MOLECULAR SIMULATIONS

1. Dynamic Processes: Lecture 1 Lecture Notes MOLECULAR SIMULATIONS ALL YOU (N)EVER WANTED TO KNOW Julia M. Goodfellow

2. 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

3. 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

4. What is molecular simulation/modelling ? • Quantum Mechanical Methods • Knowledge based methods • Classical Methods based on concept of energy function describing interaction between atoms

5. 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

6. DYNAMICS • Multiple Conformations • rms - atomic fluctuations • occurrence of hydrogen bonds • anisotropic thermal elipsoids • correlation functions

7. THERMODYNAMICS • POTENTIAL ENERGY • FREE ENERGY CHANGE • RELATIVE BINDING ENERGY • STABILITY OF CHEMICAL MODIFICATION • PARTITION COEFFICIENTS • REDOX POTENTIALS

8. 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

9. 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

10. 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

11. 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

12. 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

13. 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

14. 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

15. 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

16. 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

17. 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

18. 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