Molecular modelling Zdeněk Kříž National Centre for Biomolecular Research Brno, Czech Republic zdenek@chemi.muni.cz Computational chemistry Computational chemistry is a branch of chemistry that uses principles of computer science to assist in solving chemical problems. It uses the results of theoretical chemistry, incorporated into efficient computer programs, to calculate the structures and properties of molecules and solids. Its necessity arises from the well-known fact that apart from relatively recent results concerning the Hydrogen molecular ion, the quantum n-body problem cannot be solved analytically, much less in closed form. Molecular modelling encompasses all theoretical methods and computational techniques used to model or mimic the behaviour of molecules. The techniques are used in the fields of computational chemistry, computational biology and materials science for studying molecular systems ranging from small chemical systems to large biological molecules and material assemblies. Molecular modelling Quantum mechanics approach vs. Molecular mechanics approach Exact solution of Schroedinger Equation. Using parameters. Fast, but not usable for chemical reactions study Outline  Conformational analysis  Potential energy (hyper)surface/Free energy (hyper)surface  Searching methods  Single coordinate driving method - SCD  Results of CICADA searching  Molecular Mechanics  Molecular Dynamics Conformational analysis Conformational analysis Potential / free energy Free Energy Bonds Angles Improper Dihedral Torsions Electrostatics Van der Waals Constant NVT: Helmholtz free energy A=U-TS , Where U= - average energy Constatnt NPT Gibbs free energy G=U+PV-TS=H-TS Empirical Potential Energy Function Bonds Angles Improper Dihedral Torsions Electrostatics Van der Waals Potential / free energy hypersurface Searching PES ● Grid search ● Metropolis Monte Carlo method ● Simulated annealing ● Distance geometry search ● Homology modelling ● Fragment approach ● Genetic algorithms ● Chain growth algorithms Grid search method Grid search method Grid search method NGP=∏ i=1 k 360/torsion stepi N torsions 3 4 5 6 7 N conformers 1728 20736 248832 2985984 3.6 E7 Step size 30 degrees Time: 1 conformer per 1 second: 3 torsions – 29 min, 4 torsions – 6 hours, 5 torsions – 69 hours, 7 torsion – 417 days Problem of combinatorial explosion Grid search method ● How to solve problem with combinatorial explosion? – Energy cutoff – Coarse grain grid – Fragment base approach – Single coordinate driving method Grid search method Grid search method ● Advantage: – Explore all conformational space systematically. – All possible minima can be found. ● Lack: – Time consuming combinatorial explosion. – Can not be used for large and flexible systems. – Limitation for ring systems. Metropolis Monte Carlo 1 generate state x0 2 find state x1 next to x0 3 calculate E(x1), E(x0) if (E(x1)E(x0)) { make x0 = x1 with probability } 4 cycle until x1 does not change Px0 x1= Px1 Px0 =e −E x1 −Ex0 kT Metropolis Monte Carlo Metropolis Monte Carlo ● Advantage: – Fast and powerful method for large flexible systems. – Useful for ring systems. – As an additional option chiral centers can be preserved to their original geometry or inverted during conformational search. ● Lack: – Only energy criterion for search. – No real end point like for systematic search. Molecular dynamicsEnergy ? Simulated anealing ● Global optimization technique based on Monte Carlo method. ● Number of accepted conformations is dependent on simulation temperature. – High simulation temperature = many states will be accepted. – Low simulation temperature = majority of generated states will be rejected. Simulated anealing 0 set Tmax 1 generate state x0 2 find state x1 next to x0 3 calculate E(x1), E(x0) if (E(x1)E(x0)) { make x0 = x1 with Metropolis criterion } 4 cycle until x1 does not change 5 cool down system and cycle from 1 with x1 state Simulated anealing Simulated anealingEnergy Heating phase Slow cooling Distance geometry ● Reduction of degrees of freedom by experimentally known geometry data ● Crystallography, NMR (NOE) ● Constraints and penalty functions ● Time-averaged constraints Distance geometry Distance geometry ● Advantage: – Very accurate in the systems for which experimental data are available (NMR, X-ray). – Useful for refining structure of proteins and nucleic acids. – Can generate several conformations that are consistent with experimental data – additional information about flexibility of the system. ● Lack: – Requires experimental data. Single coordinate driving method CICADA – Channel In Conformational Space Analalysed by Driver Approach CICADA approach ● Systematic search method. ● Solve problem of combinatorial explosion. ● Explore only low energy areas of energy surface. ● Good parallelization = useful for larger systems. ● Used also as docking method. ● Minimization using TINKER software CICADA approach ● Why TINKER? ● Free with source code – easy to implemented into CICADA. ● Variety of minimize routines. ● Several common parameter sets: – Amber (ff94, ff96, ff98, ff99, ff99SB), – CHARMM (19, 22, 22CMAP), – Allinger MM (MM2-1991 and MM3-2000), – OPLS (OPLS-UA, OPLS-AA), CICADA approach A + B CT CICADA approach CICADA approach NUMBER OF TORSIONS: 36 1 2 3 18 1 0 0. 3 18 19 20 1 0 0. 18 19 20 34 1 0 0. 20 34 35 36 1 0 0. 34 35 36 45 1 0 0. 36 45 46 47 1 0 0. 45 46 47 69 1 0 0. 47 69 70 71 1 0 0. 69 70 71 88 1 0 0. 71 88 89 90 1 1 0. Control parameters: DYNAM 0. ROCRIT 30. ECRIT 0.20 SEED pept PATH /home/zdenek/PCKI/ DOCKING F 1./LAST 2 301 BTCHACT 0 DRIVSTEP 20. STARTTIM 16 37 2 0 09 9 30 BACK F MULTCOEF 5 ECUT 150. CONFCUT 50.00 CICADA results Single amino acids Alanine Valine CICADA results ● Cysteine, cystine (L-Cys -S-S-L-Cys and L-Cys-S-S-D-Cys) ● Nucleic acids fragments ● Monosaccharides and oligosaccharides ● Small peptides – enkephalins and their cyclic analogues ● Small organic molecules CICADA results Enkephalins CICADA results The largest system we have studied using CICADA program 19 amino acids – C terminal domain of Casein Kinase I CKI  – natural and polyphosphorylated form CICADA results CICADA results Amyloid  – human and rat form 42 amino acids Difference in only 3 amino acids CICADA - docking CICADA - docking ● CICADA – docking – Normal conformational search of receptor or ligand – SCD docking ● rotations of ligand (3 directions) ● Translation of ligand (3 directions) CICADA - docking Catechine –-cyclodextrin docking using CICADA software Molecular Mechanics ● Atoms in molecules described using classical mechanics (balls and springs) ● Usable for large systems such a proteins and nucleic acids ● No real energy based on physical background ● Force fields Force fields Force fields Force fields – non bonded VdW Electrostatic Force fields Force field - equations Force fields -types ● MM2, MM3 – N. A. Allinger ● AMBER – P. Kollmann ● OPLS – Jorgensen ● MMFF ● CHARMM ● Amoeba Optimization procedures ● Simplex method ● Steepest descent – first derivatives ● Conjugated gradient – first derivatives ● Newton – Raphson method – second derivatives Acknowledgment ● Grand agency of the Czech Republic ● Ministry of education, youth and sports ● Supercomputer center Brno ● Prof. Jaroslav Koča ● Dr. Petr Kulhanek ● Jakub Štěpán