Protein Structure Prediction

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S.Will, 18.417, Fall 2011 mn Acids Amino

S.Will, 18.417, Fall 2011 eeso structure of Levels

S.Will, 18.417, Fall 2011 hita nne,1961: Anﬁnsen, Christian ⇒ ⇒ aiesrcue=mnmmo h reenergy free the of minimum = structure sequence proteins) native the globular small in for is least structure (at native about information all hypthesis: dogma/thermodynamic Anﬁnsen’s machinery vitro) folding (in external state no functional into refolds RNase denatured • • • ieial accessible kinetically stable unique rti tutr Prediction Structure Protein

S.Will, 18.417, Fall 2011 poen odi ilscnst seconds to milliseconds in fold proteins BUT: yu eita:poenfligi o trial-and-error not experiment: is Thought folding protein Levinthal: Cyrus • • • • sue3sae o aho h 0 h n s odangles bond psi and phi 200 the of each for states aa) 3 (101 assume bonds peptide 100 with protein reso antd ogrta h g fteuniverse the of age the 60 than over longer still magnitude secon, of per orders samples quadrillion one assuming ⇒ 3 200 ≈ 10 eita’ aao,1969 Paradox, Levinthal’s 95 conformations PARADOX

S.Will, 18.417, Fall 2011 rvn forces: Driving • • • rnilso odn Esnily Understood ’Essentially’ Folding of Principles omto fitaoeua yrgnbnsb eryall nearly atoms by polar atoms bonds buried and hydrogen groups intramolecular buried of of formation packing water void-free nearly from away close, groups non-polar of hiding yrpoi eﬀect Hydrophobic eovsLvnhlsParadox Levinthal’s resolves odn Funnel Folding · Van-der-Waals · Electrostatic

S.Will, 18.417, Fall 2011 oetF evc.Polmsolved Problem Service. F. Robert uut8 August th cec:polmsolved? problem Science: , ti n oefloigsie nprdb ib u eoeWaldisp¨uhl] Jerome Xu, Jinbo by inspired slides following some and [this ∗ ( ∗ oto) cec,2008. Science, of). sort

S.Will, 18.417, Fall 2011 nraigAcrc fPeitos lwybtSteadily but Slowly Predictions: of Accuracy Increasing h cuayo h rti-odn models. improved protein-folding steadily the but of slowly accuracy have the modelers Computer rise. Steady

CorrectlyAligned(%) 100 20 40 60 80 0 CASP1 Easy CASP2 CASP3 CASP4 a gtdfiut Difficult Target difficulty CASP5 CASP6 CASP7

S.Will, 18.417, Fall 2011 rti ofrain) ilsdsac ewe conformations. in between atoms distance of Yields coordinates conformations). (here, protein coordinates of vectors two Compares Deviation Square Mean Root = RMSD ti ple osprmoe tutrs ratrmnmzn over minimizing after or algorithm) structures, (Kabsch superimposed rotations/translations to applied is it orientation; on depends RMSD RMSD( v , w = ) itnebten3 structures 3D between Distance = r r n n 1 1 X X ( k v v ix i − − w w i ix k ) 2 2 ( + v iy − w iy ) 2 ( + v iz − w iz ) 2

S.Will, 18.417, Fall 2011 CASP/CAFASP

S.Will, 18.417, Fall 2011 • • • Public Blind: Drawback: • • • • • • edeeytoyears two every third-party Held unbiased the by Evaluated community structure by Organized oecnesaerlcatt ees hi structures their release to reluctant are centers Some Blindness centers structure by competition determined after be to structures Experimental < 0 targets 100 CASP/CAFASP

S.Will, 18.417, Fall 2011 APCFS Schedule CASP/CAFASP

S.Will, 18.417, Fall 2011 • • • e od(F targets (NF) Fold New Homology odRcgiin(R targets (FR) Recognition Fold • • • • • • osmlrfl nPDB in fold similar No locle oprtv oeig(M targets PDB (CM) in Modeling protein Comparative homologous called distant Also PDB a in has protein HM: homologous Hard a has HM: Easy targets (HM) Modeling a iia odi PDB in fold similar a Has etPoenCategory Protein Test

S.Will, 18.417, Fall 2011 • • • • tg :Bcbn Prediction Backbone 1: Stage tg :SrcueReﬁnement Structure 4: Stage Packing Side-Chain 3: Stage Modeling Loop 2: Stage • • • rti threading Protein modeling Homology prediction initio Ab rti tutr Prediction Structure Protein

S.Will, 18.417, Fall 2011 • • • rmpestlbayo Dmtf (=fragments) motifs 3D of library pre-set from assembly Fragment Dynamics Molecular models Discrete-state / models Lattice apigtegoa ofrainspace conformation global the Sampling biii Prediction: Ab-initio

S.Will, 18.417, Fall 2011 Example 1989) Dill, & (Lau HP-Model The • • tutrsaedsrt,sml,ad2D and simple, discrete, are structures interaction hydrophobic only model atc oes h ipetPoenModel Protein Simplest The Models: Lattice H H H • • • • Sl-viigWalk Self-Avoiding lattice square overlaps: a without on drawn are structures (C- backbone only model alphabet nryfnto aosHH-contacts favors function energy P P P { H , P } / hydrophobic/polar = H/P ; α positions ) Z 2

S.Will, 18.417, Fall 2011 HH-contact Example 1989) Dill, & (Lau HP-Model The • • tutrsaedsrt,sml,ad2D and simple, discrete, are structures interaction hydrophobic only model atc oes h ipetPoenModel Protein Simplest The Models: Lattice H H H • • • • Sl-viigWalk Self-Avoiding lattice square overlaps: a without on drawn are structures (C- backbone only model alphabet nryfnto aosHH-contacts favors function energy P P P { H , P } / hydrophobic/polar = H/P ; α positions ) Z 2

S.Will, 18.417, Fall 2011 O-atc models Oﬀ-lattice Lattice: Without Space Structure Discrete structures possible of set Lattices = sequence a of space Structure • • • • • • iceerotational discrete problem combinatorial gets prediction Structure enumerated be can Structures space structure the discretizes Lattice eae da agn peeModel Sphere Tangent idea: related library fragment atc oes iceeSrcueSpace Structure Discrete Models: Lattice φ/ψ age ftebackbone the of -angles

S.Will, 18.417, Fall 2011 agn peeModel Sphere Tangent H H H P P P

S.Will, 18.417, Fall 2011 H iecanmodels chain Side H P P P H

S.Will, 18.417, Fall 2011 A Deﬁnition lattice saset a is ~ ~ u 0 L , ∈ of ~ v L ∈ atc points lattice L implies Lattices ~ u + uhthat such ~ v , ~ u − ~ v ∈ L

S.Will, 18.417, Fall 2011 ui atc = Lattice Cubic ui Lattice Cubic Z 3

S.Will, 18.417, Fall 2011 aeCnee ui atc (FCC) Lattice Cubic Face-Centered C = FCC {

y x z ! ∈ Z 3 | x + y + z even }

S.Will, 18.417, Fall 2011 aeCnee ui atc (FCC) Lattice Cubic Face-Centered C = FCC {

y x z ! ∈ Z 3 | x + y + z even }

S.Will, 18.417, Fall 2011 Measures • • • opr ﬀltieado-atc structure on-lattice and oﬀ-lattice Compare lattice on approximation best PDB Generate database from structures protein Use dRMSD cRMSD ( ( ,ω ω, ,ω ω, 0 0 = ) = ) h etLattice? Best The D D ij ij 0 s s = = n n 1 k k ( ω ω 1 n ≤ X ( 0 ( i − i i ) 1 ≤ ) − n 1) − k / ω ω ω 2 ( ( 0 j ( i 1 ) ) j ≤ k ) X − i k < j ω ≤ 0 n ( ( i ) D k ij 2 − D ij 0 ) 2

S.Will, 18.417, Fall 2011 prxmto eed lotol ncmlxt ftemodel the of complexity on only almost depends Approximation Conclusion iceesaemdl fpoensrcueJunlo Molecular of Journal of structure 1995 protein accuracy Biology, of and complexity models The state Levitt. discrete Michael Park, H. Britt atc prxmto oeResults Some - Approximation Lattice oycnee ui BC .92.14 2.59 (BCC) cubic body-centered aecnee ui FC .81.46 1.78 (FCC) cubic face-centered atc RS cRMSD dRMSD Lattice ui .42.34 2.84 cubic td yPr n Levitt and Park by Study

S.Will, 18.417, Fall 2011 • • rdcino oa tutrsi lblrpoen.JMlBiol. Mol J proteins. globular knowledge-based in the structures to local approach of An prediction from force. ensembles mean conformational of of potentials Calculation (1990) MJ Sippl structures: Macromolecules crystal approximation. protein quasi-chemical eﬀective from of energies Estimation contact (1985) interresidue R Jernigan S, Miyazawa biii Potentials Ab-initio ttsia oetas 20 Potentials: Statistical atc/iceeMdl:Piws Potentials Pairwise Models: Lattice/Discrete • • • • HHdohbc =otv,NNgtv,X=Neutral) N=Negative, P=Postive, (H=Hydrophobic, HPNX HP oeta fma oc (Sippl) force mean of potential (Myiazawa-Jernigan) approximation quasi-chemical × 0aioacids amino 20

S.Will, 18.417, Fall 2011 iuae neln eei Algorithms Genetic & Annealing Simulated • • • • vnfrsml oes antpoeoptimality prove cannot models: simple for landscape Even energy in optima local Find methods models search protein Heuristic complex or simple to Applicable tcatcLclSearch Local Stochastic

S.Will, 18.417, Fall 2011 • • • e tutrsgnrtdb pligmvsfo a from moves space applying structure by the generated in structures neighbors New are structures new Idea: structures structures existing new from generates systematically search Stochastic oeSt:LclMvsadPvtMoves Pivot and Moves Local Sets: Move • • io moves pivot moves local oeset move

S.Will, 18.417, Fall 2011 oa oecagstepstoso one ubrof number bounded a time. of a positions at the monomers changes move local A Explanation oa Moves Local

S.Will, 18.417, Fall 2011 io oertts(n/rrflcs rfi structure prefix a reflects) (and/or rotates move pivot A Explanation around ω ( i ). io Moves Pivot ω (1) ..ω ( i )

S.Will, 18.417, Fall 2011 • • • high temperature on structures worse depends to going allow Sometimes structures better to going Prefer by moves space random structure applying the through repeatedly walk random a Perform low T T cetams nybte structures better only almost accept : cetams l structures all almost accept : iuae neln Idea — Annealing Simulated T

S.Will, 18.417, Fall 2011 Remarks sequence for structure optimal an Find • • • • • edntknow. don’t we Otherwise: for only cooling. optimum slow global exponentially the ﬁnding for Guarantee criterion Metropolis = rule Acceptance Co h eprtr down) temperature the (Cool steps simulation Perform structure random with Start • • nyacp e tutr,i.e. structure, new to accept move only local random a apply iuae neln Algorithm — Annealing Simulated • • rwt probability with or if either E ( s ω , 0 ) < exp( E ( − s ω ω , ( E ) ( s ω ω ω , s → := 0 ) (temperature T ω − ω 0 0 E ( s ω , )) ) T )

S.Will, 18.417, Fall 2011 • • e tutrsaegnrtdfo xsigby existing from generated are structures of New population to annealing simulated structures of idea the Extend • • rsoe admmrigtostructures two merging random = move Crossover pivot random = Mutation Hbi)GntcAgrtm—Idea — Algorithm Genetic (Hybrid)

S.Will, 18.417, Fall 2011 ida pia tutr o sequence for structure optimal an Find h Hbi)GntcAgrtm[ne&Moult] [Unger& Algorithm Genetic (Hybrid) The • • ipepoenmdl ora fMlclrBooy 1996. a Biology, in Molecular folding of dominate Journal interactions model. Local protein Moult. simple J and Unger R eeaerno tr ouain(..20structures) 200 Repeat (e.g. population start random Generate • • • average to compared is population.) offspring in each energy of criterion energy the Metropolis to (Here: due only offspring crossover Accept by population offspring Generate structures all Mutate s

S.Will, 18.417, Fall 2011 • • • • saltm steps time small for calculated are Changes motion of laws Newton’s Applies CHARMM) AMBER, (e.g. potentials ﬁeld force Uses protein a of motion the Simulates E nonbonded onslk h liaesolution ultimate the like sounds atoms; between forces considering • • • E bonded mle hnvbaino system ⇒ of vibration error than discretization smaller avoid to enough small frsmlto time simulation for critical intensive computationally E total nodro etscns=10 = femtoseconds of order in = = = E E E electrostatic bond bonded oeua Dynamics Molecular − stretch + E + nonbonded + E E van angle − der − − − bend 15 Waals seconds! + E rotation − along − bond

S.Will, 18.417, Fall 2011 • • • • • • arptnilmn-oypotentials potential/many-body Pair MD Quantum solvent explicit/implicit (instabilities) numerically solved equations Newton’s molecules) small comparably (from empirical ﬁelds force gap Simulation ai o rti odn case? ( folding protein for valid millisecond least at need we proteins, small folding 10 For steps: billion one Assume ebraseto oeua mechanics” molecular of “embarrassment iiain fM r o exclusively not are MD of Limitations atro opttoa resources computational of matter a oeua yais Limits Dynamics: Molecular − 15 × 10 9 ssil10 still is ) − 6

S.Will, 18.417, Fall 2011 • • • • • ii ofrainlsac pc yuig9e motifs 9mer using Rationale by space search model conformational grained Limit coarse in search Carlo Monte eetcniae o reﬁnement for fragments candidates compatible Select swapping by generated structures New • • • • • a rdc ag ra fpoenb acigsqec to sequence matching by protein of motifs protein areas full large of predict independently Can fold often structures Local lsesadrtre oteue spredictions as user ﬁve the best to the returned of and each clusters center from the taken conformations of structures of structure Representative number deviation greatest rms the N- with within one is cluster Best and energy on size based structural clustered are structures Accepted rgetAsml:Rosetta Assembly: Fragment

S.Will, 18.417, Fall 2011 a oet.An.Rv ice,2008. with Biochem, Modeling Rev. Macromolecular Annu. Baker. Rosetta. David and Das Rhiju oet:Famn sebyadReﬁnement and Assembly Fragment Rosetta: c b Polar residues Negatively chargedPositively residues chargedHydrophobic residues residues Hydrogen bonds Nonpolar atoms

S.Will, 18.417, Fall 2011 Rosetta tmclvlprediction, level atomic a oeo Rosetta: of More de-novo ln rdcinRsls(CASP6) Results Prediction Blind < 2 ;ab 09 eius 1.6/1.4 residues, 70/90 a/b: A; ˚ b Foldit A ˚

S.Will, 18.417, Fall 2011 Protein Structure Prediction

• Stage 1: Backbone Prediction – Ab initio folding – Homology modeling – Protein threading • Stage 2: Loop Modeling • Stage 3: Side-Chain Packing • Stage 4: Structure Refinement

The picture is adapted from http://www.cs.ucdavis.edu/~koehl/ProModel/fillgap.html

April 22nd, 2009 18.417 Lecture 20: Comparative modeling and side-chain packing 18/49 Sometimes grouped “Comparative Modeling”

• Homology modeling – identification of homologous proteins through sequence alignment

– structure prediction through placing residues into “corresponding” positions of homologous structure models

• Protein threading – make structure prediction through identification of “good” sequence- structure fit

April 22nd, 2009 18.417 Lecture 20: Comparative modeling and side-chain packing 19/49 PDB New Fold Growth

April 22nd, 2009 18.417 Lecture 20: Comparative modeling and side-chain packing 20/49 Homology Modeling

Query DRVYIHPFADRVYIHPFA Sequence: • PSI-BLAST • HMM • Smith-Waterman algorithm

Protein sequence classification database

The Best Match

April 22nd, 2009 18.417 Lecture 20: Comparative modeling and side-chain packing 21/49 Protein Structure Prediction

• Stage 1: Backbone Prediction – Ab initio folding – Homology modeling – Protein threading • Stage 2: Loop Modeling • Stage 3: Side- Chain Packing • Stage 4: Structure Refinement

The picture is adapted from http://www.cs.ucdavis.edu/~koehl/ProModel/fillgap.html

April 22nd, 2009 18.417 Lecture 20: Comparative modeling and side-chain packing 22/49 Protein Threading

• Make a structure prediction through finding an optimal alignment (placement) of a protein sequence onto each known structure (structural template)

– “alignment” quality is measured by some statistics-based scoring function

– best overall “alignment” among all templates may give a structure prediction

• Step 1: Construction of Template Library • Step 2: Design of Scoring Function • Step 3: Alignment • Step 4: Template Selection and Model Construction

April 22nd, 2009 18.417 Lecture 20: Comparative modeling and side-chain packing 23/49 Protein Threading

Query Sequence: DRVYIHPFADRVYIHPFA

The Best Match

April 22nd, 2009 18.417 Lecture 20: Comparative modeling and side-chain packing 24/49 Protein Threading

April 22nd, 2009 18.417 Lecture 20: Comparative modeling and side-chain packing 25/49 Threading Model

• Each template is parsed as a chain of cores. Two adjacent cores are connected by a loop. Cores are the most conserved segments in a protein.

• No gap allowed within a core.

• Only the pairwise contact between two core residues are considered because contacts involved with loop residues are not conserved well.

• Global alignment employed

April 22nd, 2009 18.417 Lecture 20: Comparative modeling and side-chain packing 26/49 Scoring Function

how preferable to put how well a residue two particular fits a structural residues nearby: E_p environment: E_s (Pairwise potential) (Fitness score)

sequence similarity between query and alignment gap template proteins: E_m penalty: E_g (Mutation score) (gap score) How consistent of the secondary structures: E_ss

E= E_p +E_s +E_m +E_g +E_ss

Minimize E to find a sequence-template alignment

April 22nd, 2009 18.417 Lecture 20: Comparative modeling and side-chain packing 27/49 Scoring: Fitness Score

occurring probability of amino acid a with s

occurring probability of amino acid a

occurring probability of solvent accessibility s

April 22nd, 2009 18.417 Lecture 20: Comparative modeling and side-chain packing 28/49 Scoring: Pairwise Potential

occurring probability of a and b with distance < cutoff

occurring probability of amino acid a

occurring probability of amino acid b

April 22nd, 2009 18.417 Lecture 20: Comparative modeling and side-chain packing 29/49 Scoring: Secondary Structure

1. Difference between predicted secondary structure and template secondary structure

2. PSIPRED for secondary structure prediction

April 22nd, 2009 18.417 Lecture 20: Comparative modeling and side-chain packing 30/49 Scoring: Mutational Score

Could be based on chemical similarity, etc, etc.

April 22nd, 2009 18.417 Lecture 20: Comparative modeling and side-chain packing 31/49 Contact Graph

1. Each residue as a vertex template 2. One edge between two residues if their spatial distance is within given cutoff. 3. Cores are the most conserved segments in the template

April 22nd, 2009 18.417 Lecture 20: Comparative modeling and side-chain packing 32/49 Simplified Contact Graph

April 22nd, 2009 18.417 Lecture 20: Comparative modeling and side-chain packing 33/49 Alignment Example

April 22nd, 2009 18.417 Lecture 20: Comparative modeling and side-chain packing 34/49 Alignment Example

April 22nd, 2009 18.417 Lecture 20: Comparative modeling and side-chain packing 35/49 Calculation of Alignment Score

April 22nd, 2009 18.417 Lecture 20: Comparative modeling and side-chain packing 36/49 Threading Algorithms

• NP-Hard problem – Can be reduced to MAX-CUT

• Approximation Algorithm – Interaction-frozen algorithm (A. Godzik et al.) – Monte Carlo sampling (S.H. Bryant et al.) – Double dynamic programming (D. Jones et al.)

• Exact Algorithm – Branch-and-bound (R.H. Lathrop and T.F. Smith) – PROSPECT-I uses divide-and-conquer (Y. Xu et al.) – Linear programming by RAPTOR (J. Xu et al.)

April 22nd, 2009 18.417 Lecture 20: Comparative modeling and side-chain packing 37/49 Linear & Integer Program

maximize

Linear Program z= 6x+5y Linear function Integer Program Subject to

3x+y<=11 -x+2y<=5 Linear contraints x, y>=0

Integral contraints x, y integer (nonlinear)

April 22nd, 2009 18.417 Lecture 20: Comparative modeling and side-chain packing 38/49 Variables

• x(i,l) denotes core i is aligned to sequence position l • y(i,l,j,k) denotes that core i is aligned to position l and core j is aligned to position k at the same time.

April 22nd, 2009 18.417 Lecture 20: Comparative modeling and side-chain packing 39/49 LP Formulation

a: singleton score parameter b: pairwise score parameter

Each y variable is 1 if and only if its two x variable are 1

Each core has only one alignment position

April 22nd, 2009 18.417 Lecture 20: Comparative modeling and side-chain packing 40/49 Online Servers

http:// www.bioinformatics.uw aterloo.ca/~j3xu/raptor/ index.php

http://robetta.bakerlab.org/index.html

http://www.sbg.bio.ic.ac.uk/~phyre/

April 22nd, 2009 18.417 Lecture 20: Comparative modeling and side-chain packing 41/49 Protein Structure Prediction

• Stage 1: Backbone Prediction – Ab initio folding – Homology modeling – Protein threading • Stage 2: Loop Modeling • Stage 3: Side- Chain Packing • Stage 4: Structure The picture is adapted from http://www.cs.ucdavis.edu/~koehl/ProModel/fillgap.html Refinement

April 22nd, 2009 18.417 Lecture 20: Comparative modeling and side-chain packing 42/49 Protein Side-Chain Packing

• Problem: given the backbone coordinates of a protein, predict the coordinates of the side- chain atoms

• Insight: a protein structure is a geometric object with special features

• Method: decompose a protein structure into some very small blocks

April 22nd, 2009 18.417 Lecture 20: Comparative modeling and side-chain packing 43/49 Side-Chain Packing

0.3

0.2 0.3 0.7 0.1

0.1 0.4 0.1

0.6

clash

Each residue has many possible side-chain positions. Each possible position is called a rotamer. Need to avoid atomic clashes.

April 22nd, 2009 18.417 Lecture 20: Comparative modeling and side-chain packing 44/49 Energy Function

Assume rotamer A(i) is assigned to clash penalty residue i. The side-chain packing quality is measured by 10

clash penalty 0.82 1 occurring preference The higher the occurring probability, the smaller the value : distance between two atoms :atom radii

Minimize the energy function to obtain the best side-chain packing.

April 22nd, 2009 18.417 Lecture 20: Comparative modeling and side-chain packing 45/49 Many Methods

• NP-hard [Akutsu, 1997; Pierce et al., 2002] and NP- complete to achieve an approximation ratio O(N) [Chazelle et al, 2004] • Dead-End Elimination: eliminate rotamers one-by- one • SCWRL: biconnected decomposition of a protein structure [Dunbrack et al., 2003] – One of the most popular side-chain packing programs

• Linear integer programming [Althaus et al, 2000; Eriksson et al, 2001; Kingsford et al, 2004] – The formulation similar to that used in RAPTOR

April 22nd, 2009 18.417 Lecture 20: Comparative modeling and side-chain packing 46/49 Dead-end elimination

• Conformation consists of N residues, each with a set of r possible rotomers

• Simplification: Global conformation energy formulated as 2 parts: • Sum of all interactions between backbone and N residues • Sum of all pairwise interactions between i*i residues (residues i, j, rotatmers r, s)

N N−1 N E total = ∑ E(ir ) + ∑ ∑ E(ir, js) i=1 i=1 j= i+1

nd € April 22 , 2009 18.417 Lecture 20: Comparative modeling and side-chain packing 47/49 Dead-end elimination

• If two rotamers r, s at residue position i

• can eliminate rotamer s, if pairwise energy between ir and all other sideschains is always higher than pairwise energy between is and all other sidechains

Eliminate ir iff:

E(ir ) − E(is) +

∑min E(ir, j) +∑min E(is, j) > 0 j≠i j≠i

€ http://www.ch.embnet.org/CoursEMBnet/Pages3D08/slides/SIB-PhD-Day2_p.pdf April 22nd, 2009 18.417 Lecture 20: Comparative modeling and side-chain packing 48/49 Dead-end elimination

• Apply iteratively to all rotamer pairs

• After each elimination, energy landscape changes so could cause new elimination that couldn’t have happened before

April 22nd, 2009 18.417 Lecture 20: Comparative modeling and side-chain packing 49/49