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Internal Motility in Stiffening Actin-Myosin Networks

We present a study on filamentous actin solutions containing heavy meromyosin subfragments of myosin II motor molecules. We focus on the viscoelastic phase behavior and internal dynamics of such networks during ATP depletion. Upon simultaneously using micro-rheology and fluorescence microscopy as complementary experimental tools, we find a sol-gel transition accompanied by a sudden onset of directed filament motion. We interpret the sol-gel transition in terms of myosin II enzymology, and suggest a "zipping" mechanism to explain the filament motion in the vicinity of the sol-gel transition.

physics.bio-ph↗

From polymers to proteins -- novel phases of short compact tubes

A framework is presented for understanding the common character of proteins. Proteins are linear chain molecules. However, the simple model of a polymer viewed as spheres tethered together does not account for many of the observed characteristics of protein structures. The authors show here that proteins may be regarded as tubes of nonzero thickness. This approach allows one to bridge the conventional compact polymer phase with a novel phase employed by Nature to house biomolecular structures. The continuum description of a tube (or a sheet) of arbitrary thickness entails using appropriately chosen many-body interactions rather than two-body interactions. The authors suggest that the structures of folded proteins are selected based on geometrical considerations and are poised at the edge of compaction, thus accounting for their versatility and flexibility. This approach also offers an explanation for why helices and sheets are the building blocks of protein structures.

cond-mat.stat-mech↗

Effective Fitness Landscapes for Evolutionary Systems

In evolution theory the concept of a fitness landscape has played an important role, evolution itself being portrayed as a hill-climbing process on a rugged landscape. In this article it is shown that in general, in the presence of other genetic operators such as mutation and recombination, hill-climbing is the exception rather than the rule. This descrepency can be traced to the different ways that the concept of fitness appears --- as a measure of the number of fit offspring, or as a measure of the probability to reach reproductive age. Effective fitness models the former not the latter and gives an intuitive way to understand population dynamics as flows on an effective fitness landscape when genetic operators other than selection play an important role. The efficacy of the concept is shown using several simple analytic examples and also some more complicated cases illustrated by simulations.

nlin.AO↗

Jigsaw model of the origin of life

It is suggested that life originated in a three-step process referred to as the jigsaw model. RNA, proteins, or similar organic molecules polymerized in a dehydrated carbon-rich environment, on surfaces in a carbon-rich environment, or in another environment where polymerization occurs. These polymers subsequently entered an aqueous environment where they folded into compact structures. It is argued that the folding of randomly generated polymers such as RNA or proteins in water tends to partition the folded polymer into domains with hydrophobic cores and matching shapes to minimize energy. In the aqueous environment, hydrolysis or other reactions fragmented the compact structures into two or more matching molecules, occasionally producing simple living systems, also known as autocatalytic sets of molecules. It is argued that the hydrolysis of folded polymers such as RNA or proteins is not random. The hydrophobic cores of the domains are rarely bisected due to the energy requirements in water. Hydrolysis preferentially fragments the folded polymers into pieces with complementary structures and chemical affinities. Thus the probability of producing a system of matched, interacting molecules in prebiotic chemistry is much higher than usually estimated. Environments where this process may occur are identified. For example, the jigsaw model suggests life may have originated at a seep of carbonaceous fluids beneath the ocean. The polymerization occurred beneath the sea floor. The folding and fragmentation occurred in the ocean. The implications of this hypothesis for seeking life or prebiotic chemistry in the Solar System are explored.

nlin.AO↗

Capture of the Lamb: Diffusing Predators Seeking a Diffusing Prey

We study the capture of a diffusing "lamb" by diffusing "lions" in one dimension. The capture dynamics is exactly soluble by probabilistic techniques when the number of lions is very small, and is tractable by extreme statistics considerations when the number of lions is very large. However, the exact solution for the general case of three or more lions is still not known.

cond-mat.stat-mech↗

Specificity and stability in topology of protein networks

Molecular networks guide the biochemistry of a living cell on multiple levels: its metabolic and signalling pathways are shaped by the network of interacting proteins, whose production, in turn, is controlled by the genetic regulatory network. To address topological properties of these two networks we quantify correlations between connectivities of interacting nodes and compare them to a null model of a network, in which al links were randomly rewired. We find that for both interaction and regulatory networks, links between highly connected proteins are systematically suppressed, while those between a highly-connected and low-connected pairs of proteins are favored. This effect decreases the likelihood of cross talk between different functional modules of the cell, and increases the overall robustness of a network by localizing effects of deleterious perturbations.

cond-mat.soft↗

Hierarchical organization of modularity in metabolic networks

Spatially or chemically isolated functional modules composed of several cellular components and carrying discrete functions are considered fundamental building blocks of cellular organization, but their presence in highly integrated biochemical networks lacks quantitative support. Here we show that the metabolic networks of 43 distinct organisms are organized into many small, highly connected topologic modules that combine in a hierarchical manner into larger, less cohesive units, their number and degree of clustering following a power law. Within Escherichia coli the uncovered hierarchical modularity closely overlaps with known metabolic functions. The identified network architecture may be generic to system-level cellular organization.

cond-mat.soft↗

Base pair dynamic assisted charge transport in DNA

An 1d model with time-dependent random hopping is proposed to describe charge transport in DNA. It admits to investigate both diffusion of electrons and their tunneling between different sites in DNA. The tunneling appears to be strongly temperature-dependent. Observations of a strong (exponential) as well as a weak distance dependence of the charge transfer in DNA can be explained in the framework of our model.

cond-mat.soft↗

Topological and geometrical entanglement in a model of circular DNA undergoing denaturation

The linking number (topological entanglement) and the writhe (geometrical entanglement) of a model of circular double stranded DNA undergoing a thermal denaturation transition are investigated by Monte Carlo simulations. By allowing the linking number to fluctuate freely in equilibrium we see that the linking probability undergoes an abrupt variation (first-order) at the denaturation transition, and stays close to 1 in the whole native phase. The average linking number is almost zero in the denatured phase and grows as the square root of the chain length, N, in the native phase. The writhe of the two strands grows as the square root of N in both phases.

cond-mat.stat-mech↗

A simple model of DNA denaturation and mutually avoiding walks statistics

Recently Garel, Monthus and Orland (Europhys. Lett. v 55, 132 (2001)) considered a model of DNA denaturation in which excluded volume effects within each strand are neglected, while mutual avoidance is included. Using an approximate scheme they found a first order denaturation. We show that a first order transition for this model follows from exact results for the statistics of two mutually avoiding random walks, whose reunion exponent is c > 2, both in two and three dimensions. Analytical estimates of c due to the interactions with other denaturated loops, as well as numerical calculations, indicate that the transition is even sharper than in models where excluded volume effects are fully incorporated. The probability distribution of distances between homologous base pairs decays as a power law at the transition.

cond-mat.stat-mech↗

Selective advantage of topological disorder in biological evolution

We examine a model of biological evolution of Eigen's quasispecies in a holey fitness landscape, where the fitness of a site is either 0 (lethal site) or a uniform positive constant (viable site). So, the evolution dynamics is determined by the topology of the genome space. It is modeled by the random Bethe lattice. We use the effective medium and single-defect approximations to find the criteria, under which the localized quasispecies cloud is created. We find that shorter genomes, which are more robust to random mutations than average, represent a selective advantage which we call ``topological''. A way of assessing empirically the relative importance of reproductive success and topological advantage is suggested.

cond-mat.stat-mech↗

An Analytical Approach to Neuronal Connectivity

This paper describes how realistic neuromorphic networks can have their connectivity properties fully characterized in analytical fashion. By assuming that all neurons have the same shape and are regularly distributed along the two-dimensional orthogonal lattice with parameter $Δ$, it is possible to obtain the accurate number of connections and cycles of any length from the autoconvolution function as well as from the respective spectral density derived from the adjacency matrix. It is shown that neuronal shape plays an important role in defining the spatial spread of network connections. In addition, most such networks are characterized by the interesting phenomenon where the connections are progressively shifted along the spatial domain where the network is embedded. It is also shown that the number of cycles follows a power law with their respective length. Morphological measurements for characterization of the spatial distribution of connections, including the adjacency matrix spectral density and the lacunarity of the connections, are suggested. The potential of the proposed approach is illustrated with respect to digital images of real neuronal cells.

cond-mat.dis-nn↗

Elastic interaction between "hard'' or "soft" pointwise inclusions on biological membranes

We calculate the induced elastic-interaction between pointwise membrane inclusions that locally interact up to quadratic order with the membrane curvature tensor. For isotropic inclusions, we recover the usual interaction proportional to the inverse fourth power of the separation, however with a prefactor showing a non-trivial dependence on the rigidity $Γ$ of the quadratic potential. In the large $Γ$ limit, corresponding to ``hard'' inclusions, we recover the standard prefactor first obtained by Goulian et al. [Europhys. Lett. \textbf{22}, 145 (1993)]. In the small $Γ$ limit, corresponding to "soft" inclusions, we recover the recent result of Marchenko and Misbah [Eur. Phys. J. E \textbf{8}, 477 (2002)]. This shows that the latter result bears no fundamental discrepancy with previous works, but simply corresponds to the limit of soft inclusions. We discuss how the same inclusion can be depicted as hard or soft according to the degree of coarse-graining of the pointwise description. Finally, we argue that conical transmembrane proteins should be fundamentally considered as hard inclusions.

cond-mat.soft↗

Nonlinear Relaxation in Population Dynamics

We analyze the nonlinear relaxation of a complex ecosystem composed of many interacting species. The ecological system is described by generalized Lotka-Volterra equations with a multiplicative noise. The transient dynamics is studied in the framework of the mean field theory and with random interaction between the species. We focus on the statistical properties of the asymptotic behaviour of the time integral of the i-th population and on the distribution of the population and of the local field.

cond-mat.stat-mech↗

Gauge Symmetry and Neural Networks

We propose a new model of neural network. It consists of spin variables to describe the state of neurons as in the Hopfield model and new gauge variables to describe the state of synapses. The model possesses local gauge symmetry and resembles lattice gauge theory of high-energy physics. Time dependence of synapses describes the process of learning. The mean field theory predicts a new phase corresponding to confinement phase, in which brain loses ablility of learning and memory.

cond-mat.dis-nn↗

An evolutionary model for simple ecosystems

In this review some simple models of asexual populations evolving on smooth landscapes are studied. The basic model is based on a cellular automaton, which is analyzed here in the spatial mean-field limit. Firstly, the evolution on a fixed fitness landscape is considered. The correspondence between the time evolution of the population and equilibrium properties of a statistical mechanics system is investigated, finding the limits for which this mapping holds. The mutational meltdown, Eigen's error threshold and Muller's ratchet phenomena are studied in the framework of a simplified model. Finally, the shape of a quasi-species and the condition of coexistence of multiple species in a static fitness landscape are analyzed. In the second part, these results are applied to the study of the coexistence of quasi-species in the presence of competition, obtaining the conditions for a robust speciation effect in asexual populations.

cond-mat.stat-mech↗

Catastrophic senescence of the Pacific salmon without mutation-accumulation

We derive catastrophic senescence of the Pacific salmon from an aging model which was recently proposed by Stauffer. The model is based on the postulates of a minimum reproduction age and a maximal genetic lifespan. It allows for self-organization of a typical age of first reproduction and a typical age of death. Our Monte Carlo simulations of the population dynamics show that the model leads to catastrophic senescence for semelparous reproduction as it occurs in the case of salmon, but to a more gradually increase of senescence for iteroparous reproduction.

cond-mat↗

Bacterial Evolution and Bak-Sneppen Model

Recently, Lenski et al [Elena,Lenski,Travisano] have carried out several experiments on bacterial evolution. Their findings support the theory of punctuated equilibrium in biological evolution. They have further quantified the relative contributions of adaptation, chance and history to bacterial evolution. In this paper, we show that a modified $M$-trait Bak-Sneppen model can explain many of the experimental results in a qualitative manner.

cond-mat.stat-mech↗