Exploring protein's optimal HP configurations by self-organizing mapping

Self-organizing map (SOM) has been used in protein folding prediction when the HP model is employed. The existing work uses a square-like shape lattice with l = m x n points to represent the optimal compact structure of a sequence of l amino acids. In this paper, a general l'-size sequence of amino acids is self-organized in a two dimensional lattice with l (> l') points. The obtained minimum configuration then has a flexible shape, in contrast to the compact structure limited in the lattice. To fulfil this extension, a new self-organizing map (SOM) technique is proposed to deal with the difficulty of the unsymmetric input and output spaces. New competition rules in the training phase are introduced and a local search method is applied to overcome the multi-mapping phenomena. Several HP benchmark examples with up to 36 amino acids are tested to verify the effectiveness of the proposed approach in this paper.     

Emergence of highly designable protein-backbone conformations in an off-lattice model

Despite the variety of protein sizes, shapes, and backbone configurations found in nature, the design of novel protein folds remains an open problem. Within simple lattice models it has been shown that all structures are not equally suitable for design. Rather, certain structures are distinguished by unusually high designability: the number of amino acid sequences for which they represent the unique lowest energy state; sequences associated with such structures possess both robustness to mutation and thermodynamic stability. Here we report that highly designable backbone conformations also emerge in a realistic off-lattice model. The highly designable conformations of a chain of 23 amino acids are identified and found to be remarkably insensitive to model parameters. Although some of these conformations correspond closely to known natural protein folds, such as the zinc finger and the helix-turn-helix motifs, others do not resemble known folds and may be candidates for novel fold design.     

Statistical mechanics of integral membrane protein assembly

During the synthesis of integral membrane proteins (IMPs), the hydrophobic amino acids of the polypeptide sequence are partitioned mostly into the membrane interior and hydrophilic amino acids mostly into the aqueous exterior. Using a many-body statistical mechanics model, we analyze the minimum free energy state of polypeptide sequences partitioned into α-helical transmembrane (TM) segments and the role of thermal fluctuations. Results suggest that IMP TM segment partitioning shares important features with general theories of protein folding. For random polypeptide sequences, the minimum free energy state at room temperature is characterized by fluctuations in the number of TM segments with very long relaxation times. Moreover, simple assembly scenarios do not produce a unique number of TM segments due to jamming phenomena. On the other hand, for polypeptide sequences corresponding to actual IMPs, the minimum free energy structure with the wild-type number of segments is free of number fluctuations due to an anomalously large gap in the energy spectrum. Now, simple assembly scenarios do reproduce the minimum free energy state without jamming. Finally, we find a threshold number of random point mutations where the size of the anomalous gap is reduced to the point that the wild-type ground state is destabilized and number fluctuations reappear.     

High-resolution structural validation of the computational redesign of human U1A protein

Achieving atomic-level resolution in the computational design of a protein structure remains a challenging problem despite recent progress. Rigorous experimental tests are needed to improve protein design algorithms, yet studies of the structure and dynamics of computationally designed proteins are very few. The NMR structure and backbone dynamics of a redesigned protein of 96 amino acids are compared here with the design target, human U1A protein. We demonstrate that the redesigned protein reproduces the target structure to within the uncertainty of the NMR coordinates, even as 65 out of 96 amino acids were simultaneously changed by purely computational methods. The dynamics of the backbone of the redesigned protein also mirror those of human U1A, suggesting that the protein design algorithm captures the shape of the potential energy landscape in addition to the local energy minimum.     

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.     

Germline transformation with Drosophila mutant actin genes induces constitutive expression of heat shock genes

Two Drosophila mutants KM75 and HH5, which are mutated in the act88F actin gene specific for the indirect flight muscles (IFM), synthesize heat shock proteins (hsps) constitutively in a tissue-specific manner. We have introduced cloned mutant act88F genes into a strain containing the wild-type act88F allele by P-element-mediated transformation. Flies transformed with a 4.05 kb KM75 act88F gene fragment encoding the p42 actin variant express both p42 and hsps specifically in the IFM. Using normal/mutant chimeric genes, the mutation sites of KM75 and HH5 were mapped within the sequence encoding the last 72 amino acids of actin. An in vitro mutated gene encoding a protein that lacks the 72 carboxy-terminal amino acids also induces constitutive hsp synthesis.     

Guiding conformation space search with an all-atom energy potential

The most significant impediment for protein structure prediction is the inadequacy of conformation space search. Conformation space is too large and the energy landscape too rugged for existing search methods to consistently find near-optimal minima. To alleviate this problem, we present model-based search, a novel conformation space search method. Model-based search uses highly accurate information obtained during search to build an approximate, partial model of the energy landscape. Model-based search aggregates information in the model as it progresses, and in turn uses this information to guide exploration toward regions most likely to contain a near-optimal minimum. We validate our method by predicting the structure of 32 proteins, ranging in length from 49 to 213 amino acids. Our results demonstrate that model-based search is more effective at finding low-energy conformations in high-dimensional conformation spaces than existing search methods. The reduction in energy translates into structure predictions of increased accuracy.     

Trading accuracy for speed: A quantitative comparison of search algorithms in protein sequence design

Finding the minimum energy amino acid side-chain conformation is a fundamental problem in both homology modeling and protein design. To address this issue, numerous computational algorithms have been proposed. However, there have been few quantitative comparisons between methods and there is very little general understanding of the types of problems that are appropriate for each algorithm. Here, we study four common search techniques: Monte Carlo (MC) and Monte Carlo plus quench (MCQ); genetic algorithms (GA); self-consistent mean field (SCMF); and dead-end elimination (DEE). Both SCMF and DEE are deterministic, and if DEE converges, it is guaranteed that its solution is the global minimum energy conformation (GMEC). This provides a means to compare the accuracy of SCMF and the stochastic methods. For the side-chain placement calculations, we find that DEE rapidly converges to the GMEC in all the test cases. The other algorithms converge on significantly incorrect solutions; the average fraction of incorrect rotamers for SCMF is 0.12, GA 0.09, and MCQ 0.05. For the protein design calculations, design positions are progressively added to the side-chain placement calculation until the time required for DEE diverges sharply. As the complexity of the problem increases, the accuracy of each method is determined so that the results can be extrapolated into the region where DEE is no longer tractable. We find that both SCMF and MCQ perform reasonably well on core calculations (fraction amino acids incorrect is SCMF 0.07, MCQ 0.04), but fail considerably on the boundary (SCMF 0.28, MCQ 0.32) and surface calculations (SCMF 0.37, MCQ 0.44).     

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.     

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     

Amino Acid Starvation Has Opposite Effects on Mitochondrial and Cytosolic Protein Synthesis

Amino acids are essential for cell growth and proliferation for they can serve as precursors of protein synthesis, be remodelled for nucleotide and fat biosynthesis, or be burnt as fuel. Mitochondria are energy producing organelles that additionally play a central role in amino acid homeostasis. One might expect mitochondrial metabolism to be geared towards the production and preservation of amino acids when cells are deprived of an exogenous supply. On the contrary, we find that human cells respond to amino acid starvation by upregulating the amino acid-consuming processes of respiration, protein synthesis, and amino acid catabolism in the mitochondria. The increased utilization of these nutrients in the organelle is not driven primarily by energy demand, as it occurs when glucose is plentiful. Instead it is proposed that the changes in the mitochondrial metabolism complement the repression of cytosolic protein synthesis to restrict cell growth and proliferation when amino acids are limiting. Therefore, stimulating mitochondrial function might offer a means of inhibiting nutrient-demanding anabolism that drives cellular proliferation.     

最小Hamilton路算法在蛋白质结构预测中的应用

本文对蛋白质loop结构进行了反向研究,即对由n个残基构成的loop已知其空间结构,求匹配的n个氨基酸残基序列.把loop的3D信息转化为一个加权完全图Kn模型,然后求加权Kn图的最小Hamilton路.这条H路对应与寻找一个氨基酸残基序列,使该序列能够折叠成这个立体结构模型.根据Bayesian定律得到一个加权表,应用对loop的预测问题,取得预期的结果.     

利用粒子群算法在菱形网格上预测蛋白质结构

本文在菱形网格上研究讨论了二维HP模型。首先,将蛋白质结构预测问题转化成一个数学问题,并简化成氨基酸序列中每个氨基酸与网格格点的匹配问题。为了解决这个数学问题,我们改进并扩展了经典的粒子群算法。为了验证算法和模型的有效性,我们对一些典型的算例进行数值模拟。通过与方格网上得到的蛋白质构象进行比较,菱形网上的蛋白质构象更自然,更接近真实。我们进一步比较了菱形网格上的紧致构象和非紧致构象。结果显示我们的模型和算法在菱形网格上预测氨基酸序列的蛋白质结构是有效的有意义的。     

Tau protein binds to microtubules through a flexible array of distributed weak sites

Tau protein plays a role in the extension and maintenance of neuronal processes through a direct association with microtubules. To characterize the nature of this association, we have synthesized a collection of tau protein fragments and studied their binding properties. The relatively weak affinity of tau protein for microtubules (approximately 10(-7) M) is concentrated in a large region containing three or four 18 amino acid repeated binding elements. These are separated by apparently flexible but less conserved linker sequences of 13-14 amino acids that do not bind. Within the repeats, the binding energy for microtubules is delocalized and derives from a series of weak interactions contributed by small groups of amino acids. These unusual characteristics suggest tau protein can assume multiple conformations and can pivot and perhaps migrate on the surface of the microtubule. The flexible structure of the tau protein binding interaction may allow it to be easily displaced from the microtubule lattice and may have important consequences for its function.     

A Pareto-Optimal Refinement Method for Protein Design Scaffolds

Computational design of protein function involves a search for amino acids with the lowest energy subject to a set of constraints specifying function. In many cases a set of natural protein backbone structures, or “scaffolds”, are searched to find regions where functional sites (an enzyme active site, ligand binding pocket, protein – protein interaction region, etc.) can be placed, and the identities of the surrounding amino acids are optimized to satisfy functional constraints. Input native protein structures almost invariably have regions that score very poorly with the design force field, and any design based on these unmodified structures may result in mutations away from the native sequence solely as a result of the energetic strain. Because the input structure is already a stable protein, it is desirable to keep the total number of mutations to a minimum and to avoid mutations resulting from poorly-scoring input structures. Here we describe a protocol using cycles of minimization with combined backbone/sidechain restraints that is Pareto-optimal with respect to RMSD to the native structure and energetic strain reduction. The protocol should be broadly useful in the preparation of scaffold libraries for functional site design.     

Protein evolution within a structural space

Understanding of the evolutionary origins of protein structures represents a key component of the understanding of molecular evolution as a whole. Here we seek to elucidate how the features of an underlying protein structural “space” might impact protein structural evolution. We approach this question using lattice polymers as a completely characterized model of this space. We develop a measure of structural comparison of lattice structures that is analogous to the one used to understand structural similarities between real proteins. We use this measure of structural relatedness to create a graph of lattice structures and compare this graph (in which nodes are lattice structures and edges are defined using structural similarity) to the graph obtained for real protein structures. We find that the graph obtained from all compact lattice structures exhibits a distribution of structural neighbors per node consistent with a random graph. We also find that subgraphs of 3500 nodes chosen either at random or according to physical constraints also represent random graphs. We develop a divergent evolution model based on the lattice space which produces graphs that, within certain parameter regimes, recapitulate the scale-free behavior observed in similar graphs of real protein structures.     

Molecular characterization of mutant actin genes which induce heat-shock proteins in Drosophila flight muscles

Heat-shock proteins (hsps) are constitutively induced by the mutant actins in the Drosophila indirect flight muscles (IFM). We compared primary structures of the mutant actin genes (KM75 and HH5) which induce hsps and of the non-inducing alleles (KM129 and KM88). The KM75 actin has lost 20 amino acids at the C-terminus. The HH5 actin has only one amino acid substitution, from Gly-336 to Ser. In KM129, the C-terminal part of actin is replaced by novel amino acids. KM88 is a null allele, with an amber mutation early in the coding region of the mutated actin gene. Although all of the KM75, HH5 and KM129 actins have defects near the C-terminus, only hsp-inducing mutant actins cause enlargement of the IFM nuclei as well as a disruption of myofibrils even in the presence of two copies of the normal genes. We further consider the underlying mechanisms linking these features of the hsp-inducing alleles.     

On Hydrophobicity and Conformational Specificity in Proteins

In this study we examine the distribution of hydrophobic residues in a nonredundant set of monomeric globular single-domain proteins. We find that the total fraction of hydrophobic residues is roughly constant and has no discernible dependence on protein size. This results in a decrease of the hydrophobicity of the core as the size of proteins increases. Using a normalized measure, and by comparing with sets of randomly reshuffled sequences, we show that this change in the composition of the core is statistically significant and robust with respect to which amino acids are considered hydrophobic and to how buried residues are defined. Comparison with model sequences optimized for stability, while still required to retain their native state as a unique minimum energy conformation, suggests that the size-independence of the total fraction of hydrophobic residues could be a result of requiring proteins to be conformationally specific.     

Solvent-amino acid interaction energies in three-dimensional-lattice Monte Carlo simulations of a model 27-mer protein: Folding thermodynamics and kinetics

Amino acid residue-solvent interactions are required for lattice Monte Carlo simulations of model proteins in water. In this study, we propose an interaction-energy scale that is based on the interaction scale by Miyazawa and Jernigan. It permits systematic variation of the amino acid-solvent interactions by introducing a contrast parameter for the hydrophobicity, C(s), and a mean attraction parameter for the amino acids, omega. Changes in the interaction energies strongly affect many protein properties. We present an optimized energy parameter set for best representing realistic behavior typical for many proteins (fast folding and high cooperativity for single chains). Our optimal parameters feature a much weaker hydrophobicity contrast and mean attraction than does the original interaction scale. The proposed interaction scale is designed for calculating the behavior of proteins in bulk and at interfaces as a function of solvent characteristics, as well as protein size and sequence.