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At least 1,135 records · Page 63Linked to original sources

arXiv2003

Modeling DNA Structure, Elasticity and Deformations at the Base-pair Level

We present a generic model for DNA at the base-pair level. We use a variant of the Gay-Berne potential to represent the stacking energy between neighboring base-pairs. The sugar-phosphate backbones are taken into account by semi-rigid harmonic springs with a non-zero spring length. The competition of these two interactions and the introduction of a simple geometrical constraint leads to a stacked right-handed B-DNA-like conformation. The mapping of the presented model to the Marko-Siggia and the Stack-of-Plates model enables us to optimize the free model parameters so as to reproduce the experimentally known observables such as persistence lengths, mean and mean squared base-pair step parameters. For the optimized model parameters we measured the critical force where the transition from B- to S-DNA occurs to be approximately $140{pN}$. We observe an overstretched S-DNA conformation with highly inclined bases that partially preserves the stacking of successive base-pairs.

cond-mat.soft↗

arXiv2003

Stability of Negative Image Equilibria in Spike-Timing Dependent Plasticity

We investigate the stability of negative image equilibria in mean synaptic weight dynamics governed by spike-timing dependent plasticity (STDP). The neural architecture of the model is based on the electrosensory lateral line lobe (ELL) of mormyrid electric fish, which forms a negative image of the reafferent signal from the fish's own electric discharge to optimize detection of external electric fields. We derive a necessary and sufficient condition for stability, for arbitrary postsynaptic potential functions and arbitrary learning rules. We then apply the general result to several examples of biological interest.

physics.bio-ph↗

arXiv2003

Properties of highly clustered networks

We propose and solve exactly a model of a network that has both a tunable degree distribution and a tunable clustering coefficient. Among other things, our results indicate that increased clustering leads to a decrease in the size of the giant component of the network. We also study SIR-type epidemic processes within the model and find that clustering decreases the size of epidemics, but also decreases the epidemic threshold, making it easier for diseases to spread. In addition, clustering causes epidemics to saturate sooner, meaning that they infect a near-maximal fraction of the network for quite low transmission rates.

cond-mat.stat-mech↗

arXiv2003

Diffusion limited friendship network: A model for six degrees of separation

A dynamic model of a society is studied where each person is an uncorrelated and non-interacting random walker. A dynamical random graph represents the acquaintance network of the society whose nodes are the individuals and links are the pairs of mutual friendships. This network exhibits a novel percolation like phase transition in all dimensions. On introducing simultaneous death and birth rates in the population we show that the friendship network shows the six degrees of separation for ever after where the precise value of the network diameter depends on the death/birth rate. A SIS type model of disease spreading shows that this society remains always healthy if the population density is less than certain threshold value.

cond-mat.stat-mech↗

arXiv2003

Synapse efficiency diverges due to synaptic pruning following over-growth

In the development of the brain, it is known that synapses are pruned following over-growth. This pruning following over-growth seems to be a universal phenomenon that occurs in almost all areas -- visual cortex, motor area, association area, and so on. It has been shown numerically that the synapse efficiency is increased by systematic deletion. We discuss the synapse efficiency to evaluate the effect of pruning following over-growth, and analytically show that the synapse efficiency diverges as O(log c) at the limit where connecting rate c is extremely small. Under a fixed synapse number criterion, the optimal connecting rate, which maximize memory performance, exists.

cond-mat.dis-nn↗

arXiv2003

Epidemic processes with immunization

We study a model of directed percolation (DP) with immunization, i.e. with different probabilities for the first infection and subsequent infections. The immunization effect leads to an additional non-Markovian term in the corresponding field theoretical action. We consider immunization as a small perturbation around the DP fixed point in d<6, where the non-Markovian term is relevant. The immunization causes the system to be driven away from the neighbourhood of the DP critical point. In order to investigate the dynamical critical behaviour of the model, we consider the limits of low and high first infection rate, while the second infection rate remains constant at the DP critical value. Scaling arguments are applied to obtain an expression for the survival probability in both limits. The corresponding exponents are written in terms of the critical exponents for ordinary DP and DP with a wall. We find that the survival probability does not obey a power law behaviour, decaying instead as a stretched exponential in the low first infection probability limit and to a constant in the high first infection probability limit. The theoretical predictions are confirmed by optimized numerical simulations in 1+1 dimensions.

cond-mat.stat-mech↗

arXiv2003

Structure optimization in an off-lattice protein model

We study an off-lattice protein toy model with two species of monomers interacting through modified Lennard-Jones interactions. Low energy configurations are optimized using the pruned-enriched-Rosenbluth method (PERM), hitherto employed to native state searches only for off lattice models. For 2 dimensions we found states with lower energy than previously proposed putative ground states, for all chain lengths $\ge 13$. This indicates that PERM has the potential to produce native states also for more realistic protein models. For $d=3$, where no published ground states exist, we present some putative lowest energy states for future comparison with other methods.

cond-mat.stat-mech↗

arXiv2003

A food-web based unified model of "macro"- and "micro-" evolution

We incorporate the generic hierarchical architecture of foodwebs into a "{\it unified}" model that describes both "micro" and "macro" evolutions within a single theoretical framework. This model describes the "micro" -evolution in detail by accounting for the birth, ageing and natural death of individual organisms as well as prey-predator interactions on a hierarchical dynamic food web. It also provides a natural description of random mutations and speciation/orgination of species as well as their extinctions. The distribution of lifetimes of species follows an approximate power law only over a limited regime.

cond-mat.stat-mech↗

arXiv2003

Statistical mechanics of RNA folding: importance of alphabet size

We construct a minimalist model of RNA secondary-structure formation and use it to study the mapping from sequence to structure. There are strong, qualitative differences between two-letter and four or six-letter alphabets. With only two kinds of bases, there are many alternate folding configurations, yielding thermodynamically stable ground-states only for a small set of structures of high designability, i.e., total number of associated sequences. In contrast, sequences made from four bases, as found in nature, or six bases have far fewer competing folding configurations, resulting in a much greater average stability of the ground state.

cond-mat.stat-mech↗

arXiv2003

Characterizing Width Uniformity by Wave Propagation

This work describes a novel image analysis approach to characterize the uniformity of objects in agglomerates by using the propagation of normal wavefronts. The problem of width uniformity is discussed and its importance for the characterization of composite structures normally found in physics and biology highlighted. The methodology involves identifying each cluster (i.e. connected component) of interest, which can correspond to objects or voids, and estimating the respective medial axes by using a recently proposed wavefront propagation approach, which is briefly reviewed. The distance values along such axes are identified and their mean and standard deviation values obtained. As illustrated with respect to synthetic and real objects (in vitro cultures of neuronal cells), the combined use of these two features provide a powerful description of the uniformity of the separation between the objects, presenting potential for several applications in material sciences and biology.

cond-mat.dis-nn↗

arXiv2003

Adsorption of mono- and multivalent cat- and anions on DNA molecules

Adsorption of monovalent and multivalent cat- and anions on a deoxyribose nucleic acid (DNA) molecule from a salt solution is investigated by computer simulation. The ions are modelled as charged hard spheres, the DNA molecule as a point charge pattern following the double-helical phosphate strands. The geometrical shape of the DNA molecules is modelled on different levels ranging from a simple cylindrical shape to structured models which include the major and minor grooves between the phosphate strands. The densities of the ions adsorbed on the phosphate strands, in the major and in the minor grooves are calculated. First, we find that the adsorption pattern on the DNA surface depends strongly on its geometrical shape: counterions adsorb preferentially along the phosphate strands for a cylindrical model shape, but in the minor groove for a geometrically structured model. Second, we find that an addition of monovalent salt ions results in an increase of the charge density in the minor groove while the total charge density of ions adsorbed in the major groove stays unchanged. The adsorbed ion densities are highly structured along the minor groove while they are almost smeared along the major groove. Furthermore, for a fixed amount of added salt, the major groove cationic charge is independent on the counterion valency. For increasing salt concentration the major groove is neutralized while the total charge adsorbed in the minor groove is constant. DNA overcharging is detected for multivalent salt. Simulations for a larger ion radii, which mimic the effect of the ion hydration, indicate an increased adsorbtion of cations in the major groove.

cond-mat.soft↗

arXiv2002

Hierarchical population model with a carrying capacity distribution

A time- and space-discrete model for the growth of a rapidly saturating local biological population $N(x,t)$ is derived from a hierarchical random deposition process previously studied in statistical physics. Two biologically relevant parameters, the probabilities of birth, $B$, and of death, $D$, determine the carrying capacity $K$. Due to the randomness the population depends strongly on position, $x$, and there is a distribution of carrying capacities, $Π(K)$. This distribution has self-similar character owing to the imposed hierarchy. The most probable carrying capacity and its probability are studied as a function of $B$ and $D$. The effective growth rate decreases with time, roughly as in a Verhulst process. The model is possibly applicable, for example, to bacteria forming a "towering pillar" biofilm. The bacteria divide on randomly distributed nutrient-rich regions and are exposed to random local bactericidal agent (antibiotic spray). A gradual overall temperature change away from optimal growth conditions, for instance, reduces bacterial reproduction, while biofilm development degrades antimicrobial susceptibility, causing stagnation into a stationary state.

physics.bio-ph↗

arXiv2003

Motion of rotatory molecular motor and chemical reaction rate

We examine the dependence of the physical quantities of the rotatory molecular motor, such as the rotation velocity and the proton translocation rate, on the chemical reaction rate using the model based only on diffusion process. A peculiar behavior of proton translocation is found and the energy transduction efficiency of the motor protein is enhanced by this behavior. We give a natural explanation that this behavior is universal when certain inequalities between chemical reaction rates hold. That may give a clue to examine whether the motion of the molecular motor is dominated by diffusion process or not.

physics.bio-ph↗

arXiv2003

Universality and Shannon entropy of codon usage

The distribution functions of the codon usage probabilities, computed over all the available GenBank data, for 40 eukaryotic biological species and 5 chloroplasts, do not follow a Zipf law, but are best fitted by the sum of a constant, an exponential and a linear function in the rank of usage. For mitochondriae the analysis is not conclusive. A quantum-mechanics-inspired model is proposed to describe the observed behaviour. These functions are characterized by parameters that strongly depend on the total GC content of the coding regions of biological species. It is predicted that the codon usage is the same in all exonic genes with the same GC content. The Shannon entropy for codons, also strongly depending on the exonic GC content, is computed.

cond-mat↗

arXiv2004

Reparametrizing loop entropy weights: Effect on DNA melting curves

Recent advances in the understanding of the melting behavior of double-stranded DNA with statistical mechanics methods lead to improved estimates of the weight factors for the dissociation events of the chains, in particular for interior loop melting. So far, in the modeling of DNA melting, the entropy of denaturated loops has been estimated from the number of configurations of a closed self-avoiding walk. It is well understood now that a loop embedded in a chain is characterized by a loop closure exponent c which is higher than that of an isolated loop. Here we report an analysis of DNA melting curves for sequences of a broad range of lengths (from 10 to 10^6 base pairs) calculated with a program based on the algorithms underlying MELTSIM. Using the embedded loop exponent we find that the cooperativity parameter is one order of magnitude bigger than current estimates. We argue that in the melting region the double helix persistence length is greatly reduced compared to its room temperature value, so that the use of the embedded loop closure exponent for real DNA sequences is justified.

cond-mat.stat-mech↗

arXiv2003

Robustness of retrieval properties against imbalance between long-term potentiation and depression of spike-timing-dependent plasticity

Spike-timing-dependent plasticity (STDP) has recently been shown in some physiological studies. STDP depends on the precise temporal relationship of pre- and post-synaptic spikes. Many authors have indicated that a precise balance between long-term potentiation (LTP) and long-term depression (LTD) of STDP is significant for a stable learning. However, a situation in which the balance is maintained precisely is inconceivable in the brain. Using a method of the statistical neurodynamics, we show robust retrieval properties of spatio-temporal patterns in an associative memory model against the imbalance between LTP and LTD. When the fluctuation of LTD is assumed to obey a Gaussian distribution with mean 0 and variance $δ^2$, the storage capacity takes a finite value even at large $δ$. This means that the balance between LTP and LTD of STDP need not to be maintained precisely, but must be maintained on average. Furthermore, we found that a basin of attraction becomes smaller as $δ$ increases while an initial critical overlap remains unchanged.

cond-mat.dis-nn↗

arXiv2003

The Error and Repair Catastrophes: A Two-Dimensional Phase Diagram in the Quasispecies Model

This paper develops a two gene, single fitness peak model for determining the equilibrium distribution of genotypes in a unicellular population which is capable of genetic damage repair. The first gene, denoted by $ σ_{via} $, yields a viable organism with first order growth rate constant $ k > 1 $ if it is equal to some target ``master'' sequence $ σ_{via, 0} $. The second gene, denoted by $ σ_{rep} $, yields an organism capable of genetic repair if it is equal to some target ``master'' sequence $ σ_{rep, 0} $. This model is analytically solvable in the limit of infinite sequence length, and gives an equilibrium distribution which depends on $ μ\equiv L\eps $, the product of sequence length and per base pair replication error probability, and $ \eps_r $, the probability of repair failure per base pair. The equilibrium distribution is shown to exist in one of three possible ``phases.'' In the first phase, the population is localized about the viability and repairing master sequences. As $ \eps_r $ exceeds the fraction of deleterious mutations, the population undergoes a ``repair'' catastrophe, in which the equilibrium distribution is still localized about the viability master sequence, but is spread ergodically over the sequence subspace defined by the repair gene. Below the repair catastrophe, the distribution undergoes the error catastrophe when $ μ$ exceeds $ \ln k/\eps_r $, while above the repair catastrophe, the distribution undergoes the error catastrophe when $ μ$ exceeds $ \ln k/f_{del} $, where $ f_{del} $ denotes the fraction of deleterious mutations.

cond-mat.stat-mech↗

arXiv2003

Analysis of the intraspinal calcium dynamics and its implications on the plasticity of spiking neurons

The influx of calcium ions into the dendritic spines through the N-metyl-D-aspartate (NMDA) channels is believed to be the primary trigger for various forms of synaptic plasticity. In this paper, the authors calculate analytically the mean values of the calcium transients elicited by a spiking neuron undergoing a simple model of ionic currents and back-propagating action potentials. The relative variability of these transients, due to the stochastic nature of synaptic transmission, is further considered using a simple Markov model of NMDA receptos. One finds that both the mean value and the variability depend on the timing between pre- and postsynaptic action-potentials. These results could have implications on the expected form of synaptic-plasticity curve and can form a basis for a unified theory of spike time-dependent, and rate based plasticity.

physics.bio-ph↗