arXiv subjects

Michele Vendruscolo

Publications and source records attributed to Michele Vendruscolo.

At least 37 records · Page 2Linked to original sources

arXiv2007

Importance of Metastable States in the Free Energy Landscapes of Polypeptide Chains

We show that the interplay between excluded volume effects, hydrophobicity, and hydrogen bonding of a tube-like representation of a polypeptide chain gives rise to free energy landscapes that exhibit a small number of metastable minima corresponding to common structural motifs observed in proteins. The complexity of the landscape increases only moderately with the length of the chain. Analysis of the temperature dependence of these landscapes reveals that the stability of specific metastable states is maximal at a temperature close to the mid-point of folding. These mestastable states are therefore likely to be of particular significance in determining the generic tendency of proteins to aggregate into potentially pathogenic agents.

cond-mat.soft↗

arXiv2004

Looking at structure, stability, and evolution of proteins through the principal eigenvector of contact matrices and hydrophobicity profiles

We review and further develop an analytical model that describes how thermodynamic constraints on the stability of the native state influence protein evolution in a site-specific manner. To this end, we represent both protein sequences and protein structures as vectors: Structures are represented by the principal eigenvector (PE) of the protein contact matrix, a quantity that resembles closely the effective connectivity of each site; Sequences are represented through the ``interactivity'' of each amino acid type, using novel parameters that are correlated with hydropathy scales. These interactivity parameters are more strongly correlated than the other hydropathy scales that we examine with: (1) The change upon mutations of the unfolding free energy of proteins with two-states thermodynamics; (2) Genomic properties as the genome-size and the genome-wide GC content; (3) The main eigenvectors of the substitution matrices. The evolutionary average of the interactivity vector correlates very strongly with the PE of a protein structure. Using this result, we derive an analytic expression for site-specific distributions of amino acids across protein families in the form of Boltzmann distributions whose ``inverse temperature'' is a function of the PE component. We show that our predictions are in agreement with site-specific amino acid distributions obtained from the Protein Data Bank, and we determine the mutational model that best fits the observed site-specific amino acid distributions. Interestingly, the optimal model almost minimizes the rate at which deleterious mutations are eliminated by natural selection.

q-bio.BM↗

arXiv2004

Prediction of site-specific amino acid distributions and limits of divergent evolutionary changes in protein sequences

We derive an analytic expression for site-specific stationary distributions of amino acids from the Structurally Constrained Neutral (SCN) model of protein evolution with conservation of folding stability. The stationary distributions that we obtain have a Boltzmann-like shape, and their effective temperature parameter, measuring the limit of divergent evolutionary changes at a given site, can be predicted from a site-specific topological property, the principal eigenvector of the contact matrix of the native conformation of the protein. These analytic results, obtained without free parameters, are compared with simulations of the SCN model and with the site-specific amino acid distributions obtained from the Protein Data Bank. These results also provide new insights into how the topology of a protein fold influences its designability, i.e. the number of sequences compatible with that fold. The dependence of the effective temperature on the principal eigenvector decreases for longer proteins, a possible consequence of the fact that selection for thermodynamic stability becomes weaker in this case.

q-bio.BM↗

arXiv2004

The principal eigenvector of contact matrices and hydrophobicity profiles in proteins

With the aim to study the relationship between protein sequences and their native structures, we adopt vectorial representations for both sequence and structure. The structural representation is based on the Principal Eigenvector of the fold's contact matrix (PE). As recently shown, the latter encodes sufficient information for reconstructing the whole contact matrix. The sequence is represented through a Hydrophobicity Profile (HP), using a generalized hydrophobicity scale that we obtain from the principal eigenvector of a residue-residue interaction matrix and denote it as interactivity scale. Using this novel scale, we define the optimal HP of a protein fold, and predict, by means of stability arguments, that it is strongly correlated with the PE of the fold's contact matrix. This prediction is confirmed through an evolutionary analysis, which shows that the PE correlates with the HP of each individual sequence adopting the same fold and, even more strongly, with the average HP of this set of sequences. Thus, protein sequences evolve in such a way that their average HP is close to the optimal one, implying that neutral evolution can be viewed as a kind of motion in sequence space around the optimal HP. Our results indicate that the correlation coefficient between N-dimensional vectors constitutes a natural metric in the vectorial space in which we represent both protein sequences and protein structures, which we call Vectorial Protein Space. In this way, we define a unified framework for sequence to sequence, sequence to structure, and structure to structure alignments. We show that the interactivity scale is nearly optimal both for the comparison of sequences with sequences and sequences with structures.

q-bio.BM↗

arXiv2004

Reconstruction of protein structures from a vectorial representation

We show that the contact map of the native structure of globular proteins can be reconstructed starting from the sole knowledge of the contact map's principal eigenvector, and present an exact algorithm for this purpose. Our algorithm yields a unique contact map for all 221 globular structures of PDBselect25 of length $N \le 120$. We also show that the reconstructed contact maps allow in turn for the accurate reconstruction of the three-dimensional structure. These results indicate that the reduced vectorial representation provided by the principal eigenvector of the contact map is equivalent to the protein structure itself. This representation is expected to provide a useful tool in bioinformatics algorithms for protein structure comparison and alignment, as well as a promising intermediate step towards protein structure prediction.

q-bio.BM↗

arXiv2004

Inhibition of protein crystallization by evolutionary negative design

In this perspective we address the question: why are proteins seemingly so hard to crystallize? We suggest that this is because of evolutionary negative design, i.e. proteins have evolved not to crystallize, because crystallization, as with any type of protein aggregation, compromises the viability of the cell. There is much evidence in the literature that supports this hypothesis, including the effect of mutations on the crystallizability of a protein, the correlations found in the properties of crystal contacts in bioinformatics databases, and the positive use of protein crystallization by bacteria and viruses.

q-bio.BM↗

arXiv2002

Lack of self-averaging in neutral evolution of proteins

We simulate neutral evolution of proteins imposing conservation of the thermodynamic stability of the native state in the framework of an effective model of folding thermodynamics. This procedure generates evolutionary trajectories in sequence space which share two universal features for all of the examined proteins. First, the number of neutral mutations fluctuates broadly from one sequence to another, leading to a non-Poissonian substitution process. Second, the number of neutral mutations displays strong correlations along the trajectory, thus causing the breakdown of self-averaging of the resulting evolutionary substitution process.

cond-mat↗

arXiv2002

Statistical properties of neutral evolution

Neutral evolution is the simplest model of molecular evolution and thus it is most amenable to a comprehensive theoretical investigation. In this paper, we characterize the statistical properties of neutral evolution of proteins under the requirement that the native state remains thermodynamically stable, and compare them to the ones of Kimura's model of neutral evolution. Our study is based on the Structurally Constrained Neutral (SCN) model which we recently proposed. We show that, in the SCN model, the substitution rate decreases as longer time intervals are considered, and fluctuates strongly from one branch of the evolutionary tree to another, leading to a non-Poissonian statistics for the substitution process. Such strong fluctuations are also due to the fact that neutral substitution rates for individual residues are strongly correlated for most residue pairs. Interestingly, structurally conserved residues, characterized by a much below average substitution rate, are also much less correlated to other residues and evolve in a much more regular way. Our results could improve methods aimed at distinguishing between neutral and adaptive substitutions as well as methods for computing the expected number of substitutions occurred since the divergence of two protein sequences.

cond-mat↗

arXiv2002

Connectivity of neutral networks and structural conservation in protein evolution

Protein structures are much more conserved than sequences during evolution. Based on this observation, we investigate the consequences of structural conservation on protein evolution. We study seven of the most studied protein folds, finding out that an extended neutral network in sequence space is associated to each of them. Within our model, neutral evolution leads to a non-Poissonian substitution process, due to the broad distribution of connectivities in neutral networks. The observation that the substitution process has non-Poissonian statistics has been used against the original Kimura's neutral theory, while our model shows that this is a generic property of neutral evolution with structural conservation. Our model also predicts that the substitution rate can strongly fluctuate from one branch to another of the evolutionary tree. The average sequence similarity within a neutral network is close to the threshold of randomness, as observed for families of sequences sharing the same fold. Nevertheless, some positions are more difficult to mutate than others. We compare such structurally conserved positions to positions conserved in protein evolution, suggesting that our model can be a valuable tool to distinguish structural from functional conservation in databases of protein families. These results indicate that a synergy between database analysis and structurally-based computational studies can increase our understanding of protein evolution.

cond-mat.soft↗

arXiv2001

Automated assignment of SCOP and CATH protein structure classification from FSSP scores

We present an automated procedure to assign CATH and SCOP classifications to proteins whose FSSP score is available. CATH classification is assigned down to the topology level and SCOP classification to the fold level. As the FSSP database is updated weekly, this method makes it possible to update also CATH and SCOP with the same frequency. Our predictions have a nearly perfect success rate when ambiguous cases are discarded. These ambiguous cases are intrinsic in any protein structure classification, which relies on structural information alone. Hence, we introduce the notion of ``twilight zone for structure classification''. We further suggest that in order to resolve these ambiguous cases other criteria of classification, based also on information about sequence and function, must be used.

cond-mat.soft↗

arXiv2000

Structurally constrained protein evolution: results from a lattice simulation

We simulate the evolution of a protein-like sequence subject to point mutations, imposing conservation of the ground state, thermodynamic stability and fast folding. Our model is aimed at describing neutral evolution of natural proteins. We use a cubic lattice model of the protein structure and test the neutrality conditions by extensive Monte Carlo simulations. We observe that sequence space is traversed by neutral networks, i.e. sets of sequences with the same fold connected by point mutations. Typical pairs of sequences on a neutral network are nearly as different as randomly chosen sequences. The fraction of neutral neighbors has strong sequence to sequence variations, which influence the rate of neutral evolution. In this paper we study the thermodynamic stability of different protein sequences. We relate the high variability of the fraction of neutral mutations to the complex energy landscape within a neutral network, arguing that valleys in this landscape are associated to high values of the neutral mutation rate. We find that when a point mutation produces a sequence with a new ground state, this is likely to have a low stability. Thus we tentatively conjecture that neutral networks of different structures are typically well separated in sequence space. This results indicates that changing significantly a protein structure through a biologically acceptable chain of point mutations is a rare, although possible, event.

cond-mat.stat-mech↗

arXiv1999

Folding Lennard-Jones proteins by a contact potential

We studied the possibility to approximate a Lennard Jones interaction by a pairwise contact potential. First we used a Lennard-Jones potential to design off-lattice, protein-like heteropolymer sequences, whose lowest energy (native) conformations were then identified by Molecular Dynamics. Then we turned to investigate whether one can find a pairwise contact potential, whose ground states are the contact maps associated with these native conformations. We show that such a requirement cannot be satisfied exactly - i.e. no such contact parameters exist. Nevertheless, we found that one can find contact energy parameters for which an energy minimization procedure, acting in the space of contact maps, yields maps whose corresponding structures are close to the native ones. Finally we show that when these structures are used as the initial point of a Molecular Dynamics energy minimization process, the correct native folds are recovered with high probability.

cond-mat.stat-mech↗

arXiv1999

Protein folding using contact maps

We present the development of the idea to use dynamics in the space of contact maps as a computational approach to the protein folding problem. We first introduce two important technical ingredients, the reconstruction of a three dimensional conformation from a contact map and the Monte Carlo dynamics in contact map space. We then discuss two approximations to the free energy of the contact maps and a method to derive energy parameters based on perceptron learning. Finally we present results, first for predictions based on threading and then for energy minimization of crambin and of a set of 6 immunoglobulins. The main result is that we proved that the two simple approximations we studied for the free energy are not suitable for protein folding. Perspectives are discussed in the last section.

cond-mat.soft↗

arXiv1998

Neutral evolution of model proteins: diffusion in sequence space and overdispersion

We simulate the evolution of model protein sequences subject to mutations. A mutation is considered neutral if it conserves 1) the structure of the ground state, 2) its thermodynamic stability and 3) its kinetic accessibility. All other mutations are considered lethal and are rejected. We adopt a lattice model, amenable to a reliable solution of the protein folding problem. We prove the existence of extended neutral networks in sequence space -- sequences can evolve until their similarity with the starting point is almost the same as for random sequences. Furthermore, we find that the rate of neutral mutations has a broad distribution in sequence space. Due to this fact, the substitution process is overdispersed (the ratio between variance and mean is larger than one). This result is in contrast with the simplest model of neutral evolution, which assumes a Poisson process for substitutions, and in qualitative agreement with biological data.

cond-mat.stat-mech↗

arXiv1998

Hydrophobicity and Unique Folding of Selected Polymers

In suitable environments, proteins, nucleic acids and certain synthetic polymers fold into unique conformations. This work shows that it is possible to construct lattice models of foldable heteropolymers by expressing the energy only in terms of individual properties of monomers, such as the exposure to the solvent and the steric factor.

cond-mat.soft↗

arXiv1998

Elusive Unfoldability: Learning a Contact Potential to Fold Crambin

We investigate the extent to which the commonly used standard pairwise contact potential can be used to identify the native fold of a protein. Ideally one would hope that a universal energy function exists, for which the native folds of all proteins are the respective ground states. Here we pose a much more restricted question: is it possible to find a set of contact parameters for which the energy of the native contact map of a single protein (crambin) is lower than that of all possible physically realizable decoy maps. We seek such a set of parameters by perceptron learning, a procedure which is guaranteed to find such a set if it exists. We found that it is extremely hard (and most probably, impossible) to fine tune contact parameters that will assign all alternative conformations higher energy than that of the native map. This finding clearly indicates that it is impossible to derive a general pairwise contact potential that can be used to fold any given protein. Inclusion of additional energy terms, such as hydrophobic (solvation), hydrogen bond or multi-body interactions may help to attain foldability within specific structural families.

cond-mat.soft↗

arXiv1997

Recovery of Protein Structure from Contact Maps

We present an efficient algorithm to recover the three dimensional structure of a protein from its contact map representation. First we show that when a physically realizable map is used as target, our method generates a structure whose contact map is essentially similar to the target. Furthermore, the reconstructed and original structures are similar up to the resolution of the contact map representation. Next we use non-physical target maps, obtained by corrupting a physical one; in this case our method essentially recovers the underlying physical map and structure. Hence our algorithm will help to fold proteins, using dynamics in the space of contact maps. Finally we investigate the manner in which the quality of the recovered structure degrades when the number of contacts is reduced.

cond-mat.soft↗

arXiv1997

Stability Threshold as a Selection Principle for Protein Design

The sensitivity of the native states of protein-like heteropolymers to mutations modelled as perturbations in the interaction potential between amino acids is studied. The stability threshold against mutations is shown to be zero for random heteropolymers on a lattice in two dimensions, whereas a design procedure modelling evolution produces a non-zero threshold. We introduce an evolution-like protein design procedure based on an optimization of the stability threshold that is shown to naturally ensure thermodynamic stability as well.

cond-mat.soft↗