A Genetic Programming Challenge: Evolving the Energy Function for Protein Structure Prediction

Evolving energy functionfor protein structure prediction

Paweł [email protected]

Natalio Krasnogor, Jonathan Garibaldi

Department of Computer ScienceBen-Gurion University of the Negev Beer Sheva, Israel

2009-06-30

mailto:[email protected]

Outline

1 Introduction

2 Protein energy models

3 Genetic Programming problem formulation

4 Results

5 Conclusions

Pawe l Widera Evolving energy function for PSP 2009-06-30 2 / 26

Protein structure predictionFrom 1D sequence to 3D structure

LFSKELRCMMYGFGDDQNPYTESVDILEDLVIEFITEMTHKAMSIFSEEQLNRYEMYRRSAFPKAAIKRLIQSITGTSVSQNVVIAMSGISKVFVGEVVEEALDVCEKWGEMPPLQPKHMREAVRRLKSKGQIP

Protein basics20 aminoacidalphabetsequence encodesstructurestructuredetermines activity


International prediction contestCritical Assessment of techniques for protein Structure Prediction

CASP factsbiannual competition started in 1994parallel prediction and experimental verificationmodel assesment by human experts

Prediction difficultycomparative modelling (sequence similarity)fold recognition (new or existing)ab initio modelling (first principles)


Ab initio predictor schemaFrom sequence to the final model

Target sequence

Secondarystructureprediction

Foldrecognition

and threading

Initial ab initio prediction

Optimisation

Clustering

Final models

PSIPRED

SAM-T02

JUFO

PSI-BLAST


Ab initio predictor schemaFrom sequence to the final model

Target sequence

Secondarystructureprediction

Foldrecognition

and threading

Initial ab initio prediction

Optimisation

Clustering

Final models

PSIPRED

SAM-T02

JUFO

PSI-BLAST


The algorithm of foldingAnfinsen’s thermodynamic hypothesis [Anfinsen, 1973]

[Dill and Chan, 1997]

Refolding experimentfolds to the samenative statenative state isenergetically stable

Energy funnelroll down freeenergy hillavoid local minimatraps


Model assesmentCorrelation between energy and similarity to native

Similarity measure

RMSD =

√√√√ 1N

i=N∑i=1

δ2i

Decoys generated byI-TASSER[Wu et al., 2007]

Robetta[Rohl et al., 2004]


Model assesmentCorrelation between energy and similarity to native

Similarity measure

RMSD =

√√√√ 1N

i=N∑i=1

δ2i

Decoys generated byI-TASSER[Wu et al., 2007]

Robetta[Rohl et al., 2004]


All-atom force fieldFolding simulation ∑bonds

ik l

i2 (l − l0i )+∑angles

ikθi2 (θ − θ0

i )+∑torsionsi

Vωi2 [1 + cos(niωi − φi)]+∑N−1

i=1∑N

j=i+1

{4εij

[(σijrij

)12−(

σijrij

)6]

+qi qj

4πε0rij

}Intermolecular forces

bond forces (stretching, bending, rotating)short range forces (Pauli repulsion, van der Waals’ interactions)electrostatic forces (Coulomb’s law)

Rosetta@home in CASP7140k computers (37 TFLOPS) — 500k CPU hours per domain


All-atom force fieldFolding simulation ∑bonds

ik l

i2 (l − l0i )+∑angles

ikθi2 (θ − θ0

i )+∑torsionsi

Vωi2 [1 + cos(niωi − φi)]+∑N−1

i=1∑N

j=i+1

{4εij

[(σijrij

)12−(

σijrij

)6]

+qi qj

4πε0rij

}Intermolecular forces

bond forces (stretching, bending, rotating)short range forces (Pauli repulsion, van der Waals’ interactions)electrostatic forces (Coulomb’s law)

Rosetta@home in CASP7140k computers (37 TFLOPS) — 500k CPU hours per domain


Simplified knowledege-based potentialProtein structure prediction

i − 1

i

i + 1

n̂ib̂i v̂i

Example

Estiff =∑

i

(−λv̂i · v̂i+4 − λ

∣∣∣b̂i · b̂i+2

∣∣∣− λΘ1(i) + Θ2(i) + Θ3(i))

Eenv =∑

i V (NPi ,NAi ,NOi ,Ai)


Energy functionWeighted sum of terms vs. evolved function

F (~T ) = w1 ∗ T1 + . . .wn ∗ Tn[Zhang et al., 2003]

F (~T ) = T1∗T3w1∗log(T2)

+ sin(

T4−w2∗T1T5∗exp(cos(w1∗T3))

)GP input

terminals:T1, . . . ,T8

functions:add sub mul divsin cos exp lograndom ephemeralsin range [0,1]

GP tree examplesize = 60depth = 17




F (~T ) = T1∗T3w1∗log(T2)

+ sin(


)GP input







F (~T ) = T1∗T3w1∗log(T2)

+ sin(


)GP input





Fitness evaluationEvolutionary objective

1 construction of the reference ranking RR(decoys sorted by similarity to native)

2 ranking decoys using evolved energy function RE(decoys sorted by energy)

3 rankings comparison - RR vs. RE4 fitness = average distance for all proteins


Reference ranking constructionCorrelation between energy and similarity to native

R0

RMSD

0

3.2

1

2.1

2

5.2

3

1.2

4

3.5

5

2.1

6

4.8

7

3.5

R1 3 1 5 0 4 7 6 2

R2 3.0 1.5 7.0 0.0 4.5 1.5 6.0 4.5

Ranking typesR1 - permutation of indicesR2 - averaged ranks


Rankings comparisonMeasure of distance between rankings

4 3 2 1 53 4 1 5 21 1 1 4 3→ 10

1 45

35

25

15 → 4.6

Distance functionsLevenshtein edit distance - O(n)

Kendall Tau distance - O(n(n−1)2 )

Spearman footrule distance - O(12n2)

Ranks weightinglinearsigmoid


Rankings comparisonMeasure of distance between rankings

4 3 2 1 53 4 1 5 21 1 1 4 3→ 10

1 45

35

25

15 → 4.6

Distance functionsLevenshtein edit distance - O(n)

Kendall Tau distance - O(n(n−1)2 )

Spearman footrule distance - O(12n2)

Ranks weightinglinearsigmoid


Decoys samplingSelection vs. noise reduction

Simple selectiontopuniformrandom

Bin based selectionequal sizeequal distance


























Experiment design


Evolutionary progressFitness throughout generations

0 200 400 600 800 1000

generation

0.0010

0.0015

0.0020

0.0025

0.0030

0.0035

0.0040

fitness

levenshtein-steadystate

0 200 400 600 800 1000

generation

0.34

0.36

0.38

0.40

0.42

fitness

spearman-generational

0 200 400 600 800 1000

generation

0.500

0.505

0.510

0.515

0.520

fitness

kendall-generational

ObservationsRound I - early saturationRound II - small but constant improvement


Evolutionary progressFitness throughout generations

0 200 400 600 800 1000

generation

0.32

0.34

0.36

0.38

0.40

0.42

0.44

fitness

spearman-linear-ts8-generational

0 200 400 600 800 1000

generation

0.42

0.44

0.46

0.48

0.50

0.52

0.54

fitness

spearman-sigmoid-ts8-elitism

0 200 400 600 800 1000

generation

0.500

0.505

0.510

0.515

0.520

0.525

fitness

kendall-ts4-generational

ObservationsRound I - early saturationRound II - small but constant improvement


Landscape analysisFitness distribution for the random walk


Landscape analysisFitness distribution for the random walk

d-100 d-58 f-100 f-42 random-100 top-100 uniform-100 all0.3

0.4

0.5

0.6

0.7

0.8

fitness


Population diveristy analysisGenotype - Phenotype - Fitness mapping

Diversity measuresF - fitness entropy(frequency ofduplicates)P - root mean squaredistance betweenrankingsG - number of uniquetrees <#T, #NT, depth>






Improvement over random walkIs the evolution any good?

decoys set improvement avg best

all 0.78% 0.710uniform-100 0.96% 0.711random-100 1.28% 0.713top-100 1.93% 0.702s-42 7.76% 0.713s-100 7.64% 0.772d-58 8.21% 0.780d-100 10.88% 0.804


Best evolved energy functionsComparison to naive combination of energy terms

Correlation to RMSDd-100 0.76(generational+ADF)all decoys 0.30(steady-state+elitism)best single term 0.24worst single term -0.20naive combination ofterms 0.12original I-TASSERenergy 0.44 (0.51/0.65)











Comparison to weighted sum of termsNelder-Mead downhill simplex optimisation

spearman-sigmoid correlation

method d-100 all d-100 all

simplex 0.734 0.638 0.650 0.166GP 0.835 *0.714 0.740 *0.200


Distribution of terminals and operatorsDid the evolution discovered any knowledge?

energy term correlation

T1 (E13) 0.03± 0.11T2 (E14) 0.20± 0.17T3 (E15) 0.15± 0.15T4 (Estiff ) 0.24± 0.22T5 (EHB) −0.16± 0.20T6 (Epair ) 0.01± 0.14T7 (Eelectro) −0.20± 0.23T8 (Eenv ) 0.04± 0.16

average 0.06

Use of energy termsmost frequent: T4, T5

least frequent: T1, T6

Use of operatorsmost frequentadd, divleast frequentsin, cos, log





average 0.06








average 0.06








average 0.06





Summary

ConclusionsGP evolved function outperforms linear combination of weightsGP choice of energy terms reflects their correlation to RMSDdecoys from real prediction process are more difficult to assesbloat control is necessary to evolve more compact functions

Ideas for the futuremore complex total fitnessdistance measured using ProCKSI consensusRosetta generated decoysadditional energy terms (SA, RCH)


http://www.procksi.net

Summary

ConclusionsGP evolved function outperforms linear combination of weightsGP choice of energy terms reflects their correlation to RMSDdecoys from real prediction process are more difficult to assesbloat control is necessary to evolve more compact functions

Ideas for the futuremore complex total fitnessdistance measured using ProCKSI consensusRosetta generated decoysadditional energy terms (SA, RCH)


http://www.procksi.net

Thank you!

AcknowledgementsThis work was supported by Marie CurieAction MEST-CT-2004-7597 under theSixth Framework Programme of theEuropean Community.

Ben Gurion University of the Negev’sDistinguished Scientists Visitor Programand Prof. Moshe Sipper.

[email protected]


mailto:[email protected]

Publications

1 P. Widera, J.M. Garibaldi, N. KrasnogorEvolutionary design of the energy function for proteinstructure predictionIn IEEE Congress on Evolutionary Computation, CEC’09,p1305–1312, Trondheim, Norway, May 2009

2 P. Widera, J.M. Garibaldi, N. KrasnogorGP challange: evolving the energy function for proteinstructure predictionsubmitted to Genetic Programming and Evolvable Machines, 2008


References

Anfinsen, C. (1973).Principles that Govern the Folding of Protein Chains.Science, 181(4096):223–30.

Dill, K. A. and Chan, H. S. (1997).From Levinthal to pathways to funnels.Nat Struct Mol Biol, 4(1):10–19.

Rohl, C. A., Strauss, C. E. M., Misura, K. M. S., and Baker, D. (2004).Protein Structure Prediction Using Rosetta.In Brand, L. and Johnson, M. L., editors, Numerical Computer Methods, Part D, volume Volume 383 of Methods inEnzymology, pages 66–93. Academic Press.

Wu, S., Skolnick, J., and Zhang, Y. (2007).Ab initio modeling of small proteins by iterative TASSER simulations.BMC Biol, 5(1):17.

Zhang, Y., Kolinski, A., and Skolnick, J. (2003).TOUCHSTONE II: A New Approach to Ab Initio Protein Structure Prediction.Biophys. J., 85(2):1145–1164.


Education

A Genetic Programming Challenge: Evolving the Energy Function for Protein Structure Prediction