Hard-sphere limit of soft-sphere model for granular materials: Stiffness dependence of steady granular flow

Dynamical behavior of steady granular flow is investigated numerically in the inelastic hard sphere limit of the soft sphere model. We find distinctively different limiting behaviors for the two flow regimes, i.e., the collisional flow and the frictional flow. In the collisional flow, the hard sphere limit is straightforward; the number of collisions per particle per unit time converges to a finite value and the total contact time fraction with other particles goes to zero. For the frictional flow, however, we demonstrate that the collision rate diverges as the power of the particle stiffness so that the time fraction of the multiple contacts remains finite even in the hard sphere limit although the contact time fraction for the binary collisions tends to zero.Comment: 10 figures. Typos removed. to appear in Phys. Rev.

Linear stability analysis of rapid granular flow on a slope and density wave formation

The linear stability of rapid granular flow on a slope under gravity against the longitudinal perturbation is analyzed using hydrodynamic equations. It is demonstrated that the steady flow uniform along the flow direction becomes unstable against the long-wavelength perturbations longitudinal to the flow direction for certain parameter ranges to form the density wave, in contrast with the finite wavelength instability against the transverse perturbation (Forterre & Pouliquen 2002). It is shown that the instability can be understood as the the long-wave instability of the kinematic waves in a quasi-one dimensional system. The results are compared with our previous molecular dynamics simulations (Mitarai & Nakanishi 2001), where the spontaneous density wave formation has been found.Comment: 25 pages, 15 figures, submitted to J. Fluid Mech.; larger parameter range investigated, discussions revise

Control of ribosome traffic by position-dependent choice of synonymous codons

Messenger RNA encodes a sequence of amino acids by using codons. For most amino acids there are multiple synonymous codons that can encode the amino acid. The translation speed can vary from one codon to another, thus there is room for changing the ribosome speed while keeping the amino acid sequence and hence the resulting protein. Recently, it has been noticed that the choice of the synonymous codon, via the resulting distribution of slow- and fast-translated codons, affects not only on the average speed of one ribosome translating the messenger RNA (mRNA) but also might have an effect on nearby ribosomes by affecting the appearance of "traffic jams" where multiple ribosomes collide and form queues. To test this "context effect" further, we here investigate the effect of the sequence of synonymous codons on the ribosome traffic by using a ribosome traffic model with codon-dependent rates, estimated from experiments. We compare the ribosome traffic on wild type sequences and sequences where the synonymous codons were swapped randomly. By simulating translation of 87 genes, we demonstrate that the wild type sequences, especially those with a high bias in codon usage, tend to have the ability to reduce ribosome collisions, hence optimizing the cellular investment in the translation apparatus. The magnitude of such reduction of the translation time might have a significant impact on the cellular growth rate and thereby have importance for the survival of the species.Comment: 12 pages, 6 Figures. This is an author-created, un-copyedited version of an article accepted for publication in Physical Biology. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from i

Disturbance accelerates the transition from low- to high- diversity state in a model ecosystem

The effect of disturbance on a model ecosystem of sessile and mutually competitive species [Mathiesen et al. Phys. Rev. Lett. 107, 188101 (2011); Mitarai et al. Phys. Rev. E 86, 011929 (2012) ] is studied. The disturbance stochastically removes individuals from the system, and the created empty sites are re-colonized by neighbouring species. We show that the stable high-diversity state, maintained by occasional cyclic species interactions that create isolated patches of meta-populations, is robust against small disturbance. We further demonstrate that finite disturbance can accelerate the transition from the low- to high-diversity state by helping creation of small patches through diffusion of boundaries between species with stand-off relation.Comment: 8 pages, 8 figures. Typos correcte

Dynamic competition between transcription initiation and repression: Role of nonequilibrium steps in cell-to-cell heterogeneity

Transcriptional repression may cause transcriptional noise by a competition between repressor and RNA polymerase binding. Although promoter activity is often governed by a single limiting step, we argue here that the size of the noise strongly depends on whether this step is the initial equilibrium binding or one of the subsequent unidirectional steps. Overall, we show that nonequilibrium steps of transcription initiation systematically increase the cell-to-cell heterogeneity in bacterial populations. In particular, this allows also weak promoters to give substantial transcriptional noise.Comment: 5 pages, 3 fiugres. Figure and text update

Ribosome collisions and Translation efficiency: Optimization by codon usage and mRNA destabilization

Individual mRNAs are translated by multiple ribosomes that initiate translation with a few seconds interval. The ribosome speed is codon dependant, and ribosome queuing has been suggested to explain specific data for translation of some mRNAs in vivo. By modelling the stochastic translation process as a traffic problem, we here analyze conditions and consequences of collisions and queuing. The model allowed us to determine the on-rate (0.8 to 1.1 initiations per sec) and the time (1 sec) the preceding ribosome occludes initiation for Escherichia coli lacZ mRNA in vivo. We find that ribosome collisions and queues are inevitable consequences of a stochastic translation mechanism that reduce the translation efficiency substantially on natural mRNAs. The cells minimize collisions by having its mRNAs being unstable and by a highly selected codon usage in the start of the mRNA. The cost of mRNA breakdown is offset by the concomitant increase in translational efficiency.Comment: 5 figures, 3 table