On a Generalized Levinthal's Paradox: The Role of Long- and Short Range Interactions in Complex Bio-molecular Reactions, Including Protein and DNA Folding

The current protein folding literature is reviewed. Two main approaches to the problem of folding were selected for this review: geometrical and biophysical. The geometrical approach allows the formulation of topological restrictions on folding, that are usually not taken into account in the construction of physical models. In particular, the topological constraints do not allow the known funnel-like energy landscape modeling, although most common methods of resolving the paradox are based on this method. The very paradox is based on the fact that complex molecules must reach their native conformations (complexes that result from reactions) in an exponentially long time, which clearly contradicts the observed experimental data. In this respect we considered the complexity of the reactions between ligands and proteins. On this general basis, the folding-reaction paradox was reformulated and generalized. We conclude that prospects for solving the paradox should be associated with incorporating a topology aspect in biophysical models of protein folding, through the construction of hybrid models. However, such models should explicitly include long-range force fields and local cell biological conditions, such as structured water complexes and photon/phonon/soliton waves, ordered in discrete frequency bands. In this framework, collective and coherent oscillations in, and between, macromolecules are instrumental in inducing intra- and intercellular resonance, serving as an integral guiding network of life communication: the electrome aspect of the cell. Yet, to identify the actual mechanisms underlying the bonds between molecules (atoms), it will be necessary to perform dedicated experiments to more definitely solve the particular time paradox. © 2017 Elsevier Ltd.The present results were partially obtained in the frame of state task of Ministry of Education and Science of Russia 1.4539.2017/8.9

A Novel Multi-objectivisation Approach for Optimising the Protein Inverse Folding Problem

In biology, the subject of protein structure prediction is of continued interest, not only to chart the molecular map of the living cell, but also to design proteins of new functions. The Inverse Folding Problem (IFP) is in itself an important research problem, but also at the heart of most rational protein design approaches. In brief, the IFP consists in finding sequences that will fold into a given structure, rather than determining the structure for a given sequence - as in conventional structure prediction. In this work we present a Multi Objective Genetic Algorithm (MOGA) using the diversity-as-objective (DAO) variant of multi-objectivisation, to optimise secondary structure similarity and sequence diversity at the same time, hence pushing the search farther into wide-spread areas of the sequence solution-space. To control the high diversity generated by the DAO approach, we add a novel Quantile Constraint (QC) mechanism to discard an adjustable worst quantile of the population. This DAO-QC approach can efficiently emphasise exploitation rather than exploration to a selectable degree achieving a trade-off producing both better and more diverse sequences than the standard Genetic Algorithm (GA). To validate the final results, a subset of the best sequences was selected for tertiary structure prediction. The super-positioning with the original protein structure demonstrated that meaningful sequences are generated underlining the potential of this work