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

Crystallography, Birkbeck WHY DO SIMULATIONS? Numerical simulations fall between experiments and theoretical methods n Where there are no available experimental data n Where it is difficult or impossible to get exptl data n Add atomic insight

Crystallography, Birkbeck AIMS AND OBJECTIVES n 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 ? n Quantum Mechanical Methods n Knowledge based methods n Classical Methods based on concept of energy function describing interaction between atoms

Crystallography, Birkbeck CONFORMATION n EXPERIMENTAL ANALYSIS (1) X-RAY refinement (2) NMR - structure determination from NOEs. n HOMOLOGY MODELLING Optimization of models n ‘ENERGY’ CALCULATIONS (1) conformation in solution (2) conformation of complex

Crystallography, Birkbeck DYNAMICS n Multiple Conformations n rms - atomic fluctuations n occurrence of hydrogen bonds n anisotropic thermal elipsoids n correlation functions

Crystallography, Birkbeck THERMODYNAMICS n POTENTIAL ENERGY n FREE ENERGY CHANGE n RELATIVE BINDING ENERGY n STABILITY OF CHEMICAL MODIFICATION n PARTITION COEFFICIENTS n REDOX POTENTIALS

Crystallography, Birkbeck Methods n Energy Minimization: based on using mathematical methods to optimize a function to its minimum value n Monte Carlo: based on probability of change in energy between different conformations n Molecular Dynamics: based on Newton’s Laws of Motion

Crystallography, Birkbeck MONTE CARLO SIMULATIONS n one could make random moves, calculate energy, add energy* probability to get average n instead make random move and choose whether to accept according to probability and then just add energies n state n, make random move to n’ n DEnn’ = En’ - En n If DEnn’ < 0, Accept n 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

Crystallography, Birkbeck Molecular Dynamics n Uses time trajectory as systems evolves due to Newton’s Laws of Motion n F = M x A n know mass & calculate force from derivative of potential energy, so get acceleration A n a = dV/dt where v is velocity n v = dx/dt where x is position n Solve differential equations numerically using standard methods Verlet, Beeman, Gear n solutions are iterative over small time steps typically 1 fs; n generates trajectory through microstates which obey ensemble constraint (NVT) and hence one can calculate averages

Crystallography, Birkbeck Non-standard techniques n ‘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 n ‘free energy’ calculations n non-equilibrium systems n joint QM/MD calculations

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 n What interactions are important ? n How do you represent them ? n 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

Crystallography, Birkbeck Software and hardware n Software: lots - amber, insight/discover, sybyl, quanta/charmm etc n Hardware: PC to CRAY T3D n Requirements: Initial Model/Set Up Running Simulation Analysis and Validation

Crystallography, Birkbeck initial requirements n Starting configuration of atoms n info about the molecule - nos of atoms, atom types, connectivity (bonds, angles, torsions), partial electronic charge n info about how atoms interact - covalent bonds, angles and torsions: non-covalent LJ, electrostatics, H-bond n Solvent ? n control: Vol, P, Temp, time step

Crystallography, Birkbeck VALIDATION n Everyone gets good qualitative agreement with experimental data n Totally ad hoc n choose sensible starting model n check that it is behaving properly especially at the beginning n thorough analysis of many parameters - even if you cannot publish them all n choose the right level of detail

Crystallography, Birkbeck Future - n improve assumptions n validation n need to improve - long range and short range electrostatics n need to improve precision of all interactions as compromise between many weak interactions n need to increase time beyond ns to ms n Need to get quicker so that we can ‘play’ with system. difficult when it takes 3-6 months a calculation

Crystallography, Birkbeck ATOMISTIC SIMULATIONS n APPLICATION AREAS (A) environmental effects on peptide stability: role of solvents in stabilising/ destabilising secondary structure (B) conformation of chemically modified dnas n NOVEL ALGORITHMS Protein folding/unfolding - solvent insertion into cavities; stability and unfolding of different protein architecture n VALIDATION development of systematic protocols for assessing simulations