Protein folding. A theoretical view Alexei Finkelstein Institute of Protein Research, Russian Academy of Sciences, Pushchino, Moscow Region, Russia University of Orange Free State Bloemfontain, South Africa September 5, 2007

TWO protein folding problems: TWO protein folding problems: 1)How does protein structure fold? 1)How does protein structure fold? √ 2)How to predict protein structure from the chain’s a. a. sequence? from the chain’s a. a. sequence? U N

BASIC FACTS: Protein chains has unique sequence & unique 3D structure & unique 3D structure Protein chain can fold spontaneously (RNase, Anfinsen, 1961; RNase, Merrifield, 1969) RNase, Merrifield, 1969) Folding time: in vivo: Biosynthesis + Folding < 10–20 min in vitro : from microseconds to hours

BASIC FACTS: Protein chains has unique sequence & unique 3D structure & unique 3D structure Protein chain can fold spontaneously (RNase, Anfinsen, 1961; RNase, Merrifield, 1969) RNase, Merrifield, 1969) Folding time: in vivo: Biosynthesis + Folding < 10–20 min in vitro : from microseconds to hours For:Water-soluble single-domain proteins; or separate domains

How CAN protein fold in a “bio-reasonable” time? How CAN protein fold in a “bio-reasonable” time? Levinthal paradox (1968): Random exhaustive enumeration Special pathway? Folding intermediates? Native protein structure refolds from various starts, i.e., it behaves as thermodynamically stable. HOW CAN it be found - within seconds - among zillions of the others? U N RANDOM

Is “Levinthal paradox” a paradox at all?

L -dimensional “Golf course”

Zwanzig, 1992; Bicout & Szabo, 2000 Is “Levinthal paradox” a paradox at all? …any tilt of energy surface solves this “paradox”… (?) “Funnel” L -dimensional “Golf course”

Cunning simplicity of a “funnel” (without phase separation) folding - NO simultaneous explanation to (I) “all-or-none” transition (II) folding within non-astron. time at mid-transition at mid-transition UN E E L -dimensional “folding funnel”? ~L L- ST Resistance 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 kinetics: Segava, Sugihara,1984) Funnel helps, but ONLY when N is much more stable than U !!

Phillips (1965) hypothesis: folding nucleus is formed by the N-end of the nascent protein chain, and the remaining chain wraps around it. folding nucleus is formed by the N-end of the nascent protein chain, and the remaining chain wraps around it. for single-domain proteins: NO: Goldenberg & Creighton, 1983: circular permutants: circular permutants: N-end has no special role in the in vitro folding. N-end has no special role in the in vitro folding. A special pathway?

Phillips (1965) hypothesis: folding nucleus is formed by the N-end of the nascent protein chain, and the remaining chain wraps around it. folding nucleus is formed by the N-end of the nascent protein chain, and the remaining chain wraps around it. for single-domain proteins: NO: Goldenberg & Creighton, 1983: circular permutants: circular permutants: N-end has no special role in the in vitro folding. N-end has no special role in the in vitro folding. A special pathway? However, for many-domain proteins: Folding from N-end domain,  domain after domain DO NOT CONFUSE N-END DRIVEN FOLDING WITHIN DOMAIN (which seems to be absent) and N-DOMAIN DRIVEN FOLDING IN MANY-DOMAIN PROTEIN (which is observed indeed)

NOW: NOW: NOW: NOW: pre-molten MOLTEN globule globule GLOBULE HYPOTHESIS: Stages in the mechanism of self-organization of protein molecules O.B.Ptitsyn, Dokl. Akad. Nauk SSSR. 1973; 210: Folding intermediates?

PROTEINFOLDING: current picture (Dobson, 2003) e

U N MG pre-MG TRUE: FOLDING with observable (accumulating in experiment) intermediatesU N = MG = MG INDEED, NO exhaustive enumeration when N is much more stable then U Hierarchic (stepwise) folding avoids many “bad” pathways

U N MG pre-MG TRUE: FOLDING with observable (accumulating in experiment) intermediatesU N = MG = MG Special pathway - Folding intermediates - they help, but ONLY when N is much more stable than U !! INDEED, NO exhaustive enumeration when N is much more stable then U Hierarchic (stepwise) folding avoids many “bad” pathways

U N BUT ALSO: FOLDING WITHOUT ANY observable intermediates UN NO hierarchic folding – NO “special pathways”, NO explanation of non-astron. folding time at “all-or-none” transition, especially close to mid-transition Cunning simplicity of hierarchic folding as applied to resolve the Levinthal paradox All-or-none transition All-or-none transition for 1-domain proteins for 1-domain proteins (in thermodynamics: Privalov,1974; 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): Special pathway? Folding intermediates? “Funnel”? Can help…, but ONLY when N is much more stable then U … Native protein structure refolds from various starts, i.e., it behaves as if thermodynamically stable. HOW can it be found - within seconds - among zillions of the others? SEARCH TIME AT SEARCH TIME AT MID-TRANSITION= ??? MID-TRANSITION= ??? U N RANDOM

Kinetics vs. stability: 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: What to predict? What to design?

Kinetics vs. stability: 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: What to predict? What to design? (railway? airport?) (railway? airport?)

However: Is there a contradiction between the “foldable” structure and the “most stable” structure?! NO! Computer experiments (Shakhnovich et al, ); general theory (Finkelstein et al., ) general theory (Finkelstein et al., ) √ Kinetics vs. stability: 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: What to predict? What to design?

Nucleation: Folding with phase separation folding interm. L 1

Nucleation occurs at the “all-or-none” transition (N and U states are observed only): Nucleation results from the “energy gap” Nucleation results from the “energy gap” Energy landscape Energy landscape The “energy gap” is: - necessary for unique protein structure - necessary for fool-proof protein action - necessary for fool-proof protein action - necessary for direct U  N transition - necessary for direct U  N transition - necessary for fast folding - necessary for fast foldingUN gap

Nucleation: Folding with phase separation folding interm. L 1

Nucleation: Folding with phase separation “Detailed Balance”: at given conditions, folding pathway = unfolding pathway folding interm. = unfolding interm. L 1

Nucleation: 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  T tr S = H folding pathway  unfolding pathway close to mid-transition  TS  90%H “close to”  T  90%T tr indeed:  T  300 o K,  T tr  330 o K

Nucleation: Folding with phase separation “Detailed Balance”: at given conditions, folding pathway = unfolding pathway  F # ~ L 2/3  surface tension a) micro-; b) loops [from melting] [from Flory]  F # /RT ~ ( 1 / 2  3 / 2 ) L 2/3 Ln(k f ) ~ folding interm. = unfolding interm. L 1

↓ Corr. = 0.7 loops At mid-transition intermediates do not matter…

↓ ΔF N ↓ ↓ ΔF N ↓ 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:  lnk f  - 1 / 2  F N /RT 2) Large gap  large acceleration before “rollover” caused by intermediates M at “bio-conditions” ↓ ΔF N ↓ ↓ ΔF N ↓  GAP  

α -helices decrease effective chain length. THIS HELPS TO FOLD! Corr. = 0.84 α -HELICES ARE PREDICTED FROM THE AMINO 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:

choice of one structure out of zillions REQUIRES very precise estimate of interactions choice of one structure out of two DOES NOT require too precise estimate of interactions 2) One still cannot predict protein structure from the a. a. sequence without homologues… WHY?? sequence without homologues… WHY??  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 State Bloemfontain, South Africa September 4, 2007

U: stable N: stable unstable semi-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 # ~ L 2/3 Rearrangement of 1 residue takes 1-10 ns # L 1 ns Detailed Balance: at given conditions, folding pathway = unfolding pathway Consider thermodynamic mid-transition U ↔ N.

L 1 ns  F # ~ ( 1 / 2  3 / 2 ) L 2/3 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 # ~ L 2/3  surface tension F (U) a) micro-; b) loops = compact folded nucleus: ~1/2 of the chain F (N) micro:  F #  L 2/3  [  / 4 ] ;     2RT 0 [experiment] loops:  F # ≤ L 2/3  1 / 2 [ 3 / 2 RT  ln(L 1/3 ) ]  e -N/(  100) [Flory] [knots]