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### MOLECULAR SIMULATIONS

Lecture Notes

ALL YOU (N)EVER WANTED TO KNOW

Julia M. Goodfellow

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

AIMS AND OBJECTIVES

- Please see overview of the course on ‘Dynamic Processes’ which lists the aims and objectives of this course unit and each letter

What is molecular simulation/modelling ?

- Quantum Mechanical Methods
- Knowledge based methods
- Classical Methods based on concept of energy function describing interaction between atoms

CONFORMATION

- EXPERIMENTAL ANALYSIS
(1) X-RAY refinement

(2) NMR - structure determination from NOEs.

- HOMOLOGY MODELLING
Optimization of models

- ‘ENERGY’ CALCULATIONS
(1) conformation in solution

(2) conformation of complex

DYNAMICS

- Multiple Conformations
- rms - atomic fluctuations
- occurrence of hydrogen bonds
- anisotropic thermal elipsoids
- correlation functions

THERMODYNAMICS

- POTENTIAL ENERGY
- FREE ENERGY CHANGE
- RELATIVE BINDING ENERGY
- STABILITY OF CHEMICAL MODIFICATION
- PARTITION COEFFICIENTS
- REDOX POTENTIALS

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

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
- if exp DEnn’/KT < x, reject

Molecular Dynamics

- 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

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

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

FORCE FIELDS

- 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

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

initial requirements

- 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

VALIDATION

- 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

Future -

- 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 calculation

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

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