction that he had been the instrument of calling into action a sentiment that did the foreigner so much credit. Meanwhile the heat of noon passed, and Ashley’s horse stood with patient dejection in the shadow of the huge cactus to which he had been tethered, not even taking advantage of the freedom allowed by the length of the rope, so little temptation to browse was offered by the sparse and coarse tufts of herbage which struggled into existence here and there. The time wore on, and an occasional stamp attested his disapprobation of a master who lay prone upon
- 37. the ground under a mesquite tree when the sun shone hottest, and who when the cool breeze of afternoon swept over the silent spot, stood long and still beside the grave he had not sought, and yet felt infinite reluctance to leave. It was a foolish thought, but as he gazed across the broad valley to the great square of buildings set among the fields, the youth imagined how indeed the dead man might at times steal forth to visit again those fertile scenes where he had lived and loved. As he stood there, Ashley could see the people like pigmies passing in and out the great gateway, or going from hut to hut in the village. There was one figure—it seemed that of a woman—which his eye sought from time to time, as it appeared and disappeared in the corn and bean fields, and at last came out on the open road that lay between them and the reduction-works. He was becoming quite fascinated by its hesitating yet persistent progress, when he was startled by a sound; and glancing up, he saw a man leaning upon the crumbling wall and regarding him with a gaze so bewildered, so fixed, that involuntarily he moved a step toward him. The stranger started, as if some frightful spell had been broken. Ashley saw that he crossed himself, and muttered some invocation; yet that he had not the look of a nervous man or a coward, but rather of a somnambulist pacing the earth under the impulse of some horrible dream. The man was not ill-looking,—no, decidedly not; and though his skin was deeply browned as if from much exposure, and his cheek bones were prominent, giving his face a certain cast below the eyes that was plebeian or Indian in character, the eyes themselves were dilated and brilliant, and the straight nose and pointed beard gave him the air of a Spanish cavalier, though he wore the broad sombrero and serape of a common soldier of the rural order. Perhaps on ordinary occasions even a more practised eye than that of Ashley Ward would have accepted the stranger for what he purported to be; but the American with an extraordinary feeling of repulsion little accounted for by the mere sense of intrusion caused by the man’s unexpected appearance, at once leaped to the conclusion that his dress—though he had no appearance of strangeness in it—was virtually a disguise, and that instead of a
- 38. soldier of the ranks, the man before him was of no ordinary position or character. The new-comer seemed to have risen out of the ground, so stealthily had he approached. It would have been quite possible for him, tall as he was, to have skirted the wall without observation from any one within the enclosure. But undoubtedly he had taken no precaution in that solitary place, which except at funeral times was shunned as the haunt of ghosts and ill-omened birds and reptiles, and thus had come unexpectedly upon the motionless figure of the tall young man clothed in a plain riding-suit of black, with bright conspicuous locks at the moment uncovered, and fair-skinned face of a characteristic American type,—all unremarkable in themselves but associated in the mind of the observer with one whom he had seen but twice or thrice, and this on the mad night when the moon had shone down upon a victim quivering in the death-agony above which he had exulted. The two men held each the other’s gaze in silence for a full minute, both unmindful of the common courtesy usual in such chance encounters in solitary places. Then recovering from the superstitious awe which had overpowered him, the Mexican stepped over the broken wall. Ashley noticed as he did so that heavy silver spurs were on his heels, and that the fringed sides of his leathern trousers were stained as though with hard riding, and that, as if from habit, rather than any purpose of menace, his nervous hand closed upon the pistol in his scarlet band, as with a few long strides he reached the spot on which Ashley stood with that air of defiance which a sudden intrusion upon a solitude however secure naturally arouses in a man who is neither a coward nor an adept in the self- command that is perhaps the most perfect substitute for invincible courage. “Señor,” said the Mexican, “your pistols are on your saddle. You are right; this is an evil habit to wear them so readily at one’s side. Pardon me if in my surprise I assumed an attitude of menace; but these are troublous times. One scarcely expects to find a cavalier alone in such a place.” He looked around him with a smile, which did
- 39. not hinder a quiver of the lip expressing an excitement which his commonplace words denied. Ashley regarded the speaker with ever increasing repugnance. It was true his pistols hung from the saddle, but there was a small knife in his belt, and his hand wandered to it stealthily as he answered: “Señor, I make no inquiry why you are here, and on foot, —which you must acknowledge might well cause some curiosity in this place; but in all courtesy I trust your errand is a happier one than mine. Whatever it is, I will not intrude upon it longer than will suffice to plant this cross.” And with an air of perfect security, yet with his knife in hand, he bent to the work, which the other regarded with an almost incredulous gaze,—the preservation of a grave or its tokens being a sort of sentimentality to which by tradition and training he was a stranger; and to see it exhibited for the first time in this God’s acre of laborers, almost sufficed to dissipate the impression the unexpected encounter had made upon him. As Ashley quietly pursued his work, the new-comer had an opportunity to look at him narrowly. After all, this one was like many another American! Yet there was something in the young man’s appearance that brought the sweat to the brow of the soldier; he pushed back his hat, and breathed hard. As he did so, Ashley braced the cross against his knee. The action brought the letters into clear and direct view. The eyes of the Mexican rested upon them. He fell back a step or two in superstitious awe, involuntarily exclaiming: “Cristo! was he buried here? And who are you?” Ashley glanced up. There was a revelation to him in the questioner’s disordered and ashy countenance. He dropped the cross, sprang over the grave, and seized the stranger by the right arm. “Who are you who ask?” he cried. “What do you know of the man who is buried there?” “My faith! you are a brave man to put such questions!” retorted the new-comer, wrenching himself free. Ashley had spoken in English, but the violence of his act had interpreted his words. “Take your pistols and defend yourself, if you are here for vengeance. Kill him? Yes; I killed him as I would a dog. Faith, I thought it was his accursed ghost that had risen to challenge me!”
- 40. “I am his cousin! Assassin, give me reasons for your deed!” cried Ashley, furiously, yet with a remembrance that to every criminal should be allowed some chance of justification. But the Mexican seemed little inclined to profit by it. “Reasons!” cried he. “Yes, such reasons as I gave him when I thrust the knife into his heart.” He raised his pistol and fired. The shot passed so close to Ashley’s temple that he heard it whiz through the air. In the same instant the two men clinched. The horse, which during the controversy had plunged and reared madly, broke away, and careering over the graves galloped wildly down the hillside. A fresh horse with its rider at the same instant dashed into the enclosure, and a voice cried, “For God’s sake my General! what adventure is this? Mount! mount! there is no time to be lost!” The combatants at the sound of a third voice had involuntarily paused. Had the knife in the hand of the American been in that of the Mexican it would have sheathed itself in his opponent’s heart; but Ashley, less ready in its use, arrested his hand midway. His passion half spent, the scarcely healed wound throbbing in his shoulder, his strength exhausted, he had much ado to keep himself from staggering. “A touch of my sabre would finish him,” said the new-comer coolly, as he reined in his restive horse, and put his hand on the long weapon swinging from his saddle. But the soldier stopped him. “No killing in cold blood,” he exclaimed. “’Tis a madman, but his fury is over. What brings you here, Reyes? Were you not to wait at the rendezvous?” “Wait!” he retorted, “this is no time to wait! We are already a day too late. A thousand men are on the road before us, my General! We let them pass us this morning as we lingered on the opposite side of the mountain in the Devil’s gate!” “And the troops are there still?” cried the other furiously. “Where is Choolooke? Did you not think to bring me a horse? Back to the Zahuan, man! We must begin the march this very night. I know Ruiz; he will yield in a moment at sight of me!” “Not he!” answered Reyes. “He has a new patroness; Doña Isabel herself is with him.”
- 41. “Isabel!” cried the officer with an oath. “Ah, then, Tres Hermanos is partisan at last! Carrhi! my lady Isabel shall find what she has begun shall be soon ended!” He put a small silver whistle to his lips and blew a shrill blast, which was answered by a neigh. A black horse lifted its head and looked over the wall with a gaze of almost human intelligence. “He followed me at a word,” exclaimed Reyes, “and stood by the wall like a statue when I bade him. Never was there such another horse as your black Choolooke, my General. Even the stampede of that unbroken brute that was tethered here could not startle him.” “Ay, I discipline horses better than I do men,—eh, Choolooke?” The horse with its jingling accoutrements had cantered into the enclosure, and with one bound his owner was in the saddle. All had passed in the few minutes in which Ashley was recovering breath, and in utter bewilderment endeavoring to gain some insight into the meaning of this rapid transformation scene, of which he himself had formed a part. As his late opponent sprang into the saddle, he could have fancied he heard the sound of the bugle, so alert were the man’s movements, so soldierly his bearing. But in the midst of his involuntary admiration he did not forget the extraordinary relations in which they stood to each other. He threw himself before the horse at the imminent risk of being trampled down. “Your name!” he cried. “By your own admission you are my cousin’s murderer. We must meet again! I am Ashley Ward; and you?” “Out of the way!” cried the rider, checking his horse by a dexterous turn of his hand. “My name? Ah, yes! Tell them there,” and he nodded in the direction of the hacienda, “they will soon have reason never to forget it!” He hesitated; plunged the spurs into his already impatient steed, and dashed furiously away, followed by Reyes; then rose in his stirrups to shout back in defiance the name —“Ramirez!”
- 42. XXXI. Ramirez! Ashley’s heart bounded, his brain throbbed dizzily yet acutely. Here was no obscure assassin, who once escaping him would perhaps be lost forever. The name was on every lip with those of Juarez, Ortega, Degollado, Miramon, and a score of other popular chieftains who of one party or another, or of independent factions, attracted to themselves a host of followers, more by their own personal magnetism than for the sake of any principles they represented. In that time of anarchy any head that rose above the common herd led enthusiastic multitudes, who followed a nod and applauded to the echo even one deed of daring. But Ramirez held his prestige by no such recent and uncertain tenure; throughout the long years of revolution he had been a central figure in the bloody drama. Even his recent defeat at El Toro and his subsequent disappearance had added but a fresh glamor of mystery to his adventurous career, without detracting from the almost superstitious awe with which he was regarded. It was believed that he would reappear when and where least expected. Ashley Ward had smiled covertly at the strange and daring escapades attributed to this man. He had become in his mind a figure of romance; and here in the broad day he had risen before him, the self-denounced murderer of John Ashley,—and as suddenly as he had come, so had he escaped him. Thinking no more of the cross, which had fallen upon the ground, hiding beneath it the name that had been so long preserved for so strange a purpose, Ashley Ward turned from the sunken graves and striding across the mounds, scarred and broken by the sacrilegious tread of the horses’ feet, stood for a moment upon the broken wall,
- 43. scanning the country in his excitement for some sign of the desperate men who but a few moments before had urged their restive steeds up the steep path and disappeared over the crest of the hill. He saw his own recreant steed galloping toward the hacienda walls, keeping the high-road, on past the reduction-works and the long stretch of open country beyond, and plunging and rearing at the fatal mesquite-tree. The superstitious vaqueros had instinctively imbued their animals with the same irrational terrors in which they had themselves been trained. Yet no sight of ghost or smell of blood lingered there to rouse memory or vengeance. Their waiting-place had been that long-forgotten grave upon the desolate hillside. Ashley leaped from the wall and rapidly began the descent to the valley. The sun was still high in the heavens, for the scene we have recorded had passed in less than a brief quarter of an hour. As he walked on, gradually falling into a more natural pace, the whole matter took definite form and coherence in his mind. That which had been so unexpected, so unnatural, seemed to be the event to which his whole journey to Mexico, all his wanderings, his strange and wearisome experiences, had inevitably and naturally tended. And then arose a point beyond. His work at Tres Hermanos seemed ended; the primal cause of his being there was forgotten. The definite thought now in his mind was to reach the hacienda, provide himself anew with horse, guide, and arms, and follow on the path which Ramirez had chosen, and upon which he would sooner or later re-appear, decoyed by the rich booty that Doña Isabel had intrusted to the weak and presumably faithless Ruiz. Could he reach and warn her in time? Ashley’s scarce-healed wound was throbbing painfully, the way was long, the heat intense; yet he pressed on resolutely, though at last he staggered as he went. He sat down to rest awhile among the dry rushes of the spent watercourse, under a straggling cottonwood- tree, the few poor leaves of which scarcely sufficed to shade him from the fierce rays of the sun. A fever heat was in his veins; wild theories and speculations passed through his brain,—some of them, perhaps, not far from being keys to the mystery of that tragedy
- 44. which that day for the first time had become to his mind other than a vague and gloomy fantasy. Now, like the murderer himself, it was real, absorbing, appalling. The young man rose and again pressed on. After the descent to the long rude wall of the reduction-works, he skirted it slowly, thinking as he went how changed the aspect of the place must be since his cousin had ridden forth to his death. How proudly John had written, and almost vauntingly, of the prosperity his management had inaugurated, of the crowds of laden animals that passed in and out of the wide gates, of the men who led their slow, laborious lives among those primitive mills and wide floors of trodden ores. Ashley glanced at the great square mass of walls and towers of Tres Hermanos, glistening in the distance. To his weary eye it looked far away; yet doubtless he thought it had been but the ride of a few eager minutes to the lover, as he went at midnight to cast a glance at the walls that circled his mistress, or to rein his horse beneath her window that he might win a word or glance from her who whispered from above. These, Ashley had heard, were lovers’ ways in Mexico; he did not know that no maiden of Tres Hermanos ever occupied one of the few apartments whose windows opened toward the outer air. Yet as he debated the matter with himself, it became more and more probable to him that John Ashley had upon the fatal night been actually within the walls of the hacienda, and been stealthily followed thence by his treacherous rival,—for what, he thought, even to a Spaniard, could justify so foul a murder but the falseness of his mistress, the triumph of a hated rival? Pedro’s taciturnity and gloom Ashley construed as proofs of his complicity in the crime. Even then Ramirez had been a chieftain of renown, and Pedro in his youth had been a soldier, a free rider, of whom strange tales were told. Was it not probable that he had opened the gate at a comrade’s bidding,—or, more likely still, had bidden him wait beneath the tree where the favored lover was wont to mount his horse, and so take him unawares? Ashley remembered that such, it had been said, had been the manner of his cousin’s taking off. He had been slain with the swiftness and sureness of a secret and unhesitating avenger.
- 45. The ardent youth railed at the mocking chances that had combined to suffer Ramirez to escape him in the unpremeditated struggle in which they had clinched with a deadly enmity. In such a struggle he could have found himself the victor without remorse, or could have died without regret; but it was not in his nature to follow a man for blood. Yet neither could he shut his ears to that cry for vengeance, for justice, which seemed ringing through the sultry stillness,—the more importunate as the possibilities of their attainment shaped themselves in his mind. That this must be a personal matter between himself and Ramirez was clear. At any time it would probably have been useless for an alien to have denounced so popular and influential a man as the proud and daring revolucionario. To attempt his arrest for a murder committed years before and probably in rivalry for a lady’s favor, would be but to throw a new mystery about him, and add a fresh legend of romance to those which already made him rather a character of ideal chivalry than of mere vulgar, every-day lawlessness and semi-barbarity. Though the brilliant adventurer was now under a temporary cloud, one threat of attack from law would make him again a popular idol; indeed it was likely that a pronunciamiento in his favor would be the immediate result, and that in falling into his hands the American would lose, if not his life, at least all opportunity either of obtaining the satisfaction of the law for his cousin’s death, or of investigating further those doubts and probabilities which he had forgotten, but which now came upon him with redoubled force. The excited Ashley planned in his mind to refresh himself upon reaching the hacienda, and demanding horse and guide to set forth upon that very night, hoping to rejoin the force at daybreak. It was useless, he reflected, to waste further time in idle questionings. It was to Doña Isabel herself he would appeal, and warning her of the danger that threatened her from the bandit chieftain, induce her to make common cause with him against one who for years must have been their common enemy. Impossible was it for him to solve the mystery of the relations in which the several actors in this strange drama in which he was so unexpectedly taking part, stood either to
- 46. one another, or to himself. There was but one fact certain; by that alone he could connect himself with beings who seemed almost of another world,—the one undoubted fact of the discovery of John Ashley’s murderer. Ashley’s ready apprehension of the public mind had been helped by what he knew to be the actual state of affairs in the ranks to which Doña Isabel had intrusted the safety of her person, trusting to the resources which were at her command, and to the present ascendency of Gonzales, to bind those soldiers of fortune to the cause she had espoused. Perhaps none knew better than she the elements that an alluring chance of gain or a transient enthusiasm had drawn together; but she could not know how near the fire lay to the straw, and how at her very side were those who in the name of patriotism—or, like Chinita, for a personal sentiment as unexplainable as it was imaginative and ardent—would sacrifice her dearest plans, and think it a grand and noble deed to raise the ubiquitous and dashing Ramirez upon the fall of the slow and cautious Gonzales. Ashley had imperfectly comprehended the scheme or its bearings; he had little understood, and felt but little interest in, those strange complexities and personalities of Mexican politics; but now a sudden party zeal and horror of treason seized him. Where was Pedro Gomez, who, having played traitor once, might do so a hundred times more? Where was Pepé? Had he rejoined the troops, or had the detour to the graveyard been but a clever plan for eluding them? Were these, and perhaps Ruiz too, the tools of Ramirez? Yet the latter had appeared to have ridden far; the news of the gathering and departure of the troops had appeared to have astounded as much as it had enraged him. Who had carried the news to Reyes? The way was long and the youth’s excitement waning; his recent illness and still aching wound began to declare their effects. In his full vigor Ashley Ward would have found the walk under the glaring sunshine—which, though no longer vertical, was fierce and blinding as it neared the western hilltops—more than he would have chosen for an afternoon’s stroll. Weak as he was, and becoming painfully conscious that he had fasted since morning, he was glad to lean
- 47. sometimes against the high adobe wall and measure with his eye the slowly decreasing distance. It was a landmark on his way when he caught sight of the heavy gate set in the wall of the reduction- works; he knew then just how much farther he must go. He had no thought of actually approaching it, but he noticed with surprise that one heavy valve was slightly ajar; and with that sudden collapse which is apt to assail the overtasked frame at the unexpected sight of an open door, however meagre the entertainment it may suggest, he dragged himself onward with the natural belief that he should find within some servant or attaché of the great house. But when he reached the gate and looked through the narrow aperture, a perfect stillness reigned within. No horse stamped in the courtyard; no spurred heel rang on the pavement. Great cacti were pushing their gaunt and prickly branches into the narrow space, as if stretching longing arms out into the wide world from which they had been so long shut in. With some effort Ashley thrust back the strong and aggressive barrier, and forced his way in. Rank grass, which was at that season yellow and matted, had grown up between the cobble-stones, and raised them in little heaps, over which the lizards ran. One—fiery red —stopped as Ashley’s boot-heel woke the echoes, and turned a wondering ear, then glided swiftly on. Between the main building and the offices there was a small arched lobby, through which one entered the great court, upon which piles of broken ores and the long dried masses were spread. In this lobby in the olden time the workmen had been stopped by the watchman or gatekeeper and searched,—a proceeding to which they daily submitted with indifference, holding their arms on high while the practised searcher ran his hands over their thin and scanty garments, shook out the coarse serape and tattered sombrero, peered among the rows of glistening teeth and under the tongue, for those fragments of rich ore or amalgam which in spite of all precautions, or by the connivance of the searcher, reached the outer world, netting in the aggregate a considerable surplus to the income of the laborers, which found its way to the gambling tables, or was spent in the adornment of their wives,—as was proved by the great
- 48. decline in the village of the manufacture of filagree ornaments of quaint and delicate designs upon the closing of the Garcia mining- works. Ashley, with a feeling of curiosity or a sense of impending action, which renewed his strength as a tonic might have done, noticed that the door upon the side of the lobby that opened into the main building or living rooms was also ajar. He glanced in, but except where the long ray of light stole in through the aperture, which his person partially obscured, all was so dim that he saw only imperfectly a few scattered articles of furniture,—and they appeared to be so old and battered that they were scarce worth the protection which the great padlock and rusty key, hanging from a staple in the door, indicated had been afforded them. With a feeling of awe, Ashley remembered that his cousin must have lived, and perhaps had lain dead, in that room. With nervous energy he thrust open the door, and the light streamed in. He started as his eyes fell upon the floor. It was of large square bricks, thickly spread with the dust of many years, but impressed with footprints so blurred that, dazzled as his eyes were, he could not tell whether they were those of man, woman, or child. They seemed mysterious, ghostly. There was no sound of human presence. His heart beat as it had not done in all the excitement of that day. “I am here! I have been waiting as you bade me,” said a low, frightened voice. The words came so unexpectedly that Ashley scarce understood them. He stepped forward and glanced around searchingly. In the farther corner of the room a female figure was in the act of rising from a low seat on which it had crouched. The face was half-averted, the dark reboso was drawn over it with the left hand, the right was outstretched as if in supplicating, almost compulsory, welcome. “Good God!”—“Dios mio!” The ejaculations were simultaneous; the girl sank to the floor, the young man involuntarily drew back. “Señorita!” he exclaimed in a voice of incredulity, “Señorita, you here and alone?” “Maria Sanctissima! not the General Ramirez!” he heard her moan; yet in the fright and confusion there seemed an accent of relief.
- 49. “Don ’Guardo! Oh, what has brought you here? Oh, Señor, believe me—” “Do not distress yourself to explain, Señorita,” interrupted Ashley, coldly. “Rise, I beg, and I will go at once; but that you may not waste more time in waiting, I will tell you that the man you speak of will not be here to-day. And,” he added, with an intensity that startled even himself, “if there is justice in heaven or upon earth, never again shall he fulfil a lover’s tryst upon a spot that by any other than a demon would be shunned as a scene of gentle dalliance, if not abhorred as the theatre of a crime that should have blasted his whole life!” The girl threw back her head-covering and looked up in uncomprehending amaze. As her gaze caught Ashley’s both colored, both averted their eyes in confusion. Ashley recoiled before hers, so childlike, so honest. “Chata!” he murmured; “Chata!” involuntarily extending toward her his hand in deprecation, in entreaty, in protection. She clasped it as a frightened child might, and clinging to it rose to her feet, swaying a little and bending low, not with weakness, but with shame. “I dared not disobey him,” she murmured at last. “I dared not disobey.” Ashley dropped her hand,—almost flung it from him. The girl’s face crimsoned; she opened her lips, hesitated, then clasping her hands together, cried, “It is not as you think. Oh, rather than the truth, would to God it were! I am not the child of Don Rafael and Doña Rita! Jose Ramirez is my father!”
- 50. XXXII. “José Ramirez is my father!” Had her words been a thunderbolt hurled at Ashley’s feet, they could not have astounded him more. The daughter of Ramirez! “I do not believe it! I cannot believe it!” he exclaimed, with no thought for courteous words. “Oh, that is a tale for a jealous lover! but I am not one. Anything, anything rather than that, Señorita, would serve to explain the reason of your presence here!” “Why have I spoken?” cried the young girl with tears. “Why have I broken my promise, and only to be disbelieved and scorned? O, Señor, I know not what it was in you that wrung the words from me! Did he not command me to be silent till he gave me leave to speak? He is my father, yet I have disobeyed his first command. In the letter the woman brought me, two days after he left El Toro, and in which he commanded me to meet him here upon this day, he enjoined secrecy again and again; and yet I forgot. Miserable girl that I am!” Ashley had lived among Mexicans long enough to learn something of their ideas of filial duty. No matter how vile, how cruel, how debased the parent may be, the duty of the child is perfect obedience and respect; the petted infant in its most wilful moments ceases its passionate cries to kiss the father’s hand; the young man deprives himself, his wife and children, to minister to his aged parents; he who cannot or will not work, esteems it a pious act to become a bandit upon the highway rather than that his father or mother shall look to him for food or even for luxuries in vain,—and thus he comprehended the remorse of this conscience-stricken child, as the conviction rushed over him that her belief might indeed be true. There was that in the contour of her face which resembled that
- 51. of Ramirez more markedly than the mere general type that in her babyhood had given her that resemblance to Rosario, which daily grew less, and indeed had never been apparent to Ashley; though in her face he had traced resemblances which had puzzled and bewildered him, and which as he gazed upon her now became still more confusing. As they had been conversing, Ashley and Chata had gradually drawn near to the door, where the light fell full upon the agitated girl. Yes, in the square brows, the heavily fringed lids resting upon the olive cheeks,—too broad beneath the eyes for beauty, but singularly delicate about the mouth and chin,—so far she resembled Ramirez; or was it but a common Aztec type? The mouth itself, sensitive, refined,—which should have parted but for laughter,— quivered with emotion, and the large gray eyes she lifted to Ashley’s were singularly grave and earnest. Where had he seen such a mouth, such eyes? The contrasts and combinations in the face confused him. Never had he seen its counterpart, yet fancy might under other circumstances have led him upon wild theories. That face familiar, yet strange, had haunted him since he had first seen it. Vainly he had sought in his memory for some picture, some dream, with which to connect it. Now, though he had seen Ramirez, though Chata declared herself his child, the same feeling of uncertainty, of tantalizing familiarity yet strangeness, remained; the association of one with the other did not even momentarily satisfy him. He was not conscious that the face appealed to his imagination rather than to his memory, or that it had always awakened an interest different from that with which he had looked upon others. Certainly its beauty had not delighted him; even as he looked at her now, the witching, glowing, ever-changing countenance of Chinita rose before him. “Strange! strange!” he murmured. “What can be the mystery that from the first has seemed to hover around you, to separate you from the rest?” “Ah, yes!” she said humbly. “I have realized that myself. Oh, for a long, long time I have felt as a stranger among them all,—they so good, so true; and I—O God, who am I? Ah, I used to pity Chinita, but they have given her her proper place. It must have been a
- 52. worthy one, or Doña Isabel would not have made her her child. But when they separate me from Don Rafael what shall I be?” “Do not think of it. He—this Ramirez—is gone, perhaps never to return,” said Ashley, soothingly. “And if not, why should you go with him? Appeal to Don Rafael, to Doña Feliz.” “Doña Rita has told me already that would be worse than useless,” replied Chata. “Don Rafael and Doña Feliz have already interfered in his plans for me; to thwart him further would be to make him their deadly enemy. Oh, you know not, Señor, what men like Don José Ramirez will do; and yet he is my father!” Her voice failed in an agony of terror and shame. Ashley’s words died on his lips. Here was a grief he could hardly understand, against which he could offer no advice to one whose education and mind were so different from his own. What could he say to her to lessen the burden of her grief? Surely not, as he would have done to Chinita, that she should strive to content herself in a destiny which would raise her from an obscure station to wealth,—for the revolutionary chieftain, he supposed, had never-failing resources,— and to a certain dignity, as the daughter of a popular hero. He could have imagined Chinita as glorying in such a position, and Rosario as reigning with a thousand airs and graces in the miniature court around her; but here was a child, a very child, shrinking from the possible contact with cruel and conscience-hardened adventurers, and stricken to the heart by the thought of losing the heritage of an honest name. Presently Chata spoke again, as though to speak to this stranger in whom she had involuntarily confided was, in spite of her self- reproach, to lay her long repression, her doubts and fears, before a shrine. Almost incoherently, in the rapid utterance of overwhelming excitement, she poured forth the story of the interview of Ramirez and Doña Rita which she had overheard in the garden at El Toro. In her earnestness she did not even omit the project which had been discussed for uniting her future with that of Ruiz. Ashley’s teeth became set and his lips pressed each other as he listened. Here indeed was confirmation of the villain’s claim; and yet—and yet—
- 53. “It cannot be!” he interrupted. “I cannot believe it. You say yourself, your very being recoils from him—ah, it must be for some deep cause you hate him so! And I too—I hate him. Did I not tell you I have a long arrear of wrong to settle, and—” “You!” she ejaculated wonderingly. “What wrong can he have done to you? Was it he who robbed and wounded you?” “No, no!” he answered. “Those were but the chances of travel. There is something far greater than that; but while you believe him to be your father, I will not talk to you of avenging myself. I should be a brute indeed to add a feather’s weight to your trouble. Do not think of that again; but believe me, there is some mystery neither of us understands. The truth may be far from what you think it. I will demand it of Don Rafael, of Doña Feliz—they must know.” She was looking at him wonderingly, almost in awe, with those large, clear, gray eyes, which seemed to have in them the reflection of a purer, calmer sky than the intense and fiery one beneath which she was born. As he looked at her, her very dress seemed a disguise, so entirely did she seem disassociated from the scenes in which he found her. “Ah,” she said hopelessly, clasping her hands, “you do not know my people as I do. I have not asked Don Rafael or Doña Feliz to tell me the secret of my birth. They have concealed it for some weighty reason, and until the time comes when they judge it right for me to know, I might plead with them in vain. By going to them I should but lose their love, and become the object of their suspicion and doubt. Oh, I could not endure that, I would not endure it! Doña Rita is changed, is cold, distrustful; and why should I by useless haste bring their anger upon her? No, no, Señor, I beg, I entreat you, say nothing to Don Rafael. Let me be in peace as long as I may. My father has not come to-day; perhaps he has forgotten me!” “You reason wildly,” said Ashley. “I cannot understand these strange duplicities; yet I know it is quite true I should gain nothing by direct questioning. What have I ever gained? No, it is to Doña Isabel I will go, and to Ramirez himself. But promise me, Chata,” he added earnestly, “promise me, by all you hold most sacred, never to leave the hacienda to meet him or any messenger of his. Promise for
- 54. your own sake, and I swear I will leave no measure untried to free you from this strange bondage.” He had expressed himself with difficulty throughout, but she caught his meaning eagerly. “Oh, if I dared to promise!” she murmured. “But it is the duty of the child to obey. Besides, he would tell me the truth; even this very day I thought I should have known the wretched story,—oh, I am sure it is a wretched one! Well, I have a respite,—a little respite. Go, Señor; you have been kind,—be kind still by being silent. I must go; the sun will soon set. Ah, unfortunate that I am, the men will be coming in from the fields, the women will be at their doors,—how shall I ever return without being seen?” Here was indeed a difficulty. The strictly nurtured girl had never in her life been outside the precincts of the village alone; that she then should be, and with a young man, would occasion endless gossip. The two involuntary culprits looked at each other with blank faces,— Ashley in absolute dismay, for he had heard of the strict requirements of Mexican customs and etiquette, and knew to what cruel innuendo this young girl had exposed herself. He realized then for the first time how great her courage had been in venturing forth in obedience to the command of Ramirez. “Chata, Chata! for God’s sake,” he cried, “go at once! I will remain. Your mad freak will be pardoned this time, when they see you are alone.” “Alone!” she echoed, a crimson flush suffusing her face as she fully realized the significance of his words, and saw that with a sudden faintness he leaned against the wall, spent with excitement and fatigue. “Yes, yes,” he said wearily, “none will know I am here. The night will soon pass; in the morning I will wander in to one of the huts. They will fancy I was lost on the mountain. None will think—you will be safe.” “I am safe,” said the girl with sudden resolution. “Would a woman of your own country leave you to hunger and shiver through all the night in a desolate place like this? Ah,” she added with a long-drawn breath and a tremor, “even ghosts are here.”
- 55. Ashley smiled. “I do not fear them,” he said. “I fear but for you. Go! go at once! And yet before you go, promise!—promise me never to run these risks again; never in any place to meet Ramirez!” In his earnestness he clasped her hand and gazed eagerly into her limpid eyes. “I promise, yes, I promise,” she said hurriedly. “But I will not leave you,—weak, fasting, fainting!” She looked up at him with the angelic pity in her face that innocent children feel before they have learned distrust. Ashley read the perfect trust, the perfect guilelessness, of her tender nature. Rather, he thought, would he die than cast a cloud upon her name; and what, after all, would matter the privations of a few hours? That he must not be seen in the neighborhood for some time after her unusual wanderings was a foregone conclusion. How should he combat her resolution? Truly, this gentle girl had deep springs of action within her. For duty and right she could be a very heroine. As these thoughts passed through his mind, a sudden breeze stole through the open gate and reached the lobby; there was a faint smell of cactus flowers, and a rustle of the dry grass. The effect was weird and ghostly. A shadow fell between them. Had the sun plunged down beneath the western hills? They glanced up and started apart,—Doña Feliz was before them. The ordinarily grave and self-possessed woman was for a moment the most agitated of the three. She gasped for breath. She had been walking fast, but it was not that alone which caused the earth apparently to reel beneath her. She had found Chata, whose disappearance from the hacienda she had discovered at the moment when a cry had run through the house that the horse of the young American had returned riderless; that the youth had doubtless met an evil fate. She had found them both,—and together! She pressed her hands over her eyes as though to shut out some horrid vision; a moan broke from her lips,—then she caught Chata in her arms and glared at Ashley with concentrated anguish and fury. Had one guilty thought possessed him, or had he meditated a doubtful act, her glance would have covered him with confusion. As it was, he read in her expressive face and gesture a volume of deep and terrible significance, far different from that which an anxious
- 56. duenna ordinarily casts upon the imagined trifler with the affections of her charge. Nothing of that assumption of virtuous indignation, yet of flattered satisfaction, which in the midst of remonstrance gives indication of a certain sympathy and inclination to condone the offence in consideration of its cause, was apparent. Doña Feliz evidently had in her mind no lover’s venial follies. This meeting was to her a tragedy,—the very culmination of woes. Ashley read something of this in her expression and gesture, and hastened to reassure her, by giving a partial account of the reasons of his return. The anxious guardian of innocence would perhaps have thought his turning aside at the instance of Pepé to view his cousin’s grave, his lingering there, the departure of the servant, the flight of his horse, all a fabrication, but for the meeting with his cousin’s murderer, which the young man recounted with startling brevity and force, unconsciously regaining in the recital much of the excitement and deep indignation which had thrilled him at the time of the encounter, and which had gradually subsided amid the new complications that Chata’s words had opened before him. Involuntarily Ashley refrained from any allusion to the fact that the young girl had ventured forth to meet this man Ramirez; and acute though she was, it did not suggest itself to Doña Feliz, who seemed lost in wonder at the almost miraculous chance which after so many years had brought into contact the secret murderer and him whose mission it seemed to avenge the innocent blood. In his recital, Ashley had not mentioned the name of the self-confessed assassin. Doña Feliz did not ask it,—perhaps she inferred that it remained unknown to him,—yet Ashley was certain his identity was no problem to her. Had she guessed the secret all these years? Had she screened the guilty and fostered the innocent, at the same time? Deep as was her interest in his tale, full as was her acceptance of the fact that the meeting of Ashley Ward and Chata was purely accidental, Doña Feliz did not exhibit a tithe of that horror and dismay which was depicted upon the countenance of Chata, who listened breathlessly,—her lips apart, her hair pushed back, her startled eyes opened wide. Ashley would gladly have recalled his
- 57. words as he looked at her. Every particle of color had faded from her face. In her absorption in Ashley’s words, Doña Feliz had ceased to regard or even remember the young girl, who suddenly recalled herself to that lady’s mind. “Doña Feliz,” she murmured in an agonized and pleading voice, “when my mother forsook me, why did you not suffer me to die? Oh why, why did I live to hear such horrors, to know such wretchedness as this?” As if in a frenzy, before either thought to stop her, or found words with which to answer or recall her, she ran out from the lobby,—her small figure passing unimpeded through the cactus-guarded gateway,—and fled across the plain toward the hacienda. She was young and strong,—excitement lent wings to her feet. Doña Feliz and Ashley standing together in the gateway looked at each other in amazement. The girl continued her flight until she reached the outskirts of the village. There a horseman stopped her. Even at that distance they recognized Don Rafael, and saw that Chata clung to him passionately when he dismounted. “She is safe!” murmured Doña Feliz. “Rafael will know how to account for her presence with him.” “Yes,” thought Ashley; “these Mexicans fortunately know how to coin a plausible tale as well for a good cause as for a bad one.” They saw that Don Rafael, placing Chata on his horse before him, had turned in the direction of the hacienda, and was signalling to the vaqueros lingering in uncertainty at the gate. “They will be here in a few moments, Señor,” said Doña Feliz, calmly. “We must lock the gates and conceal the keys. You must be found outside of, not within, these walls.” Ashley assented, and within a few moments, and in silence, their necessary task was accomplished. Doña Feliz then led the way toward the village, walking rapidly as though impelled by the agitation of her thoughts or a desire to escape question. Ashley kept pace with her with some effort, though the chill which had come with the grayness of evening over the landscape revived and strengthened him. The breeze was whistling in the tall corn in the
- 58. fields as they passed them; the cattle were lowing in the yards; the distant sound of horses’ feet was beginning to be heard; the riders like gray columns were seen approaching. Ashley laid his hand upon the arm of Doña Feliz. She turned and looked at him. His face was to her a volume of reproach and question. Her voice broke forth in a great sob. “Ashley! Ashley!” she exclaimed, “do you not comprehend that a vow stronger than death controls me? Ask me nothing, but follow the indications which the good God—Fate—Providence—has given you. The time may come—for strange things are happening in our land—when I may be free once more. Now I may only watch and wait and pray. Ah! what hard tasks for a woman such as I am! But I have vowed; I cannot retract!” “You are wrong!” cried Ashley. “How strange that a woman of so much intelligence, of a conscience so pure, can suffer herself to be led by the spurious customs and traditions that pride and priestcraft together have fastened upon her people! But your very reticence, Doña Feliz, confirms my beliefs. I will go as you recommend, as my own judgment urged me, to follow the clew I have so unexpectedly obtained. Do not think that a vulgar and wolfish desire for vengeance alone actuates me; but justice must be done. Even for Chata’s sake, this man must not be suffered to continue his course unchecked.” He would have added more, but Gabriel and Pancho, the vaqueros, came galloping up with vivas and cries of welcome. “Praised be our Holy Mother, and all the saints!” exclaimed one. “Don Rafael told us you were safe. Who would have thought the Señora and the niña Chatita would have found you no farther away than deaf and blind Refugio’s? Ay, Doña Feliz, without seeking, finds more than will a dozen unlucky ones, though they have spectacles and lanterns to aid them. In the name of reason, Don ’Guardo, how happened your nag to throw you and gallop back thus? He is manageable enough with any of us—” and there was a suspicion of irony in the solicitude of the horseman, which did not escape Ashley as he answered,— “To-morrow you shall have the whole tale. These roads of yours are no place for a man to linger on alone. But for the present,
- 59. remember I have a wound not too well healed, and am more anxious for supper than for recounting adventures.” “Ah! ah! he was stopped on the road by banditti,—and has escaped.” The vaqueros regarded Ashley with vastly increased respect. Their numbers were augmented as they neared the hacienda; and when the party reached the gates, wild rumors of Ashley’s prowess were already flying from mouth to mouth. Ashley did not present an imposing figure as he passed in between the crowds of admiring women; but he served to turn their thoughts from the unprecedented appearance of Chata, which was but unsatisfactorily explained by Don Rafael’s ready fiction that she and Doña Feliz had been piously visiting at the hut of old Refugio, and that upon the arrival of Ashley there, the young girl had hastened to meet her father, and give him news of the American’s safety. “Doña Feliz is even too careful of her grandchildren,” said some of the more liberal. “What harm would have come to the maiden from a walk of a few minutes, or a few words spoken, with an honorable young man such as he seems to be? Now, if it were Don Alonzo, or that gay young Captain Ruiz, for example!” Rosario, who had been leaning over the balcony as Ashley arrived, heard something of what was said, and smiled. She was not at all ready to believe that Chata’s walk had extended only as far as the hut of blind Refugio; and that it had not been made in company with Doña Feliz she was quite certain. But she had no time just then to interest herself in Chata’s affairs,—her own were far too engrossing; for the new clerk whom Carmen, at Doña Isabel’s request, had sent from Guanapila, evidently was much more intent upon studying the charms of Rosario than his new duties, and in seeking favor in her eyes than in those of the administrador himself. The new clerk was Don Alonzo, and Don Alonzo was a handsome fellow, with the face of an angel, Doña Rita said,—a contrast indeed to that little brown monkey Captain Ruiz; and Rosario smiled coyly, and did not gainsay her. The next morning at an unusually early hour this same Don Alonzo tapped on Ashley’s door. “Pardon, Señor,” he said, “but the horses
- 60. and servants are ready, and I have orders myself to accompany you beyond the boundaries of Tres Hermanos.” The announcement was not a surprise. Ashley had arranged his departure with Don Rafael upon the preceding evening. He dressed hastily, and while partaking of his cup of chocolate, glanced often around him, in expectation of the appearance of Don Rafael or his mother; but in vain. The American could no longer hope to learn at a parting moment what each had chosen to withhold. Irrationally, and against all likelihood, he ventured to hope that Chata might steal forth for a farewell word. He laughed at himself afterward for the thought, saying that the air of intrigue had begun to affect his own brain. Sooner than was usual, even in that land of early movement, Don Alonzo warned him it was growing late. It was not too late or early for Rosario to wave her little brown hand from her mother’s window in token of adieu. Ashley did not see it, but he for whom it was intended did. So with more foreboding and reluctance than he could have imagined possible but a few hours before, Ashley once more rode forth from Tres Hermanos,—this time with a definite object, from which he felt there could be no turning back, no possible end but his own death or the downfall of a man to whom but yesterday he had been utterly indifferent, but who to-day was inseparable from all his thoughts, his passions, his purposes,—Ramirez the revolucionario, the declared murderer of John Ashley, the declared father of the young girl who seemed the very incarnation of honor and sensibility, of tenderness and purity.
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