Polymer principles and protein folding.

The origin and evolution of protein folds are among the most challenging, long-standing problems in biology. We developed Protein Fold Evolution Simulator (PFES), a computational approach that simulates evolution of globular folds from random amino acid sequences with atomistic details. PFES introduces random mutations in a population of protein sequences, evaluates the effect of mutations on protein structure, and selects a new set of proteins for further evolution. Iteration of this process allows tracking the evolutionary trajectory of a changing protein fold that evolves under selective pressure for protein fold stability, interaction with other proteins, or other features shaping the fitness landscape. We employed PFES to show how stable, globular protein folds could evolve from random amino acid sequences as monomers or in complexes with other proteins. The simulations reproduce the evolution of many simple folds of natural proteins as well as emergence of distinct folds not known to exist in nature. We show that evolution of small globular protein folds from random sequences, on average, takes 1.15 to 3 amino acid replacements per site, depending on the population size, with some simulations yielding stable folds after as few as 0.2 replacements per site. These values are lower than the characteristic numbers of replacements in conserved proteins during the time since the Last Universal Common Ancestor, suggesting that simple protein folds can evolve from random sequences relatively easily and quickly. PFES tracks the complete evolutionary history from simulations and can be used to test hypotheses on protein fold evolution.

Chapter 4 - Nuclear magnetic resonance spectroscopy for protein structure, folding, and dynamics

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.

Levinthal's paradox is that finding the native folded state of a protein by a random search among all possible configurations can take an enormously long time. Yet proteins can fold in seconds or less. Mathematical analysis of a simple model shows that a small and physically reasonable energy bias against locally unfavorable configurations, of the order of a few kT, can reduce Levinthal's time to a biologically significant size.

Artificial Intelligence has a high potential to solve many real-world problems. In the recent years researchers are dealing with one of the biggest complications in biology, which is protein folding. With the assistance of technology, we can foresee how proteins fold from a chain of amino acids into 3D shapes that do life's errands. There are mainly three big problems associated with folding of proteins. The first problem is there any particular folding code. The second one there is a folding system. Then the final problem is we able to determine the 3D structure of proteins. Proteins are the microscopic machines and structural building blocks of our cells. They carry out important functions like breaking down foods, storing oxygen and forming scaffolds to help cells keep their shape. Each one is built up of one amino acid chain that folds in on itself into a mostly defined structure. Each part of our body and in any other organism is made either from or by proteins and this is true for every living creature, even for viruses. The structure of very small proteins can be foreseen using the computer method. This article is all about the protein folding problem with more spotlights on the role of AI-based systems in protein structure forecasts. The motivation behind this article is to convey an overall understanding of AI-based answers for protein folding problems.

This Perspective is intended to raise questions about the conventional interpretation of protein folding. According to the conventional interpretation, developed over many decades, a protein population can visit a vast number of conformations under unfolding conditions, but a single dominant native population emerges under folding conditions. Accordingly, folding comes with a substantial loss of conformational entropy. How is this price paid? The conventional answer is that favorable interactions between and among the side chains can compensate for entropy loss, and moreover, these interactions are responsible for the structural particulars of the native conformation. Challenging this interpretation, the Perspective introduces a proposal that high energy (i.e., unfavorable) excluding interactions winnow the accessible population substantially under physical–chemical conditions that favor folding. Both steric clash and unsatisfied hydrogen bond donors and acceptors are classified as excluding interactions, so called because conformers with such disfavored interactions will be largely excluded from the thermodynamic population. Both excluding interactions and solvent factors that induce compactness are somewhat nonspecific, yet together they promote substantial chain organization. Moreover, proteins are built on a backbone scaffold consisting of α‐helices and strands of β‐sheet, where the number of hydrogen bond donors and acceptors is exactly balanced. These repetitive secondary structural elements are the only two conformers that can be both completely hydrogen‐bond satisfied and extended indefinitely without encountering a steric clash. Consequently, the number of fundamental folds is limited to no more than ~10,000 for a protein domain. Once excluding interactions are taken into account, the issue of “frustration” is largely eliminated and the Levinthal paradox is resolved. Putting the “bottom line” at the top: it is likely that hydrogen‐bond satisfaction represents a largely under‐appreciated parameter in protein folding models.

The spontaneous folding of protein has posed a fundamental problem popularly known as Levinthal paradox. Effort has been harnessed both in vivo and in vitro to obtain the native (functional) structure of proteins which is the most stable thermodynamically from the experimental and theoretical point of view. A coarse-grained simplified model has been a very useful tool for the study of protein structure by representing proteins as linear and self-avoiding chains which contain two types of monomers H (hydrophobic) and P (polar) on a lattice model. We present the results of numerical studies of the energy landscape on three sequences of amino acid and distinct funnels were generated with contact interactions to obtain the ground state conformation on a square lattice using a move-biased Monte Carlo simulation (MBMC). This method is very efficient and outperforms the conventional Monte Carlo method in the state-of-the-art results.

1. Introduction 1112. Levinthal's paradox and energy landscapes 1152.1 Including randomness in the energy function 1212.2 Some effects of energetic correlations between structurally similar states 1263. Resolution of problems by funnel theory 1283.1 Physical origin of free-energy barriers 1334. Generic mechanisms in folding 1384.1 Collapse, generic and specific 1394.2 Helix formation 1394.3 Nematic ordering 1414.4 Microphase separation 1425. Signatures of a funneled energy landscape 1456. Statistical Hamiltonians and self-averaging 1527. Conclusions and future prospects 1568. Acknowledgments 1579. Appendix: Glossary of terms 15710. References 158The current explosion of research in molecular biology was made possible by the profound discovery that hereditary information is stored and passed on in the simple, one-dimensional (1D) sequence of DNA base pairs (Watson & Crick, 1953). The connection between heredity and biological function is made through the transmission of this 1D information, through RNA, to the protein sequence of amino acids. The information contained in this sequence is now known to be sufficient to completely determine a protein's geometrical 3D structure, at least for simpler proteins which are observed to reliably refold when denatured in vitro, i.e. without the aid of any cellular machinery such as chaperones or steric (geometrical) constraints due to the presence of a ribosomal surface (for example Anfinsen, 1973) (see Fig. 1). Folding to a specific structure is typically a prerequisite for a protein to function, and structural and functional probes are both often used in the laboratory to test for the in vitro yield of folded proteins in an experiment.

Special issue on protein folding: experimental and theoretical approaches

We discuss the statistical mechanical foundation for the two-state transition in the protein folding of small globular proteins. In the standard arguments of protein folding, the statistical search for the ground state is carried out from astronomically many conformations in the configuration space. This leads us to the famous Levinthal's paradox. To resolve the paradox, Gō first postulated that the two-state transition — all-or-none type transition — is very crucial for the protein folding of small globular proteins and used the Gō's lattice model to show the two-state transition nature. Recently, there have been accumulated many experimental results that support the two-state transition for small globular proteins. Stimulated by such recent experiments, Zwanzig has introduced a minimal statistical mechanical model that exhibits the two-state transition. Also, Finkelstein and coworkers have discussed the solution of the paradox by considering the sequential folding of a small globular protein. On the other hand, recently Iguchi have introduced a toy model of protein folding using the Rubik's magic snake model, in which all folded structures are exactly known and mathematically represented in terms of the four types of conformations: cis-, trans-, left and right gauche-configurations between the unit polyhedrons. In this paper, we study the relationship between the Gō's two-state transition, the Zwanzig's statistical mechanics model and the Finkelsteinapos;s sequential folding model by applying them to the Rubik's magic snake models. We show that the foundation of the Gō's two-state transition model relies on the search within the equienergy surface that is labeled by the contact order of the hydrophobic condensation. This idea reproduces the Zwanzig's statistical model as a special case, realizes the Finkelstein's sequential folding model and fits together to understand the nature of the two-state transition of a small globular protein by calculating the physical quantities such as the free energy, the contact order and the specific heat. We point out the similarity between the liquid-gas transition in statistical mechanics and the two-state transition of protein folding. We also study morphology of the Rubik's magic snake models to give a prototype model for understanding the differences between α-helices proteins and β-sheets proteins.

How Well Evolved Is The Folding Code?

To better understand how amino acid sequence encodes protein structure, we engineered mutational pathways that connect three common folds (3α, β−grasp, and α/β−plait). The structures of proteins at high sequence-identity intersections in the pathways (nodes) were determined using NMR spectroscopy and analyzed for stability and function. To generate nodes, the amino acid sequence encoding a smaller fold is embedded in the structure of an ~50% larger fold and a new sequence compatible with two sets of native interactions is designed. This generates protein pairs with a 3α or β−grasp fold in the smaller form but an α/β−plait fold in the larger form. Further, embedding smaller antagonistic folds creates critical states in the larger folds such that single amino acid substitutions can switch both their fold and function. The results help explain the underlying ambiguity in the protein folding code and show that new protein structures can evolve via abrupt fold switching.

Protein folding is a hierarchical event, in which transiently formed local structural elements assemble to yield the native conformation. In principle, multiple paths glide down the energy landscape, but, in practice, only a few of the paths are highly traveled. Here, the literature is reviewed in this light, and, particularly, a hierarchical, building block protein-folding model is presented, putting it in the context of a broad range of experimental and theoretical results published over the past few years. The model is based on two premises: First, although the local building block elements may be unstable, they nevertheless have higher population times than all alternate conformations; and, second, protein folding progresses through a combinatorial assembly of these elements. Through the binding of the most favorable building block conformers, there is a redistribution of the conformers in solution, propagating the protein-folding reaction. We describe the algorithm, and illustrate its usefulness, then we focus on its utility in assigning simple vs complex folding pathways, on chaperonin-assisted folding, on its relevance to domain-swapping processes, and on its relevance and relationship to disconnectivity graphs and tree diagrams. Considering protein folding as initiating from local transient structural elements is consistent with available experimental and theoretical results. Here, we have shown that, early in the folding process, sequential interactions are likely to take place, even if the final native fold is a complex, nonsequential one. Such a route is favorable kinetically and entropically. Through the construction of anatomy trees, the model enables derivation of the major folding pathways and their bumps, and qualitatively explains the kinetics of protein folding.

Protein folding involves a large number of steps and conformations in which the folding protein samples different thermodynamic states characterized by local minima. Kinetically trapped on- or off-pathway intermediates are metastable folding intermediates towards the lowest absolute energy minima, which have been postulated to be the natively folded state where intramolecular interactions dominate, and the amyloid state where intermolecular interactions dominate. However, this view largely neglects the rich polymorphism found within amyloid species. We review the protein folding energy landscape in view of recent findings identifying specific transition routes among different amyloid polymorphs. Observed transitions such as twisted ribbon→crystal or helical ribbon→nanotube, and forbidden transitions such helical ribbon↛crystal, are discussed and positioned within the protein folding and aggregation energy landscape. Finally, amyloid crystals are identified as the ground state of the protein folding and aggregation energy landscape.

In this contribution we shall try to argue that no folding scenario—be it hierachical, nonhierarchical, nucleation, etc.—needs to be invoked to solve Levinthal's paradox: It fails on its own grounds.