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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
What is Computational Biology ?
  • Structural Biology & Biophysics
  • Computational Chemistry of Biological Molecules
  • Genomics and Proteomics
  • Systems Biology
molecular simulations in structural biology
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
protein folding structure prediction refinement
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)
computational tools for biophysical modeling
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)
scoring functions
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
atomic force fields
Atomic Force Fields:

torsion

stretching

bending

non-bonded

slide11

C5

C7ax

C7eq

Conformations of alanine dipeptide

aR

aL

effects of solvation
Effects of Solvation

MD simulation, RMSD from native:

explicit solvent
Explicit Solvent
  • Most accurate/detailed.
  • Expensive.
  • Requires averaging over solvent coordinates.
  • Difficult to obtain relative free energies of solute conformations.
implicit solvent
Implicit Solvent
  • Solvent continuum.
  • Based on solvent PMF.
  • Reduced dimensionality.
  • Relative free energies from single point effective potential energy calculations.

e, r, ...

agbnp analytical generalized born non polar
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)

slide17

Generalized Born Model

Charging Free Energy in linear dielectric medium:

Bi is the Born radius of atom i defined by:

slide18

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)

slide19

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”

slide20

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”

folding funnels and binding energy landsapes
Folding Funnels and Binding Energy Landsapes

Binding Energy Landscapes

Folding Funnels

agbnp remd
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
protein folding and kinetic network models

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
the hairpin of b1 domain of protein g
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

the b hairpin of b1 domain of protein g
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)

the b hairpin of b1 domain of protein g1
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)

slide28

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

slide31

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”)

slide32

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

slide33

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

slide34

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

peptide folding benchmarks for the opls aa agbnp effective potential
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.

induced conformational changes and allosteric transitions
Induced Conformational Changes and Allosteric Transitions
  • Signalling and regulation of enzymatic activity, transport, gene transcription.
ribose binding protein transport and chemotaxis
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)

the ribose binding protein rbp
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).

calculating populations by umbrella sampling
Calculating Populations by Umbrella Sampling

Count

Biasing Potential

Hinge Angle (degrees)

Unbiased Conformational Populations (WHAM)

ribose free rbp population
Ribose-free RBP: Population
  • The open state is the most populated.
  • Open state exists in wide array of conformations.
ribose bound rbp population
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.
slide43

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.
hinge bending and twisting population distribution
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.
predicted intermediate for ribose release
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).

conclusions
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.
conformational equilibria and free energy profiles for the allostery of the ribose binding protein

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

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