MM | MD | Theory | Forcefield | Basic steps | Limitation | Enhanced MD

1. Molecular Dynamics : Basics
Ajay Murali
Msc Biotechnology
VIT

2. Introduction
 Molecular dynamics is the study of motion of molecules in explicit conditions.
 The concept behind MD is solving Newton's 2nd law of motion to find the position of atom
as time proceeds.
 MD offers a robust way to study kinetics and underlying static and thermodynamics
properties in real time through computer simulation.
 Limited computational capacity and models to correctly represent the system impedes the
development of MD.
 Once perfected the MD can offer endless possibilities of application and might ultimately
help us answer many a questions that had made us curious.

3. What to expect !!
 Molecular dynamics - General introduction and types
 Force Fields (FF) and Potentials
 Steps in MD procedure
 Types of FF and Solvation models
 Periodic boundary and PBC
 Minimum image convention and Cutoff distance
 Thermostat and Barostat.
 Integrator Algorithm
 Limitations and Applications
 Using GROMACS
 Discussion
 Conclusion

4. 0.1
0.1
Conformers
What is Molecular Dynamics ?
 A statistical approach trying to find out the evolution of a system with respect to time.
 Basically the study of motion of molecules based on the “ergodic hypothesis”
 “Given a long time scale, all the microstate has equal probability of occurrence “
 Thus it gives out the detailed description of the “Boltzmann distribution/Gibbs distribution” {
conformation to energy graph}
http://crystal.med.upenn.edu/sharp-lab-pdfs/2015SharpMatschinsky_Boltz1877_Entropy17.pdf
Leipzig: J. A. Barth. 1898.

5. Major ways to account for MD !!
Quantum Mechanics
Solves the schrodinger wave
equation for getting the positions
Computationally intensive
More accurate method of MD
Monte Carlo Simulation
More of a mathematical
and statistical approach on
finding the conformers
probability and statistical
techniques helps to pin
down on the position
Less accurate but faster and
compuationally cheapl
Molecular Mechanics
Utilises newtonian mechanics
to find position
More of a approximation
methods
Will not be able to explain
the chemical reactivity involved
Molecular dynamics

6. Its a Quantum world !!
 Its is now well versed that the physic of subatomic particle does not behave as same as
that of macroscopic world which is better explained by Newtonian mechanics
 Therefore Quantum mechanics is the physics which can better help us in understanding
microscopic world
 QM is based on the schrodinger's wave equation
https://iopscience.iop.org/article/10.1088/0143-0807/17/2/017 https://pubs.acs.org/doi/10.1021/acs.jctc.7b01195

7. Monte Carlo simulation
 An alternative method to discover low-energy
regions of the space of atomic arrangements
 Instead of using Newton’s laws to move
atoms,consider random moves
 Takes into account changes to a randomly
selected dihedral angle, or to multiple dihedral
angles simultaneously and then
 Evaluate energy linked with resulting atom
positions to decide upon whether or not to
“accept” each move you consider
https://en.wikipedia.org/wiki/Monte_Carlo_molecular_modelin
g

8. Metropolis criterion in MC simulation !
Metropolis criterion ensures that simulation will sample the Boltzmann distribution,it
calculate the PE difference (ΔU) between the before & after move position
The Metropolis criterion for accepting a move is
– If ΔU ≤ 0, accept the move
– If ΔU > 0, accept the move with probability
On long enough runs, the probability of observing a particular arrangement of atoms is
given by the Boltzmann distribution
If one gradually reduces the temperature T during the simulation,this becomes a
minimization strategy (“simulated annealing”).

9. Molecular Mechanics and MD ?
If to be successful pre-requisite has to be satified
The set of initial conditions (initial position and velocity of all particle)
The interaction potentials for deriving the force on the system
Utilising the initial pre-requisite it solves for the newtonian equations for motion
𝑓
= 𝑚 ∗ 𝑎
𝑓 = −𝛻𝑉
−𝑑𝑉
𝑑𝑡
= 𝑚𝑖 ∗
𝑑2𝑟
𝑑𝑡2
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4026342
/
https://en.wikipedia.org/wiki/Molecular_mechanics

10. O H
H
OH
H
OH
H
O
H
H
Force fields and Potentials
Force Fields are a set of predifined parameter and potential defined as to carry/defining out
MD simulation and analysis
 From earlier equation it is understood that force is the negative difeerential of potential
energy ... !! What is potential energy and what make it ?? !!
 Bonded and Non-bonded potentials contribution to Potential energy
electrostatic interactions van der Waals forces
e
+
e
+
e
+
e-
e-e-

11. Force fields and Potentials
 Force Fields are a set of predifined parameter and potential defined as to carry/defining out
MD simulation and analysis
 From earlier equation it is understood that force is the negative difeerential of potential
energy ... !! What is potential energy and what make it ?? !!
 Bonded and Non-bonded potentials contribution to Potential energy

12. Steps in performing a MD
Selection of interaction model
Selection of boundary conditions
Selection of initial conditions (positions,velocities . . . )
Selection of ensemble (NVE, NVT, NPT . . . )
Selection of target temperature,density/pressure . . .
Selection of integrator, thermostat, barostat . . .
Perform simulation until equilibration is reached (property dependent)
Perform production simulation to collect thermodynamic averages, positions, velocities
Analyze the results via post-processing
http://www.gromacs.org/Documentation/Howtos/Steps_to_Perform_a_Simulation

13. Types of Forcefield
 They are a combination of parameters (van der Waals radii, bond order etc..) and the
mathematical equations to calculate the particle interaction
 There is no universal force field which works for all particle because of the huge variability
in the interaction
FORCEFIELD THEIR USE
MM2,MM3, MM4 proteins,DNA,lipid and small molecule
CHARMM “
AMBER “
OPLS “
GROMOS protein, DNA, sugar
UFF elements in periodic table
MMFF small drugs and drug complex with proteins
https://www.neutron-sciences.org/articles/sfn/pdf/2011/01/sfn201112009pdf
https://www.researchgate.net/post/How_to_choose_force_fields_for
olecular_dynamics_simulation

14. Solvation Model
Molecule to be simulated must be immersed in proper solvation medium like water , organic
solvents or lipid bilayer to mimic their natural environment
Provides the dielectric constant that affect the electrostatic interaction ,a key determinant
among molecular interaction
EXPLICIT MODEL IMLICIT MODEL
Physical Presence Of Water Mimics The Dielectric Effect By
Placing A Continuous
Homogeneous Medium With Bulk
Dielectric Constant
SPC,SPC/E,TIP3P,TIP4P,TIP5P Distance Dependent Dielectric ,
GliBot,GBMB,Poisson Bosson
Surface Area
More Accurate ,Computationally
Expensive
Less Accurate, Computationally
Expensive
https://courses.physics.illinois.edu/phys466/sp2011/projects
/2011/Protein_Solvent_Models_Sikanar_David.pdf https://en.wikipedia.org/wiki/Solvent_model

15. Periodic boundary condition PBC and why ?
“ During simulation it is of top priority that number of particles
remain constant in the system, Instability in number may
happen as particles are always in motion.”
This is accomplished by boundary condition which place a
restriction on motion for particle beyond the boundary.
If not done the MD process will crash.
Types
 Boundary condition with harmonic restraints - obsolete not
used
 Periodic boundary condition - commonly used
 Small box replicated in all directions
 A particle that leaves the box on one side is
replaced by an image particle that enters from
the other side
 There are no walls and no surface particles
Cell where simulation happens
https://nanohub.org/resources/7577/download/Martini_L5_Boundar
yConditions.pdf
http://www.people.virginia.edu/~lz2n/mse627/notes/Bo
df

16. Periodic boundary condition PBC and why ?
“ During simulation it is of top priority that number of particles
remain constant in the system, Instability in number may
happen as particles are always in motion.”
This is accomplished by boundary condition which place a
restriction on motion for particle beyond the boundary.
If not done the MD process will crash.
Types
Periodic boundary condition -Limitations

New artificial correlations

Problem in long range interactions

nearest image not always energetic,spliting of molecules
Alternatives?

Space filling unit cell

Surface of a (hyper) sphere
Cell where simulation happens
https://nanohub.org/resources/7577/download/Martini_L5_Boundar
yConditions.pdf
http://www.people.virginia.edu/~lz2n/mse627/notes/Bo
df

17. Non-bonded interactions and use of minimum image and cut-off
NBs consist of longe and short range intearction thus elucidation these the most severe
during simulation
The difficulty usally resonate exponentially with the no.of particles
The minimum image and spherical cut-off lowers the comp.expense.
By minimum image convention “The interaction is calculated with
the closest atom or image inside the cutoff”.
When periodic boundary conditions and cutoff are being used, the cutoff should not be so
large that a particle “sees” its own image
 “The cutoff have to be no more than half the length of the cell”
http://manual.gromacs.org/2019-beta3/reference-
manual/algorithms/molecular-dynamics.html#neighbor-searchi

18. Searching for neighbours
 It is a waste of time to calculate the distances between atoms to decide whether they have
justified the cut off and then to calculate their interaction energy.So it is better to keep a list
of interacting atom beforehand and then find their interaction energy.
 The Verlet neighbor list : Maintain list of neighbour pairs closer than the radius (rc) and a
buffer radius r(skin)
 Keep updating after every 25 times steps,since
 each timestep of MD and MC iteration doesn't change
 the distance that much
 The cell method/Linked list
 Domain decomposition
https://onlinelibrary.wiley.com/doi/abs/10.1002/jcc.540100709

19. Statistical Ensemble
MICRO-CANONICAL
/NVE
• Constant no of
paricle
• Constant volume
• Constant energy
• Resemble a
isolated system
CANONICAL/NVT
• Biological system
• Constant number
of particle
• Constant volume
• Constant
temperature
ISOTHERMAL/
ISOBARIC/NPT
• Invitro
chemical
system
ʮVT/GRANT
CANONICAL
• Physical
solid state
system
Otherwise large number of virtual copies (sometimes infinitely many) of
a system, considered all at once, each of which represents a possible
state that the real system might be in.
A statistical ensemble is a probability distribution for
the state of the system. https://en.wikipedia.org/wiki/Statistical_ensemble_(mathemati
l_physics)
https://ocw.mit.edu/courses/physics/8-08-statistical-physics-ii-
spring-2005/lecture-notes/microcanonical_en.pdf

20. Thermostat and Barostat
http://manual.gromacs.org/2019-beta3/reference-manual/algorithms/molecular-
dynamics.html#temperature-coupling
http://manual.gromacs.org/2019-beta3/reference-
manual/algorithms/molecular-
dynamics.html#pressure-coupling

21. Integrater Algorithm
 1.Verlet Based integrator
Verlet algorithm
Velocity verlet
Leap frog algorithm
 2.The Gear predictor-corrector
https://nanohub.org/resources/7575/do
wnload/Martini_L3_IntegrationAlgorithm
s.pdf
https://link.springer.com/chapter/10.1007/978-1-4612-4066-
2_10

22. Selection of Time-step
 A balance is needed in choosing the timestep.
 Too short timestep lead to a very expensive solution of the equations of motion, and leads
to a limited coverage of phase space and also causes round off errors
 Too large of a timestep leads to instabilities
https://doi.org/10.1016/0010-4655(86)90113-X http://citeseerx.ist.psu.edu/viewdoc/download?doi=
10.1.1.597.5016&rep=rep1&type=pdf

23. Com.Expense of MD too High !!! why?
Many time steps (millions to trillions) and enormous amount of computation at every time
step
Mostly by non-bonded interactions, as these act between every pair of atoms.
In a system of N atoms, the number of non-bonded terms is proportional to N2
Can we ignore interactions beyond atoms separated by more than some fixed cutoff
distance?
For van der Waals interactions, yes. These forces fall off quickly with distance.
For electrostatics, no. These forces does not fall off slowly with distance.

24. Limitations of MD
MD operates based on Born-Oppenheimer approximation,thus only the nucleus is consider
 That limits the application of MD in analysing the chemical reactivity (bond
forming/breaking)
 New force field are developed for dealing with this “reactive force-field” -ReaxFF(Through a
geometry dependent parametrization of reactants and products)
Atomic charges of each atoms are fixed which does not allow any charge polarizability over
time
 “polarizable FF have been developed to deal with this,they develop electronic redistribution
in response to an external electric field.”
Approximation in MD on limited sampling can cause random errors which is more
pronounced while extended runs.

25. Limitation of MD (contind)
 The PES is approximated by a function which gives potential energy as a function of
coordinates and forces are obtained as a gradient of potential energy
 problem with this approximation:
 PES is really the solution of electronic Schrodinger equation with born- Oppenheimer
approximation , and designing a potential function to approximate Schrodinger equation is
a difficult task

26. Enhanced Sampling !!
 Specialized or modified form of MD
simulation has been developed to address
the specific problem and achieve the
objectives in a more efficient manner.
 However it leads to compromise in the
accuracy for speed and based on the
principle of balance of accuracy and
speed.
 This includes accelerated molecular
dynamics (AMD), simulated annealing,
steered molecular dynamics (SMD),
targeted molecular dynamics (TMD),
replica exchange molecular dynamics
(REMD), reduced molecular dynamics
(RMD), Langevin dynamics and
Brownian dynamics.

27. Enhanced Sampling (contd..) !!
 SAMD
 Avoids chances that the procedure stucks in local minima
 This is more effective conformational sampling technique used to explore the
conformational space of the molecule than conventional MD simulation.
 TMD
 MD technique explores the conformational path between initial and final conformation of
the molecule.
 A biased force/potential is applied which propels the molecule towards final conformation
and negates the effect of random thermal motion. It helps to speed up the conformational
change to achieve its final state at faster rate than conventional MD approach.

28. Enhanced Sampling (contd..) !!
 TMD
It is useful for simulation of molecular process which requires larger sampling time
(microsecond or longer) like opening and closing of ion channels or transporters or large
movement of domains in kinases.
It is a type of steered dynamics and hence a non-equilibrium dynamics method and cannot be
used to calculate the equilibrium properties like ΔG
 REMD
 performed at different temperature simultaneously to generate different replica (different
conformation of same the molecule) and they are allowed to exchange between replicas to
produce new and hybrid conformation
 cross the energy barrier at very faster rate, usually applied in protein folding and peptide
chemical space elucidation

29. Application of MD
 Protein structure prediction
 Protein folding kinetics and mechanics
 Conformational Dynamics
 Global optimizations
 DNA/RNA simulations
 Membrane protein /Lipid layer simulations
 NMR and X-ray structure refinement
 To find the thermodynamic property
 Chemical reaction and solvent effect
Change of kinetics to physical properties
Refinement of Homology models
Conformational analysis of peptides
Protein Folding
Transport of ions/opening closing of
Transporters
Refinement of Protein-Ligand complex
Calculation of Binding Free energy

30. GROMACS Installation v2020
 Prerequisite
 cmake 3.17.1.tar.gz
 fftw3.3.8.tar.gz
 gromacs-2020.tar.gz
 ---Installing cmake-----------------------------------
Require a C compiler
 $sudo apt-get install g++
Requires openSSL library
 $sudo apt-get install libssl-dev
Extracting and navigating to the directory
 $tar -xvf cmake3.17.1.tar.gz && cd cmake3.17.1
Configuration and installation of cmake
 $./bootstrap --prefix=/etc/cmake && make && make install

31. GROMACS Installation v2020 (contind..)
 -------Installing the fftw-3.3.8 (Optional - either you can compile from source or otherwise
using cmake--------
 $tar -xvf fftw-3.3.8.tar.gz
 $cd fftw-3.3.8 && ./configure && make && sudo make install
 ---------Installing gromacs------------------
 $tar -xvf gromacs.2020.1.tar.gz
 $cd gromacs.2020.1
 $mkdir build && cd build
 $cmake .. -DGMX_BUILD_OWN_FFTW=ON -DREGRESSIONTEST_DOWNLOAD=ON
 $make && sudo make install
 $source /usr/local/gromac/bin/GMXRC
 $gmx --help