Modelling cytoskeletal traffic: an interplay between passive diffusion and active transport

We introduce the totally asymmetric exclusion process with Langmuir kinetics (TASEP-LK) on a network as a microscopic model for active motor protein transport on the cytoskeleton, immersed in the diffusive cytoplasm. We discuss how the interplay between active transport along a network and infinite diffusion in a bulk reservoir leads to a heterogeneous matter distribution on various scales. We find three regimes for steady state transport, corresponding to the scale of the network, of individual segments or local to sites. At low exchange rates strong density heterogeneities develop between different segments in the network. In this regime one has to consider the topological complexity of the whole network to describe transport. In contrast, at moderate exchange rates the transport through the network decouples, and the physics is determined by single segments and the local topology. At last, for very high exchange rates the homogeneous Langmuir process dominates the stationary state. We introduce effective rate diagrams for the network to identify these different regimes. Based on this method we develop an intuitive but generic picture of how the stationary state of excluded volume processes on complex networks can be understood in terms of the single-segment phase diagram.Comment: 5 pages, 7 figure

Bertrand-Edgeworth competition in an almost symmetric oligopoly

We analyze a Bertrand-Edgeworth game in homogeneous product industry, under effcient rationing, constant marginal cost until full capacity utilization, and identical technology across firms. We solve for the equilibrium and establish its uniqueness for capacity configurations in the mixed strategy region of the capacity space such that the capacities of the largest and smallest firm are sufficiently close.Bertrand-Edgeworth competition; mixed strategy equilibrium; almost symmetric oligopoly; Mixed strategy equilibrium

Bertrand-Edgeworth games under oligopoly with a complete characterization for the triopoly

The paper extends the analysis of price competition among capacity-constrained sellers beyond the cases of duopoly and symmetric oligopoly. We first provide some general results for the oligopoly and then focus on the triopoly, providing a complete characterization of the mixed strategy equilibrium of the price game. The region of the capacity space where the equilibrium is mixed is partitioned according to the features of the mixed strategy equilibrium arising in each subregion. Then computing the mixed strategy equilibrium becomes a quite simple task. The analysis reveals features of the mixed strategy equilibrium which do not arise in the duopoly (some of them have also been discovered by Hirata (2008)).Bertrand-Edgeworth; Price game; Oligopoly; Triopoly; Mixed strategy equilibrium

Precision radiative corrections to the Dalitz plot of baryon semileptonic decays including the spin-momentum correlation of the decaying baryon and the emitted charged lepton

We calculate the radiative corrections to the angular correlation between the polarization of the decaying baryon and the direction of the emitted charged lepton in the semileptonic decays of spin one-half baryons to order (\alpha/\pi)(q/M_1). The final results are presented, first, with the triple integration of the bremsstrahlung photon ready to be performed numerically and, second, in an analytical form. A third presentation of our results in the form of numerical arrays of coefficients to be multiplied on the quadratic products of form factors is discussed. This latter may be the most practical one to use in Monte Carlo simulations. A series of crosschecks is performed. The results are useful in the analysis of the Dalitz plot of precision experiments involving light and heavy quarks and is not compromised to fixing the form factors at predetermined values. It is assumed that the real photons are kinematically discriminated. Otherwise, our results have a general model-independent applicability.Comment: 8 pages, RevTex4, 5 tables, no figures. Shortened version; results and conclusions remain unchange

Precision radiative corrections to the semileptonic Dalitz plot with angular correlation between polarized decaying and emitted baryons: Effects of the four-body region

Analytical radiative corrections of order (\alpha/\pi)(q/M_1) are calculated for the four-body region of the Dalitz plot of baryon semileptonic decays when the s_1 \cdot p_2 correlation is present. Once the final result is available, it is possible to exhibit it in terms of the corresponding final result of the three-body region following a set of simple changes in the latter. We cover two cases, a charged and a neutral polarized decaying baryon.Comment: Revtex4, 7 pages, no figure

Motor proteins traffic regulation by supply-demand balance of resources

In cells and in vitro assays the number of motor proteins involved in biological transport processes is far from being unlimited. The cytoskeletal binding sites are in contact with the same finite reservoir of motors (either the cytosol or the flow chamber) and hence compete for recruiting the available motors, potentially depleting the reservoir and affecting cytoskeletal transport. In this work we provide a theoretical framework to study, analytically and numerically, how motor density profiles and crowding along cytoskeletal filaments depend on the competition of motors for their binding sites. We propose two models in which finite processive motor proteins actively advance along cytoskeletal filaments and are continuously exchanged with the motor pool. We first look at homogeneous reservoirs and then examine the effects of free motor diffusion in the surrounding medium. We consider as a reference situation recent in vitro experimental setups of kinesin-8 motors binding and moving along microtubule filaments in a flow chamber. We investigate how the crowding of linear motor proteins moving on a filament can be regulated by the balance between supply (concentration of motor proteins in the flow chamber) and demand (total number of polymerised tubulin heterodimers). We present analytical results for the density profiles of bound motors, the reservoir depletion, and propose novel phase diagrams that present the formation of jams of motor proteins on the filament as a function of two tuneable experimental parameters: the motor protein concentration and the concentration of tubulins polymerized into cytoskeletal filaments. Extensive numerical simulations corroborate the analytical results for parameters in the experimental range and also address the effects of diffusion of motor proteins in the reservoir.Comment: 31 pages, 10 figure

Radiative corrections to the three-body region of the Dalitz plot of baryon semileptonic decays with angular correlation between polarized emitted baryons and charged leptons: The initial-baryon rest frame case

We complement the results for the radiative corrections to the s2.l angular correlation of baryon semileptonic decays of Ref. [1] with the final results in the rest frame of the decaying baryon.Comment: 7 pages, Revtex4, no figure