Subject: RE: SUMMARY - Levinthal Paradox

From: Tom Ngo <[email-masked]>
Date: Tue, 3 Aug 1999 12:23:47 -0700

Jati, the following paper is also online:

J. Thomas Ngo, Joe Marks and Martin Karplus, "Computational Complexity,
Protein Structure Prediction, and the Levinthal Paradox," in The Protein
Folding Problem and Tertiary Structure Prediction, Kenneth Merz, Jr. and
Scott LeGrand, eds., pp. 433-506, Birkhauser, Boston, 1994. 

ftp://ftp.interval.com/pub/papers/ngo/merz.ps.gz

--Tom

> -----Original Message-----
> From: JATI KASTANJA [mailto:[email-masked]]
> Sent: Tuesday, August 03, 1999 9:22 AM
> To: [email-masked]
> Subject: CCL:SUMMARY - Levinthal Paradox
> 
> 
> 
> Dear all, 
> I've obtained a lot of helpful responses. I'd like to thank everybody 
> who spent his time in giving me some suggestions with regard to  
> the "Levinthal Paradox".  
> Many thanks to Raman, Rick, Carlos, John, Jim, Peter, Tom and 
> any other person I might have forgotten. 
> 
> Regards, Jati 
> 
> Subsequent a list of suggestions and papers which deal with the  
> Levinthal Paradox 
> ----------------------------------------------- 
> >Peter S. Shenkin wrote 
> If you do find the Journal, you will find that it contains only 
> a passing reference to what has become known as the Levinthal 
> paradox.  The idea really derives from a comment Cyrus once 
> made at a 
> meeting. 
> 
> The idea is this.  Take a 100-residue protein.  Let's suppose each 
> residue can have only, say, 3 conformational states.  Then there 
> are 3^100, or about 10^48, possible states.  Now suppose the 
> protein 
> can explore a new state with every moleculear vibration.  
> Suppose  
> each vibration takes about a femtosecond.  Then exploring all  
> the states would take about 10^48 fs, or 10^33 s.  There are about 
> 10^8 
> s 
> in a year, so exploring all the states would take about 10^25 years. 
> But this is longer than the age of the universe.   
> 
> Now, in order for a protein to fold into its global 
> thermodynamic energy minimum, the folding process has to 
> be ergodic.  That is, it has to explore all its states 
> within the time-span of the process.  But protein folding takes 
> typically seconds to minutes.  So a protein can't be folding  
> into its thermodynamic energetic minimum, since it can't 
> possibly find it in so short a time. 
> 
> Therefore, protein folding must be a kinetically controlled process. 
> I.e., proteins fold to the most accessible minimum, rather than the  
> most stable minimum.  In this, protein folding must resemble the 
> kinetically controlled reactions of organic (and bio-) chemistry. 
> 
> The reason it's considered a "paradox" is that most people 
> don't believe it (at least for globular proteins as small 
> as 100 residues). Cyrus didn't believe it either, in fact. 
> But it is fun to think about, and it's great for impressing 
> people at cocktail parties.  (You have to go to the right cocktail  
> parties, though. :-) ) 
> 
> -P. 
> 
> ----------------------------------------------- 
> >C.S.Raman wrote:   
> Well, the list I have provided at the end of this mail should 
> help you track down all the literature pertinent to this problem. 
> 
> {*} Until now I am unsuccessful in finding out the journal where 
> Cyrus  
> {*} Levinthal first published something about this paradox.  
> 
> Cy's article is one of the most MISQUOTED in the literature. 
> His original work was presented in a symposium: 
> Levinthal, C (1969) in Mossbauer Spectroscopy in Biological 
> Systems, (ed) Debrunner, P., & Tsibris, J.C.M., P. 22-24, 
> University of Illinois, Urbana Champaign. How to Fold 
> Graciously. 
> 
> Levinthal also published an article in J. Chim. Phys. (1968) 
> 65: 44-45 entitled "Are there pathways for protein folding?", 
> which is usually quoted as being the source of the paradox. 
> This is incorrect and this article makes no mention of it. 
> 
> 1. Dill KA. 
> Polymer principles and protein folding. 
> Protein Science, 1999 Jun, 8(6):1166-80. 
> 
> 2. Yon JM. 
> Protein folding: concepts and perspectives. 
> Cellular and Molecular Life Sciences, 1997 Jul, 53(7):557-67. 
> 
> 3. Finkelstein, AV; Badretdinov, AY. 
> Physical reason for fast folding of the stable spatial structure of 
> proteins: A solution of the Levinthal paradox. 
> MOLECULAR BIOLOGY, 1997 MAY-JUN, V31 N3:391-398. 
> 
> 4. Shakhnovich EI. 
> Theoretical studies of protein-folding thermodynamics and 
> kinetics. 
> Current Opinion in Structural Biology, 1997 Feb, 7(1):29-40. 
> 
> 5. Dill KA; Chan HS. 
> >From Levinthal to pathways to funnels. 
> Nature Structural Biology, 1997 Jan, 4(1):10-9. 
> 
> 8. Finkelstein AV; Badretdinov AYa. 
> Rate of protein folding near the point of thermodynamic 
> equilibrium 
> between the coil and the most stable chain fold [published erratum 
> appears 
> in Fold Des 1998;3(1):67]. 
> Folding and Design, 1997, 2(2):115-21. 
> 
> 9. Lattman EE. 
> Remembering Cy Levinthal [editorial]. 
> Proteins, 1995 Oct, 23(2):i. 
> 
> 10. Karplus M; Sali A. 
> Theoretical studies of protein folding and unfolding. 
> Current Opinion in Structural Biology, 1995 Feb, 5(1):58-73. 
> 
> 11. Durup, J. 
> On ''Levinthal paradox'' and the theory of protein folding. 
> THEOCHEM-JOURNAL OF MOLECULAR STRUCTURE, 
> 1998 FEB 9, V424 N1- 2:157-169. 
> 
> 12. Karplus, M. 
> The Levinthal paradox: yesterday and today. 
> FOLDING & DESIGN, 1997, V2 N4:S69-S75. 
> 
> 13. HONIG B. 
> LEVINTHAL,CYRUS - IN MEMORIAM. 
> PROTEINS-STRUCTURE FUNCTION AND GENETICS, 
> 1991, V11 N4:239-241. 
> 
> 14. LATTMAN E. 
> LEVINTHAL,CYRUS MAY 2, 1922 NOVEMBER 4, 1990 - IN 
> MEMORIAM. 
> PROTEINS-STRUCTURE FUNCTION AND GENETICS, 
> 1990, V8 N4:R1-R1. 
> 
> I hope this helps. 
> -raman 
> --------------------------------------------------- 
> >Tom Ngo and Joe Marks wrote:
> Also relevant to your inquiry are the references below.  We argue 
> in the 
> > first paper that the astronomical number of conformational 
> states does not, 
> > by itself, give reason to conclude that folding should take 
> exponential 
> > time.  We show how the theory of NP-completeness can be 
> brought to bear on 
> > questions related to folding times. 
> >  
> > * J. Thomas Ngo, Joe Marks and Martin Karplus, 
> "Computational Complexity, 
> > Protein Structure Prediction, and the Levinthal Paradox," in The 
> Protein 
> > Folding Problem and Tertiary Structure Prediction, Kenneth 
> Merz, Jr. and 
> > Scott LeGrand, eds., pp. 433-506, Birkhauser, Boston, 1994. 
> >  
> > * J. Thomas Ngo and Joe Marks, "Computational Complexity of 
> a Problem in 
> > Molecular Structure Prediction," Protein Engineering 5(4):313-
> 321, June 
> > 1992. 
> The second paper above is on my web site, 
> http://www.merl.com/people/marks/index.html. 
> 
> -- Joe Marks 
> > --Tom Ngo 
> 
> ------------------------------------------------------------------ 
> > Rick Venable wrote:      
> I've appended a quick search result for "levinthal paradox"-- some 
> of 
> these papers (e.g. those by Dill, Karplus, or Shakhnovich) may 
> hopefully 
> refer to the original statement of the paradox.  
> 
>    Parker JMR 
>     The relationship between peptide plane rotation (PPR) and 
> similar 
> conformations 
>     J COMPUT CHEM 20: (9) 947-955 JUL 15 1999  
> 
>    Iguchi K 
>     Exactly solvable model of protein folding: Rubik's magic snake 
> model 
>     INT J MOD PHYS B 13: (4) 325-361 FEB 10 1999  
> 
>    Hamacher K, Wenzel W 
>     Scaling behavior of stochastic minimization algorithms in a 
> perfect 
> funnel landscape 
>     PHYS REV E 59: (1) 938-941 Part B JAN 1999  
> 
>    Durup J 
>     On "Levinthal paradox" and the theory of protein folding 
>     THEOCHEM-J MOL STRUC 424: (1-2) 157-169 FEB 9 1998 
>  
> 
>    Finkelstein AV, Badretdinov AY 
>     Physical reason for fast folding of the stable spatial 
> structure of 
> proteins: A solution of the 
>     Levinthal paradox 
>     MOL BIOL+ 31: (3) 391-398 MAY-JUN 1997  
> 
>    Karplus M 
>     The Levinthal paradox: yesterday and today 
>     FOLD DES 2: (4) S69-S75 1997  
> 
>    Finkelstein AV, Badretdinov AY 
>     Rate of protein folding near the point of thermodynamic 
> equilibrium 
> between the coil and the 
>     most stable chain fold 
>     FOLD DES 2: (2) 115-121 1997  
> 
>    Shakhnovich EI 
>     Theoretical studies of protein-folding thermodynamics and 
> kinetics 
>     CURR OPIN STRUC BIOL 7: (1) 29-40 FEB 1997  
> 
>    Mirny LA, Abkevich V, Shakhnovich EI 
>     Universality and diversity of the protein folding scenarios: A 
> comprehensive analysis with the 
>     aid of a lattice model 
>     FOLD DES 1: (2) 103-116 1996  
> 
>    Nakamura H, Tanimura R, Kidera A 
>     Side-chain conformations cooperatively restricted in protein 
> secondary structure .2. Side-chain 
>     configurational entropies of alpha-helices in the folding nuclei 
>     P JPN ACAD B-PHYS 72: (7) 149-152 SEP 1996  
> 
>    Su ZD, Arooz MT, Chen HM, et al. 
>     Least activation path for protein folding: Investigation of 
> staphylococcal nuclease folding by 
>     stopped-flow circular dichroism 
>     P NATL ACAD SCI USA 93: (6) 2539-2544 MAR 19 1996  
> 
>    KARPLUS M, SALI A 
>     THEORETICAL-STUDIES OF PROTEIN-FOLDING AND 
> UNFOLDING 
>     CURR OPIN STRUC BIOL 5: (1) 58-73 FEB 1995  
> 
>    PERKYNS JS, PETTITT BM 
>     PEPTIDE CONFORMATIONS ARE RESTRICTED BY 
> SOLUTION STABILITY 
>     J PHYS CHEM-US 99: (1) 1-2 JAN 5 1995  
> 
>    GULUKOTA K, WOLYNES PG 
>     STATISTICAL-MECHANICS OF KINETIC 
> PROOFREADING IN PROTEIN-FOLDING 
> IN-VIVO 
>     P NATL ACAD SCI USA 91: (20) 9292-9296 SEP 27 1994  
> 
>    ABKEVICH VI, GUTIN AM, SHAKHNOVICH EI 
>     SPECIFIC NUCLEUS AS THE TRANSITION-STATE FOR 
> PROTEIN-FOLDING - 
> EVIDENCE FROM 
>     THE LATTICE MODEL 
>     BIOCHEMISTRY-US 33: (33) 10026-10036 AUG 23 1994  
> 
>    SALI A, SHAKHNOVICH E, KARPLUS M 
>     HOW DOES A PROTEIN FOLD 
>     NATURE 369: (6477) 248-251 MAY 19 1994  
> 
>    DILL KA, YUE K, FIEBIG K 
>     PROTEIN-FOLDING - DRIVING FORCES AND THE 
> LEVINTHAL PARADOX 
>     BIOPHYS J 66: (2) A241-A241 Part 2 FEB 1994  
> 
>    DILL KA 
>     FOLDING PROTEINS - FINDING A NEEDLE IN A 
> HAYSTACK 
>     CURR OPIN STRUC BIOL 3: (1) 99-103 FEB 1993  
> 
>    CHAN HS, DILL KA 
>     ENERGY LANDSCAPES AND THE COLLAPSE 
> DYNAMICS OF  HOMOPOLYMERS 
>     J CHEM PHYS 99: (3) 2116-2127 AUG 1 1993  
> 
>    FIEBIG KM, DILL KA 
>     PROTEIN CORE ASSEMBLY PROCESSES 
>     J CHEM PHYS 98: (4) 3475-3487 FEB 15 1993  
>