128,811 research outputs found

    Modeling the Role of the Cell Cycle in Regulating Proteus mirabilis Swarm-Colony Development

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    We present models and computational results which indicate that the spatial and temporal regularity seen in Proteus mirabilis swarm-colony development is largely an expression of a sharp age of dedifferentiation in the cell cycle from motile swarmer cells to immotile dividing cells (also called swimmer or vegetative cells.) This contrasts strongly with reaction-diffusion models of Proteus behavior that ignore or average out the age structure of the cell population and instead use only density-dependent mechanisms. We argue the necessity of retaining the explicit age structure, and suggest experiments that may help determine the underlying mechanisms empirically. Consequently, we advocate Proteus as a model organism for a multiscale understanding of how and to what extent the life cycle of individual cells affects the macroscopic behavior of a biological system

    Diffusion entropy and waiting time statistics of hard x-ray solar flares

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    We analyze the waiting time distribution of time distances τ\tau between two nearest-neighbor flares. This analysis is based on the joint use of two distinct techniques. The first is the direct evaluation of the distribution function ψ(τ)\psi(\tau), or of the probability, Ψ(tau)\Psi(tau), that no time distance smaller than a given τ\tau is found. We adopt the paradigm of the inverse power law behavior, and we focus on the determination of the inverse power index μ\mu, without ruling out different asymptotic properties that might be revealed, at larger scales, with the help of richer statistics. The second technique, called Diffusion Entropy (DE) method, rests on the evaluation of the entropy of the diffusion process generated by the time series. The details of the diffusion process depend on three different walking rules, which determine the form and the time duration of the transition to the scaling regime, as well as the scaling parameter δ\delta. With the first two rules the information contained in the time series is transmitted, to a great extent, to the transition, as well as to the scaling regime. The same information is essentially conveyed, by using the third rules, into the scaling regime, which, in fact, emerges very quickly after a fast transition process. We show that the significant information hidden within the time series concerns memory induced by the solar cycle, as well as the power index μ\mu. The scaling parameter δ\delta becomes a simple function of μ\mu, when memory is annihilated. Thus, the three walking rules yield a unique and precise value of μ\mu if the memory is wisely taken under control, or cancelled by shuffling the data. All this makes compelling the conclusion that μ=2.138±0.01\mu = 2.138 \pm 0.01.Comment: 23 pages, 13 figure

    Averaging approach to phase coherence of uncoupled limit-cycle oscillators receiving common random impulses

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    Populations of uncoupled limit-cycle oscillators receiving common random impulses show various types of phase-coherent states, which are characterized by the distribution of phase differences between pairs of oscillators. We develop a theory to predict the stationary distribution of pairwise phase difference from the phase response curve, which quantitatively encapsulates the oscillator dynamics, via averaging of the Frobenius-Perron equation describing the impulse-driven oscillators. The validity of our theory is confirmed by direct numerical simulations using the FitzHugh-Nagumo neural oscillator receiving common Poisson impulses as an example

    Reaction-diffusion kinetics on lattice at the microscopic scale

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    Lattice-based stochastic simulators are commonly used to study biological reaction-diffusion processes. Some of these schemes that are based on the reaction-diffusion master equation (RDME), can simulate for extended spatial and temporal scales but cannot directly account for the microscopic effects in the cell such as volume exclusion and diffusion-influenced reactions. Nonetheless, schemes based on the high-resolution microscopic lattice method (MLM) can directly simulate these effects by representing each finite-sized molecule explicitly as a random walker on fine lattice voxels. The theory and consistency of MLM in simulating diffusion-influenced reactions have not been clarified in detail. Here, we examine MLM in solving diffusion-influenced reactions in 3D space by employing the Spatiocyte simulation scheme. Applying the random walk theory, we construct the general theoretical framework underlying the method and obtain analytical expressions for the total rebinding probability and the effective reaction rate. By matching Collins-Kimball and lattice-based rate constants, we obtained the exact expressions to determine the reaction acceptance probability and voxel size. We found that the size of voxel should be about 2% larger than the molecule. MLM is validated by numerical simulations, showing good agreement with the off-lattice particle-based method, eGFRD. MLM run time is more than an order of magnitude faster than eGFRD when diffusing macromolecules with typical concentrations in the cell. MLM also showed good agreements with eGFRD and mean-field models in case studies of two basic motifs of intracellular signaling, the protein production-degradation process and the dual phosphorylation cycle. Moreover, when a reaction compartment is populated with volume-excluding obstacles, MLM captures the non-classical reaction kinetics caused by anomalous diffusion of reacting molecules

    Cycle expansions for intermittent diffusion

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    We investigate intermittent diffusion using cycle expansions, and show that a truncation based on cycle stability achieves reasonable convergence.Comment: 6 pages, revtex, 4 figure
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