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Topic: Levinthal paradox

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Protein structure prediction

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	[No title]
		Levinthal’s study of the bacterial gene for the enzyme alkaline phosphatase showed that there was a collinear relationship between a gene and the amino acid sequence of the protein it specifies.
		Levinthal’s ability to quantify the magnitude of the protein folding problem gave birth to the “Levinthal paradox,” a calculation that predicts that proteins would never fold in a reasonable amount of time given the principles understood at the time and that remain elusive to this day.
		Levinthal was a member of the National Academy of Sciences and was an NAS representative to the United Nations Educational, Scientific, and Cultural Organization.
	www.columbia.edu /cu/biology/faculty/chasin/cyrus.html (2941 words)

	Levinthal's Paradox (Site not responding. Last check: 2007-08-20)
		Very few people have actually read the original paper on Levinthal's paradox, even though it is extensively cited.
		Professor Levinthal then showed a short motion picture which illustrated the synthesis of a polypeptide structure and the process of then forming a desired interaction via the most favored energy path as displayed on the computer controlled oscilloscope.
		The relevance of these studies to Mossbauer spectroscopy may be in the understanding of small perturbations of polypeptide structures and their effect on the Mossbauer nucleus.
	www.sdsc.edu /~nair/levinthal.html (1185 words)

	Paradox@Everything2.com
		In Mage the Ascension, Paradox (with a capital P) is how reality responds to mages who decide that their will is how things should be done.
		Don't confuse a simply difficult problem with a real paradox, or you'll never work out which of the lying or truthful monsters is guarding the gate to safety.
		Use a paradox to illustrate inconsistency in an opponents argument.
	www.everything2.com /index.pl?node=paradox (1156 words)

	Citations: Are there pathways for protein folding - Levinthal (ResearchIndex)
		to pose the famous Levinthal Paradox : a protein has too many conformations to fold by a random search of conformational space, and must fold by a directed pathway With the results of the present study we have a quantitative relationship between m, the complexity or number of states per residue,.
		The essence of the paradox is that in theory a protein is expected to require exponential time to fold, given an arbitrary starting configuration, whereas in practice proteins are observed to fold....
		Protein folding, the Levinthal paradox and rapidly mixing Markov..
	citeseer.ist.psu.edu /context/540026/0 (1323 words)

	Introduction
		Some have tried to resolve Levinthal's paradox by hypothesizing a reduction in the number of states that the protein has to search through.
		Seeking to resolve Levinthal's paradox by reducing the search space may be unproductive in a more fundamental sense, for it ignores a basic fallacy in Levinthal's paradox: namely the assumption that each point in configuration space is equally likely.
		Levinthal was effectively assuming that the PES is totally flat.
	www-wales.ch.cam.ac.uk /~jon/PhD2/node34.html (2816 words)

	Why YASARA?
		Back in 1966, Cyrus Levinthal (known even to first-year biochemistry students thanks to the "Levinthal Paradox" of protein folding) published a clairvoyant article in Scientific American (fig.3) that marks the official beginning of molecular graphics and interactive modeling.
		Having pointed out the importance of true interaction between the user and the program during modeling ("..it is our experience that an investigator, who is looking at a molecule can frequently understand the reason for a local minimum and by making a small alteration in the structure can return the program to its downhill path.
		Fig.3: Cyrus Levinthal's clairvoyant article from 1966 - most of it is even more valid today than back in these early times of molecular modeling.
	www.yasara.org /why.htm (403 words)

	CHEM 440 lectures
		I have made the argument in class that evolution has acted to select for amino acid sequences that fold into a well-defined native state that (despite the overall modest stability of the folded state) is well-separated in free energy from other conformations.
		The Levinthal paradox suggests that sequences may have also been selected for on the basis of well-defined folding pathways.
		State the Levinthal paradox, and explain its implications for protein folding.
	guweb2.gonzaga.edu /faculty/cronk/chemistry/CHEM440/lectures.cfm?L=9 (1262 words)

	Levinthal's Paradox
		The fact that many naturally-occurring proteins fold reliably and quickly to their native state despite the astronomical number of possible configurations has come to be known as Levinthal's Paradox.
		The paper usually cited has proved remarkably difficult to get hold of, which is itself a paradox given the frequency of citation.
		It is reproduced verbatim below, in the hope that it will be of use and interest to people working in the field of protein folding or relaxation dynamics in general.
	www-wales.ch.cam.ac.uk /~mark/levinthal/levinthal.html (1227 words)

	Brainstorms: The nature of proteins: Sub-optimal design?
		From my understanding, Levinthal's paradox simply means that proteins do not reach their native structures by randomly sampling structure space, but rather do so deterministically.
		Typically it is argued that the protein first collapses rapidly to a compact conformation and that the subsequent search is through the greatly reduced space of these compact states[232,233,234].
		Until contrary evidence appears, basically resolving levinthal's paradox, I think we can assume that the proteome is optimal.
	www.iscid.org /boards/ubb-get_topic-f-6-t-000256-p-2.html (3442 words)

	NDSA
		The Levinthal Paradox states that it is impractical for an unfolded polypeptide chain to randomly search the entire conformational space available before reaching its native folded state.
		This suggests that there could be a "magic force" directing the folding of polypeptide chain to its native structure.
		The finding of such sequential patterns should be significant to our ability to predict the secondary structures of protein sequences, and ultimately improve our ability to predict protein ternary structures.
	astro.temple.edu /~feng/Bioinformatics/NDSA.htm (564 words)

	How Does a Protein Fold?
		In this section we consider the problem of how a polypeptide folds into a compact, active, globular protein, with its 3d structure determined by its sequence.
		We first review the famous Levinthal paradox which presents a very pessimistic viewpoint suggesting that proteins will never find their native structure because of the overwhelming entropy of nonfolded states.
		We then describe how this paradox can be resolved by recognizing the entropy-reducing effect of compaction of the protein into a disordered random coil, and then finally we describe the importance of sequence in defining a well-defined native state.
	www.uic.edu /classes/phys/phys450/MARKO/N013.html (1919 words)

	PFP
		The paradox is due to the fact that proteins are shown to fold into their native state in a finite, if not short amount of time, however, theoretically the protein must “choose” its native state by shifting through all of the possible tertiary conformations, which would take an infinite amount of time.
		In order to solve the problem one must discard factors which ultimately play a role in determining the the tertiary structure, so that your answer may resemble the native fold, but it will not be the native fold.
		Levinthal C (1969) 22-24 Mossbauer Spectroscopy in Biological Systems: Proceedings of a meeting held at Allerton House, Monticello, IL.
	www.msu.edu /~mullenli/PFP.htm (5833 words)

	Sandwalk: How Proteins Fold
		Obviously, there's something wrong with the assumptions behind what came to be known as the Levinthal Paradox.
		As a matter of fact, the paradox was never really a paradox since the whole point of the calculation was to shown that proteins did not fold by randomly searching though the conceptual universe of all possible shapes.
		The final structure of a protein minimizes the energy of the random coil by burying hydrophobic amino acids in the interior of the molecule.
	sandwalk.blogspot.com /2007/02/how-proteins-fold.html (2079 words)

	Harvard Department of Chemistry and Chemical Biology
		The approach to a solution of these problems is based on utilization and development of modern analytical methods of statistical mechanics such as replicas, renormalization group etc. and numeric studies of non-traditional lattice models with exhaustively enumerated conformations.
		These simulations make it possible to address the "Levinthal paradox" and develop a theory of kinetics of protein folding.
		Within this project also is an evolutionary question of the way in which sequences which are able to fold evolved.
	www.chem.harvard.edu /research/faculty/eugene_shakhnovich.php (398 words)

	Current Projects Page
		If one considers molecular dynamics all-atom simulations with explicit solvation, then one is clearly a minimum of six orders of magnitude too slow (nanoseconds versus milliseconds at best) to simulate the folding process itself.
		It is clearly impossible for a protein to systematically search through the myriad of combinations of possible local conformations of the individual residues (the Levinthal paradox), and experimental data suggests that folding paths are followed with probable nucleation of secondary structure.
		This suggests a hierarchical approach to the problem; determine the secondary structure elements and then their three-dimensional arrangement.
	www.cmd.wustl.edu /Current_Projects.htm (895 words)

	Computational Complexity, Protein Structure Prediction, and the Levinthal Paradox - Ngo, Marks, Karplus (ResearchIndex)
		Computational Complexity: Protein structure prediction and the Levinthal paradox.
		1 Levinthal's paradox (context) - the, of et al.
		1 The Levinthal paradox revisited (context) - New, NY et al.
	citeseer.ist.psu.edu /ngo94computational.html (1520 words)

	JBSD Online
		Loop Fold Structure of Proteins: Resolution of Levinthalâs Paradox (p.
		According to Levinthal a protein chain of ordinary size would require enormous time to sort its conformational states before the final fold is reached.
		Key words: Levinthalâs paradox, protein folding, chain conformation, closed loops, loop fold structure.
	www.jbsdonline.com /index.cfm?d=3011&c=4084&p=11131&do=detail (103 words)

	Fast protein folding on downhill energy landscape -- Cavalli et al. 12 (8): 1801 -- Protein Science
		Dill, K.A. and Chan, H.S. From Levinthal to pathways to funnels.
		Dinner, A.R. and Karplus, M. Comment on the communication "The key to solving the protein-folding problem lies in an accurate description of the denatured state" by van Gunsteren et al.
		Karplus, M. The Levinthal paradox: Yesterday and today.
	www.proteinscience.org /cgi/content/full/12/8/1801 (1992 words)

	[No title]
		Trp-cys-lys-leu-arg-asn-gly-val +2 [Chymotrypsin can cleave after Leu under some conditions- NH2 terminus is positive, COOH is negative] What is Levinthal's paradox and what does it tell us about protein folding?
		Levinthal’s paradox is that from mathematical estimation, it should take proteins much longer to fold than it actually does.
		This paradox tells us that the process for protein folding is not random as assumed by Levinthal in his calculations.
	dixonlab.biochem.med.umich.edu /biochem/archive/courses/bc415_515/downloads/Review34answers.doc (575 words)

	Lecture 5 Feb 2007 (Site not responding. Last check: 2007-08-20)
		No, as was first explained by Cyrus Levinthal, there is not enough time.
		Or, the answer to Levinthal' s paradox is that proteins are a lot smarter than they look.
		Protein folding: from the levinthal paradox to structure prediction
	faculty.smu.edu /svik/6312/Lectures/5Feb.html (1647 words)

	Order in unfolded proteins
		The supposed “search” turns out to be much simpler and faster than Levinthal imagined.
		The most far-reaching consequence of my research is that it resolves Levinthal’s paradox by itself.
		If proteins fold from a state that has one dominant structure to another with a different dominant structure then Levinthal’s extended search disappears.
	homepages.nyu.edu /~kc689/dissertation.html (614 words)

	Topics in Bioinformatics
		The native state is characterized by sterically allowed conformations that energetically favorable, see chapter "ab initio protein structure prediction".
		Sampling of all the possible conformations and deciding which conformation conforms to the above steric and energetic conditions would take forever (Levinthal paradox).
		The folding pathway occurs via unstable intermediates (unstable because even the native state is so marginally more stable than the unfolded state).
	www.cs.cmu.edu /~blmt/Seminar/SeminarMaterials/folding.html (424 words)

	FORCASP - CASP Forums Site - Pushchino (P0203) - 263 predictions: 263 3D
		On the contrary, a nucleation mechanism of folding can account for all these major features simultaneously and resolves the Levinthal paradox.
		The author is grateful to N.S. Bogatyreva for discussions and assistance, and acknowledges a support of an International Research Scholar's Award from the Howard Hughes Medical Institute and of the Russian Foundation for Basic Research.
		A nucleation/condensation mechanism does indeed resolve the Levinthal paradox, but this scheme is perfectly consistent with the folding funnel, and it is hierarchic.
	www.forcasp.org /paper1899.html (197 words)

	Review
		The corollary of this postulate is the thermodynamic control of protein folding, meaning that the native conformation is at the minimum of Gibbs free energy.
		This statement was discussed by Levinthal in a consideration of the short time required by the folding process in vitro as well as in vivo, which is order of seconds or minutes [7].
		Such a situation is referred to as the Levinthal paradox and has dominated discussions for the last three decades, leading to different models for the folding pathway.
	www.jcmm.ro /content.jsp?pageId=356 (9846 words)

	Research Interest (Site not responding. Last check: 2007-08-20)
		This problem is commonly described as the Levinthal paradox: an unfolded protein does not have the time needed to explore all possible conformations, and yet it apparently folds rapidly to the single most stable conformation.
		Two hypotheses have been proposed to solve the paradox.
		The existence of such hidden intermediates thus supports the intermediate hypothesis for solving the Levinthal paradox.
	bai.nci.nih.gov /research.html (861 words)

	Introduction (Site not responding. Last check: 2007-08-20)
		One of the major theories and the most interesting seems to be this Framework model.
		This model gets around Cyrus Levinthal's paradox that random configurations would take an immense about of time that a protein does not have.
		This funnel theory says that proteins fold in directed energy pathways and do not sample the entire space.
	people.ucsc.edu /~sheng/protein/folding2.htm (68 words)

	SFB 504 glossary: References
		Fiedler, K., Walther, E. and Nickel, S. Inductive social cognition: Experiments on the Simpson paradox.
		Levinthal, D.A. and March, J.G. A Model for Adaptive Organizational Search.
		Levinthal, D.A. and March, J.G. The Myopia of Learning.
	www.sfb504.uni-mannheim.de /glossary/glosslit.htm (2451 words)

	Abstracts 1998
		The current thrust of the theoretical literature, however bypasses this potentially paralysing paradox by shifting its focus from the management of tangibles to that of intangible assets and knowledge.
		As globalization becomes a reality and hypercompetition is pervasive, organizational learning theorists (e.g, Levinthal and March, 1993; Nass, 1994; Nonak, 1994) hold that the art of management itself could also benefit from continuous improvement.
		However to cope with tasks of this kind it is indispensable first of all to grasp well why and how the Human, Biological, Ecological, Technological and Educational worlds (structural circumstances which rather paradoxically have made possible the emergence and evolvement of our magnificent civilization) tend to be increasingly unsustainable.
	www.isss.org /1998meet/abstract.htm (18093 words)

	CHE 530/730 homework 1
		Tell how the use of denaturants can be used to show the connection between protein struncture and function (via the Anfinson experiment)
		Describe the Levinthal Paradox and proposed solutions to it
		Why is their formation so much more rapid than the complex predictions of the Levinthal paradox?
	people.eku.edu /brockm/courses/che530/hmwk1.html (1642 words)

	Publications - Honiglab_public
		Honig, B., Kabat, E., Katz, L., Levinthal, C. and Wu, T. Model-Building of Neurohypophyseal Hormones.
		Honig, B., Ray, A. and Levinthal, C. Conformational Flexibility and Protein Folding: Rigid structural fragments connected by flexible joints in subtilisin BPN.
		Honig, B. Protein Folding: From the Levinthal Paradox to Structure Prediction.
	wiki.c2b2.columbia.edu /honiglab_public/index.php/Publications (4858 words)

	Yaakov (Koby) Levy research group
		Protein folding has long been viewed as being rich in complexities.
		With the development of the energy landscape theory, our view of protein folding, however, has greatly simplified from the hopelessly complex one first presented by Levinthal’s paradox.
		Because of their funneled energy landscapes, global structural measures of similarity to the native state are clearly adequate for describing the folding progression for most natural proteins.
	www.weizmann.ac.il /Structural_Biology/faculty_pages/Levy/research.html (933 words)

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