How proteins manage to fold and how chaperones manage to assist the folding.

This review presents the current understanding of (i) spontaneous self-organization of spatial structures of protein molecules, and (ii) possible ways of chaperones' assistance to this process. Specifically, we overview the most important features of spontaneous folding of proteins (mostly, of the single-domain water-soluble globular proteins): the choice of the unique protein structure among zillions of alternatives, the nucleation of the folding process, and phase transitions within protein molecules. We consider the main experimental facts on protein folding, both in vivo and in vitro, of both kinetic and thermodynamic nature.

Physics of Ice Nucleation and Antinucleation: Action of Ice-Binding Proteins.

Ice-binding proteins are crucial for the adaptation of various organisms to low temperatures. Some of these, called antifreeze proteins, are usually thought to inhibit growth and/or recrystallization of ice crystals. However, prior to these events, ice must somehow appear in the organism, either coming from outside or forming inside it through the nucleation process.

Correction: Finkelstein et al. How Can Ice Emerge at 0 °C? 2022, , 981.

We regret to state that our article "How Can Ice Emerge at 0 °C?" [...

Protein folding problem: enigma, paradox, solution.

The ability of protein chains to spontaneously form their three-dimensional structures is a long-standing mystery in molecular biology. The most conceptual aspect of this mystery is how the protein chain can find its native, "working" spatial structure (which, for not too big protein chains, corresponds to the global free energy minimum) in a biologically reasonable time, without exhaustive enumeration of all possible conformations, which would take billions of years. This is the so-called "Levinthal's paradox.

How Can Ice Emerge at 0 °C?

The classical nucleation theory shows that bulk water freezing does not occur at temperatures above ≈ -30 °C, and that at higher temperatures ice nucleation requires the presence of some ice-binding surfaces. The temperature and rate of ice nucleation depend on the size and level of complementarity between the atomic structure of these surfaces and various H-bond-rich/depleted crystal planes. In our experiments, the ice nucleation temperature was within a range from -8 °C to -15 °C for buffer and water in plastic test tubes.

Calculation of Crystal-Solution Dissociation Constants.

The calculation of dissociation constants is an important problem in molecular biophysics. For such a calculation, it is important to correctly calculate both terms of the binding free energy; that is, the enthalpy and entropy of binding. Both these terms can be computed using molecular dynamics simulations, but this approach is very computationally expensive, and entropy calculations are especially slow.

Sublimation Entropy and Dissociation Constants Prediction by Quantitative Evaluation of Molecular Mobility in Crystals.

Prediction of binding free energies (or dissociation constants) is a crucial challenge for computational biochemistry. One of the main problems here consists in fast and accurate evaluation of binding entropy, which is far more time-consuming than evaluation of binding enthalpy. Here, we offer a fast and rather accurate approach to evaluate the sublimation entropy (i.

There and back again: Two views on the protein folding puzzle.

The ability of protein chains to spontaneously form their spatial structures is a long-standing puzzle in molecular biology. Experimentally measured folding times of single-domain globular proteins range from microseconds to hours: the difference (10-11 orders of magnitude) is the same as that between the life span of a mosquito and the age of the universe. This review describes physical theories of rates of overcoming the free-energy barrier separating the natively folded (N) and unfolded (U) states of protein chains in both directions: "U-to-N" and "N-to-U".

Reduction of the Search Space for the Folding of Proteins at the Level of Formation and Assembly of Secondary Structures: A New View on the Solution of Levinthal's Paradox.

The complete volume of the protein conformation space is, by many orders of magnitude, smaller at the level of secondary structure elements than that at the level of amino acid residues; the latter, according to Levinthal's estimate, scales approximately as 10(2 L), with L being the number of residues in the chain, whereas the former, as demonstrated in this paper, scales no faster than ∼L(N), with N being the number of the secondary structure elements, which is approximately equal to L/15. This drastic decrease in the exponent (L/15 instead of 2 L) explains why sampling of the conformation space does not contradict the ability of the protein chain to find its most stable fold.

Restrictions to protein folding determined by the protein size.

Experimentally measured rates of spontaneous folding of single-domain globular proteins range from microseconds to hours: the difference (11 orders of magnitude!) is akin to the difference between the life span of a mosquito and the age of the Universe. We show that physical theory with biological constraints outlines the possible range of folding rates for single-domain globular proteins of various size and stability, and that the experimentally measured folding rates fall within this narrow "golden triangle" built without any adjustable parameters, filling it almost completely. This "golden triangle" also successfully predicts the maximal allowed size of the "foldable" protein domains, as well as the maximal size of protein domains that fold under solely thermodynamic (rather than kinetic) control.

Golden triangle for folding rates of globular proteins.

The ability of protein chains 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 (11 orders of magnitude) is akin to the difference between the life span of a mosquito and the age of the universe. Here, we show that physical theory with biological constraints outlines a "golden triangle" limiting the possible range of folding rates for single-domain globular proteins of various size and stability, and that the experimentally measured folding rates fall within this narrow triangle built without any adjustable parameters, filling it almost completely.

FoldAmyloid: a method of prediction of amyloidogenic regions from protein sequence.

Motivation: Amyloidogenic regions in polypeptide chains are very important because such regions are responsible for amyloid formation and aggregation. It is useful to be able to predict positions of amyloidogenic regions in protein chains.

Results: Two characteristics (expected probability of hydrogen bonds formation and expected packing density of residues) have been introduced by us to detect amyloidogenic regions in a protein sequence.

ComSin: database of protein structures in bound (complex) and unbound (single) states in relation to their intrinsic disorder.

Most of the proteins in a cell assemble into complexes to carry out their function. In this work, we have created a new database (named ComSin) of protein structures in bound (complex) and unbound (single) states to provide a researcher with exhaustive information on structures of the same or homologous proteins in bound and unbound states. From the complete Protein Data Bank (PDB), we selected 24 910 pairs of protein structures in bound and unbound states, and identified regions of intrinsic disorder.

Intrinsic disorder in protein interactions: insights from a comprehensive structural analysis.

We perform a large-scale study of intrinsically disordered regions in proteins and protein complexes using a non-redundant set of hundreds of different protein complexes. In accordance with the conventional view that folding and binding are coupled, in many of our cases the disorder-to-order transition occurs upon complex formation and can be localized to binding interfaces. Moreover, analysis of disorder in protein complexes depicts a significant fraction of intrinsically disordered regions, with up to one third of all residues being disordered.

Understanding the folding rates and folding nuclei of globular proteins.

The first part of this paper contains an overview of protein structures, their spontaneous formation ("folding"), and the thermodynamic and kinetic aspects of this phenomenon, as revealed by in vitro experiments. It is stressed that universal features of folding are observed near the point of thermodynamic equilibrium between the native and denatured states of the protein. Here the "two-state" ("denatured state" <--> "native state") transition proceeds without accumulation of metastable intermediates, but includes only the unstable "transition state".

More compact protein globules exhibit slower folding rates.

We have demonstrated that, among proteins of the same size, alpha/beta proteins have on the average a greater number of contacts per residue due to their more compact (more "spherical") structure, rather than due to tighter packing. We have examined the relationship between the average number of contacts per residue and folding rates in globular proteins according to general protein structural class (all-alpha, all-beta, alpha/beta, alpha+beta). Our analysis demonstrates that alpha/beta proteins have both the greatest number of contacts and the slowest folding rates in comparison to proteins from the other structural classes.

Different packing of external residues can explain differences in the thermostability of proteins from thermophilic and mesophilic organisms.

Motivation: Understanding the basis of protein stability in thermophilic organisms raises a general question: what structural properties of proteins are responsible for the higher thermostability of proteins from thermophilic organisms compared to proteins from mesophilic organisms?

Results: A unique database of 373 structurally well-aligned protein pairs from thermophilic and mesophilic organisms is constructed. Comparison of proteins from thermophilic and mesophilic organisms has shown that the external, water-accessible residues of the first group are more closely packed than those of the second. Packing of interior parts of proteins (residues inaccessible to water molecules) is the same in both cases.

Prediction of amyloidogenic and disordered regions in protein chains.

The determination of factors that influence protein conformational changes is very important for the identification of potentially amyloidogenic and disordered regions in polypeptide chains. In our work we introduce a new parameter, mean packing density, to detect both amyloidogenic and disordered regions in a protein sequence. It has been shown that regions with strong expected packing density are responsible for amyloid formation.

FoldUnfold: web server for the prediction of disordered regions in protein chain.

Unlabelled: Identification of disordered regions in polypeptide chains is very important because such regions are essential for protein function. A new parameter, namely mean packing density of residues has been introduced to detect disordered regions in a protein sequence. We have demonstrated that regions with weak expected packing density would be responsible for the appearance of disordered regions.

Is it possible to predict amyloidogenic regions from sequence alone?

Identification of potentially amyloidogenic regions in polypeptide chains is very important because the amyloid fibril formation can be induced in most normal proteins. In our work we suggest a new method to detect amyloidogenic regions in protein sequence. It is based on the assumption that packing is tight inside an amyloid and therefore regions which could potentially pack well would have a tendency to form amyloids.

Entropy capacity determines protein folding.

Search and study of the general principles that govern kinetics and thermodynamics of protein folding generate a new insight into the factors controlling this process. Here, based on the known experimental data and using theoretical modeling of protein folding, we demonstrate that there exists an optimal relationship between the average conformational entropy and the average energy of contacts per residue-that is, an entropy capacity-for fast protein folding. Statistical analysis of conformational entropy and number of contacts per residue for 5829 protein structures from four general structural classes (all-alpha, all-beta, alpha/beta, alpha+beta) demonstrates that each class of proteins has its own class-specific average number of contacts (class alpha/beta has the largest number of contacts) and average conformational entropy per residue (class all-alpha has the largest number of rotatable angles phi, psi, and chi per residue).