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I. Ispolatov

Publications and source records attributed to I. Ispolatov.

At least 19 recordsLinked to original sources
arXiv2009

Speciation due to hybrid necrosis in plant-pathogen models

We develop a model for speciation due to postzygotic incompatibility generated by autoimmune reactions. The model is based on predator-prey interactions between a host plants and their pathogens. Such interactions are often frequency-dependent, so that pathogen attack is focused on the most abundant plant phenotype, while rare plant types may escape pathogen attack. Thus, frequency dependence can generate disruptive selection, which can give rise to speciation if distant phenotypes become reproductively isolated. Based on recent experimental evidence from {\it Arabidopsis}, we assume that at the molecular level, incompatibility between strains is caused by epistatic interactions between two proteins in the plant immune system, the guard and the guardee. Within each plant strain, immune reactions occur when the guardee protein is modified by a pathogen effector, and the guard subsequently binds to the guardee, thus precipitating an immune response. However, when guard and guardee proteins come from phenotypically distant parents, a hybrid's immune system can be triggered by erroneous interactions between these proteins even in the absence of pathogen attack, leading to severe autoimmune reactions in hybrids. Our model shows how phenotypic variation generated by frequency-dependent host-pathogen interactions can lead to postzygotic incompatibility between extremal types, and hence to speciation.

q-bio.PE↗
arXiv2007

Propagation of large concentration changes in reversible protein binding networks

We study how the dynamic equilibrium of the reversible protein-protein binding network in yeast Saccharomyces cerevisiae responds to large changes in abundances of individual proteins. The magnitude of shifts between free and bound concentrations of their immediate and more distant neighbors in the network is influenced by such factors as the network topology, the distribution of protein concentrations among its nodes, and the average binding strength. Our primary conclusion is that, on average, the effects of a perturbation are strongly localized and exponentially decay with the network distance away from the perturbed node, which explains why, despite globally connected topology, individual functional modules in such networks are able to operate fairly independently. We also found that under specific favorable conditions, realized in a significant number of paths in the yeast network, concentration perturbations can selectively propagate over considerable network distances (up to four steps). Such "action-at-a-distance" requires high concentrations of heterodimers along the path as well as low free (unbound) concentration of intermediate proteins.

q-bio.MN↗
arXiv2007

Detection of the dominant direction of information flow in densely interconnected regulatory networks

Finding the dominant direction of flow of information in densely interconnected regulatory or signaling networks is required in many applications in computational biology and neuroscience. This is achieved by first identifying and removing links which close up feedback loops in the original network and hierarchically arranging nodes in the remaining network. In mathematical language this corresponds to a problem of making a graph acyclic by removing as few links as possible and thus altering the original graph in the least possible way. Practically in all applications the exact solution of this problem requires an enumeration of all combinations of removed links, which is computationally intractable. We introduce and compare two algorithms: the deterministic, 'greedy' algorithm that preferentially cuts the links that participate in the largest number of feedback cycles, and the probabilistic one based on a simulated annealing of a hierarchical layout of the network which minimizes the number of ``backward'' links going from lower to higher hierarchical levels. We find that the annealing algorithm outperforms the deterministic one in terms of speed, memory requirement, and the actual number of removed links. Implications for system biology and directions for further research are discussed.

q-bio.MN↗
arXiv2006

Finding mesoscopic communities in sparse networks

We suggest a fast method to find possibly overlapping network communities of a desired size and link density. Our method is a natural generalization of the finite-$T$ superparamegnetic Potts clustering introduced by Blatt, Wiseman, and Domany (Phys. Rev. Lett. v.76, 3251 (1996) and the recently suggested by Reichard and Bornholdt (Phys. Rev. Lett. v.93, 21870 (2004)) annealing of Potts model with global antiferromagnetic term. Similarly to both preceding works, the proposed generalization is based on ordering of ferromagnetic Potts model; the novelty of the proposed approach lies in the adjustable dependence of the antiferromagnetic term on the population of each Potts state, which interpolates between the two previously considered cases. This adjustability allows to empirically tune the algorithm to detect the maximum number of communities of the given size and link density. We illustrate the method by detecting protein complexes in high-throughput protein binding networks.

q-bio.MN↗
arXiv2005

Binaries and core-ring structures in self-gravitating systems

Low energy states of self-gravitating systems with finite angular momentum are considered. A constraint is introduced to confine cores and other condensed objects within the system boundaries by gravity alone. This excludes previously observed astrophysically irrelevant asymmetric configurations with a single core. We show that for an intermediate range of a short-distance cutoff and small angular momentum, the equilibrium configuration is an asymmetric binary. For larger angular momentum or for a smaller range of the short distance cutoff, the equilibrium configuration consists of a central core and an equatorial ring. The mass of the ring varies between zero for vanishing rotation and the full system mass for the maximum angular momentum $L_{max}$ a localized gravitationally bound system can have. The value of $L_{max}$ scales as $\sqrt{\ln(1/x_0)}$, where $x_0$ is a ratio of a short-distance cutoff range to the system size. An example of the soft gravitational potential is considered; the conclusions are shown to be valid for other forms of short-distance regularization.

cond-mat.stat-mech↗
arXiv2005

Cliques and duplication-divergence network growth

A population of complete subgraphs or cliques in a network evolving via duplication-divergence is considered. We find that a number of cliques of each size scales linearly with the size of the network. We also derive a clique population distribution that is in perfect agreement with both the simulation results and the clique statistic of the protein-protein binding network of the fruit fly. In addition, we show that such features as fat-tail degree distribution, various rates of average degree growth and non-averaging, revealed recently for only the particular case of a completely asymmetric divergence, are present in a general case of arbitrary divergence.

q-bio.MN↗
arXiv2004

Duplication-divergence model of protein interaction network

We show that the protein-protein interaction networks can be surprisingly well described by a very simple evolution model of duplication and divergence. The model exhibits a remarkably rich behavior depending on a single parameter, the probability to retain a duplicated link during divergence. When this parameter is large, the network growth is not self-averaging and an average vertex degree increases algebraically. The lack of self-averaging results in a great diversity of networks grown out of the same initial condition. For small values of the link retention probability, the growth is self-averaging, the average degree increases very slowly or tends to a constant, and a degree distribution has a power-law tail.

q-bio.MN↗
arXiv2004

Anomalously slow phase transitions in self-gravitating systems

Kinetics of collapse and explosion transitions in microcanonical self-gravitating ensembles is analyzed. A system of point particles interacting via an attractive soft Coulomb potential and confined to a spherical container is considered. We observed that for 100--200 particles collapse takes $10^3$ -- $10^4$ particle crossing times to complete, i. e., it is by 2-3 orders of magnitude slower than velocity relaxation. In addition, it is found that the collapse time decreases rapidly with the increase of the softcore radius. We found that such an anomalously long collapse time is caused by the slow energy exchange between a higher-temperature compact core and relatively cold diluted halo. The rate of energy exchange between the faster modes of the core particles and slower-moving particles of the halo is exponentially small in the ratio of the frequencies of these modes. As the softcore radius increases, and the typical core modes become slower, the ratio of core and halo frequencies decreases and the collapse accelerates. Implications to astrophysical systems and phase transition kinetics are discussed.

cond-mat.stat-mech↗
arXiv2003

Collapses and explosions in self-gravitating systems

Collapse and reverse to collapse explosion transition in self-gravitating systems are studied by molecular dynamics simulations. A microcanonical ensemble of point particles confined to a spherical box is considered; the particles interact via an attractive soft Coulomb potential. It is observed that the collapse in the particle system indeed takes place when the energy of the uniform state is put near or below the metastability-instability threshold (collapse energy), predicted by the mean-field theory. Similarly, the explosion in the particle system occurs when the energy of the core-halo state is increased above the explosion energy, where according to the mean field predictions the core-halo state becomes unstable. For a system consisting of 125 -- 500 particles, the collapse takes about $10^5$ single particle crossing times to complete, while a typical explosion is by an order of magnitude faster. A finite lifetime of metastable states is observed. It is also found that the mean-field description of the uniform and the core-halo states is exact within the statistical uncertainty of the molecular dynamics data.

cond-mat.stat-mech↗
arXiv2002

Phase diagram of self-attracting systems

Phase diagram of microcanonical ensembles of self-attracting particles is studied for two types of short-range potential regularizations: self-gravitating fermions and classical particles interacting via attractive soft $-(r^2+r_0^2)^{-1/2}$ Coulomb potential. When the range of regularization is sufficiently short, the self-attracting systems exhibit gravitational or collapse-like transition. As the fermionic degeneracy or the softness radius increases, the gravitational phase transition crosses over to a normal first-order phase transition, becomes second-order at a critical point, and finally disappears. Applicability of a commonly used saddle-point or mean-field approximation and importance of metastable states is discussed.

cond-mat.stat-mech↗
arXiv2001

Modeling eruptions of Karymsky volcano

A model is proposed to explain temporal patterns of activity in a class of periodically exploding Strombolian-type volcanos. These patterns include major events (explosions) which follow each other every 10-30 minutes and subsequent tremor with a typical period of 1 second. This two-periodic activity is thought to be caused by two distinct mechanisms of accumulation of the elastic energy in the moving magma column: compressibility of the magma in the lower conduit and viscoelastic response of the almost solid magma plug on the top. A release of the elastic energy happens when a stick-slip dynamic phase transition in a boundary layer along the walls of the conduit occurs; this phase transition is driven by the shear stress accumulated in the boundary layer. The first-order character and intrinsic hysteresis of this phase transition explains the long periods of inactivity in the explosion cycle. Temporal characteristics of the model are found to be qualitatively similar to the acoustic and seismic signals recorded at Karymsky volcano in Kamchatka.

physics.geo-ph↗
arXiv2001

Collapse in $1/r^α$ interacting systems

Collapse, or a gravitational-like phase transition is studied in a microcanonical ensemble of particles with an attractive $1/r^α$ potential. A mean field continuous integral equation is used to determine a saddle-point density profile that extremizes the entropy functional. For all $0<α<3$, a critical energy is determined below which the entropy of the system exhibits a discontinuous jump. If an effective short-range cutoff is applied, the entropy jump is finite; if not, the entropy diverges to $+\infty$. A stable integral equation solution represents a state with maximal entropy; the reverse is always true only for a modified integral equation introduced here.

cond-mat.stat-mech↗
arXiv2001

On first-order phase transition in microcanonical and canonical non-extensive systems

Two examples of Microcanonical Potts models, 2-dimensional nearest neighbor and mean field, are considered via exact enumeration of states and analytical asymptotic methods. In the interval of energies corresponding to a first order phase transition, both of these models exhibit a convex dip in the entropy vs energy plot and a region with negative specific heat within the dip. It is observed that in the nearest neighbor model the dip flattens and disappears as the lattice size grows, while in the mean field model the dip persists even in the limit of an infinite system. If formal transitions from microcanonical to canonical ensembles and back are performed for an infinite but non-extensive system, the convex dip in the microcanonical entropy plot disappears.

cond-mat.stat-mech↗
arXiv2000

Correlation functions in decorated lattice models

Occupation probabilities for primary-secondary-primary cell strings and correlation functions for primary sites of a decorated lattice model are expressed through the well-studied partition function and correlation functions of the Ising model. The results are analogous to those found in related lattice models of hydrophobic interactions and are interpreted in similar terms.

cond-mat.stat-mech↗
arXiv2000

Symmetry effects and equivalences in lattice models of hydrophobic interaction

We establish the equivalence of a recently introduced discrete model of the hydrophobic interaction, as well as its extension to continuous state variables, with the Ising model in a magnetic field with temperature-dependent strength. In order to capture the effect of symmetries of the solvent particles we introduce a generalized multi-state model. We solve this model - which is not of the Ising type - exactly in one dimension. Our findings suggest that a small increase in symmetry decreases the amplitude of the solvent-mediated part of the potential of mean force between solute particles and enhances the solubility in a very simple fashion. High symmetry decreases also the range of the attractive potential. This weakening of the hydrophobic effect observed in the model is in agreement with the notion that the effect is entropic in origin.

cond-mat.stat-mech↗
arXiv2000

Phase Transition in a Traffic Model with Passing

We investigate a traffic model in which cars either move freely with quenched intrinsic velocities or belong to clusters formed behind slower cars. In each cluster, the next-to-leading car is allowed to pass and resume free motion. The model undergoes a phase transition from a disordered phase for the high passing rate to a jammed phase for the low rate. In the disordered phase, the cluster size distribution decays exponentially in the large size limit. In the jammed phase, the cluster size distribution has a power law tail and in addition there is an infinite-size cluster. Mean-field equations, describing the model in the framework of Maxwell approximation, correctly predict the existence of phase transition and adequately describe the disordered phase; properties of the jammed phase are studied numerically.

cond-mat.stat-mech↗
arXiv1999

Particle Systems with Stochastic Passing

We study a system of particles moving on a line in the same direction. Passing is allowed and when a fast particle overtakes a slow particle, it acquires a new velocity drawn from a distribution P_0(v), while the slow particle remains unaffected. We show that the system reaches a steady state if P_0(v) vanishes at its lower cutoff; otherwise, the system evolves indefinitely.

cond-mat.stat-mech↗