Md simulation and stochastic simulation

Stochastic Simulation,
Molecular Dynamic
Simulation
Prepared by:
Abdul Ahad 20685
Presented to:
Dr. Ghulam Abbas
Riphah
International
University,
Faisalabad

Simulation
• The process of designing a mathematical or logical
model of a real system and then conducting
computer based experiments with the model to
describe, explain and predict the behavior of real
system.

Steps involved in creating simulations
• Gather and prepare accurate data to reflect the real world.
• Create mathematical formulaealgorithms to generate output data from
that which is input.
• Create graphs or other output displays for the information.
• Verify and validate the data by re-testing scenarios to ensure that the same
result occurs.

Advantages of Simulations
• Safety – able to test or experiment without harming the person or environment.
• Economic saving – from the use of simulations to design and test new products
before prototypes or finalizing the product.
• Projection – can look into future and highlight potential impacts and address them
before they occur.
• Visualization – can see and understand relationships. Can speed up or slow down
time.
• Replication – able to look at things under a variety of different scenarios.

Stochastic
• Taken from Greek word stokhastikos "able to guess”.
• Stochastic refers to a variable process where the outcome involves some
“randomness” and has some uncertainty.
• It is mathematical term and is closely related to randomness and
probabilistic and can be contrasted to the idea of “deterministic”.

Stochastic Simulation
• A stochastic simulation is a simulation of a system that has variables that can
change stochastically (randomly) with individual probabilities.
• Realizations of these random variables are generated and inserted into a model of
the system. Outputs of the model are recorded, and then the process is repeated
with a new set of random values.These steps are repeated until a sufficient amount
of data is gathered. In the end, the distribution of the outputs shows the most
probable estimates as well as a frame of expectations regarding what ranges of
values the variables are more or less likely to fall in.

• In order to determine the next event in a stochastic
simulation, the rates of all possible changes to the state
of the model are computed, and then ordered in an
array. Next, the cumulative sum of the array is taken,
and the final cell contains the number R, where R is the
total event rate.This cumulative array is now a discrete
cumulative distribution, and can be used to choose the
next event by picking a random number z~U(0,R) and
choosing the first event, such that z is less than the rate
associated with that event.

Uses
• Stochastic
simulation
plays
fundamental
role in the
following fields;

Real life
Applications
The Monte Carlo Simulation is an
example of stochastic model used in
finance.
It can simulate how a portfolio may
perform on the probability distributions
of individual stock runs.
Also applied to insurance industry,
telecommunication and traffic control
etc.

Stochastic vs Deterministic Model
In Deterministic Model; the
output of the model is fully
determined by the values of
parameters and initial conditions.
A process is deterministic if the
future is determined by its
present and past states.
A stochastic model is a random
process which evolves in time.
Even if we have full knowledge of
current state of system, we can
not be sure of the effect in future
periods. It’s a collection of
random variables.

Molecular Simulation
• This is a computational method used to simulate physical movements of
atoms and molecules depending on time and force field chosen under
different conditions(temperature, pressure, force).

MD Simulation: Introduction
• One of the principle tools in the theoretical study of biological molecules
• Calculates the time dependent behavior of a molecular system
• Provides detailed information on the fluctuations and conformational
changes of proteins and nucleic acids
• Used to investigate the structure, dynamics and thermodynamics of
biological molecules and their complexes Reading Material.

Principle
• MD Simulation is based on Newton’s second
law of motion
𝐹𝑖 = 𝑚𝑖 𝑎𝑖
Where,
𝐹𝑖 is the force exerted on particle 𝑖
𝑚𝑖 is the mass of particle 𝑖
𝑎𝑖 is the acceleration of particle 𝑖

There is no analytical
solution to the
equation of motion. It
must be solved
numerically.
Numerous numerical
methods have been
developed for
integrating the
equations of motion
• -Verlet algorithm
• -Leap-frog algorithm
• -VelocityVerlet algorithm

Applications
Protein stability
Conformational changes
Protein folding
Molecular recognition: proteins, DNA, membranes,
complexes
Ion transport in biological systems Drug Design &
Structure determination (X-ray and NMR)

Advantages
• Molecular dynamics (MD) is a form of computer simulation in which atoms
and molecules are allowed to interact for a period of time.
• Because molecular systems generally consist of a vast number of particles,
it is impossible to find the properties of such complex systems analytically;
MD simulation circumvents this problem by using numerical methods.

conti..
• It represents an interface between laboratory experiments and theory.
• It can be understood as a "virtual experiment.
• It generates the most stable and the energy minimized conformations of
the protein.
• While doing so it computes many different frames or trajectories of the
same protein.

References
• https://en.wikipedia.org/wiki/Stochastic_simulation
• http://www.doc.ic.ac.uk/~jb/conferences/pasta2006/slides/stochastic-
simulation-introduction.pdf
• https://www.slideshare.net/puneetkacker/md-simulation

Md simulation and stochastic simulation

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