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Simulating biomolecular function from motions across multiple scales (I) Peter J. Bond (BII) peterjb@bii.a-star.edu.sg Structural Biology: Why the Need for Simulation? 2017 Explosion in number of structures deposited to PDB over past


  1. Simulating biomolecular function from motions across multiple scales (I) Peter J. Bond (BII) peterjb@bii.a-star.edu.sg

  2. Structural Biology: Why the Need for Simulation? 2017 • Explosion in number of structures deposited to PDB over past ~15 years… due to: year - Post-genomics era: accessibility to numerous genomes, more stable proteomes etc. - Automation in crystallization protocols, robotics. - Structural biology consortia (and money!) • Also improvements in NMR, RCSB PDB: RCSB Protein Data Bank cryoEM, & biophysical methods. https://www.rcsb.org/ 1972 • So with all this structural data, 0 125,000 no. of structures why the need for simulation? 2

  3. The Importance of Dynamics and “Landscape”… single “snapshot” ligand binding 3

  4. Methods & Associated (Typical) Scales TIME (s) Continuum 10 0 Coarse-grained (ms) 10 -3 simulation Atomic res. simulation ( µ s) 10 -6 Semi- (ns) 10 -9 empirical QM biomolecules (ps) 10 -12 Ab initio QM (fs) 10 -15 LENGTH (metres) 10 -10 10 -9 10 -8 10 -7 10 -6 10 -5 10 -4 ( µ m) (nm) 4

  5. Biomolecular Simulations: From Structure to Dynamics FF used to calculate resultant forces F i (& acceleration a i via Newton’s 2 nd law) on particle i with mass m i F i = −∇ i E system = m i a i thus we can relate gradient of PE to changes in positions / velocities as a function of time: − δ E system δ 2 r δ v i = m i δ t = m i i δ t 2 δ r i o Static structure – in vitro conditions. o Simulation: ~300 K, biological model ... o 10 3 – 10 5 atoms … o ~10 6 pair-wise interactions: “ force field” o Numerical integration of F=ma. o Coordinates calculated every 0.000000000000001 sec, ~ 1 CPU sec … 5

  6. Biomolecular Simulations: From Structure to Dynamics COMPUTATIONAL COST... real … explicit implicit (e.g. ε , ± ξ ) o Static structure – in vitro conditions. o Simulation: ~300 K, biological model ... o 10 3 – 10 5 atoms … o ~10 6 pair-wise interactions: “ force field” o Numerical integration of F=ma Periodicity mimics infinite system (e.g. cube). o Coordinates calculated every Minimum image convention. 0.000000000000001 sec, ~ 1 CPU sec … Good rule of thumb: ≥ 2 nm between “images”. 6

  7. Molecular Simulation – “Computational Microscope” • Computational modelling – now an indispensible tool for complementing traditional experiments. • Ariel Warshel: “ … the best tool we have to see how molecules are working.” (awarded Nobel Prize in Chemistry, 2013 with Levitt & Karplus). • Klaus Schulten coined the term “computational microscope”. • Not simply an in silico “imaging” technique – not just for movies … - dynamics, interactions, conformational changes, mechanisms! - no limitations on spatio-temporal “zoom”! - ability to carry out “alchemistry”! ii - ability to do “thought experiments”! - powerful tool: integrate model & experiment. But... Potential Limitations: 35 Å • Accuracy of starting model / available experimental data … • Accuracy of the underlying force field … • Limited sampling in time / space … 7

  8. Simulating (and waiting for) Motions … Zwier & Chong. Current Opinion in Pharmacology. 2010. 10:745-752. energy conformation 8

  9. The increasing power of biomolecular simulation Schlick et al. Biomolecular modeling and simulation: a field coming of age. Q Rev Biophys. 2011. 44:191-228. supercomputing power • < decade: ~10 3 ↑ simulation performance … - thanks to algorithms, architectures, cost … life cycle of E. coli - also improves FF accuracy. 9

  10. Describing Biomolecular Interactions H-bonds (electrostatic … ) Covalent, ~1-2 Å H shared by 2x δ - atoms. ~100 kcal mol -1 . ~1-5 kcal mol -1 , ~2-4 Å. Electrostatic: ~3 Å ~1-5 kcal mol -1 ( ε =80) ~50 kcal mol -1 ( ε =2) i.e. medium dependent! “Hydrophobic interactions” (entropy driven) vdW: ~0.5-1 kcal mol -1 Attractive - transient polarization (also repulsive - orbital overlap) 10

  11. Describing Biomolecular Interactions: “Force Field” quadratic E bond Morse cubic separation, r equilibrium value n = multiplicity (no. minima) φ = current angle γ = phase (minima position; x-axis) V n = barrier height (y-axis) 11

  12. Describing Biomolecular Interactions: “Force Field” E vdw = 4 ε {( σ / R ) 12 - ( σ / R ) 6 } Pair-wise sum of all possible interacting non bonded atoms i and j … O(n 2 ) Lennard-Jones E (“6-12”) potential: R Electrostatics – decays slowly (i.e. 1/ R ) … many methods to treat this.. *** Stick with FF recommendation! *** σ

  13. Energies & Force Fields (FFs)… Describe total energy of the system such that there are penalties for deviations from reference values. Energies are calculated using an § E TOTAL = E BONDED + E NON-BONDED empirically derived force field (FF) . “Balls & springs” : Bonded (+ f c / E o ), § non-bonded interactions (LJ), particle mass, size, partial charge. Parameters from where? § Fragment geometries – X-ray studies. § Biomolecules - highly specific refinements over the years (but cf. over-fitting, e.g. IDPs … ) Rotational barriers / vibrational § frequencies from spectroscopy. Charges from e.g. QM calculations. § van der Waal’s – trial and error § e.g. to match experimental densities. Thermodynamic properties … § Many accurate FFs are now available! § 13

  14. Real Simulation Codes & Force Fields CHARMM (Chemistry at Harvard Molecular Mechanics) www.charmm.org ♦ Interface through fortran like scripting language - tough! ♦ Very powerful, many different features. Slow. ♦ $600 (academic) but also free reduced-functionality version. AMBER (Assisted Model Building with Energy Refinement) www.ambermd.org ♦ Suite of about 60 programs based around a few central ones ♦ Slow on standard CPUs; fast with GPU-optimization ♦ $500 (academic) $15-20,000 (industry). GROMACS (Groningen Machine for Chemistry Simulation) www.gromacs.org ♦ Simple interface (not scripting based) ♦ The fastest codes on 100’s cores (CPU/GPU) ♦ GNU licensed (i.e. free!) NAMD (Not just Another Molecular Dynamics program) www.ks.uiuc.edu/Research/namd ♦ Optimized for many 1000’s of cores ♦ Written in C++ with a TCL-based scripting interface. ♦ Also free of charge. 14

  15. Automated Simulations … but be wary … http://bio.demokritos.gr/gromita/ - Graphical User Interface for GROMACS v4+ https://www.charmming.org -CHARMMing interface – preparation/submission/analysis. http://haddock.science.uu.nl/enmr/services/ GROMACS/main.php - Web-based portal for automated GROMACS simulations, distributed European Grid network (10 ns sims). http://py-enmr.cerm.unifi.it - similar for AMBER- based NMR refinement. http://mmb.irbbarcelona.org/MDWeb/ - Setting up /running / analysis of simulations in Amber, NAMD, GROMACS and related … http://www.bevanlab.biochem.vt.edu/ 15

  16. Simulation Workflow ♦ missing atoms / residues / loops & mutations (Pymol, Early Steps: Know your system! (PDB “headers” & papers are your friend!) Modeller, Swiss- model etc.) Obtain structure – X-ray / NMR / model ♦ oligomer state ♦ disulfides (assess via distance only?) ♦ ligands Add H’s, consider pk A , prepare topology (CGenFF, PRODRG, SwissParam, VMD QMTool – Gaussian.) Solvate + add ions Bulk / structural / F V = −∇ crystal i i water / Minimize ions Energy Aim to “relax” system, e.g.: solvent/ Equilibration ion distribution, temperature, box size/density … Cf. ensemble (e.g. NPT ) E restr = k ( r - r 0 ) 2 Geometry Production e.g. Steepest descents – follow gradient “downhill” until threshold ( Δ E or F max ) Analyze 16

  17. Assessing Errors & Convergence... Sampling & Convergence Simple - look at it! • Check distribution of properties against average – even distribution? • Calculate block averages for a single trajectory. • Calculate multiple simulation replicas and compare … (Ergodic … ) Protein structural deviation x no. steps each τ block should > τ relax 3 Comparison to Experiment C α RMSD (Å) e.g. RMSF vs B-factors 2 2 8 π 2 1 B i RMSF = Take frames 3 from here 10 0 time (ns) Care … this is a very limited indicator alone … … remember experimental error!

  18. Case Study: Theory vs Experiment & OmpA L2 L1 L3 L4 ? NMR X-ray insoluble detergent • Bacterial outer membrane protein (~100,000 per cell!) • Flickering channel formation in lipid membranes , but no obvious pore in crystal. • NMR – but gradient of flexibility along barrel in detergent micelle complex. 18

  19. • 4 monomers per unitcell, space group C2. • Detergent-mediated “protein fibre”. Bond et al, PNAS (‘06) 103 :9518- • 24 x octyltetraoxyethylene (C 8 E 4 ), 264 x H 2 O. • Loops modelled, crystal water & detergent + bulk water and ions. NVT ensemble simulation. 19

  20. crystal simulation 2 ) 2 (Å B i = [8 π 2 /3].RMSF i L1 L2 L3 L4 T1 T2 T3 Bond et al, PNAS (‘06) 103 :9518- 6 4 RMSD (Å) 2 0 0 10 20 30 40 50 time (ns) • Detergent molecules dynamically cover protein fibre – membrane-like environment. • β -barrel RMSD low. Higher for loops – low crystal density & inherent high mobility. • B-factor correlation... Missing density - vibrations, fluctuations, and lattice disorder … 20

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