A test of lattice protein folding algorithms

Intraglobular structures in multiblock copolymer chains from a Monte Carlo simulation

Multiblock copolymer chains in implicit nonselective solvents are studied by using a Monte Carlo method, which employs a parallel tempering algorithm. Chains consisting of 120 A and 120 B monomers, arranged in three distinct microarchitectures: (10-10)12, (6-6)20, and (3-3)40, collapse to globular states upon cooling, as expected. By varying both the reduced temperature T* and the compatibility between monomers ω, numerous intraglobular structures are obtained: diclusters (handshake, spiral, torus with a core, etc.), triclusters, and n clusters with n>3 (lamellar and other), which are reminiscent of the block copolymer nanophases for spherically confined geometries. Phase diagrams for various chains in the (T*,ω) space are mapped. The structure factor S(k), for a selected microarchitecture and ω, is calculated. Since S(k) can be measured in scattering experiments, it can be used to relate simulation results to an experiment. Self-assembly in those systems is interpreted in terms of competition between minimization of the interfacial area separating different types of monomers and minimization of contacts between chain and solvent. Finally, the relevance of this model to the protein folding is addressed.

Multiscale coarse-graining of the protein energy landscape

A variety of coarse-grained (CG) models exists for simulation of proteins. An outstanding problem is the construction of a CG model with physically accurate conformational energetics rivaling all-atom force fields. In the present work, atomistic simulations of peptide folding and aggregation equilibria are force-matched using multiscale coarse-graining to develop and test a CG interaction potential of general utility for the simulation of proteins of arbitrary sequence. The reduced representation relies on multiple interaction sites to maintain the anisotropic packing and polarity of individual sidechains. CG energy landscapes computed from replica exchange simulations of the folding of Trpzip, Trp-cage and adenylate kinase resemble those of other reduced representations; non-native structures are observed with energies similar to those of the native state. The artifactual stabilization of misfolded states implies that non-native interactions play a deciding role in deviations from ideal funnel-like cooperative folding. The role of surface tension, backbone hydrogen bonding and the smooth pairwise CG landscape is discussed. Ab initio folding aside, the improved treatment of sidechain rotamers results in stability of the native state in constant temperature simulations of Trpzip, Trp-cage, and the open to closed conformational transition of adenylate kinase, illustrating the potential value of the CG force field for simulating protein complexes and transitions between well-defined structural states.

Biological function originates from the dynamical motions of proteins in response to cellular stimuli. Protein dynamics arise from physical interactions that are well-predicted by detailed atomistic simulations. In order to examine large protein complexes on long timescales of biological importance, however, coarse-grained simulation approaches are needed to complement experiment. Previous coarse-grained models have proved successful for investigations involving a given protein's native structure, including protein folding and structure prediction. We construct a model capable of simulating proteins regardless of their sequence or structure. The present coarse-grained model was, however, developed rigorously from the underlying atomistic forces as opposed to knowledge-based or ad hoc parameterizations. Examination of the model predictions on various accessible timescales reveals successes and limitations of the model. While functionally relevant conformational transitions can be studied, the coarse-grained representation has some difficulty with the ab initio folding of the peptide chain into its proper structure. Our observations highlight the complex molecular nature of a protein's underlying energy landscape, offering rigorous insight into the information missing in reduced representations of the peptide chain. With these caveats in mind, the physical interaction–based, coarse-grained model will find application in simulations of a wide variety of proteins and continue to guide future coarse-graining efforts.

A sequence-compatible amount of native burial information is sufficient for determining the structure of small globular proteins

Protein tertiary structures are known to be encoded in amino acid sequences, but the problem of structure prediction from sequence continues to be a challenge. With this question in mind, recent simulations have shown that atomic burials, as expressed by atom distances to the molecular geometrical center, are sufficiently informative for determining native conformations of small globular proteins. Here we use a simple computational experiment to estimate the amount of this required burial information and find it to be surprisingly small, actually comparable with the stringent limit imposed by sequence statistics. Atomic burials appear to satisfy, therefore, minimal requirements for a putative dominating property in the folding code because they provide an amount of information sufficiently large for structural determination but, at the same time, sufficiently small to be encodable in sequences. In a simple analogy with human communication, atomic burials could correspond to the actual "language" encoded in the amino acid "script" from which the complexity of native conformations is recovered during the folding process.

Deconstructing the native state: energy landscapes, function, and dynamics of globular proteins

Proteins are highly complex molecules with features exquisitely selected by nature to carry out essential biological functions. Physical chemistry and polymer physics provide us with the tools needed to make sense of this complexity. Upon translation, many proteins fold to a thermodynamically stable form known as the native state. The native state is not static, but consists of a hierarchy of conformations, that are continuously explored through dynamics. In this review we provide a brief introduction to some of the core concepts required in the discussion of the protein native dynamics using energy landscapes ideas. We first discuss recent works which have challenged the structure-function paradigm by demonstrating function in disordered proteins. Next we examine the hierarchical organization in the energy landscapes using atomistic molecular dynamics simulations and principal component analysis. In particular, the role of direct and water-mediated contacts in sculpting the landscape is elaborated. Another approach to studying the native state ensemble is based on choosing high-resolution order parameters for computing one- or two-dimensional free energy surfaces. We demonstrate that 2D free energy surfaces provide rich thermodynamic and kinetic information about the native state ensemble. Brownian dynamics simulations on such a surface indicate that protein conformational dynamics is weakly activated. Finally, we briefly discuss implicit and coarse-grained protein models and emphasize the solvent role in determining native state structure and dynamics.

Insights from coarse-grained Gō models for protein folding and dynamics

Exploring the landscape of large scale conformational changes such as protein folding at atomistic detail poses a considerable computational challenge. Coarse-grained representations of the peptide chain have therefore been developed and over the last decade have proved extremely valuable. These include topology-based Gō models, which constitute a smooth and funnel-like approximation to the folding landscape. We review the many variations of the Gō model that have been employed to yield insight into folding mechanisms. Their success has been interpreted as a consequence of the dominant role of the native topology in folding. The role of local contact density in determining protein dynamics is also discussed and is used to explain the ability of Gō-like models to capture sequence effects in folding and elucidate conformational transitions.

Automated alphabet reduction for protein datasets

BACKGROUND

We investigate automated and generic alphabet reduction techniques for protein structure prediction datasets. Reducing alphabet cardinality without losing key biochemical information opens the door to potentially faster machine learning, data mining and optimization applications in structural bioinformatics. Furthermore, reduced but informative alphabets often result in, e.g., more compact and human-friendly classification/clustering rules. In this paper we propose a robust and sophisticated alphabet reduction protocol based on mutual information and state-of-the-art optimization techniques.

RESULTS

We applied this protocol to the prediction of two protein structural features: contact number and relative solvent accessibility. For both features we generated alphabets of two, three, four and five letters. The five-letter alphabets gave prediction accuracies statistically similar to that obtained using the full amino acid alphabet. Moreover, the automatically designed alphabets were compared against other reduced alphabets taken from the literature or human-designed, outperforming them. The differences between our alphabets and the alphabets taken from the literature were quantitatively analyzed. All the above process had been performed using a primary sequence representation of proteins. As a final experiment, we extrapolated the obtained five-letter alphabet to reduce a, much richer, protein representation based on evolutionary information for the prediction of the same two features. Again, the performance gap between the full representation and the reduced representation was small, showing that the results of our automated alphabet reduction protocol, even if they were obtained using a simple representation, are also able to capture the crucial information needed for state-of-the-art protein representations.

CONCLUSION

Our automated alphabet reduction protocol generates competent reduced alphabets tailored specifically for a variety of protein datasets. This process is done without any domain knowledge, using information theory metrics instead. The reduced alphabets contain some unexpected (but sound) groups of amino acids, thus suggesting new ways of interpreting the data.

Evaluating and optimizing computational protein design force fields using fixed composition-based negative design

An accurate force field is essential to computational protein design and protein fold prediction studies. Proper force field tuning is problematic, however, due in part to the incomplete modeling of the unfolded state. Here, we evaluate and optimize a protein design force field by constraining the amino acid composition of the designed sequences to that of a well behaved model protein. According to the random energy model, unfolded state energies are dependent only on amino acid composition and not the specific arrangement of amino acids. Therefore, energy discrepancies between computational predictions and experimental results, for sequences of identical composition, can be directly attributed to flaws in the force field's ability to properly account for folded state sequence energies. This aspect of fixed composition design allows for force field optimization by focusing solely on the interactions in the folded state. Several rounds of fixed composition optimization of the 56-residue beta1 domain of protein G yielded force field parameters with significantly greater predictive power: Optimized sequences exhibited higher wild-type sequence identity in critical regions of the structure, and the wild-type sequence showed an improved Z-score. Experimental studies revealed a designed 24-fold mutant to be stably folded with a melting temperature similar to that of the wild-type protein. Sequence designs using engrailed homeodomain as a scaffold produced similar results, suggesting the tuned force field parameters were not specific to protein G.

Maximum entropy approach for deducing amino Acid interactions in proteins

We present a maximum entropy approach for inferring amino acid interactions in proteins subject to constraints pertaining to the mean numbers of various types of equilibrium contacts for a given sequence or a set of sequences. We have carried out several kinds of tests for a two-dimensional lattice model with just two types of amino acids with very promising results. We also show that the method works very well even when the mean numbers of contacts are not known and therefore can be applied to real proteins.

Protein sequence design based on the topology of the native state structure

Computational design of sequences for a given structure is generally studied by exhaustively enumerating the sequence space or by searching in such a large space, which is prohibitively expensive. However, we point out that the protein topology has a wealth of information, which can be exploited to design sequences for a chosen structure. In this paper, we present a computationally efficient method for ranking the residue sites in a given native-state structure, which enables us to design sequences for a chosen structure. The premise for the method is that the topology of the graph representing the energetically interacting neighbours in a protein plays an important role in the inverse-folding problem. While our previous work (which was also based on topology) used eigenspectral analysis of the adjacency matrix of interactions for ranking the residue sites in a given chain, here we use a simple but effective way of assigning weights to the nodes on the basis of secondary connections, along with primary connections. This indirectly accounts for the edge weight in the graph and removes degeneracy in the degree. The new scheme needs only a few multiplications and additions to compute the preferred ranking of the residue sites even for structures of real proteins of sizes of a few hundred amino acid residues. We use HP lattice model examples (for which exhaustive enumeration of sequences is practical) to validate our ranking approach in obtaining sequences of lowest energy for any H-P residue composition for a given native-state structure. Some examples of native structures of real proteins are also included. Quantitative comparison of the efficacy of the new scheme with the earlier schemes is made. The new scheme consistently performs better and with much lower computational cost. An optimization procedure is added to work with the new scheme in a few rare cases wherein the new scheme fails to provide the best sequence, an optimization procedure is added to work with the new scheme.

Biopolymer structure simulation and optimization via fragment regrowth Monte Carlo

An efficient exploration of the configuration space of a biopolymer is essential for its structure modeling and prediction. In this study, the authors propose a new Monte Carlo method, fragment regrowth via energy-guided sequential sampling (FRESS), which incorporates the idea of multigrid Monte Carlo into the framework of configurational-bias Monte Carlo and is suitable for chain polymer simulations. As a by-product, the authors also found a novel extension of the Metropolis Monte Carlo framework applicable to all Monte Carlo computations. They tested FRESS on hydrophobic-hydrophilic (HP) protein folding models in both two and three dimensions. For the benchmark sequences, FRESS not only found all the minimum energies obtained by previous studies with substantially less computation time but also found new lower energies for all the three-dimensional HP models with sequence length longer than 80 residues.

A reduced amino acid alphabet for understanding and designing protein adaptation to mutation

Protein sequence world is considerably larger than structure world. In consequence, numerous non-related sequences may adopt similar 3D folds and different kinds of amino acids may thus be found in similar 3D structures. By grouping together the 20 amino acids into a smaller number of representative residues with similar features, sequence world simplification may be achieved. This clustering hence defines a reduced amino acid alphabet (reduced AAA). Numerous works have shown that protein 3D structures are composed of a limited number of building blocks, defining a structural alphabet. We previously identified such an alphabet composed of 16 representative structural motifs (5-residues length) called Protein Blocks (PBs). This alphabet permits to translate the structure (3D) in sequence of PBs (1D). Based on these two concepts, reduced AAA and PBs, we analyzed the distributions of the different kinds of amino acids and their equivalences in the structural context. Different reduced sets were considered. Recurrent amino acid associations were found in all the local structures while other were specific of some local structures (PBs) (e.g Cysteine, Histidine, Threonine and Serine for the alpha-helix Ncap). Some similar associations are found in other reduced AAAs, e.g Ile with Val, or hydrophobic aromatic residues Trp with Phe and Tyr. We put into evidence interesting alternative associations. This highlights the dependence on the information considered (sequence or structure). This approach, equivalent to a substitution matrix, could be useful for designing protein sequence with different features (for instance adaptation to environment) while preserving mainly the 3D fold.

Minimalist representations and the importance of nearest neighbor effects in protein folding simulations

In order to investigate the level of representation required to simulate folding and predict structure, we test the ability of a variety of reduced representations to identify native states in decoy libraries and to recover the native structure given the advanced knowledge of the very broad native Ramachandran basin assignments. Simplifications include the removal of the entire side-chain or the retention of only the Cbeta atoms. Scoring functions are derived from an all-atom statistical potential that distinguishes between atoms and different residue types. Structures are obtained by minimizing the scoring function with a computationally rapid simulated annealing algorithm. Results are compared for simulations in which backbone conformations are sampled from a Protein Data Bank-based backbone rotamer library generated by either ignoring or including a dependence on the identity and conformation of the neighboring residues. Only when the Cbeta atoms and nearest neighbor effects are included do the lowest energy structures generally fall within 4 A of the native backbone root-mean square deviation (RMSD), despite the initial configuration being highly expanded with an average RMSD > or = 10 A. The side-chains are reinserted into the Cbeta models with minimal steric clash. Therefore, the detailed, all-atom information lost in descending to a Cbeta-level representation is recaptured to a large measure using backbone dihedral angle sampling that includes nearest neighbor effects and an appropriate scoring function.

Accuracy of sequence alignment and fold assessment using reduced amino acid alphabets

Reduced or simplified amino acid alphabets group the 20 naturally occurring amino acids into a smaller number of representative protein residues. To date, several reduced amino acid alphabets have been proposed, which have been derived and optimized by a variety of methods. The resulting reduced amino acid alphabets have been applied to pattern recognition, generation of consensus sequences from multiple alignments, protein folding, and protein structure prediction. In this work, amino acid substitution matrices and statistical potentials were derived based on several reduced amino acid alphabets and their performance assessed in a large benchmark for the tasks of sequence alignment and fold assessment of protein structure models, using as a reference frame the standard alphabet of 20 amino acids. The results showed that a large reduction in the total number of residue types does not necessarily translate into a significant loss of discriminative power for sequence alignment and fold assessment. Therefore, some definitions of a few residue types are able to encode most of the relevant sequence/structure information that is present in the 20 standard amino acids. Based on these results, we suggest that the use of reduced amino acid alphabets may allow to increasing the accuracy of current substitution matrices and statistical potentials for the prediction of protein structure of remote homologs.

Hydrophobic collapse in (in silico) protein folding

A model of hydrophobic collapse, which is treated as the driving force for protein folding, is presented. This model is the superposition of three models commonly used in protein structure prediction: (1) 'oil-drop' model introduced by Kauzmann, (2) a lattice model introduced to decrease the number of degrees of freedom for structural changes and (3) a model of the formation of hydrophobic core as a key feature in driving the folding of proteins. These three models together helped to develop the idea of a fuzzy-oil-drop as a model for an external force field of hydrophobic character mimicking the hydrophobicity-differentiated environment for hydrophobic collapse. All amino acids in the polypeptide interact pair-wise during the folding process (energy minimization procedure) and interact with the external hydrophobic force field defined by a three-dimensional Gaussian function. The value of the Gaussian function usually interpreted as a probability distribution is treated as a normalized hydrophobicity distribution, with its maximum in the center of the ellipsoid and decreasing proportionally with the distance versus the center. The fuzzy-oil-drop is elastic and changes its shape and size during the simulated folding procedure.

A permissive secondary structure-guided superposition tool for clustering of protein fragments toward protein structure prediction via fragment assembly

MOTIVATION

Secondary-Structure Guided Superposition tool (SSGS) is a permissive secondary structure-based algorithm for matching of protein structures and in particular their fragments. The algorithm was developed towards protein structure prediction via fragment assembly.

RESULTS

In a fragment-based structural prediction scheme, a protein sequence is cut into building blocks (BBs). The BBs are assembled to predict their relative 3D arrangement. Finally, the assemblies are refined. To implement this prediction scheme, a clustered structural library representing sequence patterns for protein fragments is essential. To create a library, BBs generated by cutting proteins from the PDB are compared and structurally similar BBs are clustered. To allow structural comparison and clustering of the BBs, which are often relatively short with flexible loops, we have devised SSGS. SSGS maintains high similarity between cluster members and is highly efficient. When it comes to comparing BBs for clustering purposes, the algorithm obtains better results than other, non-secondary structure guided protein superimposition algorithms.

Fast method for estimating the energy distribution of globular states of proteins

By an enumeration study, we show that the energy distributions of a lattice protein sequence on all possible compact lattice configurations can be approximated by the energy distribution of shuffled sequences on a given lattice structure. We also show that the random energy model (REM) gives a good analytical approximation for the energy distribution of shuffled sequences on lattice structures. For real proteins, when a gapped threading method is used, REM calculations systematically underestimate the mean value of the energy distributions. We found that this discrepancy can be roughly compensated by a linear correction obtained from empirical fits. This result can be used to greatly reduce the computational effort in protein threading calculations.

Growth algorithm for finding low energy configurations of simple lattice proteins

PERM and its new variant nPERMis have been developed to optimize the energy function of protein folding based on HP simple lattice model and were found to outperform all other previous fully blind general purpose algorithms. Using the concept of core-guiding and life-forecasting, we propose a new version of nPERMis, called nPERMh. A major difference with respect to nPERMis is that criteria for further growth of new residue are based on the species of current growing monomer and its position in the HP sequence. Seventeen sequences of length ranging from 46 to 124 residues were tested by nPERMh on the cubic lattice and our algorithm proved very efficient. It should be pointed out that our new version of nPERMis is exclusively designed for conformational search. We hope that similar methods will ultimately be useful for finding native states of more realistic protein models.

Exact sequence analysis for three-dimensional hydrophobic-polar lattice proteins

We have exactly enumerated all sequences and conformations of hydrophobic-polar (HP) proteins with chains of up to 19 monomers on the simple cubic lattice. For two variants of the HP model, where only two types of monomers are distinguished, we determined and statistically analyzed designing sequences, i.e., sequences that have a nondegenerate ground state. Furthermore we were interested in characteristic thermodynamic properties of HP proteins with designing sequences. In order to be able to perform these exact studies, we applied an efficient enumeration method based on contact sets.

Comparing folding codes in simple heteropolymer models of protein evolutionary landscape: robustness of the superfunnel paradigm

Understanding the evolution of biopolymers is a key element in rationalizing their structures and functions. Simple exact models (SEMs) are well-positioned to address general principles of evolution as they permit the exhaustive enumeration of both sequence and structure (conformational) spaces. The physics-based models of the complete mapping between genotypes and phenotypes afforded by SEMs have proven valuable for gaining insight into how adaptation and selection operate among large collections of sequences and structures. This study compares the properties of evolutionary landscapes of a variety of SEMs to delineate robust predictions and possible model-specific artifacts. Among the models studied, the ruggedness of evolutionary landscape is significantly model-dependent; those derived from more protein-like models appear to be smoother. We found that a common practice of restricting protein structure space to maximally compact lattice conformations results in (i.e., "designs in") many encodable (designable) structures that are not otherwise encodable in the corresponding unrestrained structure space. This discrepancy is especially severe for model potentials that seek to mimic the major role of hydrophobic interactions in protein folding. In general, restricting conformations to be maximally compact leads to larger changes in the model genotype-phenotype mapping than a moderate shifting of reference state energy of the model potential function to allow for more specific encoding via the "designing out" effects of repulsive interactions. Despite these variations, the superfunnel paradigm applies to all SEMs we have tested: For a majority of neutral nets across different models, there exists a funnel-like organization of native stabilities for the sequences in a neutral net encoding for the same structure, and the thermodynamically most stable sequence is also the most robust against mutation.

Solvation versus freezing in a heteropolymer globule

We address the response of a random heteropolymer to preferential solvation of certain monomer types at the globule-solvent interface. For each set of monomers that can comprise the molecule's surface, we represent the ensemble of allowed configurations by a Gaussian distribution of energy levels, whose mean and variance depend on the set's composition. Within such a random energy model, mean surface composition is proportional to solvation strength under most conditions. The breadth of this linear response regime arises from the approximate statistical independence of surface and volume energies. Fluctuations play a crucial role in determining the excess of solvophilic monomers at the surface, and for a diverse set of monomer types can be overcome only by very strong solvent preference.

Dynamic polyhedral models of globular proteins

We have devised several mechanical models of globular proteins by approximating them to various polyhedra (dodecahedron, truncated octahedron, icosahedron, truncated icosahedron). The models comprise hollow blocks linked together in a flexible chain. Between blocks there is a set of several reversible, weak magnetic interactions such that when the chain is agitated, it will fold into a stable polyhedral structure about the size of a hand. Folding may be followed in real time with a video camera. Key to the success of the folding process is the lightness of the chain. Several side chains may also be added to the blocks such that they come together to create a polyhedral core when the chain folds. The models have a number of similarities to globular proteins: each chain folds into a unique, but dynamic, three-dimensional structure; the instructions that determine this structure are built into the configuration of blocks; and it is difficult to predict this structure given the unfolded block configuration. Furthermore, the chains fold quickly, generally in less than a minute, several pathways are involved, and these pathways progress through elements of "native" structure. In particular, the models emphasize the importance of restricted conformational mobility in assisting the chain to fold, and also in eliminating undesirable interactions. Because of these similarities to globular proteins, we believe that the polyhedral models will, with continued development, be helpful in understanding the protein folding process, while at the same time acting as valuable educational visual aids. They might also inspire the construction of new types of microscopic, self-assembling devices.

Thermodynamics of lattice heteropolymers

We calculate thermodynamic quantities of hydrophobic-polar (HP) lattice proteins by means of a multicanonical chain-growth algorithm that connects the new variants of the Pruned-Enriched Rosenbluth Method and flat histogram sampling of the entire energy space. Since our method directly simulates the density of states, we obtain results for thermodynamic quantities of the system for all temperatures. In particular, this algorithm enables us to accurately simulate the usually difficult accessible low-temperature region. Therefore, it becomes possible to perform detailed analyses of the low-temperature transition between ground states and compact globules.

Elastic behavior of short compact polymers

In this paper, we investigate the elastic behaviors of short compact polymers using the enumeration calculation method and the HP model on a two-dimensional square lattice. Both the mean-square end-to-end distance R(2) and the ratio of R(2)/S(2) increase with lambda. However, when the elongation ratio becomes larger, the curves of R(2)/S(2) become smooth and they are close to the limit of 10.50 for different compact polymers. We also investigate the changes of interior conformations in the process of tensile elongation through calculating the probabilities of three bond angles (i.e., 90 degrees, 180 degrees, and 270 degrees). The average energy and Helmholtz free energy per bond are both negative and increase with elongation ratio lambda. In the meantime, the elastic force per bond (f ) also increases with elongation ratio lambda, and the energy contribution to the elastic force (f(U)) increases first and then drops, and there exists the maximum of f(U) in the region of lambda=1.40-1.80 for different sequences. The entropy contribution to force (f(S)) is close to zero at a small elongation ratio lambda and then increases with lambda. Some comparisons with different sequences (including nonfolding and folding sequences) are also made.

Multicanonical chain-growth algorithm

We present a temperature-independent Monte Carlo method for the determination of the density of states of lattice proteins that combines the fast ground-state search strategy of the new pruned-enriched Rosenbluth chain-growth method and multicanonical reweighting for sampling the complete energy space. Since the density of states contains all energetic information of a statistical system, we can directly calculate the mean energy, specific heat, Helmholtz free energy, and entropy for all temperatures. We apply this method to lattice proteins consisting of hydrophobic and polar monomers, and for the examples of sequences considered, we identify the transitions between native, globule, and random coil states. Since no special properties of heteropolymers are involved in this algorithm, the method applies to polymer models as well.

Growth-based optimization algorithm for lattice heteropolymers

An improved version of the pruned-enriched-Rosenbluth method (PERM) is proposed and tested on finding lowest energy states in simple models of lattice heteropolymers. It is found to outperform not only the previous version of PERM, but also all other fully blind general purpose stochastic algorithms which have been employed on this problem. In many cases, it found new lowest energy states missed in previous papers. Limitations are discussed.

Relevance of structural segregation and chain compaction for the thermodynamics of folding of a hydrophobic protein model

The relevance of inside-outside segregation and chain compaction for the thermodynamics of folding of a hydrophobic protein model is probed by complete enumeration of two-dimensional chains of up to 18 monomers in the square lattice. The exact computation of Z scores for uniquely designed sequences confirms that Z tends to decrease linearly with sigma square root of N, as previously suggested by theoretical analysis and Monte Carlo simulations, where sigma, the standard deviation of the number of contacts made by different monomers in the target structure, is a measure of structural segregation and N is the chain length. The probability that the target conformation is indeed the unique global energy minimum of the designed sequence is found to increase dramatically with sigma, approaching unity at maximal segregation. However, due to the huge number of conformations with sub-maximal values of sigma, which correspond to intermediate, only mildly discriminative, values of Z, in addition to significant oscillations of Z around its estimated value, the probability that a correctly designed sequence corresponds to a maximally segregated conformation is small. This behavior of Z also explains the observed relation between sigma and different measures of folding cooperativity of correctly designed sequences.

Protein decoy assembly using short fragments under geometric constraints

A small set of protein fragments can represent adequately all known local protein structure. This set of fragments, along with a construction scheme that assembles these fragments into structures, defines a discrete (relatively small) conformation space, which approximates protein structures accurately. We generate protein decoys by sampling geometrically valid structures from this conformation space, biased by the secondary structure prediction for the protein. Unlike other methods, secondary structure prediction is the only protein-specific information used for generating the decoys. Nevertheless, these decoys are qualitatively similar to those found by others. The method works well for all-alpha proteins, and shows promising results for alpha and beta proteins.

Randomness, Structural Uniqueness, Modularity and Neutral Evolution in Sequence Space of Model Proteins

The genotype-phenotype map for short chains of a protein-like hetero-polymer model has been characterised [9, 12]. Hydrophobic-Polar (HP) sequences on a square lattice, their structures and partition functions have been exhaustively enumerated and analysed. Homologous sequences folding uniquely into the same structure are interconnected by point mutations. These

Flat histogram simulation of lattice polymer systems

We demonstrate the use of an algorithm called the Flat Histogram sampling algorithm for the simulation of two-dimensional lattice polymer systems. Thermodynamic properties, such as the average energy or entropy and other physical quantities such as the end-to-end distance or radius of gyration can be easily calculated using this method. The ground-state energy can also be determined. We also explore the accuracy and limitations of this method.