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.     

Finding the needle in the haystack: towards solving the protein-folding problem computationally

Prediction of protein tertiary structures from amino acid sequence and understanding the mechanisms of how proteins fold, collectively known as “the protein folding problem,” has been a grand challenge in molecular biology for over half a century. Theories have been developed that provide us with an unprecedented understanding of protein folding mechanisms. However, computational simulation of protein folding is still difficult, and prediction of protein tertiary structure from amino acid sequence is an unsolved problem. Progress toward a satisfying solution has been slow due to challenges in sampling the vast conformational space and deriving sufficiently accurate energy functions. Nevertheless, several techniques and algorithms have been adopted to overcome these challenges, and the last two decades have seen exciting advances in enhanced sampling algorithms, computational power and tertiary structure prediction methodologies. This review aims at summarizing these computational techniques, specifically conformational sampling algorithms and energy approximations that have been frequently used to study protein-folding mechanisms or to de novo predict protein tertiary structures. We hope that this review can serve as an overview on how the protein-folding problem can be studied computationally and, in cases where experimental approaches are prohibitive, help the researcher choose the most relevant computational approach for the problem at hand. We conclude with a summary of current challenges faced and an outlook on potential future directions.     

Large loop conformation sampling using the activation relaxation technique, ART-nouveau method

We present an adaptation of the ART-nouveau energy surface sampling method to the problem of loop structure prediction. This method, previously used to study protein folding pathways and peptide aggregation, is well suited to the problem of sampling the conformation space of large loops by targeting probable folding pathways instead of sampling exhaustively that space. The number of sampled conformations needed by ART nouveau to find the global energy minimum for a loop was found to scale linearly with the sequence length of the loop for loops between 8 and about 20 amino acids. Considering the linear scaling dependence of the computation cost on the loop sequence length for sampling new conformations, we estimate the total computational cost of sampling larger loops to scale quadratically compared to the exponential scaling of exhaustive search methods.     

Novel approach for alpha-helical topology prediction in globular proteins: generation of interhelical restraints

The protein folding problem represents one of the most challenging problems in computational biology. Distance constraints and topology predictions can be highly useful for the folding problem in reducing the conformational space that must be searched by deterministic algorithms to find a protein structure of minimum conformational energy. We present a novel optimization framework for predicting topological contacts and generating interhelical distance restraints between hydrophobic residues in alpha-helical globular proteins. It should be emphasized that since the model does not make assumptions about the form of the helices, it is applicable to all alpha-helical proteins, including helices with kinks and irregular helices. This model aims at enhancing the ASTRO-FOLD protein folding approach of Klepeis and Floudas (Journal of Computational Chemistry 2003;24:191-208), which finds the structure of global minimum conformational energy via a constrained nonlinear optimization problem. The proposed topology prediction model was evaluated on 26 alpha-helical proteins ranging from 2 to 8 helices and 35 to 159 residues, and the best identified average interhelical distances corresponding to the predicted contacts fell below 11 A in all 26 of these systems. Given the positive results of applying the model to several protein systems, the importance of interhelical hydrophobic-to-hydrophobic contacts in determining the folding of alpha-helical globular proteins is highlighted.     

Ab initio protein folding

Ab initio protein folding methods have been developing rapidly over the past few years and, at the last Critical assessment of methods of protein structure prediction (CASP) meeting, it was shown that important progress has been made in generating structure from sequence. Both methods based on statistical potentials and methods using physics-based potentials have shown improvements. Most current methods use statistics-based potentials and the development of these is ongoing. Additionally, the inclusion of multiple sequence data in the algorithms in order to aid in finding the native structure is a common theme. The use of physics-based potentials is less developed, which means that less progress has been made in understanding why a sequence forms a structure.     

一种在格点模型上模拟蛋白质折叠结构的优化算法

蛋白质折叠问题是生物信息学中一个经典的多项式复杂程度的非确定性(non-deterministic polynomial,NP)难度问题.势能曲面变平法(ELP)是一种启发式的全局优化算法.通过对ELP方法中的直方图函数提出一种新的更新机制,并将基于贪心策略的初始构象的产生,基于牵引移动的邻域搜索策略与ELP方法相结合,为面心立方体(FCC)格点模型的蛋白质折叠问题提出一种改进的势能曲面变平(ELP+)算法.采用文献中9条常用序列作为测试集.对于每条序列,ELP+算法均能找到与文献中的算法所得到的最低能量相等或更低的能量.实验结果表明,ELP+算法是求解FCC格点模型的蛋白质折叠问题的一种有效算法.     

Generalized-ensemble algorithms for molecular simulations of biopolymers.

In complex systems with many degrees of freedom such as peptides and proteins, there exists a huge number of local-minimum-energy states. Conventional simulations in the canonical ensemble are of little use, because they tend to get trapped in states of these energy local minima. A simulation in generalized ensemble performs a random walk in potential energy space and can overcome this difficulty. From only one simulation run, one can obtain canonical-ensemble averages of physical quantities as functions of temperature by the single-histogram and/or multiple-histogram reweighting techniques. In this article we review uses of the generalized-ensemble algorithms in biomolecular systems. Three well-known methods, namely, multicanonical algorithm, simulated tempering, and replica-exchange method, are described first. Both Monte Carlo and molecular dynamics versions of the algorithms are given. We then present three new generalized-ensemble algorithms that combine the merits of the above methods. The effectiveness of the methods for molecular simulations in the protein folding problem is tested with short peptide systems.     

Protein folding: from the levinthal paradox to structure prediction.

This article is a personal perspective on the developments in the field of protein folding over approximately the last 40 years. In addition to its historical aspects, the article presents a view of the principles of protein folding with particular emphasis on the relationship of these principles to the problem of protein structure prediction. It is argued that despite much that is new, the essential elements of our current understanding of protein folding were anticipated by researchers many years ago. These elements include the recognition of the central importance of the polypeptide backbone as a determinant of protein conformation, hierarchical protein folding, and multiple folding pathways. Important areas of progress include a detailed characterization of the folding pathways of a number of proteins and a fundamental understanding of the physical chemical forces that determine protein stability. Despite these developments, fold prediction algorithms still encounter difficulties in identifying the correct fold for a given sequence. This may be due to the possibility that the free energy differences between at least a few alternate conformations of many proteins are not large. Significant progress in protein structure prediction has been due primarily to the explosive growth of sequence and structural databases. However, further progress is likely to depend in part on the ability to combine information available from databases with principles and algorithms derived from physical chemical studies of protein folding. An approach to the integration of the two areas is outlined with specific reference to the PrISM program that is a fully integrated sequence/structural-analysis/fold-recognition/homology model building software system.     

The Topology of the Energy Landscapes of Macromolecules in the Torsion Angle Space and the Principle of the Minimum Energy Dissipation Rate in Conformational Relaxation

This article discusses some basic problems of structural biology and molecular dynamics simulation methods that need to be taken into account when considering, the protein folding problem, and prediction of 3D-structures for biopolymers. A multidimensional Fourier series expansions were formulated for the energy landscapes of the systems with conformational mobility, These energy landscape representations are correct from the viewpoint of the topology of the macromolecule configuration spaces. The problem of the single global minimum on the energy landscape for proteins is discussed and is formulated in tems of phase rules for the component of Fourier expansions. This rule is formally similar to the problem of diffraction on a multidimensional cubic lattice. The calibration of biopolymer force fields and their correspondence to topologically correct energy landscapes are discussed. Equations of motion were obtained in a matrix form for the relaxation of a representative point position on a multidimensional potential energy surface. The solutions of the equations for conformational relaxation were shown to obey the principle of the minimum energy dissipation rate at a given relaxation rate of potential energy (or folding rate).     

All-atom replica exchange molecular simulation of protein BBL

Downhill folding is one of the most important predictions of energy landscape theory. Recently, the Escherichia coli 2-oxoglutarate dehydrogenase PSBD was described as a first example of global downhill folding (Garcia-Mira et al., Science 2002;298:2191), classification that has been later subject of significant controversy. To help resolve this problem, by using intensive all-atom simulation with explicit water model and the replica exchange method, we sample the phase space of protein BBL and depict the free energy landscape. We give an estimate of the free energy barrier height of 1-2 k(B)T, dependent on the way the energy landscape is projected. We also study the conformational distribution of the transition region and find that the three helices generally take the similar positions as that in the native states whereas their spatial orientations show large variability. We further detect the inconsistency between different signals by individually fitting the thermal denaturation curves of five structural features using two-state model, which gives a wide spread melting temperature of 19 K. All of these features are consistent with a picture of folding with very low cooperativities. Compared with the experimental data (Sadqi et al., Nature 2006; 442:317), our results indicate that the Naf-BBL (pH5.3) may have an even lower barrier height and cooperativity.     

Improved energy bound accuracy enhances the efficiency of continuous protein design

Flexibility and dynamics are important for protein function and a protein's ability to accommodate amino acid substitutions. However, when computational protein design algorithms search over protein structures, the allowed flexibility is often reduced to a relatively small set of discrete side‐chain and backbone conformations. While simplifications in scoring functions and protein flexibility are currently necessary to computationally search the vast protein sequence and conformational space, a rigid representation of a protein causes the search to become brittle and miss low‐energy structures. Continuous rotamers more closely represent the allowed movement of a side chain within its torsional well and have been successfully incorporated into the protein design framework to design biomedically relevant protein systems. The use of continuous rotamers in protein design enables algorithms to search a larger conformational space than previously possible, but adds additional complexity to the design search. To design large, complex systems with continuous rotamers, new algorithms are needed to increase the efficiency of the search. We present two methods, PartCR and HOT, that greatly increase the speed and efficiency of protein design with continuous rotamers. These methods specifically target the large errors in energetic terms that are used to bound pairwise energies during the design search. By tightening the energy bounds, additional pruning of the conformation space can be achieved, and the number of conformations that must be enumerated to find the global minimum energy conformation is greatly reduced. Proteins 2015; 83:1151–1164. © 2015 Wiley Periodicals, Inc.     

基于HP模型的大麻素受体CB2折叠研究

Cannabinoid receptor Type 2(简称CB2)是大麻素受体的一种亚型,因为其无中枢神经副作用,不会产生成瘾性及耐受性,显示出了非常好的开发前景和潜在的应用价值。其作为免疫调节剂、神经保护剂和抗癌药等将具有巨大市场价值。目前,CB2蛋白的空间结构还未被测定出来,对于CB2的折叠问题研究也开展的较少,为了研究大麻素受体亚型蛋白CB2的折叠问题以及方便更多的研究人员对CB2空间结构和相关药理特性的研究,本文提出了一种基于HP模型的折叠求解方法。通过使用回溯机制和蒙特卡罗方法对此优化问题进行求解,算法可有效的在全局范围内进行寻找最优解,避免了掉入局部最优问题。实验结果表明,本文方法获取的CB2蛋白空间构象具有较低的能量值,折叠情况较好。     

Protein folding: progress made and promises ahead

Over the past 25 years, enormous breakthroughs have been made in understanding protein folding mechanisms. We have now reached an exciting stage, with consensuses beginning to emerge that combine both theoretical and experimental approaches. In addition, new fields have emerged and burgeoned, including in vivo folding and the study of protein misfolding diseases. In today's post-genomic world, understanding protein folding has never been more important and the topic has wide-ranging impact in fields from structural biology to materials science.     

Dynamics of protein folding: probing the kinetic network of folding-unfolding transitions with experiment and theory

The problem of spontaneous folding of amino acid chains into highly organized, biologically functional three-dimensional protein structures continues to challenge the modern science. Understanding how proteins fold requires characterization of the underlying energy landscapes as well as the dynamics of the polypeptide chains in all stages of the folding process. In recent years, important advances toward these goals have been achieved owing to the rapidly growing interdisciplinary interest and significant progress in both experimental techniques and theoretical methods. Improvements in the experimental time resolution led to determination of the timescales of the important elementary events in folding, such as formation of secondary structure and tertiary contacts. Sensitive single molecule methods made possible probing the distributions of the unfolded and folded states and following the folding reaction of individual protein molecules. Discovery of proteins that fold in microseconds opened the possibility of atomic-level theoretical simulations of folding and their direct comparisons with experimental data, as well as of direct experimental observation of the barrier-less folding transition. The ultra-fast folding also brought new questions, concerning the intrinsic limits of the folding rates and experimental signatures of barrier-less "downhill" folding. These problems will require novel approaches for even more detailed experimental investigations of the folding dynamics as well as for the analysis of the folding kinetic data. For theoretical simulations of folding, a main challenge is how to extract the relevant information from overwhelmingly detailed atomistic trajectories. New theoretical methods have been devised to allow a systematic approach towards a quantitative analysis of the kinetic network of folding-unfolding transitions between various configuration states of a protein, revealing the transition states and the associated folding pathways at multiple levels, from atomistic to coarse-grained representations. This article is part of a Special Issue entitled: Protein Dynamics: Experimental and Computational Approaches.     

Computational protein design and large-scale assessment by I-TASSER structure assembly simulations

Protein design aims at designing new protein molecules of desired structure and functionality. One of the major obstacles to large-scale protein design are the extensive time and manpower requirements for experimental validation of designed sequences. Recent advances in protein structure prediction have provided potentials for an automated assessment of the designed sequences via folding simulations. We present a new protocol for protein design and validation. The sequence space is initially searched by Monte Carlo sampling guided by a public atomic potential, with candidate sequences selected by the clustering of sequence decoys. The designed sequences are then assessed by I-TASSER folding simulations, which generate full-length atomic structural models by the iterative assembly of threading fragments. The protocol is tested on 52 nonhomologous single-domain proteins, with an average sequence identity of 24% between the designed sequences and the native sequences. Despite this low sequence identity, three-dimensional models predicted for the first designed sequence have an RMSD of < 2 Å to the target structure in 62% of cases. This percentage increases to 77% if we consider the three-dimensional models from the top 10 designed sequences. Such a striking consistency between the target structure and the structural prediction from nonhomologous sequences, despite the fact that the design and folding algorithms adopt completely different force fields, indicates that the design algorithm captures the features essential to the global fold of the target. On average, the designed sequences have a free energy that is 0.39 kcal/(mol residue) lower than in the native sequences, potentially affording a greater stability to synthesized target folds.     

Computational Modeling of Proteins based on Cellular Automata: A Method of HP Folding Approximation

The design of a protein folding approximation algorithm is not straightforward even when a simplified model is used. The folding problem is a combinatorial problem, where approximation and heuristic algorithms are usually used to find near optimal folds of proteins primary structures. Approximation algorithms provide guarantees on the distance to the optimal solution. The folding approximation approach proposed here depends on two-dimensional cellular automata to fold proteins presented in a well-studied simplified model called the hydrophobic–hydrophilic model. Cellular automata are discrete computational models that rely on local rules to produce some overall global behavior. One-third and one-fourth approximation algorithms choose a subset of the hydrophobic amino acids to form H–H contacts. Those algorithms start with finding a point to fold the protein sequence into two sides where one side ignores H’s at even positions and the other side ignores H’s at odd positions. In addition, blocks or groups of amino acids fold the same way according to a predefined normal form. We intend to improve approximation algorithms by considering all hydrophobic amino acids and folding based on the local neighborhood instead of using normal forms. The CA does not assume a fixed folding point. The proposed approach guarantees one half approximation minus the H–H endpoints. This lower bound guaranteed applies to short sequences only. This is proved as the core and the folds of the protein will have two identical sides for all short sequences.     

Enhanced hybrid search algorithm for protein structure prediction using the 3D-HP lattice model

The problem of protein structure prediction in the hydrophobic-polar (HP) lattice model is the prediction of protein tertiary structure. This problem is usually referred to as the protein folding problem. This paper presents a method for the application of an enhanced hybrid search algorithm to the problem of protein folding prediction, using the three dimensional (3D) HP lattice model. The enhanced hybrid search algorithm is a combination of the particle swarm optimizer (PSO) and tabu search (TS) algorithms. Since the PSO algorithm entraps local minimum in later evolution extremely easily, we combined PSO with the TS algorithm, which has properties of global optimization. Since the technologies of crossover and mutation are applied many times to PSO and TS algorithms, so enhanced hybrid search algorithm is called the MCMPSO-TS (multiple crossover and mutation PSO-TS) algorithm. Experimental results show that the MCMPSO-TS algorithm can find the best solutions so far for the listed benchmarks, which will help comparison with any future paper approach. Moreover, real protein sequences and Fibonacci sequences are verified in the 3D HP lattice model for the first time. Compared with the previous evolutionary algorithms, the new hybrid search algorithm is novel, and can be used effectively to predict 3D protein folding structure. With continuous development and changes in amino acids sequences, the new algorithm will also make a contribution to the study of new protein sequences.     

Combinatorial pattern discovery approach for the folding trajectory analysis of a beta-hairpin

The study of protein folding mechanisms continues to be one of the most challenging problems in computational biology. Currently, the protein folding mechanism is often characterized by calculating the free energy landscape versus various reaction coordinates, such as the fraction of native contacts, the radius of gyration, RMSD from the native structure, and so on. In this paper, we present a combinatorial pattern discovery approach toward understanding the global state changes during the folding process. This is a first step toward an unsupervised (and perhaps eventually automated) approach toward identification of global states. The approach is based on computing biclusters (or patterned clusters)-each cluster is a combination of various reaction coordinates, and its signature pattern facilitates the computation of the Z-score for the cluster. For this discovery process, we present an algorithm of time complexity c in RO((N + nm) log n), where N is the size of the output patterns and (n x m) is the size of the input with n time frames and m reaction coordinates. To date, this is the best time complexity for this problem. We next apply this to a beta-hairpin folding trajectory and demonstrate that this approach extracts crucial information about protein folding intermediate states and mechanism. We make three observations about the approach: (1) The method recovers states previously obtained by visually analyzing free energy surfaces. (2) It also succeeds in extracting meaningful patterns and structures that had been overlooked in previous works, which provides a better understanding of the folding mechanism of the beta-hairpin. These new patterns also interconnect various states in existing free energy surfaces versus different reaction coordinates. (3) The approach does not require calculating the free energy values, yet it offers an analysis comparable to, and sometimes better than, the methods that use free energy landscapes, thus validating the choice of reaction coordinates. (An abstract version of this work was presented at the 2005 Asia Pacific Bioinformatics Conference [1].).     

Determination of three-dimensional structures of proteins from interproton distance data by dynamical simulated annealing from a random array of atoms. Circumventing problems associated with folding

A new real space method, based on the principles of simulated annealing, is presented for determining protein structures on the basis of interproton distance restraints derived from NMR data. The method circumvents the folding problem associated with all real space methods described to date, by starting from a completely random array of atoms and introducing the force constants for the covalent, interproton distance and repulsive van der Waals terms in the target function appropriately. The system is simulated at high temperature by solving Newton's equations of motion. As the values of all force constants are very low during the early stages of the simulation, energy barriers between different folds of the protein can be overcome, and the global minimum of the target function is reliably located. Further, because the atoms are initially only weakly coupled, they can move essentially independently to satisfy the restraints. The method is illustrated using two examples of small proteins, namely crambin (46 residues) and potato carboxypeptidase inhibitor (39 residues).     

Network properties of protein-decoy structures

Convergence of the vast sequence space of proteins into a highly restricted fold/conformational space suggests a simple yet unique underlying mechanism of protein folding that has been the subject of much debate in the last several decades. One of the major challenges related to the understanding of protein folding or in silico protein structure prediction is the discrimination of non-native structures/decoys from the native structure. Applications of knowledge-based potentials to attain this goal have been extensively reported in the literature. Also, scoring functions based on accessible surface area and amino acid neighbourhood considerations were used in discriminating the decoys from native structures. In this article, we have explored the potential of protein structure network (PSN) parameters to validate the native proteins against a large number of decoy structures generated by diverse methods. We are guided by two principles: (a) the PSNs capture the local properties from a global perspective and (b) inclusion of non-covalent interactions, at all-atom level, including the side-chain atoms, in the network construction accommodates the sequence dependent features. Several network parameters such as the size of the largest cluster, community size, clustering coefficient are evaluated and scored on the basis of the rank of the native structures and the Z-scores. The network analysis of decoy structures highlights the importance of the global properties contributing to the uniqueness of native structures. The analysis also exhibits that the network parameters can be used as metrics to identify the native structures and filter out non-native structures/decoys in a large number of data-sets; thus also has a potential to be used in the protein ‘structure prediction’ problem.