Protein folding. A theoretical view Alexei Finkelstein Institute of Protein Research, Russian...

Protein folding. A theoretical view

Alexei Finkelstein

Institute of Protein Research, Russian Academy of Sciences,

Pushchino, Moscow Region, Russia

University of Orange Free StateBloemfontain, South Africa

September 5, 2007

TWO protein folding problemsTWO protein folding problems::

1)1) How does protein structure fold?How does protein structure fold? √

2)2) How to predict protein structure How to predict protein structure from the chain’s a. a. sequence?from the chain’s a. a. sequence?

U NU N

BASIC FACTSBASIC FACTS::Protein chains has unique sequenceProtein chains has unique sequence & unique 3D structure& unique 3D structure

Protein chain can fold Protein chain can fold spontaneouslyspontaneously (RNase, (RNase, Anfinsen, 1961Anfinsen, 1961; ; RNase, RNase, Merrifield, 1969Merrifield, 1969))

Folding time: Folding time: in vivo: in vivo: BiosynthesisBiosynthesis ++ Folding < 10–20 min Folding < 10–20 min in vitroin vitro:: from microseconds to hoursfrom microseconds to hours

BASIC FACTSBASIC FACTS::Protein chains has unique sequenceProtein chains has unique sequence & unique 3D structure& unique 3D structure

Protein chain can fold Protein chain can fold spontaneouslyspontaneously (RNase, Anfinsen, 1961; (RNase, Anfinsen, 1961; RNase, Merrifield, 1969)RNase, Merrifield, 1969)

Folding time: Folding time: in vivo: in vivo: BiosynthesisBiosynthesis ++ Folding < 10–20 min Folding < 10–20 min in vitroin vitro:: from microseconds to hoursfrom microseconds to hours

For:For:Water-solubleWater-solublesingle-domain proteins;single-domain proteins;or separate domainsor separate domains

How CAN protein fold in a “bio-reasonable” time?How CAN protein fold in a “bio-reasonable” time?

Levinthal paradox (1968):Levinthal paradox (1968):

Random exhaustive enumerationRandom exhaustive enumerationSpecial pathway?Special pathway?Folding intermediates?Folding intermediates?

Native protein structure Native protein structure refolds from various starts, refolds from various starts, i.e., it behaves as i.e., it behaves as thermodynamically thermodynamically stablestable..

HOW CAN it be found - HOW CAN it be found - within seconds - among within seconds - among zillions of the others?zillions of the others?

U NRANDOMRANDOM

Is “Levinthal paradox” a paradox at all?

Is “Levinthal paradox” a paradox at all?

LL-dimensional-dimensional““Golf course”Golf course”

Zwanzig, 1992; Bicout & Szabo, 2000

Is “Levinthal paradox” a paradox at all?

…any tilt of energy surface solves this “paradox”… (?)

““Funnel”Funnel”LL-dimensional-dimensional

LL-dimensional-dimensional““Golf course”Golf course”

Cunning simplicity of a “funnel” Cunning simplicity of a “funnel” (without phase separation) folding(without phase separation) folding

- NO- NO simultaneous simultaneous explanation to explanation to (I) “all-or-none” transition(I) “all-or-none” transition(II) folding within non-astron. time(II) folding within non-astron. time at mid-transitionat mid-transition

UU NN

EE

EE

LL-dimensional “folding funnel”?-dimensional “folding funnel”?

~L~L

L-L-

STST

Resistance of entropy at T>0Resistance of entropy at T>0

All-or-none transition All-or-none transition for 1-domain proteins for 1-domain proteins (in thermodynamics: Privalov,1974;(in thermodynamics: Privalov,1974;in kinetics: Segava, Sugihara,1984)in kinetics: Segava, Sugihara,1984)

Funnel helps, but ONLY when Funnel helps, but ONLY when NN is much more stable than is much more stable than U U !!!!

Phillips (1965) hypothesis:Phillips (1965) hypothesis: folding nucleus is formed by the N-endfolding nucleus is formed by the N-end of the nascent protein of the nascent protein

chain, and the remaining chain wraps around it.chain, and the remaining chain wraps around it.

for single-domain proteins:for single-domain proteins: NO: NO:Goldenberg & Creighton, 1983: Goldenberg & Creighton, 1983: circular permutants: circular permutants: N-end has no special role in the N-end has no special role in the in vitro in vitro folding.folding.

A special pathway?A special pathway?

Phillips (1965) hypothesis:Phillips (1965) hypothesis: folding nucleus is formed by the N-endfolding nucleus is formed by the N-end of the nascent protein of the nascent protein

chain, and the remaining chain wraps around it.chain, and the remaining chain wraps around it.

for single-domain proteins:for single-domain proteins: NO: NO:Goldenberg & Creighton, 1983: Goldenberg & Creighton, 1983: circular permutants: circular permutants: N-end has no special role in the N-end has no special role in the in vitro in vitro folding.folding.

A special pathway?A special pathway?

HoweverHowever, , for for manymany-domain-domain proteins: proteins: Folding from N-end Folding from N-end domaindomain, , domain after domain domain after domain

DO NOT CONFUSEDO NOT CONFUSE N-ENDN-END DRIVEN FOLDING DRIVEN FOLDING WITHIN DOMAINWITHIN DOMAIN(which seems to be absent)(which seems to be absent)and and N-DOMAIN DRIVENN-DOMAIN DRIVEN FOLDING IN FOLDING IN MANYMANY-DOMAIN PROTEIN-DOMAIN PROTEIN(which is observed indeed)(which is observed indeed)

NOW: NOW:NOW: NOW:pre-molten MOLTENpre-molten MOLTEN globuleglobule GLOBULE

HYPOTHESIS:HYPOTHESIS:Stages in the mechanism of self-organization of protein molecules O.B.Ptitsyn, Dokl. Akad. Nauk SSSR. 1973; 210:1213-1215.

Folding intermediates?Folding intermediates?

PROTEINPROTEINFOLDING:FOLDING:

current picturecurrent picture(Dobson, 2003)(Dobson, 2003)

ee

UU

NN

MGMG

pre-MGpre-MG

TRUE: FOLDING with observable (accumulating in experiment) intermediates

UU

NN

= MG= MG

INDEED, INDEED, NO exhaustive enumerationNO exhaustive enumerationwhenwhen NN is much more stable thenis much more stable then UU

Hierarchic (stepwise) foldingHierarchic (stepwise) foldingavoids many “bad” pathways avoids many “bad” pathways

UU

NN

MGMG

pre-MGpre-MG

TRUE: FOLDING with observable (accumulating in experiment) intermediates

UU

NN

= MG= MG

Special pathway -Special pathway -Folding intermediates -Folding intermediates -they help, but ONLY when they help, but ONLY when NN is much more stable than is much more stable than U U !! !!

INDEED, INDEED, NO exhaustive enumerationNO exhaustive enumerationwhenwhen NN is much more stable thenis much more stable then UU

Hierarchic (stepwise) foldingHierarchic (stepwise) foldingavoids many “bad” pathways avoids many “bad” pathways

UU

NN

BUT ALSO: FOLDING WITHOUT ANY observable intermediates

UU NN

NO hierarchic foldingNO hierarchic folding – –NO “special pathways”, NO “special pathways”, NONO explanation ofexplanation ofnon-astron. folding time at non-astron. folding time at ““all-or-none” transition,all-or-none” transition,especially close to mid-transitionespecially close to mid-transition

Cunning simplicity of Cunning simplicity of hierarchic folding hierarchic folding as applied to resolve as applied to resolve the Levinthal paradoxthe Levinthal paradox

All-or-none transition All-or-none transition for 1-domain proteins for 1-domain proteins (in thermodynamics: Privalov,1974;(in thermodynamics: Privalov,1974;in kinetics: Segava, Sugihara,1984)in kinetics: Segava, Sugihara,1984)

How CAN protein fold in a “bio-reasonable” time?How CAN protein fold in a “bio-reasonable” time?

Levinthal paradox (1968):Levinthal paradox (1968):

Special pathway?Special pathway?Folding intermediates?Folding intermediates?““Funnel”?Funnel”?Can Can helphelp…, but ONLY when …, but ONLY when NN is much more stable then is much more stable then UU … …

Native protein structure Native protein structure refolds from various starts, refolds from various starts, i.e., it behaves as if i.e., it behaves as if thermodynamically thermodynamically stablestable..

HOW can it be found - HOW can it be found - within seconds - among within seconds - among zillions of the others?zillions of the others?

SEARCH TIME AT SEARCH TIME AT MID-TRANSITION= ???MID-TRANSITION= ???

U NRANDOMRANDOM

Kinetics vs. stability:Kinetics vs. stability: Native protein structure:Native protein structure: That, which folds most rapidly?That, which folds most rapidly? That, which is the most stable?That, which is the most stable?

Practical questions:Practical questions:What to predict? What to design?What to predict? What to design?

Kinetics vs. stability:Kinetics vs. stability: Native protein structure:Native protein structure: That, which folds most rapidly?That, which folds most rapidly? That, which is the most stable?That, which is the most stable?

Practical questions:Practical questions:What to predict? What to design?What to predict? What to design? ((railway? railway? airport?airport?))

However: However: Is there a contradiction between the “foldable” Is there a contradiction between the “foldable” structure and the “most stable” structure?! structure and the “most stable” structure?!

NO!NO!

Computer experiments (Shakhnovich et al, 1993-96); Computer experiments (Shakhnovich et al, 1993-96); general theory (Finkelstein et al., 1995-97) general theory (Finkelstein et al., 1995-97) √

Kinetics vs. stability:Kinetics vs. stability: Native protein structure:Native protein structure: That, which folds most rapidly?That, which folds most rapidly? That, which is the most stable?That, which is the most stable? √

Practical questions:Practical questions:What to predict? What to design?What to predict? What to design?

NucleationNucleation:: Folding with phase separation Folding with phase separation

folding interm.

L

1

NucleationNucleation occurs at theoccurs at the““all-or-none” transitionall-or-none” transition((NN and and UU states are observed only): states are observed only):

NucleationNucleation results from the “ results from the “energy gapenergy gap””

Energy landscapeEnergy landscape

The “The “energy gapenergy gap” is” is: - necessary for unique protein structure: - necessary for unique protein structure - necessary for fool-proof protein action- necessary for fool-proof protein action - necessary for direct - necessary for direct UUNN transition transition - - necessary for fast foldingnecessary for fast folding

UU NN

gapgap

NucleationNucleation:: Folding with phase separation Folding with phase separation

folding interm.

L

1

NucleationNucleation:: Folding with phase separation Folding with phase separation“Detailed Balance”: at given conditions, folding pathway = unfolding pathway

folding interm. = unfolding interm.

L

1

NucleationNucleation:: Folding with phase separation Folding with phase separation“Detailed Balance”: at given conditions, folding pathway = unfolding pathway

folding interm. = unfolding interm.

L

1

folding pathway = unfolding pathway at mid-transition TtrS = Hfolding pathway unfolding pathway close to mid-transition TS 90%H “close to” T 90%Ttr

indeed: T 300oK, Ttr 330oK

NucleationNucleation:: Folding with phase separation Folding with phase separation“Detailed Balance”: at given conditions, folding pathway = unfolding pathway

F # ~ L2/3 surface tension

a) micro-; b) loops [from melting] [from Flory]

F #/RT ~ (1/2 3/2) L2/3 Ln(kf ) ~

folding interm. = unfolding interm.

L

1

↓ ↓

Corr. = 0.7

loops

At mid-transition

intermediatesdo not matter…

↓ ↓ ↓ ΔFN ↓ ↓

ΔFN ↓

Any stable fold is automatically a focus of rapid folding pathways. No “special pathway” is needed.

U N

When globules (N & M) become more stable than U:

a

b

a

b

GAP

1) Acceleration: lnkf -1/2FN/RT

2) Large gap large acceleration before “rollover” caused by intermediates M at “bio-conditions”

↓ ↓ ↓ ΔFN ↓ ↓

ΔFN ↓

GAP

α-helices decreaseeffective chain length. THIS HELPS TO FOLD!

Corr. = 0.84

α-HELICESAREPREDICTEDFROM THEAMINO ACID SEQUENCE

In water

Ivankov D.N., Finkelstein A.V. (2004) Prediction of protein folding rates from the amino-acid sequence-predicted secondary structure. - Proc. Natl. Acad. Sci. USA, 101:8942-8944.

choice of choice of oneone structure out of structure out of zillionszillions REQUIRESREQUIRES very precise estimate of very precise estimate of interactionsinteractions

choice of choice of oneone structure out of structure out of twotwoDOES NOTDOES NOT require too precise estimate of interactionsrequire too precise estimate of interactions

2) One still cannot predict protein structure from the a. a. 2) One still cannot predict protein structure from the a. a. sequence without homologues…sequence without homologues… WHY??WHY??

GAP

GAP

Protein folding. A theoretical view

Alexei Finkelstein

Institute of Protein Research, Russian Academy of Sciences,

Pushchino, Moscow Region, Russia

Gratitude to: D.A. Dolgikh, R.I. Gilmanshin, A.E. Dyuysekina, V.N. Uversky, E.N. Baryshnikova, B.S. Melnik, V.A. Balobanov, N.S. Katina, N.A. Rodionova, R.F. Latypov, O.I Razgulyaev, E.I. Shakhnovich, A.M. Gutin, A.Ya. Badretdinov, O.V. Galzitskaya, S.O. Garbuzynskiy, D.N.Ivankov, N.S. Bogatyreva, V.E. Bychkova, G.V. Semisotnov

The Russian Acad. Sci. Program “Mol. & Cell Biology”, The Russian Foundation for Basic Research, ISSEP, HFSPO, CRDF, INTAS, The Howard Hughes Medical Institute

University of Orange Free StateBloemfontain, South Africa

September 4, 2007

U: stable N: stable

unstablesemi-folded

Consider sequential folding (with phase separation)

M: all unstable

? HOW FAST the most stable state is achieved ?

ESTIMATE free energy barrier F #

Experiment: F # ~ L2/3

Rearrangement of 1 residue takes 1-10 ns

#

L

1ns

Detailed Balance: at given conditions,folding pathway = unfolding pathway

Consider thermodynamic mid-transition U ↔ N.

L

1ns

F # ~ (1/2 3/2) L2/3

micro loops

Any stable fold is automatically a focus of rapid folding pathways. No “special pathway” is needed.

HOW FAST the most stable state is achieved? free energy barrier

F # ~ L2/3 surface tension

F (U) a) micro-; b) loops

= compact folded nucleus: ~1/2 of the chain

F (N)

micro: F # L2/3 [/4]; 2RT0

[experiment]loops: F

# ≤ L2/31/2[3/2RTln(L1/3)]e-N/(100)

[Flory] [knots]