[Physical Basis of Functioning of Antifreeze Protein].

Antifreeze proteins, expressed in cold-blooded organisms, prevent ice formation in their bodies, and thus help them to survive in extremely cold winter temperatures. However, the mechanism of action of these proteins is still not clear. In any case, it is not simply a decrease in the temperature of normal ice formation. In this work, investigating the ice-binding protein (a mutant form of the antifreeze protein cfAFP from the spruce budworm Choristoneura fumiferana, which overwinters in needles), we showed that this antifreeze protein does not at all lower the freezing point of water and, paradoxically, increases the melting point of ice. On the other hand, calculations based on the theory of crystallization show that at temperatures of 0° to -30°C ice can only appear on surfaces that contact water, but not in the body of water. These facts suggest a new perspective on the role of antifreeze proteins: their task is not (as it is commonly believed) to bind with nascent ice crystals already formed in the organism and stop their growth, but to bind to those surfaces, on which ice nuclei can appear, and thus completely inhibit the ice formation in supercooled water or biological fluid.

[Protein Biosynthesis Proofreading Is Closely Associated with the Existence of Factor-Free Ribosomal Synthesis].

Despite protein biosynthesis being studied for decades, some major questions concerning this process are still to be addressed. We elucidate a close connection between proofreading of the emerging amino acid sequence during its normal, elongation factor-dependent ribosomal biosynthesis and the existence of the factor-free synthesis of a polypeptide chain on a ribosome. In this factor-free process, the biological role of proofreading is played by a process opposite to the factor-free attachment of Aa-tRNA to the ribosome, namely, the removal via the same pathway of that Aa-tRNA, which is not complementary to the mRNA codon exhibited by the ribosome.

50+ Years of Protein Folding.

The ability of proteins to spontaneously form their spatial structures is a long-standing puzzle in molecular biology. Experimentally measured rates of spontaneous folding of single-domain globular proteins range from microseconds to hours: the difference - 10-11 orders of magnitude - is the same as between the lifespan of a mosquito and the age of the Universe. This review (based on the literature and some personal recollections) describes a winding road to understanding spontaneous folding of protein structure. The main attention is given to the free-energy landscape of conformations of a protein chain - especially to the barrier separating its unfolded (U) and the natively folded (N) states - and to physical theories of rates of crossing this barrier in both directions: from U to N, and from N to U. It is shown that theories of both these processes come to essentially the same result and outline the observed range of folding and unfolding rates for single-domain globular proteins. In addition, they predict the maximal size of protein domains that fold under solely thermodynamic (rather than kinetic) control, and explain the observed maximal size of "foldable" protein domains.

The Molten Globule Concept: 45 Years Later.

In this review, we describe traditional systems where the molten globule (MG) state has been detected and give a brief description of the solution of Levinthal's paradox. We discuss new results obtained for MG-mediated folding of "nontraditional" proteins and a possible functional role of the MG. We also report new data on the MG, especially the dry molten globule.

[Evaluation of the Accuracy of Calculation of the Standard Binding Entropy of Molecules from their Average Mobility in Molecular Crystals].

One of the main problems in attempts to predict the binding constants of molecules (or free energies of their binding) is the correct evaluation of configurational binding entropy. This evaluation is possible by methods of molecular dynamics simulation, but these simulations require a lot of computational time. Earlier, we have developed an alternative approach which allows the fast calculation of the binding entropy from summarizing the available data on sublimation of crystals. Our method is based on evaluating the mean amplitude of the movements that are restricted in the bound molecule, e.g., in a crystal, but are not restricted in the free state, e.g., in vapor. In this work, it is shown that the standard entropy of binding of molecules by crystals under standard conditions (1 atm, 25°C) can be assessed rather accurately from geometric and physical parameters of the molecule and the average amplitude of the molecule motions in crystals estimated in our previous work.

[Anomalous Kinetics of Amyloidogenesis Suggest a Competition between Oligomers and Fibrils].

Meisl et al. have recently observed an anomalous dependence of the amyloid formation rate on the protein concentration. A novel mechanism of fibril growth has been proposed by Meisl et al. to explain the abnormality; it consists in the fibril-catalyzed initiation of fibril formation with saturation of catalytic sites at high concentrations of substrates. Our article describes an alternative explanation of the anomalous kinetics, assuming that the formation of metastable oligomers competes with fibril formation by decreasing the concentration of free monomers. Oligomers are indeed observed in the course of amyloid formation, but are usually considered as seeds of amyloid fibrils rather as their competitors. However, the oligomers visually detectable by electron microscopy were shown to be close in size to those that can be derived from the anomalous dependence of the amyloid growth rate on the protein concentration, given that the anomaly results from competition between oligomer formation and amyloidogenesis.

[Intersubunit Mobility of the Ribosome].

Ribosomes are ribonucleoprotein nanoparticles synthesizing all proteins in living cells. The function of the ribosome is to translate the genetic information encoded in a nucleotide sequence of mRNA into the amino acid sequence of a protein. Each translation step (occurring after the codon-dependent binding of the aminoacyl-tRNA with the ribosome and mRNA) includes (i) the transpeptidation reaction and (ii) the translocation that unidirectionally drives the mRNA chain and mRNA-bound tRNA molecules through the ribosomal intersubunit space; the latter process is driven by the free energy of the chemical reaction of transpeptidation. Thus, the translating ribosome can be considered a conveying protein-synthesizing molecular machine. In this review we analyze the role of ribosomal intersubunit mobility in the process of translocation.

Intermediate States of Apomyoglobin: Are They Parts of the Same Area of Conformations Diagram?

Several research teams have reported detection and characterization of various apomyoglobin intermediate states different in their accumulation mode, thus putting a natural question as to proportions of these intermediates. The current report presents spectral properties of sperm whale apomyoglobin studied over a wide range of conditions with the use of circular dichroism and fluorescence techniques. Based on the experimental data, a diagram of apomyoglobin conformational states has been constructed. It shows that though induced by various denaturants, all the observed intermediates belong to one and the same area in the diagram.

[Calculation of mobility and entropy of the binding of molecules by crystals].

A simple method for evaluating a range of molecular movements in crystals has been developed. This estimate is needed to calculate the entropy of binding, in particular in protein-ligand complexes. The estimate is based on experimental data concerning the enthalpy of sublimation and saturated vapor pressure obtained for 15 organic crystals with melting temperatures of 25-80°Ð¡. For this set, we calculated the values of the average range and the corresponding average amplitude of molecular movements in crystals that constituted 0.75 ± 0.14 Å and 0.18 ± 0.03 Å, respectively. The entropy of sublimation calculated based on the average range of molecular movements in crystals was well consistent with the experimental data.

Folding of circular permutants with decreased contact order: general trend balanced by protein stability.

To examine the influence of contact order and stability on the refolding rate constant for two-state proteins, we have analysed the folding kinetics of the small beta-alpha-beta protein S6 and two of its circular permutants with relative contact orders of 0.19, 0.15 and 0.12. Data reveal a small but significant increase of the refolding rate constant (log k(f)) with decreasing contact order. At the same time, the decreased contact order is correlated to losses in global stability and alterations of the folding nucleus. When the differences in stability are accounted for by addition of Na2SO4 or by comparison of the folding kinetics at the transition mid-point, the dependence between log k(f) and contact order becomes stronger and follows the general correlation for two-state proteins. The observation emphasizes the combined action of topology and stability in controlling the rate constant of protein folding.

Cunning simplicity of protein folding landscapes.

Funnel-like landscapes are widely used to visualize protein folding. It might seem that any funnel-like energy landscape helps to avoid the 'Levinthal paradox', i.e. to avoid sampling the impossibly large number of conformations for a folding protein. This cunning suggestion, reinforced by beautiful drawings of the energy funnels, stimulated some simple models of protein folding; one of them [D.J. Bicout and A. Szabo (2000) Protein Sci., 9, 452-465] is especially straightforward and instructive. A thorough analysis of this strict funnel model (which does not consider a nucleation of phase separation in the course of folding) shows that it cannot provide a simultaneous explanation for both major features observed for protein folding: (i) folding within non-astronomical time, and (ii) co-existence of the native and the unfolded states during the folding process. On the contrary, the nucleation mechanism of protein folding can account for both these major features simultaneously.

Theoretical study of a landscape of protein folding-unfolding pathways. Folding rates at midtransition.

This paper presents a new method for calculating the folding-unfolding rates of globular proteins. The method is based on solution of kinetic equations for a network of folding-unfolding pathways of the proteins. The rates are calculated in the point of thermodynamic equilibrium between the native and completely unfolded states. The method has been applied to all the proteins listed by Jackson [Jackson, S. E. (1998) Folding Des. 3, R81-R91] and some peptides. Although the studied protein chains differ by more than 1 order of magnitude in size and exhibit two- as well as three-state kinetics in water, and their folding rates cover more than 11 orders of magnitude, the theoretical estimates are reasonable close to the experimentally measured folding rates in midtransition (the correlation coefficient being as high as 0.78). This means that the presented theory (having no adjustable parameters at all) is consistent with the experimental observations.

Folding nuclei in proteins.

When a protein folds or unfolds, it passes through many half-folded microstates. Only a few of them can accumulate and be seen experimentally, and this happens only when the folding (or unfolding) occurs far from the point of thermodynamic equilibrium between the native and denatured states. The universal features of folding, though, are observed just close to the equilibrium point. Here the 'two-state' transition proceeds without any accumulation of metastable intermediates, and only the transition state ('folding nucleus') is outlined by its key influence on the folding-unfolding kinetics. Our aim is to review recent experimental and theoretical studies of the folding nuclei.

Statistical significance of protein structure prediction by threading.

In this study, we estimate the statistical significance of structure prediction by threading. We introduce a single parameter epsilon that serves as a universal measure determining the probability that the best alignment is indeed a native-like analog. Parameter epsilon takes into account both length and composition of the query sequence and the number of decoys in threading simulation. It can be computed directly from the query sequence and potential of interactions, eliminating the need for sequence reshuffling and realignment. Although our theoretical analysis is general, here we compare its predictions with the results of gapless threading. Finally we estimate the number of decoys from which the native structure can be found by existing potentials of interactions. We discuss how this analysis can be extended to determine the optimal gap penalties for any sequence-structure alignment (threading) method, thus optimizing it to maximum possible performance.

Folding nuclei in 3D protein structures.

This paper presents and analyzes the results of several new approaches to the problem of finding the folding nucleus in a given 3D protein structure. Firstly, we show that the participation of residues in the hydrophobic core and the secondary structure of native protein has a rather modest correlation with the experimentally found phi values characterizing the participation of residues in the folding nuclei. Then we tried to find the nuclei as the free energy saddle points on the network of the folding/unfolding pathways using the branch-and-bound technique and dynamic programming. We also attempted to estimate the phi values from solving of kinetic equations for the network of protein folding/unfolding pathways. These approaches give a better correlation with experiment, and the estimated folding time is consistent with the experimentally observed rapid folding of small proteins.

Search for the most stable folds of protein chains: III. Improvement in fold recognition by averaging over homologous sequences and 3D structures.

Three-dimensional (3D) protein fold recognition by query sequence can be improved using information of fold recognition yielded by the sequences homologous to the query one. This idea is now used more and more widely. Our paper presents its consequent development. We suggest incorporating information both on the sequences homologous to the query protein sequence and the 3D structures homologous to the target (already deciphered) protein folds. We show that both these tricks, and especially their combination reduces errors in fold recognition by the threading method. Proteins 2000;40:494-501.

A theoretical search for folding/unfolding nuclei in three-dimensional protein structures.

When a protein folds or unfolds, it has to pass through many half-folded microstates. Only a few of them can be seen experimentally. In a two-state transition proceeding with no accumulation of metastable intermediates [Fersht, A. R. (1995) Curr. Opin. Struct. Biol. 5, 79-84], only the semifolded microstates corresponding to the transition state can be outlined; they influence the folding/unfolding kinetics. Our aim is to calculate them, provided the three-dimensional protein structure is given. The presented approach follows from the capillarity theory of protein folding and unfolding [Wolynes, P. G. (1997) Proc. Natl. Acad. Sci. USA 94, 6170-6175]. The approach is based on a search for free-energy saddle point(s) on a network of protein unfolding pathways. Under some approximations, this search is rapidly performed by dynamic programming and, despite its relative simplicity, gives a good correlation with experiment. The computed folding nuclei look like ensembles of those compact and closely packed parts of the three-dimensional native folds that contain a small number of disordered protruding loops. Their estimated free energy is consistent with the rapid (within seconds) folding and unfolding of small proteins at the point of thermodynamic equilibrium between the native fold and the coil.

Averaging interaction energies over homologs improves protein fold recognition in gapless threading.

Protein structure prediction is limited by the inaccuracy of the simplified energy functions necessary for efficient sorting over many conformations. It was recently suggested (Finkelstein, Phys Rev Lett 1998;80:4823-4825) that these errors can be reduced by energy averaging over a set of homologous sequences. This conclusion is confirmed in this study by testing protein structure recognition in gapless threading. The accuracy of recognition was estimated by the Z-score values obtained in gapless threading tests. For threading, we used 20 target proteins, each having from 20 to 70 homologs taken from the HSSP sequence base. The energy of the native structures was compared with the energy from 34 to 75 thousand of alternative structures generated by threading. The energy calculations were done with our recently developed Calpha atom-based phenomenological potentials. We show that averaging of protein energies over homologs reduces the Z-score from approximately -6.1 (average Z-score for individual chains) to approximately -8.1. This means that a correct fold can be found among 3 x 10(9) random folds in the first case and among 3 x 10(15) in the second. Such increase in selectivity is important for recognition of protein folds.

How homologs can help to predict protein folds even though they cannot be predicted for individual sequences.

At present, one cannot predict the 3D structure of a protein directly from its sequence alone mainly because of errors in the energy estimates. However, a recently developed simple analytical theory (Finkelstein, 1998) shows that using a set of homologs (i.e., chains with numerous amino acid mutations but with equal 3D folds) one can average the interaction energies over the homologs and predict their common 3D fold even when predictions for individual sequences are wrong because the energy parameters are known only approximately. In this work we verify this theoretical conclusion by computer simulations performed with simplified models of protein chains.