蛋白质结构的“限域下最低能量结构片段”假说与蛋白质进化的“石器时代”

蛋白质折叠问题被称为第二遗传密码,至今未破译;蛋白质序列的天书仍然是"句读之不知,惑之不解"。在最近工作的基础上,我们提出了蛋白质结构的"限域下最低能量结构片段"假说。这一假说指出,蛋白质中存在一些关键的长程强相互作用位点,这些位点相当于标点符号,将蛋白质序列的天书变成可读的句子(多肽片段)。这些片段的天然结构是在这些强长程相互作用位点限域下的能量最低状态。完整的蛋白质结构由这些"限域下最低能量结构片段"拼合而成,而蛋白质整体结构并不一定是全局性的能量最低状态。在蛋白质折叠过程中,局部片段的天然结构倾向性为强长程相互作用的形成提供主要基于焓效应的驱动力,而天然强长程相互作用的形成为局部片段的天然结构提供主要基于熵效应的稳定性。在蛋白质进化早期,可能存在一个"石器时代",即依附不同界面(比如岩石)的限域作用而稳定的多肽片段先进化出来,后由这些片段逐步进化(包括拼合)而成蛋白质。     

Fast and high precision algorithms for optimization in large-scale genomic problems

There are several very difficult problems related to genetic or genomic analysis that belong to the field of discrete optimization in a set of all possible orders. With n elements (points, markers, clones, sequences, etc.), the number of all possible orders is n!/2 and only one of these is considered to be the true order. A classical formulation of a similar mathematical problem is the well-known traveling salesperson problem model (TSP). Genetic analogues of this problem include: ordering in multilocus genetic mapping, evolutionary tree reconstruction, building physical maps (contig assembling for overlapping clones and radiation hybrid mapping), and others. A novel, fast and reliable hybrid algorithm based on evolution strategy and guided local search discrete optimization was developed for TSP formulation of the multilocus mapping problems. High performance and high precision of the employed algorithm named guided evolution strategy (GES) allows verification of the obtained multilocus orders based on different computing-intensive approaches (e.g., bootstrap or jackknife) for detection and removing unreliable marker loci, hence, stabilizing the resulting paths. The efficiency of the proposed algorithm is demonstrated on standard TSP problems and on simulated data of multilocus genetic maps up to 1000 points per linkage group.     

Heuristic energy landscape paving for protein folding problem in the three-dimensional HP lattice model

The protein folding problem, i.e., the prediction of the tertiary structures of protein molecules from their amino acid sequences is one of the most important problems in computational biology and biochemistry. However, the extremely difficult optimization problem arising from energy function is a key challenge in protein folding simulation. The energy landscape paving (ELP) method has already been applied very successfully to off-lattice protein models and other optimization problems with complex energy landscape in continuous space. By improving the ELP method, and subsequently incorporating the neighborhood strategy with the pull-move set into the improved ELP method, a heuristic ELP algorithm is proposed to find low-energy conformations of 3D HP lattice model proteins in the discrete space. The algorithm is tested on three sets of 3D HP benchmark instances consisting 31 sequences. For eleven sequences with 27 monomers, the proposed method explores the conformation surfaces more efficiently than other methods, and finds new lower energies in several cases. For ten 48-monomer sequences, we find the lowest energies so far. With the achieved results, the algorithm converges rapidly and efficiently. For all ten 64-monomer sequences, the algorithm finds lower energies within comparable computation times than previous methods. Numeric results show that the heuristic ELP method is a competitive tool for protein folding simulation in 3D lattice model. To the best of our knowledge, this is the first application of ELP to the 3D discrete space.     

A Global Minimization Algorithm for Empirical Contact Potential Functions

Global minimization algorithm is indispensable to solving the protein folding problem based upon thermodynamic hypothesis. Here we propose a pseudo potential function, contact difference(CD), for simulating empirical contact potential functions and testing global minimization algorithm. The present paper covers conformational sampling and global minimization algorithm called BML03, based upon Monte Carlo and simulated annealing, which is able to locate CD‘s global minimum and refold extended protein structures into one swith root mean square distance(RMSD) as small as 0.03 nm from the native structures. For empirieal contact potential functions, these results demonstrate that their global minimization problems may be solvable.     

用于真实蛋白质结构预测的一种新的优化方法

用"相对熵"作为优化函数,提出了一个有效快速的折叠预测优化算法.使用了非格点模型,预测只关心蛋白质主链的走向.其中只用到了蛋白质主链上的两两连续的Cα原子间的距离信息以及20种氨基酸的接触势的一个扩展形式.对几个真实蛋白质做了算法测试,预测的初始结构都为比较大的去折叠态,预测构象相对于它们天然结构的均方根偏差(RMSD)为5～7 A.从原理上讲,该方法是对能量优化的改进.     

Molecular simulation of surfactant-assisted protein refolding

Protein refolding to its native state in vitro is a challenging problem in biotechnology, i.e., in the biomedical, pharmaceutical, and food industry. Protein aggregation and misfolding usually inhibit the recovery of proteins with their native states. These problems can be partially solved by adding a surfactant into a suitable solution environment. However, the process of this surfactant-assisted protein refolding is not well understood. In this paper, we wish to report on the first-ever simulations of surfactant-assisted protein refolding. For these studies, we defined a simple model for the protein and the surfactant and investigated how a surfactant affected the folding behavior of a two-dimensional lattice protein molecule. The model protein and model surfactant were chosen such that we could capture the important features of the folding process and the interaction between the protein and the surfactant, namely, the hydrophobic interaction. It was shown that, in the absence of surfactants, a protein in an "energy trap" conformation, i.e., a local energy minima, could not fold into the native form, which was characterized by a global energy minimum. The addition of surfactants created folding pathways via the formation of protein-surfactant complexes and thus enabled the conformations that fell into energy trap states to escape from these traps and to form the native proteins. The simulation results also showed that it was necessary to match the hydrophobicity of surfactant to the concentration of denaturant, which was added to control the folding or unfolding of a protein. The surfactants with different hydrophobicity had their own concentration range on assisting protein refolding. All of these simulations agreed well with experimental results reported elsewhere, indicating both the validity of the simulations presented here and the potential application of the simulations for the design of a surfactant on assisting protein refolding.     

Conversion of the Native 24‐mer Ferritin Nanocage into Its Non‐Native 16‐mer Analogue by Insertion of Extra Amino Acid Residues

Protein assemblies with high symmetry are widely distributed in nature. Most efforts so far have focused on repurposing these protein assemblies, a strategy that is ultimately limited by the structures available. To overcome this limitation, methods for fabricating novel self‐assembling proteins have received intensive interest. Herein, by reengineering the key subunit interfaces of native 24‐mer protein cage with octahedral symmetry through amino acid residues insertion, we fabricated a 16‐mer lenticular nanocage whose structure is unique among all known protein cages. This newly non‐native protein can be used for encapsulation of bioactive compounds and exhibits high uptake efficiency by cancer cells. More importantly, the above strategy could be applied to other naturally occurring protein assemblies with high symmetry, leading to the generation of new proteins with unexplored functions.     

Kinetics of cooperative protein folding involving two separate conformational families

The master equation that describes the kinetics of protein folding is solved numerically for a portion of Staphylococcal Protein A by a Laplace transformation. The calculations are carried out with 50 local-minimum conformations belonging to two conformational families. The master equation allows for transitions among all the 50 conformations in the evolution toward the final folded equilibrium distribution of conformations. It is concluded that the native protein folds in a fast cooperative process. The global energy minimum of a native protein can be reached after a sufficiently long folding time regardless of the initial state and the existence of a large number of local energy minima. Conformations representing non-native states of the protein can transform to the native state even if they do not belong to the native conformational family. Given a starting conformation, the protein molecule can fold to its final conformation through different paths. Finally, when the folding reaches the equilibrium distribution, the protein molecule adopts a set of conformations in which the global minimum has the largest average probability.     

Contact pair dynamics during folding of two small proteins: chicken villin head piece and the Alzheimer protein beta-amyloid

The folding of an extended protein to its unique native state requires establishment of specific, predetermined, often distant, contacts between amino acid residue pairs. The dynamics of contact pair formation between various hydrophobic residues during folding of two different small proteins, the chicken villin head piece (HP-36) and the Alzheimer protein beta-amyloid (betaA-40), are investigated by Brownian dynamics (BD) simulations. These two proteins represent two very different classes-HP-36 being globular while betaA-40 is nonglobular, stringlike. Hydropathy scale and nonlocal helix propensity of amino acids are used to model the complex interaction potential among the various amino acid residues. The minimalistic model we use here employs a connected backbone chain of atoms of equal size while an amino acid is attached to each backbone atom as an additional atom of differing sizes and interaction parameters, determined by the characteristics of each amino acid. Even for such simple models, we find that the low-energy structures obtained by BD simulations of both the model proteins mimic the native state of the real protein rather well, with a best root-mean-square deviation of 4.5 A for HP-36. For betaA-40 (where a single well-defined structure is not available), the simulated structures resemble the reported ensemble rather well, with the well-known beta-bend correctly reproduced. We introduce and calculate a contact pair distance time correlation function, C(P) (ij)(t), to quantify the dynamical evolution of the pair contact formation between the amino acid residue pairs i and j. The contact pair time correlation function exhibits multistage dynamics, including a two stage fast collapse, followed by a slow (microsecond long) late stage dynamics for several specific pairs. The slow late stage dynamics is in accordance with the findings of Sali et al. Analysis of the individual trajectories shows that the slow decay is due to the attempt of the protein to form energetically more favorable pair contacts to replace the less favorable ones. This late stage contact formation is a highly cooperative process, involving participation of several pairs and thus entropically unfavorable and expected to face a large free energy barrier. This is because any new pair contact formation among hydrophobic pairs will require breaking of several contacts, before the favorable ones can be formed. This aspect of protein folding dynamics is similar to relaxation in glassy liquids, where also alpha relaxation requires highly cooperative process of hopping. The present analysis suggests that waiting time for the necessary pair contact formation may obey the Poissonian distribution. We also study the dynamics of Forster energy transfer during folding between two tagged amino acid pairs. This dynamics can be studied by fluorescence resonance energy transfer (FRET). It is found that suitably placed donor-acceptor pairs can capture the slow dynamics during folding. The dynamics probed by FRET is predicted to be nonexponential.     

A Global Minimization Algorithm for Empirical Contact Potential Functions

Introduction Basedonthethermodynamichypothesis[1],any computionalapproachforsolvingproteinfoldingprob lemsoranabinitiopredictionofproteintertiarystruc turesfromtheirprimarysequences,requiresanempiri calpotentialfunctionthathasitsglobalminimumatthe natives…     

Performance comparison of generalized born and Poisson methods in the calculation of electrostatic solvation energies for protein structures

This study compares generalized Born (GB) and Poisson (PB) methods for calculating electrostatic solvation energies of proteins. A large set of GB and PB implementations from our own laboratories as well as others is applied to a series of protein structure test sets for evaluating the performance of these methods. The test sets cover a significant range of native protein structures of varying size, fold topology, and amino acid composition as well as nonnative extended and misfolded structures that may be found during structure prediction and folding/unfolding studies. We find that the methods tested here span a wide range from highly accurate and computationally demanding PB-based methods to somewhat less accurate but more affordable GB-based approaches and a few fast, approximate PB solvers. Compared with PB solvation energies, the latest, most accurate GB implementations were found to achieve errors of 1% for relative solvation energies between different proteins and 0.4% between different conformations of the same protein. This compares to accurate PB solvers that produce results with deviations of less than 0.25% between each other for both native and nonnative structures. The performance of the best GB methods is discussed in more detail for the application for force field-based minimizations or molecular dynamics simulations.     

De novo and inverse folding predictions of protein structure and dynamics

Summary In the last two years, the use of simplified models has facilitated major progress in the globular protein folding problem, viz., the prediction of the three-dimensional (3D) structure of a globular protein from its amino acid sequence. A number of groups have addressed the inverse folding problem where one examines the compatibility of a given sequence with a given (and already determined) structure. A comparison of extant inverse protein-folding algorithms is presented, and methodologies for identifying sequences likely to adopt identical folding topologies, even when they lack sequence homology, are described. Extension to produce structural templates or fingerprints from idealized structures is discussed, and for eight-membered β-barrel proteins, it is shown that idealized fingerprints constructed from simple topology diagrams can correctly identify sequences having the appropriate topology. Furthermore, this inverse folding algorithm is generalized to predict elements of supersecondary structure including β-hairpins, helical hairpins and α/β/α fragments. Then, we describe a very high coordination number lattice model that can predict the 3D structure of a number of globular proteins de novo; i.e. using just the amino acid sequence. Applications to sequences designed by DeGrado and co-workers [Biophys. J., 61 (1992) A265] predict folding intermediates, native states and relative stabilities in accord with experiment. The methodology has also been applied to the four-helix bundle designed by Richardson and co-workers [Science, 249 (1990) 884] and a redesigned monomeric version of a naturally occurring four-helix dimer, rop. Based on comparison to the rop dimer, the simulations predict conformations with rms values of 3–4 ? from native. Furthermore, the de novo algorithms can asses the stability of the folds predicted from the inverse algorithm, while the inverse folding algorithms can assess the quality of the de novo models. Thus, the synergism of the de novo and inverse folding algorthhm approaches provides a set of complementary tools that will facilitate further progress on the protein-folding problem.     

Optimum folding pathways of proteins: their determination and properties

We develop a dynamic optimization technique for determining optimum folding pathways of proteins starting from different initial configurations. A coarse-grained Go model is used. Forces acting on each bead are (i) the friction force, (ii) forces from bond length constraints, (iii) excluded volume constraints, and (iv) attractive forces between residue pairs that are in contact in the native state. An objective function is defined as the total attractive energy between nonbonded residues, which are neighbors in the native state. The objective function is minimized over all feasible paths, satisfying bond length and excluded volume constraints. The optimization problem is nonconvex and contains a large number of constraints. An augmented Lagrangian method with a penalty barrier function was used to solve the problem. The method is applied to a 36-residue protein, chicken villin headpiece. Sequences of events during folding of the protein are determined for various pathways and analyzed. The relative time scales are compared and scaled according to experimentally measured events. Formation times of the helices, turn, and the loop agree with experimental data. We obtain the overall folding time of the protein in the range of 600 ns-1.2 micros that is smaller than the experimental result of 4-5 micros, showing that the optimal folding times that we obtain may be possible lower bounds. Time dependent variables during folding and energies associated with short- and long-range interactions between secondary structures are analyzed in modal space using Karhunen-Loeve expansion.     

Understanding the folding rates and folding nuclei of globular proteins

The first part of this paper contains an overview of protein structures, their spontaneous formation ("folding"), and the thermodynamic and kinetic aspects of this phenomenon, as revealed by in vitro experiments. It is stressed that universal features of folding are observed near the point of thermodynamic equilibrium between the native and denatured states of the protein. Here the "two-state" ("denatured state" <--> "native state") transition proceeds without accumulation of metastable intermediates, but includes only the unstable "transition state". This state, which is the most unstable in the folding pathway, and its structured core (a "nucleus") are distinguished by their essential influence on the folding/unfolding kinetics. In the second part of the paper, a theory of protein folding rates and related phenomena is presented. First, it is shown that the protein size determines the range of a protein's folding rates in the vicinity of the point of thermodynamic equilibrium between the native and denatured states of the protein. Then, we present methods for calculating folding and unfolding rates of globular proteins from their sizes, stabilities and either 3D structures or amino acid sequences. Finally, we show that the same theory outlines the location of the protein folding nucleus (i.e., the structured part of the transition state) in reasonable agreement with experimental data.     

Energy minimizations with a combination of two knowledge-based potentials for protein folding

New force fields that are both simple and accurate are needed for computationally efficient molecular simulation studies to give insight into the actual features of the protein folding process. In this work, we assess a force field based on a new combination of two coarse-grained potentials taken from the bibliography. These potentials have already been proved efficient in representing different types of interactions, namely the side-chain interactions and the backbone hydrogen bonds. Now we combine them weighing their contribution to the global energy with a very simplified parameterization. To assess this combination of potentials, we use our evolutionary method to carry out energy minimization experiments for a set of all-alpha, all-beta, and (alpha + beta) protein structures. Our results, based on the assembly of short rigid native fragments, suggest that this combination of potentials can be successfully employed in coarse-grained folding simulations.     

Understanding the role of the topology in protein folding by computational inverse folding experiments

Recent studies suggest that protein folding should be revisited as the emergent property of a complex system and that the nature allows only a very limited number of folds that seem to be strongly influenced by geometrical properties. In this work we explore the principles underlying this new view and show how helical protein conformations can be obtained starting from simple geometric considerations. We generated a large data set of C-alpha traces made of 65 points, by computationally solving a backbone model that takes into account only topological features of the all-alpha proteins; then, we built corresponding tertiary structures, by using the sequences associated to the crystallographic structures of four small globular all-alpha proteins from PDB, and analysed them in terms of structural and energetic properties. In this way we obtained four poorly populated sets of structures that are reasonably similar to the conformational states typical of the experimental PDB structures. These results show that our computational approach can capture the native topology of all-alpha proteins; furthermore, it generates backbone folds without the influence of the side chains and uses the protein sequence to select a specific fold among the generated folds. This agrees with the recent view that the backbone plays an important role in the protein folding process and that the amino acid sequence chooses its own fold within a limited total number of folds.     

Expanding the realm of ultrafast protein folding: gpW, a midsize natural single-domain with alpha+beta topology that folds downhill

All ultrafast folding proteins known to date are either very small in size (less than 45 residues), have an alpha-helix bundle topology, or have been artificially engineered. In fact, many of them share two or even all three features. Here we show that gpW, a natural 62-residue alpha+beta protein expected to fold slowly in a two-state fashion, folds in microseconds (i.e., from tau = 33 micros at 310 K to tau = 1.7 micros at 355 K). Thermodynamic analyses of gpW reveal probe dependent thermal denaturation, complex coupling between two denaturing agents, and differential scanning calorimetry (DSC) thermogram characteristic of folding over a negligible thermodynamic folding barrier. The free energy surface analysis of gpW folding kinetics also produces a marginal folding barrier of about thermal energy ( RT) at the denaturation midpoint. From these results we conclude that gpW folds in the downhill regime and is close to the global downhill limit. This protein seems to be poised toward downhill folding by a loosely packed hydrophobic core with low aromatic content, large stabilizing contributions from local interactions, and abundance of positive charges on the native surface. These special features, together with a complex functional role in bacteriophage lambda assembly, suggest that gpW has been engineered to fold downhill by natural selection.     

A statistical model for predicting protein folding rates from amino acid sequence with structural class information

Prediction of protein folding rates from amino acid sequences is one of the most important challenges in molecular biology. In this work, I have related the protein folding rates with physical-chemical, energetic and conformational properties of amino acid residues. I found that the classification of proteins into different structural classes shows an excellent correlation between amino acid properties and folding rates of two- and three-state proteins, indicating the importance of native state topology in determining the protein folding rates. I have formulated a simple linear regression model for predicting the protein folding rates from amino acid sequences along with structural class information and obtained an excellent agreement between predicted and experimentally observed folding rates of proteins; the correlation coefficients are 0.99, 0.96 and 0.95, respectively, for all-alpha, all-beta and mixed class proteins. This is the first available method, which is capable of predicting the protein folding rates just from the amino acid sequence with the aid of generic amino acid properties and structural class information.     

Robustness of atomistic Gō models in predicting native-like folding intermediates

Go? models are exceedingly popular tools in computer simulations of protein folding. These models are native-centric, i.e., they are directly constructed from the protein's native structure. Therefore, it is important to understand up to which extent the atomistic details of the native structure dictate the folding behavior exhibited by Go? models. Here we address this challenge by performing exhaustive discrete molecular dynamics simulations of a Go? potential combined with a full atomistic protein representation. In particular, we investigate the robustness of this particular type of Go? models in predicting the existence of intermediate states in protein folding. We focus on the N47G mutational form of the Spc-SH3 folding domain (x-ray structure) and compare its folding pathway with that of alternative native structures produced in silico. Our methodological strategy comprises equilibrium folding simulations, structural clustering, and principal component analysis.