We propose a model for protein folding in vivo based on a Brownian-ratchet mechanism in the multidimensional energy landscape space. The device is able to produce directed transport taking advantage of the assumed intrinsic asymmetric properties of the proteins and employing the consumption of energy provided by an external source. Through such a directed transport phenomenon, the polypeptide finds the native state starting from any initial state in the energy landscape with great efficacy and robustness, even in the presence of different type of obstacles. This model solves Levinthal's paradox without requiring biased transition probabilities but at the expense of opening the system to an external field.
Recent high resolution experiments have provided a quantitative description of the statistical properties of interphase chromatin at large scales. These findings have stimulated a search for generic physical interactions that give rise to such specific statistical conformations. Here, we show that an active chromatin model of in-vivo folding, based on the interplay between polymer elasticity, confinement, topological constraints and active stresses arising from the (un)binding of ATP-dependent chromatin-remodeling proteins gives rise to steady state conformations consistent with these experime…
We study the protein folding problem on the base of the quantum approach we proposed recently by considering the model of protein chain with nine amino-acid residues. We introduced the concept of distance space and its projections on a $XY$-plane, and two characteristic quantities, one is called compactness of protein structure and another is called probability ratio involving shortest path. Our results not only confirmed the fast quantum folding time but also unveiled the existence of quantum intelligence hidden behind in choosing protein folding pathways.
We introduce a powerful iterative algorithm to compute protein folding pathways, with realistic all-atom force fields. Using the path integral formalism, we explicitly derive a modified Langevin equation which samples directly the ensemble of reactive pathways, exponentially reducing the cost of simulating thermally activated transitions. The algorithm also yields a rigorous stochastic estimate of the reaction coordinate. After illustrating this approach on a simple toy model, we successfully validate it against the results of ultra-long plain MD protein folding simulations for a fast folding …
We investigate the interplay between post-translational folding and escape of two small single-domain proteins at the ribosomal exit tunnel by using Langevin dynamics with coarse-grained models. It is shown that at temperatures lower or near the temperature of the fastest folding, folding proceeds concomitantly with the escape process, resulting in vectorial folding and enhancement of foldability of nascent proteins. The concomitance between the two processes, however, deteriorates as temperature increases. Our folding simulations as well as free energy calculation by using umbrella sampling s…
When described by a low-dimensional reaction coordinate, the rates of protein folding are determined by a subtle interplay between free-energy barriers and friction. While it is commonplace to extract free-energy profiles from molecular trajectories, a direct evaluation of friction is far more elusive, and one typically evaluates it indirectly via memoryless reaction rate theories. Here, using memory-kernel extraction methods founded on a generalised Langevin equation (GLE) formalism, we directly calculate the memory-dependent friction for eight fast-folding proteins, taken from a published se…
We propose a general theory to describe the distribution of protein-folding transition paths. We show that transition paths follow a predictable sequence of high-free-energy transient states that are separated by free-energy barriers. Each transient state corresponds to the assembly of one or more discrete, cooperative units, which are determined directly from the native structure. We show that the transition state on a folding pathway is reached when a small number of critical contacts are formed between a specific set of substructures, after which folding proceeds downhill in free energy. Th…
Nonnative residual interactions have attracted increasing attention in recent protein folding researches. Experimental and theoretical investigations had been set out to catch nonnative contacts that might dominate key events in protein folding. However, energetic frustrations caused by nonnative inter-residue interactions are not systematically characterized, due to the complicated folding mechanism. Recently, we studied the folding of a set of homologous all-α proteins and found that nonnative-contact-based energetic frustrations are closely related to protein native-contact networks. In thi…
We investigated the impact of hydrodynamic interactions (HI) on protein folding using a coarse-grained model. The extent of the impact of hydrodynamic interactions, whether it accelerates, retards, or has no effect on protein folding, has been controversial. Together with a theoretical framework of the energy landscape theory (ELT) for protein folding that describes the dynamics of the collective motion with a single reaction coordinate across a folding barrier, we compared the kinetic effects of HI on the folding rates of two protein models that use a chain of single beads with distinctive to…
Focusing on a small set of proteins that i) fold in a concerted, all-or-none fashion and ii) do not contain knots or slipknots, we show that the Gauss linking integral, the torsion and the number of sequence-distant contacts provide information regarding the folding rate. Our results suggest that the global topology/geometry of the proteins shifts from right-handed to left-handed with decreasing folding rate, and that this topological change is associated with an increase in the number of more sequence-distant contacts.
The protein folding problem must ultimately be solved on all length scales from the atomic up through a hierarchy of complicated structures. By analyzing the stability of the folding process using physics and mathematics, this paper shows that features without length scales, i.e. topological features, are potentially of central importance. Topology is a natural mathematical tool for the study of shape and we avail ourselves of that tool to examine the relationship between the amino acid sequence and the shapes of protein molecules. We apply what we learn to conjectures about their biological e…
We study the folding process in the shallowly knotted protein MJ0366 within two variants of a structure-based model. We observe that the resulting topological pathways are much richer than identified in previous studies. In addition to the single knot-loop events, we find novel, and dominant, two-loop mechanisms. We demonstrate that folding takes place in a range of temperatures and the conditions of most successful folding are at temperatures which are higher than those required for the fastest folding. We also demonstrate that nascent conditions are more favorable to knotting than off-riboso…
Folding protein dynamics has been an area of high interest for quite some time, especially given the increased focus on the field of Biophysics. Because folding dynamics occur on such short time scales, empirical techniques developed for more "static" protein events, such as X-ray crystallography, nuclear magnetic resonance, and green fluorescent protein (GFP) labelling, aren't as applicable. Instead, computational methods must often be used to simulate these short lived yet highly dynamic events. One such computational method that is proven to provide much valuable insight into protein foldin…
The protein folding problem is stated and a list of properties that do not depend upon specific molecules is compiled and analyzed. The relationship of this analysis to future simulations is emphasized. The choice of power and time as variables as opposed to energy and time is discussed. A wave motion model is reviewed and related to the action in classical mechanics. It is argued that the properties of the action support the idea that folding takes place in small steps. It is explained how catastrophe theory has been employed in wave motion models and how it can be used in examination of succ…
The prediction of protein secondary and tertiary structures from the primary amino acid sequence is both an incredibly important and incredibly difficult problem. Accurate prediction of a protein's native structure can provide critical insights about its function, ultimately leading to breakthoughs in drug design and disease diagnosis. The field has a rich history, from the earliest folding experiments in the 1960's to the use of state-of-the-art algorithms today; this article reviews protein folding's history with an emphasis on how modern methods are tackling the protein folding problem. Ass…
Protein folding is an indispensable process for the majority of proteins after their synthesis from ribosomes in the cell. Most in vitro protein folding studies have focused on single-domain proteins. Hence, it is important to understand the folding process of multi-domain proteins, especially when domains are discontinuous. We choose the Maltose binding protein (MBP) as a model system. In particular, we studied a mutant of MBP that folds slowly. Here, using two- and three-color single-molecule Foerster resonance energy transfer (smFRET) experiments, we study the refolding of both the domains …
Proper folding of deeply knotted proteins has a very low success rate even in structure-based models which favor formation of the native contacts but have no topological bias. By employing a structure-based model, we demonstrate that cotranslational folding on a model ribosome may enhance the odds to form trefoil knots for protein YibK without any need to introduce any non-native contacts. The ribosome is represented by a repulsive wall that keeps elongating the protein. On-ribosome folding proceeds through a a slipknot conformation. We elucidate the mechanics and energetics of its formation. …
Understanding the protein folding process is an outstanding issue in biophysics; recent developments in molecular dynamics simulation have provided insights into this phenomenon. However, the large freedom of atomic motion hinders the understanding of this process. In this study, we applied persistent homology, an emerging methods to analyze topological features in a dataset, to reveal protein folding dynamics. We developed a new method to characterize protein structure based on persistent homology and applied this method to molecular dynamics simulations of chignolin. Using principle componen…
Many aspects of the study of protein folding and dynamics have been affected by the recent advances in machine learning. Methods for the prediction of protein structures from their sequences are now heavily based on machine learning tools. The way simulations are performed to explore the energy landscape of protein systems is also changing as force-fields are started to be designed by means of machine learning methods. These methods are also used to extract the essential information from large simulation datasets and to enhance the sampling of rare events such as folding/unfolding transitions.…
We propose a new deterministic methodology to predict RNA sequence and protein folding. Is stem enough for structure prediction? The main idea is to consider all possible stem formation in the given sequence. With the stem loop energy and the strength of stem, we explore how to deterministically utilize stem information for RNA sequence and protein folding structure prediction. We use graph notation, where all possible stems are represented as vertices, and co-existence as edges. This full Stem-graph presents all possible folding structure, and we pick sub-graph(s) which give the best matching…
