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Dynamic Processes: Lecture 1
Lecture Notes
MOLECULAR SIMULATIONS
ALL YOU (N)EVER WANTED TO
KNOW
Julia M. Goodfellow
Crystallography, Birkbeck
WHY DO SIMULATIONS?
Numerical simulations fall between
experiments and theoretical methods
 Where there are no available
experimental data
 Where it is difficult or impossible to get
exptl data
 Add atomic insight
Crystallography, Birkbeck
AIMS AND OBJECTIVES
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Please see overview of the course on
‘Dynamic Processes’ which lists the
aims and objectives of this course unit
and each letter
Crystallography, Birkbeck
What is molecular
simulation/modelling ?
Quantum Mechanical Methods
 Knowledge based methods
 Classical Methods based on concept of
energy function describing interaction
between atoms
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Crystallography, Birkbeck
CONFORMATION
EXPERIMENTAL ANALYSIS
(1) X-RAY refinement
(2) NMR - structure determination from
NOEs.
 HOMOLOGY MODELLING
Optimization of models
 ‘ENERGY’ CALCULATIONS
(1) conformation in solution
Crystallography, Birkbeck
(2) conformation of complex
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DYNAMICS
Multiple Conformations
 rms - atomic fluctuations
 occurrence of hydrogen bonds
 anisotropic thermal elipsoids
 correlation functions
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Crystallography, Birkbeck
•THERMODYNAMICS
POTENTIAL ENERGY
 FREE ENERGY CHANGE
 RELATIVE BINDING ENERGY
 STABILITY OF CHEMICAL
MODIFICATION
 PARTITION COEFFICIENTS
 REDOX POTENTIALS
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Crystallography, Birkbeck
Methods
Energy Minimization: based on using
mathematical methods to optimize a
function to its minimum value
 Monte Carlo: based on probability of
change in energy between different
conformations
 Molecular Dynamics: based on
Newton’s Laws of Motion
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MONTE CARLO SIMULATIONS
one could make random moves, calculate energy,
add energy* probability to get average
 instead make random move and choose whether to
accept according to probability and then just add
energies
 state n, make random move to n’
 DEnn’ = En’ - En
 If DEnn’ < 0, Accept
 If DEnn’ > 0, make choice as follows:
– choose random nos x 0<x<1
– if exp DEnn’/KT > x, accept
Crystallography, Birkbeck– if exp DEnn’/KT < x, reject
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Molecular Dynamics
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Uses time trajectory as systems evolves due to Newton’s Laws
of Motion
F= M x A
know mass & calculate force from derivative of potential energy,
so get acceleration A
a = dV/dt where v is velocity
v = dx/dt where x is position
Solve differential equations numerically using standard
methods Verlet, Beeman, Gear
solutions are iterative over small time steps typically 1 fs;
generates trajectory through microstates which obey ensemble
constraint (NVT) and hence one can calculate averages
Crystallography, Birkbeck
Non-standard techniques
‘simulated annealing’ uses MC or MD at
high temperature to move over energy
barriers to allow conformational change
followed by cooling/min into energy
minimum
 ‘free energy’ calculations
 non-equilibrium systems
 joint QM/MD calculations
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Crystallography, Birkbeck
STATISTICAL MECHANICS
link between
atomistic representation (x,y,z,vx,vy,vz) and
thermodynamics ( macroscopic parameters such as heat
capacity)
For many body systems - lots of microstates consistent with a given
set of conditions (Temp, Pressure, Volume, Natoms)
Experimental measurements are an average over these states.
Simulations - find trajectory through all possible states and
calculate average
Crystallography, Birkbeck
FORCE FIELDS
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What interactions are important ?
How do you represent them ?
How do you parameterize them ?
Bond deformation, Bond Angle deform.,
Torsion angles, improper torsion, cross-terms
van der Waals, electrostatics, 1-4 electrostatics
hydrogen bonding
Solvent
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Software and hardware
Software: lots - amber, insight/discover,
sybyl, quanta/charmm etc
 Hardware: PC to CRAY T3D
 Requirements:
Initial Model/Set Up
Running Simulation
Analysis and Validation
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Crystallography, Birkbeck
initial requirements
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Starting configuration of atoms
info about the molecule - nos of atoms, atom
types, connectivity (bonds, angles, torsions),
partial electronic charge
info about how atoms interact - covalent
bonds, angles and torsions: non-covalent LJ,
electrostatics, H-bond
Solvent ?
control: Vol, P, Temp, time step
Crystallography, Birkbeck
VALIDATION
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Everyone gets good qualitative agreement
with experimental data
Totally ad hoc
choose sensible starting model
check that it is behaving properly especially at
the beginning
thorough analysis of many parameters - even
if you cannot publish them all
choose the right level of detail
Crystallography, Birkbeck
Future 
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improve assumptions
validation
need to improve - long range and short range
electrostatics
need to improve precision of all interactions
as compromise between many weak
interactions
need to increase time beyond ns to ms
Need to get quicker so that we can ‘play’ with
system. difficult when it takes 3-6 months a
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ATOMISTIC SIMULATIONS
APPLICATION AREAS
(A) environmental effects on peptide stability: role of
solvents in stabilising/ destabilising secondary
structure
(B) conformation of chemically modified dnas
 NOVEL ALGORITHMS
Protein folding/unfolding - solvent insertion into
cavities; stability and unfolding of different protein
architecture
 VALIDATION
development of systematic protocols for
assessing simulations
Crystallography, Birkbeck
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