Some additional remarks to the solution of the protein folding puzzle: Reply to comments on "There and back again: Two views on the protein folding puzzle"

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. We discuss the famous Levinthal's paradox of protein folding and its solution, theoretical models of protein folding and unfolding, and the dependence of the rates of these processes on the protein chain length. Special attention is paid to relatively small, single-domain, and water-soluble globular proteins whose structure and folding are much better studied and understood than those of large proteins, especially membrane or fibrous proteins. Lastly, we describe the chaperone-assisted protein folding with an emphasis on the chaperones' ability to prevent proteins from their irreversible aggregation. Since the possible assistance mechanisms connected with chaperones are still debatable, experimental data useful in selecting the most likely mechanisms of chaperone-assisted protein folding are presented.

Protein structure prediction using the evolutionary algorithm USPEX

Protein structure prediction is one of major problems of modern biophysics: current attempts to predict the tertiary protein structure from amino acid sequence are successful mostly when the use of big data and machine learning allows one to reduce the "prediction problem" to the "problem of recognition". Compared with recent successes of deep learning, classical predictive methods lag behind in their accuracy for the prediction of stable conformations. Therefore, in this work we extended the evolutionary algorithm USPEX to predict protein structure based on global optimization starting with the amino acid sequence. Moreover, we compared frequently used force fields for the task of protein structure prediction. Protein structure relaxation and energy calculations were performed using Tinker (with several different force fields) and Rosetta (with REF2015 force field) codes. To create new protein structure models in the USPEX algorithm, we developed novel variation operators. The test of the new method on seven proteins having (for simplicity) no cis-proline (with ω ≈ 0°) residues, and a length of up to 100 residues, revealed that our algorithm predicts tertiary structures of proteins with high accuracy. The comparison of the final potential energies of the predicted protein structures obtained using the USPEX and the Rosetta Abinitio approach showed that in most cases the developed algorithm found structures with close or even lower energy (Amber/Charmm/Oplsaal) and scoring function (REF2015). While USPEX has clearly demonstrated its ability to find very deep energy minima, our study showed that the existing force fields are not sufficiently accurate for accurate blind prediction of protein structures without further experimental verification.

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." In this review, we discuss the key ideas and discoveries leading to the current understanding of protein folding kinetics, including folding landscapes and funnels, free energy barriers at the folding/unfolding pathways, and the solution of Levinthal's paradox. A special role here is played by the "all-or-none" phase transition occurring at protein folding and unfolding and by the point of thermodynamic (and kinetic) equilibrium between the "native" and the "unfolded" phases of the protein chain (where the theory obtains the simplest form). The modern theory provides an understanding of key features of protein folding and, in good agreement with experiments, it (i) outlines the chain length-dependent range of protein folding times, (ii) predicts the observed maximal size of "foldable" proteins and domains. Besides, it predicts the maximal size of proteins and domains that fold under solely thermodynamic (rather than kinetic) control. Complementarily, a theoretical analysis of the number of possible protein folding patterns, performed at the level of formation and assembly of secondary structures, correctly outlines the upper limit of protein folding times.

Solution of Levinthal's Paradox and a Physical Theory of Protein Folding Times

“How do proteins fold?” Researchers have been studying different aspects of this question for more than 50 years. The most conceptual aspect of the problem is how protein can find the global free energy minimum in a biologically reasonable time, without exhaustive enumeration of all possible conformations, the so-called “Levinthal’s paradox.” Less conceptual but still critical are aspects about factors defining folding times of particular proteins and about perspectives of machine learning for their prediction. We will discuss in this review the key ideas and discoveries leading to the current understanding of folding kinetics, including the solution of Levinthal’s paradox, as well as the current state of the art in the prediction of protein folding times.

Life in Phases: Intra- and Inter- Molecular Phase Transitions in Protein Solutions

Proteins, these evolutionarily-edited biological polymers, are able to undergo intramolecular and intermolecular phase transitions. Spontaneous intramolecular phase transitions define the folding of globular proteins, whereas binding-induced, intra- and inter- molecular phase transitions play a crucial role in the functionality of many intrinsically-disordered proteins. On the other hand, intermolecular phase transitions are the behind-the-scenes players in a diverse set of macrosystemic phenomena taking place in protein solutions, such as new phase nucleation in bulk, on the interface, and on the impurities, protein crystallization, protein aggregation, the formation of amyloid fibrils, and intermolecular liquid-liquid or liquid-gel phase transitions associated with the biogenesis of membraneless organelles in the cells. This review is dedicated to the systematic analysis of the phase behavior of protein molecules and their ensembles, and provides a description of the major physical principles governing intramolecular and intermolecular phase transitions in protein solutions.