Facilitation of polymer looping and giant polymer diffusivity in crowded solutions of active particles

We study the dynamics of polymer chains in a bath of self-propelled particles (SPP) by extensive Langevin dynamics simulations in a two dimensional system. Specifically, we analyse the polymer looping properties versus the SPP activity and investigate how the presence of the active particles alters the chain conformational statistics. We find that SPPs tend to extend flexible polymer chains while they rather compactify stiffer semiflexible polymers, in agreement with previous results. Here we show that larger activities of SPPs yield a higher effective temperature of the bath and thus facilitate looping kinetics of a passive polymer chain. We explicitly compute the looping probability and looping time in a wide range of the model parameters. We also analyse the motion of a monomeric tracer particle and the polymer's centre of mass in the presence of the active particles in terms of the time averaged mean squared displacement, revealing a giant diffusivity enhancement for the polymer chain via SPP pooling. Our results are applicable to rationalising the dimensions and looping kinetics of biopolymers at constantly fluctuating and often actively driven conditions inside biological cells or suspensions of active colloidal particles or bacteria cells.Comment: 15 pages, 9 figures, IOPLaTe

Thermodynamics and Fractional Fokker-Planck Equations

The relaxation to equilibrium in many systems which show strange kinetics is described by fractional Fokker-Planck equations (FFPEs). These can be considered as phenomenological equations of linear nonequilibrium theory. We show that the FFPEs describe the system whose noise in equilibrium funfills the Nyquist theorem. Moreover, we show that for subdiffusive dynamics the solutions of the corresponding FFPEs are probability densities for all cases where the solutions of normal Fokker-Planck equation (with the same Fokker-Planck operator and with the same initial and boundary conditions) exist. The solutions of the FFPEs for superdiffusive dynamics are not always probability densities. This fact means only that the corresponding kinetic coefficients are incompatible with each other and with the initial conditions

Subordination model of anomalous diffusion leading to the two-power-law relaxation responses

We derive a general pattern of the nonexponential, two-power-law relaxation from the compound subordination theory of random processes applied to anomalous diffusion. The subordination approach is based on a coupling between the very large jumps in physical and operational times. It allows one to govern a scaling for small and large times independently. Here we obtain explicitly the relaxation function, the kinetic equation and the susceptibility expression applicable to the range of experimentally observed power-law exponents which cannot be interpreted by means of the commonly known Havriliak-Negami fitting function. We present a novel two-power relaxation law for this range in a convenient frequency-domain form and show its relationship to the Havriliak-Negami one.Comment: 5 pages; 3 figures; corrected versio

Bubble coalescence in breathing DNA: Two vicious walkers in opposite potentials

We investigate the coalescence of two DNA-bubbles initially located at weak segments and separated by a more stable barrier region in a designed construct of double-stranded DNA. The characteristic time for bubble coalescence and the corresponding distribution are derived, as well as the distribution of coalescence positions along the barrier. Below the melting temperature, we find a Kramers-type barrier crossing behaviour, while at high temperatures, the bubble corners perform drift-diffusion towards coalescence. The results are obtained by mapping the bubble dynamics on the problem of two vicious walkers in opposite potentials.Comment: 7 pages, 4 figure

Fractional Klein-Kramers equation for superdiffusive transport: normal versus anomalous time evolution in a differential L{\'e}vy walk model

We introduce a fractional Klein-Kramers equation which describes sub-ballistic superdiffusion in phase space in the presence of a space-dependent external force field. This equation defines the differential L{\'e}vy walk model whose solution is shown to be non-negative. In the velocity coordinate, the probability density relaxes in Mittag-Leffler fashion towards the Maxwell distribution whereas in the space coordinate, no stationary solution exists and the temporal evolution of moments exhibits a competition between Brownian and anomalous contributions.Comment: 4 pages, REVTe

Bubble dynamics in DNA

The formation of local denaturation zones (bubbles) in double-stranded DNA is an important example for conformational changes of biological macromolecules. We study the dynamics of bubble formation in terms of a Fokker-Planck equation for the probability density to find a bubble of size n base pairs at time t, on the basis of the free energy in the Poland-Scheraga model. Characteristic bubble closing and opening times can be determined from the corresponding first passage time problem, and are sensitive to the specific parameters entering the model. A multistate unzipping model with constant rates recently applied to DNA breathing dynamics [G. Altan-Bonnet et al, Phys. Rev. Lett. 90, 138101 (2003)] emerges as a limiting case.Comment: 9 pages, 2 figure

Differences in intestinal size, structure, and function contributing to feed efficiency in broiler chickens reared at geographically distant locations

The contribution of the intestinal tract to differences in residual feed intake (RFI) has been inconclusively studied in chickens so far. It is also not clear if RFI-related differences in intestinal function are similar in chickens raised in different environments. The objective was to investigate differences in nutrient retention, visceral organ size, intestinal morphology, jejunal permeability and expression of genes related to barrier function, and innate immune response in chickens of diverging RFI raised at 2 locations (L1: Austria; L2: UK). The experimental protocol was similar, and the same dietary formulation was fed at the 2 locations. Individual BW and feed intake (FI) of chickens (Cobb 500FF) were recorded from d 7 of life. At 5 wk of life, chickens (L1, n = 157; L2 = 192) were ranked according to their RFI, and low, medium, and high RFI chickens were selected (n = 9/RFI group, sex, and location). RFI values were similar between locations within the same RFI group and increased by 446 and 464 g from low to high RFI in females and males, respectively. Location, but not RFI rank, affected growth, nutrient retention, size of the intestine, and jejunal disaccharidase activity. Chickens from L2 had lower total body weight gain and mucosal enzyme activity but higher nutrient retention and longer intestines than chickens at L1. Parameters determined only at L1 showed increased crypt depth in the duodenum and jejunum and enhanced paracellular permeability in low vs. high RFI females. Jejunal expression of IL1B was lower in low vs. high RFI females at L2, whereas that of TLR4 at L1 and MCT1 at both locations was higher in low vs. high RFI males. Correlation analysis between intestinal parameters and feed efficiency metrics indicated that feed conversion ratio was more correlated to intestinal size and function than was RFI. In conclusion, the rearing environment greatly affected intestinal size and function, thereby contributing to the variation in chicken RFI observed across locations

From the solutions of diffusion equation to the solutions of subdiffusive one

Starting with the Green's functions found for normal diffusion, we construct exact time-dependent Green's functions for subdiffusive equation (with fractional time derivatives), with the boundary conditions involving a linear combination of fluxes and concentrations. The method is particularly useful to calculate the concentration profiles in a multi-part system where different kind of transport occurs in each part of it. As an example, we find the solutions of subdiffusive equation for the system composed from two parts with normal diffusion and subdiffusion, respectively.Comment: 11 pages, 2 figure

Subdiffusion-limited reactions

We consider the coagulation dynamics A+A -> A and A+A A and the annihilation dynamics A+A -> 0 for particles moving subdiffusively in one dimension. This scenario combines the "anomalous kinetics" and "anomalous diffusion" problems, each of which leads to interesting dynamics separately and to even more interesting dynamics in combination. Our analysis is based on the fractional diffusion equation