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What is Computational Biology ?

What is Computational Biology ?. Structural Biology & Biophysics Computational Chemistry of Biological Molecules Genomics and Proteomics Systems Biology. Molecular Simulations in Structural Biology. Molecular Structure and Function (e.g. enzymes) Protein Folding and Binding

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What is Computational Biology ?

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  1. What is Computational Biology ? • Structural Biology & Biophysics • Computational Chemistry of Biological Molecules • Genomics and Proteomics • Systems Biology

  2. Molecular Simulations in Structural Biology • Molecular Structure and Function (e.g. enzymes) • Protein Folding and Binding • DNA, RNA, Structure, Packaging, Transcription and Translation • Molecular Motors

  3. Protein folding, structure prediction, refinement • Protein folding: mechanisms, pathways, kinetics • Predict protein structure given sequence (ab-initio folding vs. homology modeling – struc. genomics ) • Protein structure determination & refinement: xray, nmr • Predict ligand-binding mode given protein structure and ligand chemical formula (docking) • Rank-score series of ligand candidates (FEP, ChemScore, LIE)

  4. Computational tools for biophysical modeling • Scoring functions (potential functions. effective potentials, effective free energy functions, knowledge based potentials) • Sampling methods (minimization, MD & MC simulations, advanced sampling methods – replica exchange) • Connection formulas for observables from simulations (statistical thermodynamics)

  5. Scoring Functions: Knowledge-Based (statistical potentials) • Empirical, simple form • Parameters from fitting structural data • Requires training Physics-Based (potential energy functions) • Transferable • Higher resolution • Slower to compute • Difficult to optimize

  6. Atomic Force Fields: torsion stretching bending non-bonded

  7. Bond Stretch Potential

  8. Torsion Angle Energy

  9. Nonbonded Potentials

  10. C5 C7ax C7eq Conformations of alanine dipeptide aR aL

  11. Effects of Solvation MD simulation, RMSD from native:

  12. Explicit Solvent • Most accurate/detailed. • Expensive. • Requires averaging over solvent coordinates. • Difficult to obtain relative free energies of solute conformations.

  13. Implicit Solvent • Solvent continuum. • Based on solvent PMF. • Reduced dimensionality. • Relative free energies from single point effective potential energy calculations. e, r, ...

  14. AGBNP(Analytical Generalized Born + Non Polar) • OPLS-AA AGBNP effective potential, an all atom model • Novel pairwise descreening Generalized Born model. • Separate terms for cavity free energy and solute-solvent van der Waals interaction energy. • Fully analytical. • Applicable to small molecules and macromolecules. Generalized Born Surface area model Born radius-based estimator E. Gallicchio, and R.M. Levy, JCC, 25, 479 (2004)

  15. Generalized Born Model Charging Free Energy in linear dielectric medium: Bi is the Born radius of atom i defined by:

  16. Non-Polar Hydration Free Energy Non-polar hydration free energy estimator: : Surface area of atom i : Estimator based on Born radius : Surface tension and van der Waals adjustable parameters R.M. Levy, L. Y. Zhang, E. Gallicchio, and A.K. Felts, JACS, 125, 9523 (2003) (proteins in water) E. Gallicchio, M. Kubo, and R.M. Levy, JPC, 104, 6271 (2000) (hydrocarbons in water)

  17. 200 K Replica exchange molecular dynamics rough energy landscapes and distributed computing MD MD MD MD MD 700 K 450 K 320 K energy Y. Sugita, Y. Okamoto Chem. Phys. Let., 314, 261 (1999) “important coordinates”

  18. 200 K Replica exchange molecular dynamics rough energy landscapes and distributed computing MD MD MD MD MD 700 K 450 K 320 K energy Y. Sugita, Y. Okamoto Chem. Phys. Let., 314, 261 (1999) “important coordinates”

  19. Folding Funnels and Binding Energy Landsapes Binding Energy Landscapes Folding Funnels

  20. AGBNP + REMD • Protein Folding • Peptides • Protein Decoys • Protein Allostery • Allosteric conformational transitions • and free energy profiles of RBP • Ligand binding • Binding Mode Prediction • Binding Free Energy Prediction

  21. F2 U2 F1 U1 Protein folding and kinetic network models • free energy surfaces of the GB1 peptide and • comparison with experiment • kinetic network model of folding pathways • for GB1 • kinetic network model of REMD • (simulations of simulations) • non-Arrhenius kinetics and replica • exchange

  22. The -Hairpin of B1 Domain of Protein G Folding nucleus of the B1 domain Blanco, Serrano. Eur. J. Biochem. 1995, 230, 634. Kobayashi, Honda, Yoshii, Munekata. Biochemistry 2000, 39, 6564. Features of a small protein: stabilized by 1) formation of secondary structure 2) association of hydrophobic residues Munoz, Thompson, Hofrichter, Eaton. Nature 1997, 390, 196. Computational studies using Explicit and Implicit solvent models Pande, PNAS 1999 Dinner,Lazaridis,Karplus,PNAS,1999 Ma & Nussinov, JMB, 2000 Pande, et al., JMB, 2001 Garcia & Sanbonmatsu, Proteins, 2001 Zhou & Berne, PNAS, 2002

  23. The b-Hairpin of B1 Domain of Protein G Simple (surf area) nonpolar model OPLS/AGBNP The potential of mean force of the capped peptide. A Felts, Y. Harano, E. Gallicchio, and R. Levy, Proteins, 56, 310 (2004)

  24. The b-Hairpin of B1 Domain of Protein G Simple (surf area) nonpolar model OPLS/AGBNP -hairpin > 90% -helix < 10% G ~ 2 kcal/mol The potential of mean force of the capped peptide. A Felts, Y. Harano, E. Gallicchio, and R. Levy, Proteins, 56, 310 (2004)

  25. Comparison of simulated and experimental NMR data experimental simulated 43 43 46 46 50 50 NOE: aN(i,i+1) NN(i,i+1) inter-strand Blanco, Rivas & Serrano (1994) Struct. Biol. 1:584 Blanco & Serrano (1995) Eur. J. Biochem. 230:634 Ha chemical shift temperature dependence: Honda, Kobayashi & Munekata (2000) JMB 295: 269 Simulated using ShiftX Neal, Nip, Zhang & Wishart (2003) J. Biomol. NMR 26:215

  26. G-peptide melting curves b coil a

  27. A kinetic network model for the G-peptide unfolded states b macrostate Kinetics are determined using the Master Equation dP(t)/dt = KP(t) or via stochastic simulation (“Gillespie algorithm”)

  28. Protein Folding Pathways from Replica Exchange Simulations and a Kinetic Network Model • Use Replica Exchange to discretize state space • Allow conformational transitions between structurally similar states • Construct master equation for the network (800,000 nodes, • 7.4 billion edges), analyze folding paths and kinetics • The majority of beta-hairpin folding trajectories pass through alpha helical intermediate states Andrec, Felts, Gallicchio & Levy (2005) PNAS, 102, 6801

  29. Folding of G-peptide from high-energy coil states occurs via a-helical intermediates b a t = 9 units ≈ 180 ns t = 2500 units ≈ 50 µs b a Fraction of hairpin conformation averaged over 2000 stochastic trajectories run at 300 K and begun from an initial state ensemble equilibrated at 700 K. 91% of 4000 temperature-quenched stochastic trajectories begun from high-energy coil states pass through states with a-helical content

  30. Evidence for a-helical intermediates in b-sheet folding and misfolding • Non-native helices have been observed in b-lactoglobulin folding • Rapid formation of a structure • Can exist as a stable thermodynamic species and as intermediates • May be important in protecting exposed ends of b-sheet from intermolecular interactions Forge, Hoshino, Kuwata, Arai, Kuwajima, Batt & Goto (2000) JMB 296:1039 Kuwata, Shastry, Cheng, Hoshino, Batt, Goto & Roder (2001) Nat. Struct. Biol. 8:151 • Amyloid b-sheets can form from a-helical precursors • Myoglobin and coiled-coil proteins can form amyloid fibrils Fändrich, Forge, Buder, Kittler, Dobson & Diekmann (2003) PNAS 100:15463 Kammerer, Dobson, Steinmetz et al. (2004) PNAS 101: 4435 • Fibril formation in amyloid b-protein may occur via a helical intermediate Kirkitadze, Condron & Teplow (2001) JMB 312:1103 Fezoui & Teplow (2002) JBC 277: 36948 • Computational and theoretical evidence • Helical structures have been observed in G-peptide simulations García & Sanbonmatsu (2001) Proteins 42:345 Zagrovic, Sorin & Pande (2001) JMB 313:151 Wei, Mousseau & Derreumaux (2004) Proteins 56:464 • Entropy-stabilized helical intermediates may be generic in b-sheet protein folding landscapes Chikenji & Kikuchi (2000) PNAS 97:14273

  31. Peptide Folding Benchmarks for the OPLS-AA/AGBNP Effective Potential Name Sequence % content Exptl RXMD AGADIR  CheY2-mu1 EDAVEALRKLQAGGY 39 45 34 CheY21 EDGVDALNKLQAGGY 2 2 2 C-peptide2 KETAAAKFERQHM 29 41 7 S-pep-analog3 AETAAAKFLREHMDS 45-63 55 9  G-peptide4 GEWTYDDATKTFTVTE 42 43  FSD15 QQYTAKIKGRTFRN- >80 59 EKELRDFIEKFKGR 1Munoz, Serrano. J. Mol. Biol.1995, 245, 275-296. 2Bierzynski, Kim, Baldwin. Proc. Natl. Acad. Sci. USA 1982, 79, 2470-2474. 3Mitchinson, Baldwin. Proteins: Struct. Funct. Genet. 1986, 1, 23-33. 4Blanco, Rivas, Serrano. Nature Struct. Biol.1994, 1, 584-590. 5Dahiyat, Mayo. Science 1997, 278, 82-87.

  32. Induced Conformational Changes and Allosteric Transitions • Signalling and regulation of enzymatic activity, transport, gene transcription.

  33. Ribose Binding Protein :Transport and Chemotaxis • Monomeric allosteric protein, well characterised experimentally. • Computational study of conformational change and allostery of RBP • using AGBNP, umbrella sampling, and WHAM. H. Shilton, S. Mowbray, Protein Science, 4, 1346-1355 (1995)

  34. The Ribose-Binding Protein (RBP) Open ribose-free Closed ribose-bound • X-ray crystal structures of closed and open forms available. • Representative of widely prevalent hinge bending motion. S. Mowbray, L. Cole, JMB, 225, 155-175 (1992). A, Bjorkman, S. Mowbray, JMB, 279, 651-664 (1998).

  35. Calculating Populations by Umbrella Sampling Count Biasing Potential Hinge Angle (degrees) Unbiased Conformational Populations (WHAM)

  36. Ribose-free RBP: Population • The open state is the most populated. • Open state exists in wide array of conformations.

  37. Ribose-bound RBP:Population • Population shifts from open to closed state. • Equilibrium shift rather than a high fidelity switch. • New ribose-bound (partially) open state at  =122o.

  38. Thermodynamics =open - closed • Open state is stabilized by conformational entropy. • Binding to ribose stabilizes closed state energetically. • -TS for ribose bound system larger because of smaller entropy associated with ribose bound closed state.

  39. Hinge Bending () and Twisting () Population Distribution Hinge Angle  Twist Angle  • Ribose Free: Mechanism of opening is as predicted by Mowbray et.al. • New ribose-bound partially open state at (122,90). • Ribose Bound: Mechanism of opening differs as open state population peak is outside path traced by crosses.

  40. Predicted Intermediate for ribose release Partially Open Ribose-bound State (30%) Closed Ribose-Bound State (70%) • Open state allows exit of ribose into membrane bound permease. • Ribose is shifted towards the face of RBP that binds to permease • Binding surface symmetric w.r.t. to ribose. A, Bjorkman, S. Mowbray, JMB, 279, 651-664 (1998).

  41. Conclusions • Description of allosteric equilibrium that links structures with thermodynamics. • Open state consists of a wide array of conformations. • Population shifts form open to closed state on binding to ribose. • Equilibrium shift rather than a high fidelity trigger. • New ribose bound open state at  = 122o. • Ribose free closed state characterised. • Open state is stabilized by conformational entropy. • Binding to ribose stabilizes closed state energetically.

  42. Conformational Equilibria and Free Energy Profiles for the Allostery of the Ribose Binding Protein

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