Are residues in a protein folding nucleus evolutionarily conserved?

Protein is the working molecule of the cell, and evolution is the hallmark of life. It is important to understand how protein folding and evolution influence each other. Several studies correlating experimental measurement of residue participation in folding nucleus and sequence conservation have reached different conclusions. These studies are based on assessment of sequence conservation at folding nucleus sites using entropy or relative entropy measurement derived from multiple sequence alignment. Here we report analysis of conservation of folding nucleus using an evolutionary model alternative to entropy-based approaches. We employ a continuous time Markov model of codon substitution to distinguish mutation fixed by evolution and mutation fixed by chance. This model takes into account bias in codon frequency, bias-favoring transition over transversion, as well as explicit phylogenetic information. We measure selection pressure using the ratio omega of synonymous versus non-synonymous substitution at individual residue site. The omega-values are estimated using the PAML method, a maximum-likelihood estimator. Our results show that there is little correlation between the extent of kinetic participation in protein folding nucleus as measured by experimental phi-value and selection pressure as measured by omega-value. In addition, two randomization tests failed to show that folding nucleus residues are significantly more conserved than the whole protein, or the median omega value of all residues in the protein. These results suggest that at the level of codon substitution, there is no indication that folding nucleus residues are significantly more conserved than other residues. We further reconstruct candidate ancestral residues of the folding nucleus and suggest possible test tube mutation studies for testing folding behavior of ancient folding nucleus.     

Energy landscape and dynamics of the beta-hairpin G peptide and its isomers: Topology and sequences

We have investigated free energy landscape [MM/PBSA + normal modes entropy] of permutations in the G peptide (41-56) from the protein G B1 domain by studying six isomers corresponding to moving the hydrophobic cluster along the beta-strands (toward the turn: T1, AGEWTYDDKTFTVTET; T2, GEDTWDYATFTVTKTE; T3, GEDDWTYATFTVTKTE; toward the end: E1, WTYDDAGETKTFTVT; E2, WEYTGDDATKTETFTV; E3, WTYEGDDATKTETFTV). The free energy terms include molecular mechanics energy, Poisson-Boltzmann electrostatic solvation energy, surface area solvation energy, and conformational entropy estimated by using normal mode analysis. From the wild type to T1, then T3, and finally T2, we see a progressively changing energy landscape, toward a less stable beta-hairpin structure. Moving the hydrophobic cluster outside toward the end region causes a greater change in the energy landscape. alpha-Helical instead of a beta-hairpin structure was the most stable form for the E2 isomer. However, no matter how much the sequence changes, for all variants studied, ideal "native" beta-hairpin topologies remain as minima (regardless of whether global or local) in the energy landscape. In general, we find that the energy landscape is dependent on the hydrophobic cluster topology and on the sequence. Our present study indicates that the key is the relative conformational energies of the different conformations. Changes in the sequence strongly modulate the relative stabilities of topologically similar regions in the energy landscape, rather than redefine the topology space. This finding is consistent with a population redistribution in the process of protein folding. The limited variation of topological space, compared with the number of possible sequence changes, may relate to the observation that the number of known protein folds are far less than the sequential allowance.     

The foldability landscape of model proteins

Molecular evolution may be considered as a walk in a multidimensional fitness landscape, where the fitness at each point is associated with features such as the function, stability, and survivability of these molecules. We present a simple model for the evolution of protein sequences on a landscape with a precisely defined fitness function. We use simple lattice models to represent protein structures, with the ability of a protein sequence to fold into the structure with lowest energy, quantified as the foldability, representing the fitness of the sequence. The foldability of the sequence is characterized based on the spin glass model of protein folding. We consider evolution as a walk in this foldability landscape and study the nature of the landscape and the resulting dynamics. Selective pressure is explicitly included in this model in the form of a minimum foldability requirement. We find that different native structures are not evenly distributed in interaction space, with similar structures and structures with similar optimal foldabilities clustered together. Evolving proteins marginally fulfill the selective criteria of foldability. As the selective pressure is increased, evolutionary trajectories become increasingly confined to “neutral networks,” where the sequence and the interactions can be significantly changed while a constant structure is maintained. © 1997 John Wiley & Sons, Inc. Biopoly 42: 427–438, 1997     

A knowledge-based move set for protein folding

The free energy landscape of protein folding is rugged, occasionally characterized by compact, intermediate states of low free energy. In computational folding, this landscape leads to trapped, compact states with incorrect secondary structure. We devised a residue-specific, protein backbone move set for efficient sampling of protein-like conformations in computational folding simulations. The move set is based on the selection of a small set of backbone dihedral angles, derived from clustering dihedral angles sampled from experimental structures. We show in both simulated annealing and replica exchange Monte Carlo (REMC) simulations that the knowledge-based move set, when compared with a conventional move set, shows statistically significant improved ability at overcoming kinetic barriers, reaching deeper energy minima, and achieving correspondingly lower RMSDs to native structures. The new move set is also more efficient, being able to reach low energy states considerably faster. Use of this move set in determining the energy minimum state and for calculating thermodynamic quantities is discussed.     

Energy Landscapes of Protein Aggregation and Conformation Switching in Intrinsically Disordered Proteins

The protein folding problem was apparently solved recently by the advent of a deep learning method for protein structure prediction called AlphaFold. However, this program is not able to make predictions about the protein folding pathways. Moreover, it only treats about half of the human proteome, as the remaining proteins are intrinsically disordered or contain disordered regions. By definition these proteins differ from natively folded proteins and do not adopt a properly folded structure in solution. However these intrinsically disordered proteins (IDPs) also systematically differ in amino acid composition and uniquely often become folded upon binding to an interaction partner. These factors preclude solving IDP structures by current machine-learning methods like AlphaFold, which also cannot solve the protein aggregation problem, since this meta-folding process can give rise to different aggregate sizes and structures. An alternative computational method is provided by molecular dynamics simulations that already successfully explored the energy landscapes of IDP conformational switching and protein aggregation in multiple cases. These energy landscapes are very different from those of ‘simple’ protein folding, where one energy funnel leads to a unique protein structure. Instead, the energy landscapes of IDP conformational switching and protein aggregation feature a number of minima for different competing low-energy structures. In this review, I discuss the characteristics of these multifunneled energy landscapes in detail, illustrated by molecular dynamics simulations that elucidated the underlying conformational transitions and aggregation processes.     

Conformational heterogeneity of an equilibrium folding intermediate quantified and mapped by scanning mutagenesis

It is challenging to experimentally define an energy landscape for protein folding that comprises multiple partially unfolded states. Experimental results are often ambiguous as to whether a non-native state is conformationally homogeneous. Here, we tested an approach combining systematic mutagenesis and a Br?nsted-like analysis to reveal and quantify conformational heterogeneity of folding intermediate states. Using this method, we resolved an otherwise apparently homogeneous equilibrium folding intermediate of Borrelia burgdorferi OspA into two conformationally distinct species and determined their relative populations. Furthermore, we mapped the structural differences between these intermediate species, which are consistent with the non-native species that we previously proposed based on native-state hydrogen exchange studies. When treated as a single state, the intermediate ensemble exhibited fractional Phi-values for mutations and Hammond-type behaviors that are often observed for folding transition states. We found that a change in relative population of the two species within the intermediate ensemble explains these properties well, suggesting that fractional Phi-values and Hammond-type behaviors exhibited by folding intermediates and transition states may arise more often from conformational heterogeneity than from a single partial structure. Our results are consistent with the presence of multiple minima in a rugged energy landscape predicted from theoretical studies. The method described here provides a promising means to probe a complex folding energy landscape.     

A novel approach for large-scale polypeptide folding based on elastic networks using continuous optimization

We present a new computationally efficient method for large-scale polypeptide folding using coarse-grained elastic networks and gradient-based continuous optimization techniques. The folding is governed by minimization of energy based on Miyazawa-Jernigan contact potentials. Using this method we are able to substantially reduce the computation time on ordinary desktop computers for simulation of polypeptide folding starting from a fully unfolded state. We compare our results with available native state structures from Protein Data Bank (PDB) for a few de-novo proteins and two natural proteins, Ubiquitin and Lysozyme. Based on our simulations we are able to draw the energy landscape for a small de-novo protein, Chignolin. We also use two well known protein structure prediction software, MODELLER and GROMACS to compare our results. In the end, we show how a modification of normal elastic network model can lead to higher accuracy and lower time required for simulation.     

Statistical mechanics of protein folding by exhaustive enumeration

It is hard to construct theories for the folding of globular proteins because they are large and complicated molecules having enormous numbers of nonnative conformations and having native states that are complicated to describe. Statistical mechanical theories of protein folding are constructed around major simplifying assumptions about the energy as a function of conformation and/or simplifications of the representation of the polypeptide chain, such as one point per residue on a cubic lattice. It is not clear how the results of these theories are affected by their various simplifications. Here we take a very different simplification approach where the chain is accurately represented and the energy of each conformation is calculated by a not unreasonable empirical function. However, the set of amino acid sequences and allowed conformations is so restricted that it becomes computationally feasible to examine them all. Hence we are able to calculate melting curves for thermal denaturation as well as the detailed kinetic pathway of refolding. Such calculations are based on a novel representation of the conformations as points in an abstract 12-dimensional Euclidean conformation space. Fast folding sequences have relatively high melting temperatures, native structures with relatively low energies, small kinetic barriers between local minima, and relatively many conformations in the global energy minimum's watershed. In contrast to other folding theories, these models show no necessary relationship between fast folding and an overall funnel shape to the energy surface, or a large energy gap between the native and the lowest nonnative structure, or the depth of the native energy minimum compared to the roughness of the energy landscape. Proteins 32:425–437, 1998. © 1998 Wiley-Liss, Inc.     

Water and molecular chaperones act as weak links of protein folding networks: energy landscape and punctuated equilibrium changes point towards a game theory of proteins

Water molecules and molecular chaperones efficiently help the protein folding process. Here we describe their action in the context of the energy and topological networks of proteins. In energy terms water and chaperones were suggested to decrease the activation energy between various local energy minima smoothing the energy landscape, rescuing misfolded proteins from conformational traps and stabilizing their native structure. In kinetic terms water and chaperones may make the punctuated equilibrium of conformational changes less punctuated and help protein relaxation. Finally, water and chaperones may help the convergence of multiple energy landscapes during protein-macromolecule interactions. We also discuss the possibility of the introduction of protein games to narrow the multitude of the energy landscapes when a protein binds to another macromolecule. Both water and chaperones provide a diffuse set of rapidly fluctuating weak links (low affinity and low probability interactions), which allow the generalization of all these statements to a multitude of networks.     

Folding of Desulfovibrio desulfuricans flavodoxin is accelerated by cofactor fly-casting

Folding of cofactor-binding proteins involves ligand binding in addition to polypeptide folding. We here assess the kinetic folding/binding landscape for Desulfovibrio desulfuricans flavodoxin that coordinates an FMN cofactor. The apo-form folds in a two-step process involving a burst-phase intermediate. Studies on Tyr98Ala and Trp60Ala variants reveal that these aromatics-that stack with the FMN in the holo-form-are not participating in the apo-protein folding pathway. However, these residues are essential for FMN interactions with the unfolded protein during refolding of holo-flavodoxin. Unfolding of wild-type holo-flavodoxin is coupled to FMN dissociation whereas for Tyr98Ala and Trp60Ala holo-variants, FMN dissociates before polypeptide unfolding. Both variants refold as apo-proteins before FMN rebinds. In sharp contrast, refolding of unfolded wild-type holo-flavodoxin is over an order of magnitude faster than that of the apo-form, the pathway does not include a burst-phase intermediate, and the speed is independent of FMN excess ratio. These observations demonstrate that FMN binds rapidly to the unfolded polypeptide and guides folding straight to the native state. As this path to functional D. desulfuricans holo-flavodoxin is faster than if the cofactor binds to pre-folded apo-protein, this is one of few examples where molecular recognition via a "fly-casting" mechanism is kinetically favored.     

Thermodynamic and kinetic exploration of the energy landscape of Borrelia burgdorferi OspA by native-state hydrogen exchange

We report a native-state hydrogen-exchange (HX) method to simultaneously obtain both thermodynamic and kinetic information on the formation of multiple excited states in a folding energy landscape. Our method exploits the inherent dispersion and pH dependence of the intrinsic HX rates to cover both the EX2 (thermodynamic) and EX1 (kinetic) regimes. At each concentration of denaturant, HX measurements are performed over a range of pH values. Using this strategy, we dissected Borrelia burgdorferi OspA, a predominantly beta-sheet protein containing a unique single-layer beta-sheet, into five cooperative units and postulated excited states predominantly responsible for HX. More importantly, we determined the interconversion rates between these excited states and the native state. The use of both thermodynamic and kinetic information from native-state HX enabled us to construct a folding landscape of this 28kDa protein, including local minima and maxima, and to discriminate on-pathway and off-pathway intermediates. This method, which we term EX2/EX1 HX, should be a powerful tool for characterizing the complex folding mechanisms exhibited by the majority of proteins.     

基于新杂合进化算法的蛋白质折叠计算

蛋白质能量最小化是蛋白质折叠的重要内容。用于蛋白质折叠的新的杂合进化算法结合了交叉和柯西变异。基于toy模型的蛋白质能量最小化算例表明,这个新的杂合进化算法是有效的。     

On the Prediction of Folding Nuclei in Globular Proteins

An approach to predicting folding nuclei in globular proteins with known three-dimensional structures is proposed. This approach is based on the pinpointing of the lowest saddle points on the barrier between the unfolded state and native structure on the free-energy landscape of a protein chain; the proposed technique uses the dynamic programming method. A comparison of calculation results with experimental data on the folding nuclei of 21 proteins shows that the model provides good Φ value predictions for protein structures determined by X-ray analysis and, less successfully, in structures determined by nuclear magnetic resonance. Consideration of the whole ensemble of transition states provides a better prediction of folding nuclei than consideration of only transition states with lowest free energies. In addition, we predict the location of folding nuclei in three-dimensional structures of some proteins whose folding kinetics is being studied, but there is no experimental evidence concerning their folding nuclei.     

Origins of globular structure in proteins

Since natural proteins are the products of a long evolutionary process, the structural properties of present-day proteins should depend not only on physico-chemical constraints, but also on evolutionary constraints. Here we propose a model for protein evolution, in which membranes play a key role as a scaffold for supporting the gradual evolution from flexible polypeptides to well-folded proteins. We suggest that the folding process of present-day globular proteins is a relic of this putative evolutionary process. To test the hypothesis that membranes once acted as a cradle for the folding of globular proteins, extensive research on membrane proteins and the interactions of globular proteins with membranes will be required.     

Distinguishing between sequential and nonsequentially folded proteins: implications for folding and misfolding.

We describe here an algorithm for distinguishing sequential from nonsequentially folding proteins. Several experiments have recently suggested that most of the proteins that are synthesized in the eukaryotic cell may fold sequentially. This proposed folding mechanism in vivo is particularly advantageous to the organism. In the absence of chaperones, the probability that a sequentially folding protein will misfold is reduced significantly. The problem we address here is devising a procedure that would differentiate between the two types of folding patterns. Footprints of sequential folding may be found in structures where consecutive fragments of the chain interact with each other. In such cases, the folding complexity may be viewed as being lower. On the other hand, higher folding complexity suggests that at least a portion of the polypeptide backbone folds back upon itself to form three-dimensional (3D) interactions with noncontiguous portion(s) of the chain. Hence, we look at the mechanism of folding of the molecule via analysis of its complexity, that is, through the 3D interactions formed by contiguous segments on the polypeptide chain. To computationally splice the structure into consecutively interacting fragments, we either cut it into compact hydrophobic folding units or into a set of hypothetical, transient, highly populated, contiguous fragments ("building blocks" of the structure). In sequential folding, successive building blocks interact with each other from the amino to the carboxy terminus of the polypeptide chain. Consequently, the results of the parsing differentiate between sequentially vs. nonsequentially folded chains. The automated assessment of the folding complexity provides insight into both the likelihood of misfolding and the kinetic folding rate of the given protein. In terms of the funnel free energy landscape theory, a protein that truly follows the mechanism of sequential folding, in principle, encounters smoother free energy barriers. A simple sequentially folded protein should, therefore, be less error prone and fold faster than a protein with a complex folding pattern.     

Reproducible polypeptide folding and structure prediction using molecular dynamics simulations

The folding of a polypeptide from an extended state to a well-defined conformation is studied using microsecond classical molecular dynamics (MD) simulations and replica exchange molecular dynamics (REMD) simulations in explicit solvent and in vacuo. It is shown that the solvated peptide folds many times in the REMD simulations but only a few times in the conventional simulations. From the folding events in the classical simulations we estimate an approximate folding time of 1-2 micros. The REMD simulations allow enough sampling to deduce a detailed Gibbs free energy landscape in three dimensions. The global minimum of the energy landscape corresponds to the native state of the peptide as determined previously by nuclear magnetic resonance (NMR) experiments. Starting from an extended state it takes about 50 ns before the native structure appears in the REMD simulations, about an order of magnitude faster than conventional MD. The calculated melting curve is in good qualitative agreement with experiment. In vacuo, the peptide collapses rapidly to a conformation that is substantially different from the native state in solvent.     

用计算机折叠蛋白质:我们走了多远?(英文)

蛋白质折叠是现代科学最具挑战性的难题之一。Anfinsen的先驱性工作已经过去数十年了,我们对蛋白质折叠的机理仍不甚了然。但值得庆幸的是,科学工作者们在解析几个模型蛋白质的折叠机理上已经取得了明显的进展。这篇综述将主要回顾在蛋白质折叠的计算研究方面的进展。受益于计算机技术的迅猛发展,在1998年首次实现了一个微秒的全原子水平的蛋白质折叠,从2000年开始,folding@home将全球分布式计算技术应用于蛋白质折叠。在经历了数十年艰苦的努力之后,天然蛋白质亚埃精度的折叠终于在2007年成功实现。近年来,一种全新的概念开始出现,人们越来越多地用网络来解释蛋白质折叠的机理。随着分子力场的不断完善,分子模拟将会在解析蛋白质折叠的机理上起到越来越重要的作用。     

Native structure-based modeling and simulation of biomolecular systems per mouse click

Background

Molecular dynamics (MD) simulations provide valuable insight into biomolecular systems at the atomic level. Notwithstanding the ever-increasing power of high performance computers current MD simulations face several challenges: the fastest atomic movements require time steps of a few femtoseconds which are small compared to biomolecular relevant timescales of milliseconds or even seconds for large conformational motions. At the same time, scalability to a large number of cores is limited mostly due to long-range interactions. An appealing alternative to atomic-level simulations is coarse-graining the resolution of the system or reducing the complexity of the Hamiltonian to improve sampling while decreasing computational costs. Native structure-based models, also called Gō-type models, are based on energy landscape theory and the principle of minimal frustration. They have been tremendously successful in explaining fundamental questions of, e.g., protein folding, RNA folding or protein function. At the same time, they are computationally sufficiently inexpensive to run complex simulations on smaller computing systems or even commodity hardware. Still, their setup and evaluation is quite complex even though sophisticated software packages support their realization.

Results

Here, we establish an efficient infrastructure for native structure-based models to support the community and enable high-throughput simulations on remote computing resources via GridBeans and UNICORE middleware. This infrastructure organizes the setup of such simulations resulting in increased comparability of simulation results. At the same time, complete workflows for advanced simulation protocols can be established and managed on remote resources by a graphical interface which increases reusability of protocols and additionally lowers the entry barrier into such simulations for, e.g., experimental scientists who want to compare their results against simulations. We demonstrate the power of this approach by illustrating it for protein folding simulations for a range of proteins.

Conclusions

We present software enhancing the entire workflow for native structure-based simulations including exception-handling and evaluations. Extending the capability and improving the accessibility of existing simulation packages the software goes beyond the state of the art in the domain of biomolecular simulations. Thus we expect that it will stimulate more individuals from the community to employ more confidently modeling in their research.

Electronic supplementary material

The online version of this article (doi:10.1186/1471-2105-15-292) contains supplementary material, which is available to authorized users.