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q-bio

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preprint2001arXiv

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.

preprint1999arXiv

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.

preprint2001arXiv

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.

preprint2000arXiv

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.

preprint2000arXiv

Theory of periodic swarming of bacteria: application to Proteus mirabilis

The periodic swarming of bacteria is one of the simplest examples for pattern formation produced by the self-organized collective behavior of a large number of organisms. In the spectacular colonies of Proteus mirabilis (the most common species exhibiting this type of growth) a series of concentric rings are developed as the bacteria multiply and swarm following a scenario periodically repeating itself. We have developed a theoretical description for this process in order to get a deeper insight into some of the typical processes governing the phenomena in systems of many interacting living units. All of our theoretical results are in excellent quantitative agreement with the complete set of available observations.

preprint2003arXiv

A Possible Mechanism of Biological Memories in terms of Quantum Fluids

A mechanism of memories, especially biological memories, is studied in terms of quantum fluids. Two-dimensional flows in central potentials $V_a(ρ)=-a^2g_aρ^{2(a-1)}$ ($a\not=0$ and $ρ=\sqrt{x^2+y^2}$) have zero-energy eigenstates that degenerate infinitely for all $a$. It is shown that stable standing waves constructed from the zero-energy flows are confined in various types of polygons which can be the minimum units of memory systems. Vortex patterns awoken in the units by stimuli correspond to the memories of the stimuli. This memory system is not a system for preserving memories as usual but that for awaking memories. The system has interesting properties; (i) the absolute economy as for the energy consumption, (ii) the infinite variety for a huge number of memories, (iii) the perfect recovery of the system from any disturbances by stimuli, and (iv) the large flexibility in the construction of the system. A process for thinking is also proposed in terms of this memory system.

preprint2002arXiv

Clustering of SNPs along a chromosome: can the neutral model be rejected?

Single nucleotide polymorphisms (SNPs) often appear in clusters along the length of a chromosome. This is due to variation in local coalescent times caused by,for example, selection or recombination. Here we investigate whether recombination alone (within a neutral model) can cause statistically significant SNP clustering. We measure the extent of SNP clustering as the ratio between the variance of SNPs found in bins of length $l$, and the mean number of SNPs in such bins, $σ^2_l/μ_l$. For a uniform SNP distribution $σ^2_l/μ_l=1$, for clustered SNPs $σ^2_l/μ_l > 1$. Apart from the bin length, three length scales are important when accounting for SNP clustering: The mean distance between neighboring SNPs, $Δ$, the mean length of chromosome segments with constant time to the most recent common ancestor, $\el$, and the total length of the chromosome, $L$. We show that SNP clustering is observed if $Δ< \el \ll L$. Moreover, if $l\ll \el \ll L$, clustering becomes independent of the rate of recombination. We apply our results to the analysis of SNP data sets from mice, and human chromosomes 6 and X. Of the three data sets investigated, the human X chromosome displays the most significan

preprint1998arXiv

Stochastic dynamics simulations in a new generalized ensemble

We develop a formulation for molecular dynamics, Langevin, and hybrid Monte Carlo algorithms in the recently proposed generalized ensemble that is based on a physically motivated realisation of Tsallis weights. The effectiveness of the methods are tested with an energy function for a protein system. Simulations in this generalized ensemble by the three methods are performed for a penta peptide, Met-enkephalin. For each algorithm, it is shown that from only one simulation run one can not only find the global-minimum-energy conformation but also obtain probability distributions in canonical ensemble at any temperature, which allows the calculation of any thermodynamic quantity as a function of temperature.

preprint1999arXiv

Kullback-Leibler and Renormalized Entropy: Applications to EEGs of Epilepsy Patients

Recently, renormalized entropy was proposed as a novel measure of relative entropy (P. Saparin et al., Chaos, Solitons & Fractals 4, 1907 (1994)) and applied to several physiological time sequences, including EEGs of patients with epilepsy. We show here that this measure is just a modified Kullback-Leibler (K-L) relative entropy, and it gives similar numerical results to the standard K-L entropy. The latter better distinguishes frequency contents of e.g. seizure and background EEGs than renormalized entropy. We thus propose that renormalized entropy might not be as useful as claimed by its proponents. In passing we also make some critical remarks about the implementation of these methods.

preprint1998arXiv

Nearly Closed Loops in Biological Systems as Electromagnetic Receptors

It is noted here that when a nearly closed loop in a biological system, such as a self-synapsing (autapsing) neuron or mutually synapsing pair, is exposed to an AC magnetic field, the induced electric fields in the insulating gaps can be many orders of magnitude larger than the average values typically discussed in the literature.$^{1,2}$ It is suggested that animal nervous systems might possibly be affected in selected spots by man-made alternating magnetic fields at weaker levels than previously supposed. Radio and microwave radiation should be considered particularly suspect.

preprint1997arXiv

A Simple Model of Evolution with Variable System Size

A simple model of biological extinction with variable system size is presented that exhibits a power-law distribution of extinction event sizes. The model is a generalization of a model recently introduced by Newman (Proc. R. Soc. Lond. B265, 1605 (1996). Both analytical and numerical analysis show that the exponent of the power-law distribution depends only marginally on the growth rate $g$ at which new species enter the system and is equal to the one of the original model in the limit $g\to\infty$. A critical growth rate $g_c$ can be found below which the system dies out. Under these model assumptions stable ecosystems can only exist if the regrowth of species is sufficiently fast.

preprint1998arXiv

Discrimination of the Healthy and Sick Cardiac Autonomic Nervous System by a New Wavelet Analysis of Heartbeat Intervals

We demonstrate that it is possible to distinguish with a complete certainty between healthy subjects and patients with various dysfunctions of the cardiac nervous system by way of multiresolutional wavelet transform of RR intervals. We repeated the study of Thurner et al on different ensemble of subjects. We show that reconstructed series using a filter which discards wavelet coefficients related with higher scales enables one to classify individuals for which the method otherwise is inconclusive. We suggest a delimiting diagnostic value of the standard deviation of the filtered, reconstructed RR interval time series in the range of $\sim 0.035$ (for the above mentioned filter), below which individuals are at risk.

preprint2003arXiv

Non-local Interaction Effects on Pattern Formation in Population Dynamics

We consider a model for population dynamics such as for the evolution of bacterial colonies which is of the Fisher type but where the competitive interaction among individuals is non-local, and show that spatial structures with interesting features emerge. These features depend on the nature of the competitive interaction as well as on its range, specifically on the presence or absence of tails in, and the central curvature of, the influence function of the interaction.

preprint1998arXiv

Large deviations for the Fleming-Viot process with neutral mutation and selection

Large deviation principles are established for the Fleming-Viot processes with neutral mutation and selection, and the corresponding equilibrium measures as the sampling rate goes to 0. All results are first proved for the finite allele model, and then generalized, through the projective limit technique, to the infinite allele model. Explicit expressions are obtained for the rate functions.

preprint1995arXiv

VLSI layouts and DNA physical mappings

We show that an important problem ($k$-ICG) in computational biology is equivalent to a colored version of a well-known graph layout problem ($k$-CVS).

preprint1994arXiv

Efficient pooling designs for library screening

We describe efficient methods for screening clone libraries, based on pooling schemes which we call ``random $k$-sets designs''. In these designs, the pools in which any clone occurs are equally likely to be any possible selection of $k$ from the $v$ pools. The values of $k$ and $v$ can be chosen to optimize desirable properties. Random $k$-sets designs have substantial advantages over alternative pooling schemes: they are efficient, flexible, easy to specify, require fewer pools, and have error-correcting and error-detecting capabilities. In addition, screening can often be achieved in only one pass, thus facilitating automation. For design comparison, we assume a binomial distribution for the number of ``positive'' clones, with parameters $n$, the number of clones, and $c$, the coverage. We propose the expected number of {\em resolved positive} clones---clones which are definitely positive based upon the pool assays---as a criterion for the efficiency of a pooling design. We determine the value of $k$ which is optimal, with respect to this criterion, as a function of $v$, $n$ and $c$. We also describe superior $k$-sets designs called $k$-sets packing designs. As a

preprint2002arXiv

Morphological Instability and Dynamics of Fronts in Bacterial Growth Models with Nonlinear Diffusion

It has been argued that there is biological and modeling evidence that a non-linear diffusion coefficient of the type D(b) = D_0 b^{k} underlies the formation of a number of growth patterns of bacterial colonies. We study a reaction-diffusion system with a non-linear diffusion coefficient introduced by Ben-Jacob et al. Due to the fact that the bacterial diffusion coefficient vanishes when the bacterial density b -> 0, the standard linear stability analysis for fronts cannot be used. We introduce an extension of the stability analysis which can be applied to such singular fronts, map out the region of stability in the D-k-plane and derive an interfacial approximation in some limits. Our linear stability analysis and sharp interface formulation will also be applicable to other examples of interface formation due to nonlinear diffusion, like in porous media or in the problem of vortex motion in superconductors.

preprint2002arXiv

A simple equation to calculate the diameters of biological vesicles

The remarkable preference of biomembranes, to constitute vesicles of certain discrete sizes is explained by using the following properties of phospholipids that are either well understood or at least documented. A. By hexagonal close-packing their fatty acyl chains form a triangular lattice. Their molecules: B. Prefer to form linear arrays that occasionally make angles of 120 degrees. C. Form relatively large hexagons. Based on these properties a model for monolayers is proposed and a simple equation derived for the calculation of diameters of vesicles. The diameters of vesicles of neurotransmitters and hormones determined by electron microscopy were compared with those obtained with the equation. Statistical analysis of this comparison revealed the model to give very significant results (p=.0002).

preprint2001arXiv

Proteinlike behavior of a spin system near the transition between ferromagnet and spin glass

A simple spin system is studied as an analog for proteins. We investigate how the introduction of randomness and frustration into the system effects the designability and stability of ground state configurations. We observe that the spin system exhibits protein-like behavior in the vicinity of the transition between ferromagnet and spin glass. Our results illuminate some guiding principles in protein evolution.

preprint2003arXiv

Sum rules for free energy and frequency distribution of DNA dinucleotides

The large discrepancy between the values of the free energy for DNA dinucleotides (or dimers) measured by different teams has raised a yet unsettled debate. Here the free energy is fitted by a three parameter empiric formula derived in the framework of the crystal basis model of genetic code. Sum rules are derived and compared satisfactorily with the data. On the basis of theoretical and phenomenological arguments, a relation between the correlation functions of dimer distribution and the free energy is assumed. From consistency conditions, sum rules are derived. A check of these conditions with different samples of experimental data is performed, allowing us to argue on the reliability of the different sets of experimental data.

preprint2002arXiv

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.

preprint2001arXiv

Emergence of highly-designable protein-backbone conformations in an off-lattice model

Despite the variety of protein sizes, shapes, and backbone configurations found in nature, the design of novel protein folds remains an open problem. Within simple lattice models it has been shown that all structures are not equally suitable for design. Rather, certain structures are distinguished by unusually high designability: the number of amino-acid sequences for which they represent the unique ground state; sequences associated with such structures possess both robustness to mutation and thermodynamic stability. Here we report that highly designable backbone conformations also emerge in a realistic off-lattice model. The highly designable conformations of a chain of 23 amino acids are identified, and found to be remarkably insensitive to model parameters. While some of these conformations correspond closely to known natural protein folds, such as the zinc finger and the helix-turn-helix motifs, others do not resemble known folds and may be candidates for novel fold design.

preprint2001arXiv

Comment on "Elasticity Model of a Supercoiled DNA Molecule"

We perform simulations to numerically study the writhe distribution of a stiff polymer. We compare with analytic results of Bouchiat and Mezard (PRL 80 1556- (1998); cond-mat/9706050).

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M. E. J. Newman contributes to research discovery and scholarly infrastructure.

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q-bio

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24 paper(s) to start with

Gauge Symmetry and Neural Networks

An evolutionary model for simple ecosystems

Nonlinear Relaxation in Population Dynamics

Effective Fitness Landscapes for Evolutionary Systems

Theory of periodic swarming of bacteria: application to Proteus mirabilis

A Possible Mechanism of Biological Memories in terms of Quantum Fluids

Clustering of SNPs along a chromosome: can the neutral model be rejected?

Stochastic dynamics simulations in a new generalized ensemble

Kullback-Leibler and Renormalized Entropy: Applications to EEGs of Epilepsy Patients

Nearly Closed Loops in Biological Systems as Electromagnetic Receptors

A Simple Model of Evolution with Variable System Size

Discrimination of the Healthy and Sick Cardiac Autonomic Nervous System by a New Wavelet Analysis of Heartbeat Intervals

Non-local Interaction Effects on Pattern Formation in Population Dynamics

Large deviations for the Fleming-Viot process with neutral mutation and selection

VLSI layouts and DNA physical mappings

Efficient pooling designs for library screening

Morphological Instability and Dynamics of Fronts in Bacterial Growth Models with Nonlinear Diffusion

A simple equation to calculate the diameters of biological vesicles

Proteinlike behavior of a spin system near the transition between ferromagnet and spin glass

Sum rules for free energy and frequency distribution of DNA dinucleotides

A simple model of DNA denaturation and mutually avoiding walks statistics

Emergence of highly-designable protein-backbone conformations in an off-lattice model

Comment on "Elasticity Model of a Supercoiled DNA Molecule"

Defensive alliances in spatial models of cyclical population interactions

12 visible researcher(s)

Bin Wang

J. Miller

Shlomo Havlin

H. Eugene Stanley

D. Thirumalai

N. P. Armitage

Philippe De Forcrand

Yu Shi

Kunihiko Kaneko

S. N. Coppersmith

Stefano Ruffo

M. E. J. Newman