The Proteome Folding Problem and Cellular Proteostasis

Stunning advances have been achieved in addressing the protein folding problem, providing deeper understanding of the mechanisms by which proteins navigate energy landscapes to reach their native states and enabling powerful algorithms to connect sequence to structure. However, the realities of the in vivo protein folding problem remain a challenge to reckon with. Here, we discuss the concept of the “proteome folding problem”—the problem of how organisms build and maintain a functional proteome—by admitting that folding energy landscapes are characterized by many misfolded states and that cells must deploy a network of chaperones and degradation enzymes to minimize deleterious impacts of these off-pathway species. The resulting proteostasis network is an inextricable part of in vivo protein folding and must be understood in detail if we are to solve the proteome folding problem. We discuss how the development of computational models for the proteostasis network’s actions and the relationship to the biophysical properties of the proteome has begun to offer new insights and capabilities.     

蛋白质折叠机理的理论研究

简要综述了近年来蛋白质折叠机理的理论研究。首先回顾了蛋白质折叠理论的发展历程,然后对折叠中间体的研究现状作了较详细的介绍。同时,对折叠机理理论研究中的几种理论模型和模拟算法作了细致评述,分析了其现状和存在的问题。最后,总结和讨论了折叠机理理论研究的现存问题及研究热点,并展望了该领域研究的发展趋势。     

Matching simulation and experiment: a new simplified model for simulating protein folding.

Simulations of simplified protein folding models have provided much insight into solving the protein folding problem. We propose here a new off-lattice bead model, capable of simulating several different fold classes of small proteins. We present the sequence for an alpha/beta protein resembling the IgG-binding proteins L and G. The thermodynamics of the folding process for this model are characterized using the multiple multihistogram method combined with constant-temperature Langevin simulations. The folding is shown to be highly cooperative, with chain collapse nearly accompanying folding. Two parallel folding pathways are shown to exist on the folding free energy landscape. One pathway contains an intermediate--similar to experiments on protein G, and one pathway contains no intermediates-similar to experiments on protein L. The folding kinetics are characterized by tabulating mean-first passage times, and we show that the onset of glasslike kinetics occurs at much lower temperatures than the folding temperature. This model is expected to be useful in many future contexts: investigating questions of the role of local versus nonlocal interactions in various fold classes, addressing the effect of sequence mutations affecting secondary structure propensities, and providing a computationally feasible model for studying the role of solvation forces in protein folding.     

Machine Learning: How Much Does It Tell about Protein Folding Rates?

The prediction of protein folding rates is a necessary step towards understanding the principles of protein folding. Due to the increasing amount of experimental data, numerous protein folding models and predictors of protein folding rates have been developed in the last decade. The problem has also attracted the attention of scientists from computational fields, which led to the publication of several machine learning-based models to predict the rate of protein folding. Some of them claim to predict the logarithm of protein folding rate with an accuracy greater than 90%. However, there are reasons to believe that such claims are exaggerated due to large fluctuations and overfitting of the estimates. When we confronted three selected published models with new data, we found a much lower predictive power than reported in the original publications. Overly optimistic predictive powers appear from violations of the basic principles of machine-learning. We highlight common misconceptions in the studies claiming excessive predictive power and propose to use learning curves as a safeguard against those mistakes. As an example, we show that the current amount of experimental data is insufficient to build a linear predictor of logarithms of folding rates based on protein amino acid composition.     

Quantitative analysis of the effects of photoswitchable distance constraints on the structure of a globular protein

Photoswitchable distance constraints in the form of photoisomerizable chemical cross-links offer a general approach to the design of reversibly photocontrolled proteins. To apply these effectively, however, one must have guidelines for the choice of cross-linker structure and cross-linker attachment sites. Here we investigate the effects of varying cross-linker structure on the photocontrol of folding of the Fyn SH3 domain, a well-studied model protein. We develop a theoretical framework based on an explicit-chain model of protein folding, modified to include detailed model linkers, that allows prediction of the effect of a given linker on the free energy of folding of a protein. Using this framework, we were able to quantitatively explain the experimental result that a longer, but somewhat flexible, cross-linker is less destabilizing to the folded state than a shorter more rigid cross-linker. The models also suggest how misfolded states may be generated by cross-linking, providing a rationale for altered dynamics seen in nuclear magnetic resonance analyses of these proteins. The theoretical framework is readily portable to any protein of known folded state structure and thus can be used to guide the design of photoswitchable proteins generally.     

Atomistic molecular simulations of protein folding

Theory and experiment have provided answers to many of the fundamental questions of protein folding; a remaining challenge is an accurate, high-resolution picture of folding mechanism. Atomistic molecular simulations with explicit solvent are the most promising method for providing this information, by accounting more directly for the physical interactions that stabilize proteins. Although simulations of folding with such force fields are extremely challenging, they have become feasible as a result of recent advances in computational power, accuracy of the energy functions or 'force fields', and methods for improving sampling of folding events. I review the recent progress in these areas, and highlight future challenges and questions that we may hope to address with these methods. I also attempt to place atomistic models into the context of the energy landscape view of protein folding, and coarse-grained simulations.     

Mechanisms of protein folding

Understanding the mechanism by which a polypeptide chain folds into its native structure is a central problem of modern biophysics. The collaborative efforts of experimental and theoretical studies recently raised the tantalizing possibility to define a unifying mechanism for protein folding. In this review we summarize some of these intriguing advances and analyze them together with a discussion on the new findings concerning the so-called downhill folding.     

Models of the structure and voltage-gating mechanism of the shaker K+ channel

In the preceding, accompanying article, we present models of the structure and voltage-dependent gating mechanism of the KvAP bacterial K+ channel that are based on three types of evidence: crystal structures of portions of the KvAP protein, theoretical modeling criteria for membrane proteins, and biophysical studies of the properties of native and mutated voltage-gated channels. Most of the latter experiments were performed on the Shaker K+ channel. Some of these data are difficult to relate directly to models of the KvAP channel's structure due to differences in the Shaker and KvAP sequences. We have dealt with this problem by developing new models of the structure and gating mechanism of the transmembrane and extracellular portions of the Shaker channel. These models are consistent with almost all of the biophysical data. In contrast, much of the experimental data are incompatible with the "paddle" model of gating that was proposed when the KvAP crystal structures were first published. The general folding pattern and gating mechanisms of our current models are similar to some of our earlier models of the Shaker channel.     

Protein folding in the post-genomic era

Protein folding is a topic of fundamental interest since it concerns the mechanisms by which the genetic message is translated into the three-dimensional and functional structure of proteins. In these post-genomic times, the knowledge of the fundamental principles are required in the exploitation of the information contained in the increasing number of sequenced genomes. Protein folding also has practical applications in the understanding of different pathologies and the development of novel therapeutics to prevent diseases associated with protein misfolding and aggregation. Significant advances have been made ranging from the Anfinsen postulate to the "new view" which describes the folding process in terms of an energy landscape. These new insights arise from both theoretical and experimental studies. The problem of folding in the cellular environment is briefly discussed. The modern view of misfolding and aggregation processes that are involved in several pathologies such as prion and Alzheimer diseases. Several approaches of structure prediction, which is a very active field of research, are described.     

Quantifying kinetic paths of protein folding

We propose a new approach to activated protein folding dynamics via a diffusive path integral framework. The important issues of kinetic paths in this situation can be directly addressed. This leads to the identification of the kinetic paths of the activated folding process, and provides a direct tool and language for the theoretical and experimental community to understand the problem better. The kinetic paths giving the dominant contributions to the long-time folding activation dynamics can be quantitatively determined. These are shown to be the instanton paths. The contributions of these instanton paths to the kinetics lead to the "bell-like" shape folding rate dependence on temperature, which is in good agreement with folding kinetic experiments and simulations. The connections to other approaches as well as the experiments of the protein folding kinetics are discussed.     

A critical assessment of the topomer search model of protein folding using a continuum explicit-chain model with extensive conformational sampling

Recently, a series of closely related theoretical constructs termed the "topomer search model" (TSM) has been proposed for the folding mechanism of small, single-domain proteins. A basic assumption of the proposed scenarios is that the rate-limiting step in folding is an essentially unbiased, diffusive search for a conformational state called the native topomer defined by an overall native-like topological pattern. Successes in correlating TSM-predicted folding rates with that of real proteins have been interpreted as experimental support for the model. To better delineate the physics entailed, key TSM concepts are examined here using extensive Langevin dynamics simulations of continuum C(alpha) chain models. The theoretical native topomers of four experimentally well-studied two-state proteins are characterized. Consistent with the TSM perspective, we found that the sizes of the native topomers increase with experimental folding rate. However, a careful determination of the corresponding probabilities that the native topomers are populated during a random search fails to reproduce the previously predicted folding rates. Instead, our results indicate that an unbiased TSM search for the native topomer amounts to a Levinthal-like process that would take an impossibly long average time to complete. Furthermore, intraprotein contacts in all four native topomers considered exhibit no apparent correlation with the experimental phi-values determined from the folding kinetics of these proteins. Thus, the present findings suggest that certain basic, generic yet essential energetic features in protein folding are not accounted for by TSM scenarios to date.     

Matching theory and experiment in protein folding.

There has been considerable progress made over the past year in linking experimental and theoretical approaches to protein folding. Recent results from several independent lines of investigation suggest that protein folding mechanisms and landscapes are largely determined by the topology of the native state and are relatively insensitive to details of the interatomic interactions. This dependence on low-resolution structural features, rather than high-resolution detail, suggests that it should be possible to describe the fundamental physics of the folding process using relatively low-resolution models. Recent experiments have set benchmarks for testing new models and progress has been made in developing theoretical models for interpreting and predicting experimental results.     

A comprehensive database of verified experimental data on protein folding kinetics

Insights into protein folding rely increasingly on the synergy between experimental and theoretical approaches. Developing successful computational models requires access to experimental data of sufficient quantity and high quality. We compiled folding rate constants for what initially appeared to be 184 proteins from 15 published collections/web databases. To generate the highest confidence in the dataset, we verified the reported lnk_f value and exact experimental construct and conditions from the original experimental report(s). The resulting comprehensive database of 126 verified entries, ACPro, will serve as a freely accessible resource ( https://www.ats.amherst.edu/protein/ ) for the protein folding community to enable confident testing of predictive models. In addition, we provide a streamlined submission form for researchers to add new folding kinetics results, requiring specification of all the relevant experimental information according to the standards proposed in 2005 by the protein folding consortium organized by Plaxco. As the number and diversity of proteins whose folding kinetics are studied expands, our curated database will enable efficient and confident incorporation of new experimental results into a standardized collection. This database will support a more robust symbiosis between experiment and theory, leading ultimately to more rapid and accurate insights into protein folding, stability, and dynamics.     

Kinetics analysis methods for approximate folding landscapes

MOTIVATION: Protein motions play an essential role in many biochemical processes. Lab studies often quantify these motions in terms of their kinetics such as the speed at which a protein folds or the population of certain interesting states like the native state. Kinetic metrics give quantifiable measurements of the folding process that can be compared across a group of proteins such as a wild-type protein and its mutants. RESULTS: We present two new techniques, map-based master equation solution and map-based Monte Carlo simulation, to study protein kinetics through folding rates and population kinetics from approximate folding landscapes, models called maps. From these two new techniques, interesting metrics that describe the folding process, such as reaction coordinates, can also be studied. In this article we focus on two metrics, formation of helices and structure formation around tryptophan residues. These two metrics are often studied in the lab through circular dichroism (CD) spectra analysis and tryptophan fluorescence experiments, respectively. The approximated landscape models we use here are the maps of protein conformations and their associated transitions that we have presented and validated previously. In contrast to other methods such as the traditional master equation and Monte Carlo simulation, our techniques are both fast and can easily be computed for full-length detailed protein models. We validate our map-based kinetics techniques by comparing folding rates to known experimental results. We also look in depth at the population kinetics, helix formation and structure near tryptophan residues for a variety of proteins. AVAILABILITY: We invite the community to help us enrich our publicly available database of motions and kinetics analysis by submitting to our server: http://parasol.tamu.edu/foldingserver/.     

Combinatorial docking approach for structure prediction of large proteins and multi-molecular assemblies

Protein folding and protein binding are similar processes. In both, structural units combinatorially associate with each other. In the case of folding, we mostly handle relatively small units, building blocks or domains, that are covalently linked. In the case of multi-molecular binding, the subunits are relatively large and are associated only by non-covalent bonds. Experimentally, the difficulty in the determination of the structures of such large assemblies increases with the complex size and the number of components it contains. Computationally, the prediction of the structures of multi-molecular complexes has largely not been addressed, probably owing to the magnitude of the combinatorial complexity of the problem. Current docking algorithms mostly target prediction of pairwise interactions. Here our goal is to predict the structures of multi-unit associations, whether these are chain-connected as in protein folding, or separate disjoint molecules in the assemblies. We assume that the structures of the single units are known, either through experimental determination or modeling. Our aim is to combinatorially assemble these units to predict their structure. To address this problem we have developed CombDock. CombDock is a combinatorial docking algorithm for the structural units assembly problem. Below, we briefly describe the algorithm and present examples of its various applications to folding and to multi-molecular assemblies. To test the robustness of the algorithm, we use inaccurate models of the structural units, derived either from crystal structures of unbound molecules or from modeling of the target sequences. The algorithm has been able to predict near-native arrangements of the input structural units in almost all of the cases, suggesting that a combinatorial approach can overcome the imperfect shape complementarity caused by the inaccuracy of the models. In addition, we further show that through a combinatorial docking strategy it is possible to enhance the predictions of pairwise interactions involved in a multi-molecular assembly.     

The evolutionary landscape of functional model proteins.

To study the distinct influences of structure and function on evolution, we propose a minimalist model for proteins with binding pockets, called functional model proteins, based on a shifted-HP model on a two-dimensional square lattice. These model proteins are not maximally compact and contain an empty lattice site surrounded by at least three nearest neighbors, thus providing a binding pocket. Functional model proteins possess a unique native state, cooperative folding and tolerance to mutation. Due to the explicit functionality in these models (by design), we have been able to explore their fitness or evolutionary landscapes, as characterized by the size and distribution of homologous families and by the complexity of the inter-relatedness of the functional model proteins. Mindful that these minimalist models are highly idealized and two-dimensional, functional model proteins should nevertheless provide a useful means for exploring the constraints of maintaining structure and function on the evolution of proteins.