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1. Random sequences and unique protein structures Alexei Finkelstein Physical theory shows that a substantial fraction (~10-4 - 10-8 %) of random amino acid sequences can form unique stable 3-D structures under physiological conditions, fold rapidly, and have architectures typical for protein molecules. The main peculiarity of a "protein- like" chain is a considerable gap dividing the energy of its lowest- energy fold from the energies of the other folds; this gap plays an essential role in thermodynamics and kinetics of folding. 2. How can a protein chain find its unique fold? The problem of how a protein chain can find its most stable structure without exhaustive sorting out of all its possible conformations is known as the "Levinthal paradox". I shall show in the lecture that attaining of the lowest-energy fold is rapid when it occurs in a vicinity of a thermodynamic "all-or-none" transition from the coil to the lowest- energy fold. Such a transition requires an "edited" chain with an enhanced stability of its lowest-energy fold. In a vicinity of the mid- transition point, all the mis- and semi-folded states cannot "trap" the folding since, even taken together, all these states are less stable than both the initial coil and the final stable fold of the chain. Therefore, a stable fold can be rather rapidly achieved here via that "nucleation and growth" folding pathway which provides a continuous entropy-by-energy compensation in the course of folding, thus providing a low transition state free energy. In the mid-transition, an N-residue chain folds normally in ~exp(N 2/3) nsec. Therefore, a 100-residue chain normally finds its most stable fold within minutes rather than in 10100 psec ~ 1080 years, according to the famous paradoxical estimate of Levinthal. 3. Introduction to protein structure prediction This is a review of the state of the art in the recognition and prediction of protein folds from their sequences. I pay a special attention to physical background of the predictive methods. In particular, I review the secondary structure predictions and the "threading" methods used for recognition of protein folds. It is shown that all the predictive methods can use only some part of the interactions operating in the chain, and that even their energies are not known precisely. This is the principal source of errors and uncertainties. The errors can be reduced by employment of many distant homologs, but this opens only a possibility to predict a secondary structure and a generalised folding pattern rather than a particular fold of a given chain with all details of the fold. ## Back to the list of abstracts