arXiv subjects

Markus Porto

Publications and source records attributed to Markus Porto.

At least 19 recordsLinked to original sources

arXiv2012

Network evolution towards optimal dynamical performance

Understanding the mutual interdependence between the behavior of dynamical processes on networks and the underlying topologies promises new insight for a large class of empirical networks. We present a generic approach to investigate this relationship which is applicable to a wide class of dynamics, namely to evolve networks using a performance measure based on the whole spectrum of the dynamics' time evolution operator. As an example, we consider the graph Laplacian describing diffusion processes, and we evolve the network structure such that a given sub-diffusive behavior emerges.

cond-mat.dis-nn↗

arXiv2009

Stochastic reconstruction of protein structures from effective connectivity profiles

We discuss a stochastic approach for reconstructing the native structures of proteins from the knowledge of the "effective connectivity", which is a one-dimensional structural profile constructed as a linear combination of the eigenvectors of the contact map of the target structure. The structural profile is used to bias a search of the conformational space towards the target structure in a Monte Carlo scheme operating on a C_alpha-chain of uniform, finite thickness. Structure information thus enters the folding dynamics via the effective connectivity, but the interaction is not restricted to pairs of amino acids that form native contacts, resulting in a free energy landscape which does not rely on the assumption of minimal frustration. Moreover, effective connectivity vectors can be predicted more readily from the amino acid sequence of proteins than the corresponding contact maps, thus suggesting that the stochastic protocol presented here could be effectively combined with other current methods for predicting native structures.

physics.bio-ph↗

arXiv2008

Fractional derivatives of random walks: Time series with long-time memory

We review statistical properties of models generated by the application of a (positive and negative order) fractional derivative operator to a standard random walk and show that the resulting stochastic walks display slowly-decaying autocorrelation functions. The relation between these correlated walks and the well-known fractionally integrated autoregressive (FIGARCH) models, commonly used in econometric studies, is discussed. The application of correlated random walks to simulate empirical financial times series is considered and compared with the predictions from FIGARCH and the simpler FIARCH processes. A comparison with empirical data is performed.

cond-mat.stat-mech↗

arXiv2007

Generating random networks with given degree-degree correlations and degree-dependent clustering

Random networks are widely used to model complex networks and research their properties. In order to get a good approximation of complex networks encountered in various disciplines of science, the ability to tune various statistical properties of random networks is very important. In this manuscript we present an algorithm which is able to construct arbitrarily degree-degree correlated networks with adjustable degree-dependent clustering. We verify the algorithm by using empirical networks as input and describe additionally a simple way to fix a degree-dependent clustering function if degree-degree correlations are given.

cond-mat.dis-nn↗

arXiv2007

Generation of arbitrarily two-point correlated random networks

Random networks are intensively used as null models to investigate properties of complex networks. We describe an efficient and accurate algorithm to generate arbitrarily two-point correlated undirected random networks without self- or multiple-edges among vertices. With the goal to systematically investigate the influence of two-point correlations, we furthermore develop a formalism to construct a joint degree distribution $P(j,k)$ which allows to fix an arbitrary degree distribution $P(k)$ and an arbitrary average nearest neighbor function $\knn(k)$ simultaneously. Using the presented algorithm, this formalism is demonstrated with scale-free networks ($P(k) \propto k^{-γ}$) and empirical complex networks ($P(k)$ taken from network) as examples. Finally, we generalize our algorithm to annealed networks which allows networks to be represented in a mean-field like manner.

cond-mat.stat-mech↗

arXiv2006

Multicomponent reaction-diffusion processes on complex networks

We study the reaction-diffusion process $A + B \to \emptyset$ on uncorrelated scale-free networks analytically. By a mean-field ansatz we derive analytical expressions for the particle pair-correlations and the particle density. Expressing the time evolution of the particle density in terms of the instantaneous particle pair-correlations, we determine analytically the `jamming' effect which arises in the case of multicomponent, pair-wise reactions. Comparing the relevant terms within the differential equation for the particle density, we find that the `jamming' effect diminishes in the long-time, low-density limit. This even holds true for the hubs of the network, despite that the hubs dynamically attract the particles.

cond-mat.stat-mech↗

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↗

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

`Generalized des Cloizeaux' exponent for self-avoiding walks on the incipient percolation cluster

We study the asymptotic shape of self-avoiding random walks (SAW) on the backbone of the incipient percolation cluster in d-dimensional lattices analytically. It is generally accepted that the configurational averaged probability distribution function for the end-to-end distance r of an N step SAW behaves as a power law for r -> 0. In this work, we determine the corresponding exponent using scaling arguments, and show that our suggested `generalized des Cloizeaux' expression for the exponent is in excellent agreement with exact enumeration results in two and three dimensions.

cond-mat.dis-nn↗

arXiv2000

Atomic scale engines: Cars and wheels

We introduce a new approach to build microscopic engines on the atomic scale that move translationally or rotationally and can perform useful functions such as pulling of a cargo. Characteristic of these engines is the possibility to determine dynamically the directionality of the motion. The approach is based on the transformation of the fed energy to directed motion through a dynamical competition between the intrinsic lengths of the moving object and the supporting carrier.

cond-mat↗

arXiv2000

Molecular motor that never steps backwards

We investigate the dynamics of a classical particle in a one-dimensional two-wave potential composed of two periodic potentials, that are time-independent and of the same amplitude and periodicity. One of the periodic potentials is externally driven and performs a translational motion with respect to the other. It is shown that if one of the potentials is of the ratchet type, translation of the potential in a given direction leads to motion of the particle in the same direction, whereas translation in the opposite direction leaves the particle localized at its original location. Moreover, even if the translation is random, but still has a finite velocity, an efficient directed transport of the particle occurs.

cond-mat↗

arXiv1999

Looking at friction through "shearons"

We study the response to shear of a one-dimensional monolayer embedded between two rigid plates, where the upper one is externally driven. The shear is shown to excite ``shearons'', which are collective modes of the embedded system with well defined spatial and temporal pattern, and which dominate the frictional properties of the driven system. We demonstrate that static friction, stick-slip events, and memory effects are well described in terms of the creation and/or annihilation of a shearon. This raises the possibility to control friction by modifying the excited shearon, which we examplify by introducing a defect at the bottom plate.

cond-mat.stat-mech↗

arXiv1999

Probability Distribution of the Shortest Path on the Percolation Cluster, its Backbone and Skeleton

We consider the mean distribution functions Phi(r|l), Phi(B)(r|l), and Phi(S)(r|l), giving the probability that two sites on the incipient percolation cluster, on its backbone and on its skeleton, respectively, connected by a shortest path of length l are separated by an Euclidean distance r. Following a scaling argument due to de Gennes for self-avoiding walks, we derive analytical expressions for the exponents g1=df+dmin-d and g1B=g1S-3dmin-d, which determine the scaling behavior of the distribution functions in the limit x=r/l^(nu) much less than 1, i.e., Phi(r|l) proportional to l^(-(nu)d)x^(g1), Phi(B)(r|l) proportional to l^(-(nu)d)x^(g1B), and Phi(S)(r|l) proportional to l^(-(nu)d)x^(g1S), with nu=1/dmin, where df and dmin are the fractal dimensions of the percolation cluster and the shortest path, respectively. The theoretical predictions for g1, g1B, and g1S are in very good agreement with our numerical results.

cond-mat.stat-mech↗