Levinthals Paradox

Many medicines are based on proteins pharmacological companies would love dearly to be able to predict, by a cheap computation, what is the equilibrium spatial shape of a polypeptide chain with a given sequence. This prediction of tertiary structme based entirely on the sequence is really a multi-billion dollar problem. What people try to do to address it in practice is to invoke an additional information, a hint apart from the sequence itself — to find other known proteins with elements of sequence similarity, and then to guess the new tertiary structure based on the elements of the known ones. This might be a nice practical solution, particularly when it works, but here in this book we are not interested in such things, for us it is almost like cheating. We want to discuss the heads-on approach in the end, this 

Can we approach this problem computationally Since it is so important a problem, we could perhaps take a very large supercomputer and just compute energies of all conformations Does this sound convincing Not really. Let s make an estimate. Say the chain is as short as 100 units. For the sake of argument suppose further that each bond of the chain can take two different conformations only, for example, right turn and left turn . (This is certainly an underestimate ) Even then the chain can have as many as 2 = (2 °) ° = (1,024) ° (1,000) ° = 10 ° conformations in 

This problem is known as Levinthal s paradox (as it was formulated by Cyrus Levinthal (1922-1990) at Columbia University in New York) protein molecule certainly cannot search through all of its conformations, yet it does find the particular one with lowest energy. It is a paradox, isn t it How does the chain manage to find the equilibrium  

we seem to be getting nowhere. We had hoped to learn about selforganization through some analogies with other physical objects. However, we have found none. That, roughly, was the state of affairs in the field in 1970s and 1980s. 

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The initial stages of folding presented a puzzle, the Levinthal paradox, that was solved by the theoreticians using a folding funnel. The final stages of folding present a problem for the experimentalists, especially the biotechnol-... 

Honig B (1999) Protein folding from the Levinthal paradox to structure prediction, J Mol Biol, 293 283-293... 

The PPR has also implications in conjunction with the thermodynamic hypothesis [86,87], the Levinthal paradox [88], the use of redundant conformations in conformational searches, and the possibility of an enhanced search procedure (projected angle method). These points lie outside the scope of the present work and will be discussed in detail in future work [89]. 

Before proteins can actively function in the living cell they must fold up into a specific 3-dimensional structure, the so-called native state (see Fig. 1). Already in the 1960 s it was recognized that the long linear polypeptides chains can adopt their native structure starting from the random coil state in a surprisingly short time. The famous Levinthal paradox states that if a peptide bond between amino acids can only adopt two conformations a relatively short protein of a hundred residues can have around 2 10 possible... 

Bioinformatics approaches to protein structure prediction and the identification of homology and similarities involve the solution of search problems. As the range of possible protein sequences and folding conformations is astronomical, appropriate pruning of the search space is inherently necessary. The so-called Levinthal paradox [4] states that even real proteins cannot try out all the possible conformations during the time they fold into... 

Assuming (optimistically) that peptide conformations can switch on the femtosecond time scale (10 s), it would take a time of order 3x 10 s, or about lO years, to search through all these possibilities to find the right one. This is a time much longer than the known age of the Universe. Yet proteins actually fold quite rapidly, in microseconds to minutes, depending on the protein and conditions. Tliis is the so-called Levinthal Paradox . 

Since we know from the coarse grained considerations that the protein-like sequences provide for a very low l3ung ground state energy, corresponding obviously to the very deep valley, we can use the landscape metaphor to hint on the resolution of the Levinthal paradox (see Section 10.3). 

But in terms of these fundamentals, we would dare to say that an important progress had been achieved over the last several years. Previously, at the time of Anfinsen, protein folding seemed a fundamental physics mystery. People could not imagine how it could be happening even in principle. Now, there is at least an overall understanding of the basic physics behind folding, as we tried to outline in the present chapter. There are lattice models, which are very much unlike proteins in many respects (too many and too obvious to list) — but which are like proteins in two most important aspects they have the same fundamental difficulties, such as Levinthal paradox, and they do fold. And we understand this model pretty well But, of course, the study continues in many directions... 

The toy is subject to Levinthal paradox it is virtually impossible to test all of its conformations, there are too many of them. Some people find the way to fold the toy quite easily others, some of them very clever, carmot do it easily or fail altogether. We do not know what kind of mental ability controls the toy folding success, and, like in proteins, we do not know how to formulate the algorithm leading to successful folding and beating the Levinthal estimate. 

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