Protein Structural Prediction

Protein Structural Prediction

Structure Determines Function

What determines structure?

• Energy• Kinematics

How can we determine structure?

• Experimental methods• Computational predictions

The Protein Folding Problem

Protein Structure Prediction

• ab initio Use just first principles: energy, geometry, and kinematics

• Homology Find the best match to a database of sequences with known 3D-

structure

• Threading

• Meta-servers and other methods

Threading

• Threading is the golden mean between homology-based prediction and molecular modeling (?)

MTYKLILN …. NGVDGEWTYTE

Main difference between homology-based prediction and threading:

Threading uses the structure to compute energy function during alignment

Threading – Overview

• Build a structural template database

• Define a sequence–structure energy function

• Apply a threading algorithm to query sequence

• Perform local refinement of secondary structure

• Report best resulting structural model

Threading Search Space

Protein Sequence X

ProteinStructure

Y

MTYKLILNGKTKGETTTEAVDAATAEKVFQYANDNGVDGEWTYTE

Threading – Template Database

• FSSP, SCOP, CATH

• Remove pairs of proteins with highly similar structures Efficiency Statistical skew in favor of large families

Threading – Energy Function


how well a residue fits a structural environment: Es

how preferable to put two particular residues nearby: Ep

alignment gap penalty: Eg

total energy: wmEm + wsEs + wpEp + wgEg + wssEss

how often a residue mutates to the template residue: Em

compatibility with local secondary structure prediction: Ess

Threading – Formulation

C1 C2 C3 C4

at1a

t2at3a

t4aλ1λ0

λ2λ3 λ4

x

uy

zv Ci

Cj

x

u v

zy

• Contact graph captures amino acid interactions

• Cores represent important local structure units

• No gaps within each core


CMG = (v, )


From Lathrop & Smith

Threading Search Space

Protein Sequence X

ProteinStructure

Y


How Hard is Threading?

CORES

How Hard is Threading?

• At least as hard as MAX-CUT

MAX-CUT: Given graph G = (V, E), find a cut (S, T) of V with maximum number of edges between S and T.

The Bad News: APX-complete even when each node has at most B edges (where B>2)

2

3

4 5

6

7

1

Reduction of MAX-CUT to Threading

• |V| cores, each core i has length 1 and corresponds to vi

• Let Ep(0,1) = 1: every edge labeled 0-1 or 1-0 gets a score of 1

• Then, size of cut = threading score

2

3

4 5

6

7

1

0 1 0 1 0 1 0 1 0 1 0 1 0 1 v1 v2 v3 v4 v5 v6 v7

Sequence consistsof |V| 01-pairs

Threading with Branch & Bound

• Set of solutions can be partitioned into subsets (branch)

• Upper limit on a subset’s solution can be computed fast (bound)

Branch & Bound1. Select subset with best

possible bound2. Subdivide it, and compute a

bound for each subset

Threading with Branch & Bound

• Key to this algorithm is tradeoff on lower bound

efficient

tight

Threading with Integer Programming

3x+y ≤ 11

-x+2y ≤ 5

x, y ≥ 0

maximize z = 6x+5y

Subject to

Linear constraints

Linear function

x, y {0, 1}Integral constraints (nonlinear)

Linear Program

Integer Program

RAPTOR: integer programming-based threadingperhaps the best protein threading system


x(i,k) denotes that core i is aligned to sequence position k

y(i,k,j,l) denotes that core i is aligned to position k and core j is aligned to position l

D(i) all positions where core i can be aligned to

R(i, j, k) set of possible alignments of core j, given that core i aligns to position k

corei (headi, taili, lengthi = taili – headi + 1)


}1,0{,

1

1

],,[,

],,[,

],1,[,1

..

),)(,(,

][,

,,),)(,(

,),)(,(

,),)(,(

),1(),(

kjlili

iDlli

kjlikjli

kjkjli

likjli

kili

ssssggppssmm

yx

x

xxy

kijRlxy

ljiRkxy

liiRkxx

ts

EWEWEWEWEWE

Minimize

Each core has only one alignment position

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

x and y represent exactly the same threading

Cores are aligned in order

Energy Function is Linear

• Sequence substitution score

• Fitness of aa in each position (example, hydrophobicity)

• Agreement with secondary structure prediction

• Pairwise interaction between two cores

• Gap between two successive cores

LP Relaxation and (again) Branch & Bound

1. Relax the integral constraint, to

x(i,j), y(i,k,j,l) 0

2. Solve the LP using a standard method(RAPTOR uses IBM’s OSL)

3. If resulting solution is integral, done

4. Else, select one non-integral variable (heuristically), and generate two subproblems by setting it to 0, and 1 -- use Branch & Bound

In practice, in RAPTOR only 1% of the instances in the test database required step 4; almost all solutions are integral !!!

CAFASP

GOAL

The goal of CAFASP is to evaluate the performance of fully automatic structure prediction servers available to the community. In contrast to the normal CASP procedure, CAFASP aims to answer the question of how well servers do without any intervention of experts, i.e. how well ANY user using only automated methods can predict protein structure. CAFASP assesses the performance of methods without the

user intervention allowed in CASP.

Performance Evaluation in CAFASP3

Servers

(54 in total)

Sum MaxSub

Score

# correct

(30 FR targets)

3ds5 robetta 5.17-5.25 15-17

pmod 3ds3 pmode3 4.21-4.36 13-14

RAPTOR 3.98 13

shgu 3.93 13

3dsn 3.64-3.90 12-13

pcons3 3.75 12

fugu3 orf_c 3.38-3.67 11-12

… … …

pdbblast 0.00 0

(http://ww.cs.bgu.ac.il/~dfischer/CAFASP3, released in December, 2002.)

Servers with name in italic are meta servers

MaxSub score ranges from 0 to 1

Therefore, maximum total score is 30

One structure where RAPTOR did best

Red: true structure

Blue: correct part of prediction

Green: wrong part of prediction

• Target Size:144

• Super-imposable size within 5A: 118

• RMSD:1.9

Some more results by other programs



Structural Motifs

beta helix

beta barrel

beta trefoil

Structural Motif Recognition

• Secondary Structure Prediction Find the helices, sheets, loops in a protein sequence

• Given an amino acid residue sequence, does it fold as a Coiled Coil? helix? barrel? Zinc finger?

• Intermediate goals towards folding• Useful information about the function of a protein• More amenable to sequence analysis, than full fold prediction

Structural Motif Recognition

1. Collect a database of known motifs and corresponding amino acid subsequences

2. Devise a method/model to “match” a new sequence to existing motif database

3. Verify computationally on a test set (divide database into training and testing subsets)

4. Verify in lab

Structural Motif Recognition Methods

• Alignment

• Neural Nets

• Hidden Markov Models

• Threading

• Profile-based Methods

• Other Statistical Methods

Predicting Coiled Coils


• NewCoils: multiply probs of frequencies in each coiled coil position


• PairCoil: multiply pairwise probs of spatially neighboring positions

• Use a sliding window of length 28

• Perfect score separation between true and false examples (false = non-coil-coil helices)

Berger et al. PNAS 1995

Predicting helices

• Helix composed of three parallel sheets

• Very few solved structures, very different from one another

• Absent in eukaryotes! Probably evolved subsequent to prok/euk split

Predicting helices

• Only available program: BetaWrap

1. The rungs subproblemGiven the location of a T2 turn of one rung, find location of T2 turn of

next rung Distribution of turn lengths Bonus/penalty for stacked pairs in the parallel strands Discard if highly charged residues in the inward-point positions of

strand

2. From a rung to multiple rungs

Find multiple initial B2-T2-B3 rungs Use sequence template based on hydrophobicity to find many

candidate rungs Find “optimal wrap” by DP + heuristic score, based on 5

consistent rungs

3. Completing the parse Find B1 strands by locally optimizing their location

Predicting helices

• BetaWrap gives scores that separate true from false helices

Bradley et al. PNAS 2001

Predicting trefoils

http://betawrappro.csail.mit.edu/

Similar idea – use a combination of domain-specific expert knowledge with statistics

WRAP-AND-PACK

WRAP: Search for antiparallel strands to “wrap” a cap

PACK: Place the side chains in the interior of the wrapped strands

Predicting Secondary Structure

• Given amino acid sequence, classify positions into helices, strands, or loops

• In general, harder than protein motif identification

• Best methods rely on Neural Networks

Similarly good separation can be achieved by SVMs

PSIPRED1. Given a sequence x, generate profile using PSI-BLAST2. Pass the profile to a pre-trained NN3. Output classification: helix / strand / loops

PSIPRED

Profile M

Training & Testing• Start with database of determined folds (<1.87 Ao)

• Remove redundancy: any pair of proteins with high similarity (found by PSI-BLAST) – 187 remaining proteins

• 3-fold cross validation

~76% classification accuracy

PSIPRED server

PSIPRED PREDICTION RESULTS

Conf: Confidence (0=low, 9=high)

Pred: Predicted secondary structure (H=helix, E=strand, C=coil)

AA: Target sequence

# PSIPRED HFORMAT (PSIPRED V2.3 by David Jones)

Conf: 9888788777656877765688766579

Pred: CCCCCCCCCCCCCCCCCCCCCCCCCCCC

AA: PEPTIDEPEPTIDEPEPTIDEPEPTIDE



AA: Target sequence


Conf: 988888600148777777885001487777778842003789

Pred: CCCCCCCCEECCCCCCCCCCCCEECCCCCCCCCCCCCCCCCC

AA: PPEEPPTTIIDDEEPPEEPPTTIIDDEEPPEEPPTTIIDDEE




AA: Target sequence


Conf: 998888872100111210012112359

Pred: CCCCCCCCCCCHHHHHHHHCCCCCCCC

AA: PTYPTYPTXXXXXXXXXXXXTEETEET




AA: Target sequence


Conf: 91025687432236422336410232027743223653334679

Pred: CCCCCCCCCCCCCCCCCCCCCCCEEEECCCCCCCCCCCCCCCCC

AA: THISISAPRXTEINSEQXENCETHISISAPRXTEINSEQXENCE

TRILOGY: Sequence–Structure Patterns

• Identify short sequence–structure patterns 3 amino acids• Find statistically significant ones (hypergeometric distribution)

Correct for multiple trials

• These patterns may have structural or functional importance

1. Pseq: R1xa-bR2xc-dR3

2. Pstr: 3 C – C distances, & 3 C – C vectors

• Start with short patterns of 3 amino acids{V, I, L, M}, {F, Y, W}, {D, E}, {K, R, H}, {N, Q}, {S, T}, {A, G, S}

• Extend to longer patterns

Bradley et al. PNAS 99:8500-8505, 2002

TRILOGY

TRILOGY: Extension

Glue together two 3-aa patterns that overlap in 2 amino acids

P-score = i:Mpat,…,min(Mseq, Mstr) C(Mseq, i) C(T – Mseq, Mstr – i) C(T, Mstr)-1

TRILOGY: Longer PatternsType-II turn between unpaired strands

NAD/RAD binding motif found in several folds

-- unit found in three proteins with the TIM-barrel fold

Helix-hairpin-helix DNA-binding motif

Four Cysteines forming 4 S-S disulfide bonds

A fold with repeated aligned -sheets

Three strands of an anti-parallel -sheet

A -hairpin connected with a crossover to a third -strand

Small Libraries of Structural Fragments for Representing Protein

Structures

Fragment Libraries For Structure Modeling

knownstructures

…

fragmentlibrary

proteinsequence

predictedstructure

Small Libraries of Protein Fragments

Kolodny, Koehl, Guibas, Levitt, JMB 2002

Goal: Small “alphabet” of protein structural fragments that can be used to represent

any structure

1. Generate fragments from known proteins2. Cluster fragments to identify common structural motifs3. Test library accuracy on proteins not in the initial set

f

Small Libraries of Protein Fragments

Dataset: 200 unique protein domains with most reliable & distinct structures from SCOP 36,397 residues

• Divide each protein domain into consecutive fragments beginning at random initial position

Library: Four sets of backbone fragments 4, 5, 6, and 7-residue long fragments

• Cluster the resulting small structures into k clusters using cRMS, and applying k-means clustering with simulated annealing Cluster with k-means Iteratively break & join clusters with simulated annealing to optimize total variance Σ(x – μ)2

f

Evaluating the Quality of a Library

• Test set of 145 highly reliable protein structures (Park & Levitt)

• Protein structures broken into set of overlapping fragments of length f

• Find for each protein fragment the most similar fragment in the library (cRMS)

Local Fit: Average cRMS value over all fragments in all proteins in the test set

Global Fit: Find “best” composition of structure out of overlapping fragments Complexity is O(|Library|N) Greedy approach extends the C best

structures so far from pos’n 1 to N

Results

C =

Documents

Protein Structural Prediction