Evolution of weighted scale-free networks in empirical data

Weighted scale-free networks exhibit two types of degree-strength relationship: linear and nonlinear relationships between them. To understand the mechanism underlying such empirical relationships, theoretical evolution models for weighted scale-free networks have been introduced for each case. However, those models have not yet been tested with empirical data. In this study, we collect temporal records of several online bulletin board systems and a movie actor network. We measure the growth rates of degree and strength of each vertex and weight of each edge within the framework of preferential attachment (PA). We also measure the probability of creating new edges between unconnected pairs of vertices. Then, based on the measured rates, linear and nonlinear growth models are constructed. We find that indeed the dynamics of creating new edges and adding weight to existing edges in a nonlocal manner is essential to reproduce the nonlinear degree-strength relationship. We also find that the degree-driven PA rule is more appropriate to real systems rather than the strength-driven one used for the linear model

Effects of molecular crowding and confinement on the spatial organization of a biopolymer

A chain molecule can be entropically collapsed in a crowded medium in a free or confined space. Here, we present a unified view of how molecular crowding collapses a flexible polymer in three distinct spaces: free, cylindrical, and (two-dimensional) slit-like. Despite their seeming disparities, a few general features characterize all these cases, even though the phi(c)-dependence of chain compaction differs between the two cases: a > a(c) and a a(c) (applicable to a coarse-grained model of bacterial chromosomes), chain size depends on the ratio a phi(c)/a(c), and "full'' compaction occurs universally at a phi(c)/a(c) approximate to 1; for a(c) > a (relevant for protein folding), it is controlled by phi(c) alone and crowding has a modest effect on chain size in a cellular environment (phi(c) approximate to 0.3). Also for a typical parameter range of biological relevance, molecular crowding can be viewed as effectively reducing the solvent quality, independent of confinement.NSERC (Canada)Korea Institute of Science and Technology Information (KISTI)Basic Science Research Program [2015R1D1A1A09057469]KIAS (Korea Institute for Advanced Study

How are molecular crowding and the spatial organization of a biopolymer interrelated

In a crowded cellular interior, dissolved biomolecules or crowders exert excluded volume effects on other biomolecules, which in turn control various processes including protein aggregation and chromosome organization. As a result of these effects, a long chain molecule can be phase-separated into a condensed state, redistributing the surrounding crowders. Using computer simulations and a theoretical approach, we study the interrelationship between molecular crowding and chain organization. In a parameter space of biological relevance, the distributions of monomers and crowders follow a simple relationship: the sum of their volume fractions rescaled by their size remains constant. Beyond a physical picture of molecular crowding it offers, this finding explains a few key features of what has been known about chromosome organization in an E. coli cell.NSERC (Canada)Korea Institute of Science and Technology Information (KISTI)Basic Science Research Program [2015R1D1A1A09057469]KIAS (Korea Institute for Advanced Study

A ring-polymer model shows how macromolecular crowding controls chromosome-arm organization in Escherichia coli

Abstract Macromolecular crowding influences various cellular processes such as macromolecular association and transcription, and is a key determinant of chromosome organization in bacteria. The entropy of crowders favors compaction of long chain molecules such as chromosomes. To what extent is the circular bacterial chromosome, often viewed as consisting of “two arms”, organized entropically by crowding? Using computer simulations, we examine how a ring polymer is organized in a crowded and cylindrically-confined space, as a coarse-grained bacterial chromosome. Our results suggest that in a wide parameter range of biological relevance crowding is essential for separating the two arms in the way observed with Escherichia coli chromosomes at fast-growth rates, in addition to maintaining the chromosome in an organized collapsed state. Under different conditions, however, the ring polymer is centrally condensed or adsorbed onto the cylindrical wall with the two arms laterally collapsed onto each other. We discuss the relevance of our results to chromosome-membrane interactions

Expansion dynamics of a self-avoiding polymer in a cylindrical pore

Inspired by recent bacterial chromosome experiments in narrow channels, we simulate the expansion (and internal) dynamics of a self-avoiding polymer under cylindrical confinement. The chain is trapped in a piston, compressed up to $20\%$ of its equilibrium length, and released unidirectionally from the right end of the piston. Our results suggest that the chain initially expands like a concentrated hard-sphere system, enters a subdiffusive regime at an intermediate time, and eventually relaxes globally to its equilibrium size. Using our results, we test a few theoretical models (e.g., a Flory-type approach), in which the blob-blob or monomer-monomer interaction determines “expansion forces,” clarifying their applicability. Our results can be used for exploring further the polymer aspect of bacterial chromosomes

Finite-size scaling in random K-satisfiability problems

We provide a comprehensive view of various phase transitions in random K-satisfiability problems solved by stochastic-local-search algorithms. In particular, we focus on the finite-size scaling (FSS) exponent, which is mathematically important and practically useful in analyzing finite systems. Using the FSS theory of nonequilibrium absorbing phase transitions, we show that the density of unsatisfied clauses clearly indicates the transition from the solvable (absorbing) phase to the unsolvable (active) phase as varying the noise parameter and the density of constraints. Based on the solution clustering (percolation-type) argument, we conjecture two possible values of the FSS exponent, which are confirmed reasonably well in numerical simulations for 2≤K≤3