Chapter 1 the physical basis of ligand binding

IN SILICO DRUG
DISCOVERY AND DESIGN
NUMERICAL COMPUTATION OF MOLECULAR DYNAMICS IN
HIV/AIDS INHIBITION RESEARCH
 BENEDIKTUS MA’DIKA
 IZZADIEN IBRAHIM
 RIFQI ALVIANSYAH

CHAPTER 1:THE PHYSICAL BASIS OF
LIGAND BINDING

1.1 INTRODUCTION
• Noncovalent binding :enzymes/substrates, ligands/receptors, or proteins/nucleic acids
• Specificity is needed to preserve the correctness of the biochemical pathways and the
integrity of the information
• Binding affinity and specificity are often provided by noncovalent interactions through
hydrogen bonds, salt bridges, tight packing of complementary molecular surfaces, and
hydrophobic forces mediated by solvent, although longer-range electrostatic interactions
also play a role, particularly in the formation of encounter complexes
• binding free energy t are specifically associated with the solute degrees of freedom: external
rotations/translations and internal vibrations.
• To isolate some of the free energy contributions more clearly, we introduce a multistep
binding path, where the ligand is first uncharged, then moved into the binding site, and
then recharged. This allows us to separate (mostly) the discussion of electrostatic and
hydrophobic effects

1.1 INTRODUCTION
• drug-like molecules can have complex energy surfaces, with polar, nonpolar, and
polarizable groups, hard and soft degrees of freedom, multiple protonation states,
possibly co-bound ions, all of which can reorganize on binding
• They must recognize dynamic, fluctuating, macromolecular targets,displace water
molecules, and compete with a host of other molecules
• In reality, the cell is crowded, stochastic, chemically open, and out of equilibrium.
This is the most basic and important framework with which to start an analysis of
biological ligand binding
• RNA and DNA have some specific properties as receptors, including a high density
of ionic phosphate groups, a corresponding ion cloud, their particular tertiary
organization, and the high flexibility of some weakly structured RNAs

1.2 DEFINING THE BOUND STATE
• conformations where the ligand is within a well-defined binding pocket would be labeled “bound.”
 deep energy well, so that ligand conformations near the boundary of the pocket will have high
energies and low statistical weights. Thus, it does not affects binding constant
 when the binding of two similar ligands to a receptor is compared, there will be some cancellation
of the boundary region contributions of each ligand.
 Even if two definitions of the binding site volume differ by a factor of 2, the two definitions of the
binding free energy would typically differ by kT log 2, just 0.4 kcal/mol at room temperature .Such
a change is not too important for a nanomolar binder at micromolar doses (a few grams in the
bloodstream).
• Experiments measure a physical signal, such as heat release or optical energy absorption, and we
should consider which conformations contribute to the experimental signal and use them as the
basis for comparison.
• The most direct approach is to compute the physical signal directly from a simulation including
include NMR chemical shifts, pKa shifts for protonation of a reporter group, fluorescence spectra,
shifts in vibrational infrared bands, and so on.
• the most common approach in free energy simulations is to compute binding free energy for one or
a few specific sites

1.3 CHEMICAL POTENTIALS AND MASS
ACTION
• Chemical potential governs binding equilibria in solution
• If the solution is dilute
• For the binding free energy, if we choose [R]° = [L]° = [RL]° = C° for simplicity
concentrations are held
fixed through some kind of
constraints
constraints are removed
the only assumptions in this derivation are infinite dilution,
nonionic solutes, and the validity of classical statistical
mechanics. The derivation holds if the solute is not dilute but
intersolute interactions are absent, as in the usual 1 M “ideal-
dilute” standard state
Biochemical applications
routinely involve ionic
ligands and/or receptors,
so it is essential to generalize
these equation for this case

1.3 CHEMICAL POTENTIALS AND MASS
ACTION
• If we consider a neutral pair of solutes X, Y that form a monovalent 1:1 salt, with [X] =
[Y]
• infinite dilution, γX has a very simple concentration dependence
• As the ion concentrations approach 0, the activity coefficients approach 1, so the law of
mass action is still valid.

1.4 FREE ENERGY CONTRIBUTIONS
ASSOCIATED WITH SOLUTE MOTIONS
• loss of solute translation entropy leads to a distinct, concentration-dependent term in the binding
free energy.
• the solute partition function and chemical potential contain several contributions associated with
its overall translation, which are all independent of the solvent and separable from the other
contributions
• rotation also leads to distinct contributions that are largely independent of the solvent (in the
dilute limit).
• intrasolute motions:
 vibrational terms associated with oscillations within an energy basin
 conformational terms associated with degrees of freedom that have several distinct energy basins
• Integrating Out the Solvent: The PMF
 Potential energy function U as a function of the solute and solvent coordinate vectors;X and Y:
U(X,Y) = Uu(X) + Uuv(X,Y) + Uv(Y)
 The configurational partition function for the whole system:

1.4 FREE ENERGY CONTRIBUTIONS
ASSOCIATED WITH SOLUTE MOTIONS
 PMF or W(X) can be interpreted by noting that δW = W − Uu is the free energy to transfer the solute from
vacuum into solvent when it is held fixed in the conformation X
• Solute Translations and Rotations
 let QX trans=(qXtrans)^nx /n X/ ! be the contribution to the partition function that arises from overall
translations of the nX solute molecules, including the nX! factor for their possible permutations.
 Rotational kinetic energy and entropy are also largely or entirely separable and independent of the solvent

• the rotational contribution to the solute partition function and chemical potential
• Solute Vibrations and Conformational Changes
 quasiharmonic model, We compute the atomic fluctuations from a molecular dynamics simulation, which
can use a realistic energy function and solvent environment.
 we compute the atomic displacement covariance matrix C, where Cij = xixj •; xi represents the
displacement of the atomic coordinate xi from its mean position, and the brackets represent a time average.
 We determine the matrix H of force constants that would lead to the observed covariances, if the solute
dynamics were harmonic, from the relation ; H = kT C^−1.
 Finally, we diagonalize a mass weighted version of H to obtain the corresponding “quasiharmonic”
vibrational modes and their enthalpy and entropy

• single vibrational mode, of frequency v and
treated quantum mechanically, contributes to
the partition function and chemical potential
according to
• To express the contribution of multiple energy
wells and conformations formally, it is helpful
to integrate out the solvent degrees of
freedom, as above (Equation 1.9), and write
the free energy or the entropy as an integral
over the remaining, 3N solute coordinates X =
(r1, …, rN):

1.8 ENTHALPY, ENTROPY, AND THEIR
COMPENSATION
• When optimizing a ligand, a rule of thumb is that “binding opposes motion”: we may
introduce groups to form new interactions, only to find that the gain in binding enthalpy is
erased because the new complex is tighter and has a lower entropy.
• For biochemical binding reactions, the measured enthalpy and entropy are usually larger
than the free energy, which implies a certain level of compensation.
• The simplest idea is that a deeper energy well, for an RL complex, will also be narrower,
leading to reduced vibrational entropy

1.9 CONFORMATIONAL SELECTION AND
INDUCED FIT
• Ligand-induced proton binding and release are the main source of
the pH dependence of the binding affinity
• With induced fit (IF), the receptor rearranges after the ligand has
become partly or fully bound
• With conformation selection(CS),the rearrangements occur before
binding, and the ligand simply selects a conformation that
preexisted—albeit with a low occupancy, and pins it in place
• In statistical physics, the concept is distinctly older: the
“fluctuation- dissipation” theorem shows that the response of a
system to a perturbation (such as ligand binding) can be
understood from its fluctuations in the absence of the
perturbation .This is the basis of linear response theory, which is
widely used in biochemistry, for example, for protein electrostatics
and ligand binding.
• In general, the binding reaction is more complex, with a series of
conformational rearrangements occurring, some before and some
after binding

1.10 ALLOSTERY AND LINKAGE
• An essential requirement in the cell is to combine and process information from multiple
channels, building up networks for signaling, energy transduction, or metabolism.
• Crosstalk between two ligands that bind the same biomolecule is referred to either as
linkage or allostery.
• The most common mechanism for allostery is for one ligand to select or induce a
conformational change that affects a second, distant binding site.
• When two ligands X, Y bind to different sites on the same receptor R, linkage occurs if
they influence each other’s binding constant
 It manifests itself when we compare the free energies ΔG(X), ΔG(Y) to bind each ligand
separately and the free energy ΔG(X, Y) to bind them simultaneously.
 If the difference ΔGXY = ΔG(X, Y) − ΔG(X) − ΔG(Y) is nonzero, there is linkage, or
couplingbetween the ligands.
 negative ΔGXY (respectively, positive) indicates cooperative (anticooperative) binding
• Linkage can be “homotropic” (X and Y are the same species) or heterotropic (X and Y are
different species).

• ΔGXY is also the free energy for the reaction XR + YR ⇋ R + XRY
 (-) system favors the right-hand state, R + XYR
• Cooperativity:whenever there are two conformations (R and T, say), with different binding
affinities for one or both ligands: ΔGR(X) ≠ ΔGT(X) and/or ΔGR(Y) ≠ ΔGT(Y)
• X and Y can be as small as two oxygen molecules targeting hemoglobin, or they can be as
complex as a tRNA and a ribosomal subunit, brought together by a translational GTPase
• Allostery is of particular interest for drug design, since it implies that more than one site
can be targeted for inhibitor or antagonist binding
the existence of a large, delocalized, conformational transition implies that still other sites
can be targeted, to block the transition and trap the system, either in its initial
conformation or in an intermediate conformation along the transition path
• Conformational trapping of kinases and ATPases/GTPases in an inactive, OFF state is an
established therapeutic strategy

• For a kinase or ATPase, we can assume the ligands are ATP and ADP the ON but not the OFF
conformation is active for binding a second partner, and ATP has a greater tendency than ADP
to stabilize the ON conformation and activate protein
 ATP preference of each state by the binding free energy differences: ΔΔGON = ΔGON(ATP) −
ΔGON (ADP), and similarly for OFF
 We characterize the ligand preference of each state by the free energy differences: ΔΔGATP =
ΔGATP(ON) − ΔGATP(OFF), and similarly for ADP
 The overall specificity : ΔΔΔG = GATP − GADP = GON − GOFF ≤ 0
 ΔΔΔG is negative by definition of the ON/OFF states; a large magnitude indicates a large
ATPase specificity
 if ON and OFF both have large preferences for their respective nucleotides, ΔΔGON is large
and negative, while ΔΔGOFF is large and positive, so that ΔΔΔG is large and negative

 overall ATP/ADP binding:ΔΔGbind = ΔGbind(ATP) − ΔGbind(ADP)
 x(ANP) = G(ON:ANP) − G(OFF:ANP)
 x(ATP) − x(ADP) =ΔΔΔG ≤ 0,
 GON ≤ Gbind ≤ GOFF
• One important route is to engineer inhibitors that act by stabilizing the inactive kinase conformation,
like the anticancer drug imatinib : different ON/OFF populations for different kinases will produce
binding specificity.
• Binding specificity for a particular kinase K, compared to another kinase K’, will be achieved if the free
energies of the OFF states are sufficiently different, even if the inhibitor binding sites are conserved
and make the same contacts
• The inhibitor will bind preferentially to the kinase with the most stable OFF conformation, say K.
• Interestingly, the K/K′ binding free energy difference will actually report on the ON/OFF free energy
difference in apo-K’ (and different inhibitors will report the same value)

Chapter 1 the physical basis of ligand binding

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