arXiv subjects

Paolo De Los Rios

Publications and source records attributed to Paolo De Los Rios.

At least 37 records · Page 2Linked to original sources

arXiv2013

Stochastic fluctuations and the detectability limit of network communities

We have analyzed the detectability limits of network communities in the framework of the popular Girvan and Newman benchmark. By carefully taking into account the inevitable stochastic fluctuations that affect the construction of each and every instance of the benchmark, we come to the conclusions that the native, putative partition of the network is completely lost even before the in-degree/out-degree ratio becomes equal to the one of a structure-less Erdös-Rényi network. We develop a simple iterative scheme, analytically well described by an infinite branching-process, to provide an estimate of the true detectability limit. Using various algorithms based on modularity optimization, we show that all of them behave (semi-quantitatively) in the same way, with the same functional form of the detectability threshold as a function of the network parameters. Because the same behavior has also been found by further modularity-optimization methods and for methods based on different heuristics implementations, we conclude that indeed a correct definition of the detectability limit must take into account the stochastic fluctuations of the network construction.

physics.soc-ph↗

arXiv2009

Vibrational entropy and the structural organization of proteins

In this paper we analyze the vibrational spectra of a large ensemble of non-homologous protein structures by means of a novel tool, that we coin the Hierarchical Network Model (HNM). Our coarse-grained scheme accounts for the intrinsic heterogeneity of force constants displayed by protein arrangements and also incorporates side-chain degrees of freedom. Our analysis shows that vibrational entropy per unit residue correlates with the content of secondary structure. Furthermore, we assess the individual contribution to vibrational entropy of the novel features of our scheme as compared with the predictions of state-of-the-art network models. This analysis highlights the importance of properly accounting for the intrinsic hierarchy in force strengths typical of the different atomic bonds that build up and stabilize protein scaffolds. Finally, we discuss possible implications of our findings in the context of protein aggregation phenomena.

q-bio.BM↗

arXiv2009

Extended navigability of small world networks: exact results and new insights

Navigability of networks, that is the ability to find any given destination vertex starting from any other vertex, is crucial to their usefulness. In 2000 Kleinberg showed that optimal navigability could be achieved in small-world networks provided that a special recipe was used to establish long range connections, and that a greedy algorithm, that ensures that the destination will be reached, is used. Here we provide an exact solution for the asymptotic behavior of such a greedy algorithm as a function of the system's parameters. Our solution enables us to show that the original claim that only a very special construction is optimal can be relaxed depending on further criteria, such as, for example, cost minimization, that must be satisfied.

cond-mat.stat-mech↗

arXiv2008

Temperature dependence of normal mode reconstructions of protein dynamics

Normal mode analysis is a widely used technique for reconstructing conformational changes of proteins from the knowledge of native structures. In this Letter, we investigate to what extent normal modes capture the salient features of the dynamics over a range of temperatures from close to T = 0 to above unfolding. We show that on the one hand, the use of normal modes at physiological temperatures is justified provided proteins are cooperative. On the other hand, it is imperative to consider several modes in order to eliminate the unpredictable temperature dependence of single- mode contributions to the protein fluctuations.

cond-mat.stat-mech↗

arXiv2008

Spectral Coarse Graining and Synchronization in Oscillator Networks

Coarse graining techniques offer a promising alternative to large-scale simulations of complex dynamical systems, as long as the coarse-grained system is truly representative of the initial one. Here, we investigate how the dynamical properties of oscillator networks are affected when some nodes are merged together to form a coarse-grained network. Moreover, we show that there exists a way of grouping nodes preserving as much as possible some crucial aspects of the network dynamics. This coarse graining approach provides a useful method to simplify complex oscillator networks, and more generally any network whose dynamics involves a Laplacian matrix.

cond-mat.dis-nn↗

arXiv2007

Diffusion-limited unbinding of small peptides from PDZ domains

PDZ domains are typical examples of binding motifs mediating the formation of protein-protein assemblies in many different cells. A quantitative characterization of the mechanisms intertwining structure, chemistry and dynamics with the PDZ function represent a challenge in molecular biology. Here we investigated the influence of native state topology on the thermodynamics and the dissociation kinetics for a complex PDZ-peptide via Molecular Dynamics simulations based on a coarse-grained description of PDZ domains. Our native-centric approach neglects chemical details but incorporates the basic structural information to reproduce the protein functional dynamics as it couples to the binding. We found that at physiological temperatures the unbinding of a peptide from the PDZ domain becomes increasingly diffusive rather than thermally activated, as a consequence of the significant reduction of the free energy barrier with temperature. In turn, this results in a significant slowing down of the process of two orders of magnitude with respect to the conventional Arrhenius extrapolation from low temperature calculations. Finally, a detailed analysis of a typical unbinding event based on the rupture times of single peptide-PDZ contacts allows to shed further light on the dissociation mechanism and to elaborate a coherent picture of the relation between function and dynamics in PDZ domains.

physics.bio-ph↗

arXiv2007

Structural efficiency of percolation landscapes in flow networks

Complex networks characterized by global transport processes rely on the presence of directed paths from input to output nodes and edges, which organize in characteristic linked components. The analysis of such network-spanning structures in the framework of percolation theory, and in particular the key role of edge interfaces bridging the communication between core and periphery, allow us to shed light on the structural properties of real and theoretical flow networks, and to define criteria and quantities to characterize their efficiency at the interplay between structure and functionality. In particular, it is possible to assess that an optimal flow network should look like a "hairy ball", so to minimize bottleneck effects and the sensitivity to failures. Moreover, the thorough analysis of two real networks, the Internet customer-provider set of relationships at the autonomous system level and the nervous system of the worm Caenorhabditis elegans --that have been shaped by very different dynamics and in very different time-scales--, reveals that whereas biological evolution has selected a structure close to the optimal layout, market competition does not necessarily tend toward the most customer efficient architecture.

cond-mat.dis-nn↗

arXiv2007

Interfaces and the edge percolation map of random directed networks

The traditional node percolation map of directed networks is reanalyzed in terms of edges. In the percolated phase, edges can mainly organize into five distinct giant connected components, interfaces bridging the communication of nodes in the strongly connected component and those in the in- and out-components. Formal equations for the relative sizes in number of edges of these giant structures are derived for arbitrary joint degree distributions in the presence of local and two-point correlations. The uncorrelated null model is fully solved analytically and compared against simulations, finding an excellent agreement between the theoretical predictions and the edge percolation map of synthetically generated networks with exponential or scale-free in-degree distribution and exponential out-degree distribution. Interfaces, and their internal organization giving place from "hairy ball" percolation landscapes to bottleneck straits, could bring new light to the discussion of how structure is interwoven with functionality, in particular in flow networks.

cond-mat.dis-nn↗

arXiv2007

Uncovering the topology of configuration space networks

The configuration space network (CSN) of a dynamical system is an effective approach to represent the ensemble of configurations sampled during a simulation and their dynamic connectivity. To elucidate the connection between the CSN topology and the underlying free-energy landscape governing the system dynamics and thermodynamics, an analytical soluti on is provided to explain the heavy tail of the degree distribution, neighbor co nnectivity and clustering coefficient. This derivation allows to understand the universal CSN network topology observed in systems ranging from a simple quadratic well to the native state of the beta3s peptide and a 2D lattice heteropolymer. Moreover CSN are shown to fall in the general class of complex networks describe d by the fitness model.

cond-mat.stat-mech↗

arXiv2006

On the origin of the Boson peak in globular proteins

We study the Boson Peak phenomenology experimentally observed in globular proteins by means of elastic network models. These models are suitable for an analytic treatment in the framework of Euclidean Random Matrix theory, whose predictions can be numerically tested on real proteins structures. We find that the emergence of the Boson Peak is strictly related to an intrinsic mechanical instability of the protein, in close similarity to what is thought to happen in glasses. The biological implications of this conclusion are also discussed by focusing on a representative case study.

cond-mat.soft↗

arXiv2006

Fractal Dimension and Localization of DNA Knots

The scaling properties of DNA knots of different complexities were studied by atomic force microscope. Following two different protocols DNA knots are adsorbed onto a mica surface in regimes of (i) strong binding, that induces a kinetic trapping of the three-dimensional (3D) configuration, and of (ii) weak binding, that permits (partial) relaxation on the surface. In (i) the gyration radius of the adsorbed DNA knot scales with the 3D Flory exponent $ν\approx 0.58$ within error. In (ii), we find $ν\approx 0.66$, a value between the 3D and 2D ($ν=3/4$) exponents, indicating an incomplete 2D relaxation or a different polymer universality class. Compelling evidence is also presented for the localization of the knot crossings in 2D.

cond-mat.soft↗

arXiv2006

The Glass-like Structure of Globular Proteins and the Boson Peak

Vibrational spectra of proteins and topologically disordered solids display a common anomaly at low frequencies, known as Boson peak. We show that such feature in globular proteins can be deciphered in terms of an energy landscape picture, as it is for glassy systems. Exploiting the tools of Euclidean random matrix theory, we clarify the physical origin of such anomaly in terms of a mechanical instability of the system. As a natural explanation, we argue that such instability is relevant for proteins in order for their molecular functions to be optimally rooted in their structures.

cond-mat.soft↗

arXiv2006

Physical realizability of small-world networks

Supplementing a lattice with long-range connections effectively models small-world networks characterized by a high local and global interconnectedness observed in systems ranging from society to the brain. If the links have a wiring cost associated to their length l, the corresponding distribution q(l) plays a crucial role. Uniform length distributions have received most attention despite indications that q(l) ~ l^{-α} exist, e.g. for integrated circuits, the Internet and cortical networks. While length distributions of this type were previously examined in the context of navigability, we here discuss for such systems the emergence and physical realizability of small-world topology. Our simple argument allows to understand under which condition and at what expense a small world results.

cond-mat.dis-nn↗

arXiv2005

Spatial small-world networks: A wiring-cost perspective

Supplementing a lattice with long-range connections effectively models small-world networks characterized by a high local and global interconnectedness observed in systems ranging from society to the brain. If the links have a wiring cost associated to their length l, the corresponding distribution q(l) plays a crucial role. Uniform length distributions have received most attention despite indications that q(l) ~ l^{-α} exist, e.g. for integrated circuits, the Internet and cortical networks. Here we discuss for such systems the emergence of small-world topology, its relationship to the wiring costs, the distribution of flows as well as the robustness with respect to random failures and overload. The main finding is that the choice of such a distribution leads to favorable attributes in most of the investigated properties.

cond-mat.dis-nn↗

arXiv2005

Slow energy relaxation of macromolecules and nano-clusters in solution

Many systems in the realm of nanophysics from both the living and inorganic world display slow relaxation kinetics of energy fluctuations. In this paper we propose a general explanation for such phenomenon, based on the effects of interactions with the solvent. Within a simple harmonic model of the system fluctuations, we demonstrate that the inhomogeneity of coupling to the solvent of the bulk and surface atoms suffices to generate a complex spectrum of decay rates. We show for Myoglobin and for a metal nano-cluster that the result is a complex, non-exponential relaxation dynamics.

cond-mat.stat-mech↗

arXiv2005

Finding instabilities in the community structure of complex networks

The problem of finding clusters in complex networks has been extensively studied by mathematicians, computer scientists and, more recently, by physicists. Many of the existing algorithms partition a network into clear clusters, without overlap. We here introduce a method to identify the nodes lying ``between clusters'' and that allows for a general measure of the stability of the clusters. This is done by adding noise over the weights of the edges of the network. Our method can in principle be applied with any clustering algorithm, provided that it works on weighted networks. We present several applications on real-world networks using the Markov Clustering Algorithm (MCL).

cond-mat.dis-nn↗

arXiv2005

Scaling exponents and probability distributions of DNA end-to-end distance

Correlation length exponent $ν$ for long linear DNA molecules was determined by direct measurement of the average end-to-end distance as a function of the contour length $s$ by means of atomic force microscopy (AFM). Linear DNA, up to 48'502 base pairs (bp), was irreversibly deposited from a solution onto silanized mica and imaged in air. Under the adsorption conditions used, the DNA is trapped onto the surface without any two-dimensional equilibration. The measured exponent is $ν= 0.589 \pm 0.006$, in agreement with the theoretical 3D value of $ν= 0.5880 \pm 0.0010$. The persistence length $\ell_p$ of DNA was estimated to be 44$\pm$3 nm, in agreement with the literature values. The distribution of the end-to-end distances for a given contour length $s$ and the exponents characterizing the distribution were determined for different $s$. For $s$ smaller or comparable to $\ell_p$, a delta function like distribution was observed, while for larger $s$, a probability distribution of the type $x^{d-1}x^g e^{-bx^δ}$ was observed with $g=0.33\pm0.22$ and $δ=2.58\pm0.76$. These values are compared to the theoretical exponents for Self-Avoiding Walk (SAW): namely $g=\frac{γ-1}ν$ and $δ=(1-ν)^{-1}$. So for $d=2$, $g\approx0.44$ and $δ=4$, while for $d=3$, $g\approx0.33$ and $δ\approx2.5$. The derived entropic exponent $γ$ is $γ=1.194\pm0.129$. The present data indicate that the DNA behaves on large length scales like a 3 dimensional SAW.

cond-mat.soft↗

arXiv2005

Functional Dynamics of PDZ Binding Domains: A Normal Mode Analysis

PDZ (Post-synaptic density-95/discs large/zonula occludens-1) domains are relatively small (80 to 120 residues) protein binding modules central in the organization of receptor clusters and in the association of cellular proteins. Their main function is to bind C-terminals of selected proteins that are recognized through specific amino-acids in their carboxyl end. Binding is associated with a deformation of the PDZ native structure and is responsible for dynamical changes in regions not in direct contact with the target. We investigate how this deformation is related to the harmonic dynamics of the PDZ structure and show that one low-frequency collective normal mode, characterized by the concerted movements of different secondary structures, is involved in the binding process. Our results suggest that even minimal structural changes are responsible of communication between distant regions of the protein, in agreement with recent Nuclear Magnetic Resonance (NMR) experiments. Thus PDZ domains are a very clear example of how collective normal modes are able to characterize the relation between function and dynamics of proteins, and to provide indications on the precursors of binding/unbonding events.

q-bio.BM↗