Modelling diffusional transport in the interphase cell nucleus

In this paper a lattice model for diffusional transport of particles in the interphase cell nucleus is proposed. Dense networks of chromatin fibers are created by three different methods: randomly distributed, non-interconnected obstacles, a random walk chain model, and a self avoiding random walk chain model with persistence length. By comparing a discrete and a continuous version of the random walk chain model, we demonstrate that lattice discretization does not alter particle diffusion. The influence of the 3D geometry of the fiber network on the particle diffusion is investigated in detail, while varying occupation volume, chain length, persistence length and walker size. It is shown that adjacency of the monomers, the excluded volume effect incorporated in the self avoiding random walk model, and, to a lesser extent, the persistence length, affect particle diffusion. It is demonstrated how the introduction of the effective chain occupancy, which is a convolution of the geometric chain volume with the walker size, eliminates the conformational effects of the network on the diffusion, i.e., when plotting the diffusion coefficient as a function of the effective chain volume, the data fall onto a master curve.Comment: 9 pages, 8 figure

Exponential families of mixed Poisson distributions

If I=(I1,…,Id) is a random variable on [0,∞)d with distribution μ(dλ1,…,dλd), the mixed Poisson distribution MP(μ) on View the MathML source is the distribution of (N1(I1),…,Nd(Id)) where N1,…,Nd are ordinary independent Poisson processes which are also independent of I. The paper proves that if F is a natural exponential family on [0,∞)d then MP(F) is also a natural exponential family if and only if a generating probability of F is the distribution of v0+v1Y1+cdots, three dots, centered+vqYq for some qless-than-or-equals, slantd, for some vectors v0,…,vq of [0,∞)d with disjoint supports and for independent standard real gamma random variables Y1,…,Yq

Some Physical Consequences of Abrupt Changes in the Multipole Moments of a Gravitating Body

The Barrab\`es-Israel theory of light-like shells in General Relativity is used to show explicitly that in general a light-like shell is accompanied by an impulsive gravitational wave. The gravitational wave is identified by its Petrov Type N contribution to a Dirac delta-function term in the Weyl conformal curvature tensor (with the delta-function singular on the null hypersurface history of the wave and shell). An example is described in which an asymptotically flat static vacuum Weyl space-time experiences a sudden change across a null hypersurface in the multipole moments of its isolated axially symmetric source. A light-like shell and an impulsive gravitational wave are identified, both having the null hypersurface as history. The stress-energy in the shell is dominated (at large distance from the source) by the jump in the monopole moment (the mass) of the source with the jump in the quadrupole moment mainly responsible for the stress being anisotropic. The gravitational wave owes its existence principally to the jump in the quadrupole moment of the source confirming what would be expected.Comment: 26 pages, tex, no figures, to appear in Phys.Rev.

Statistics of work performed on a forced quantum oscillator

Various aspects of the statistics of work performed by an external classical force on a quantum mechanical system are elucidated for a driven harmonic oscillator. In this special case two parameters are introduced that are sufficient to completely characterize the force protocol. Explicit results for the characteristic function of work and the respective probability distribution are provided and discussed for three different types of initial states of the oscillator: microcanonical, canonical and coherent states. Depending on the choice of the initial state the probability distributions of the performed work may grossly differ. This result in particular holds also true for identical force protocols. General fluctuation and work theorems holding for microcanonical and canonical initial states are confirmed

Multiple expressed MHC class II loci in salmonids; details of one non-classical region in Atlantic salmon (Salmo salar)

<p>Abstract</p> <p>Background</p> <p>In teleosts, the Major Histocompatibility Complex (MHC) class I and class II molecules reside on different linkage groups as opposed to tetrapods and shark, where the class I and class II genes reside in one genomic region. Several teleost MHC class I regions have been sequenced and show varying number of class I genes. Salmonids have one major expressed MHC class I locus (UBA) in addition to varying numbers of non-classical genes. Two other more distant lineages are also identifyed denoted L and ZE. For class II, only one major expressed class II alpha (DAA) and beta (DAB) gene has been identified in salmonids so far.</p> <p>Results</p> <p>We sequenced a genomic region of 211 kb encompassing divergent MHC class II alpha (<it>Sasa-DBA</it>) and beta (<it>Sasa-DBB</it>) genes in addition to NRGN, TIPRL, TBCEL and TECTA. The region was not linked to the classical class II genes and had some synteny to genomic regions from other teleosts. Two additional divergent and expressed class II sequences denoted DCA and DDA were also identified in both salmon and trout. Expression patterns and lack of polymorphism make these genes non-classical class II analogues. <it>Sasa-DBB</it>, <it>Sasa-DCA </it>and <it>Sasa-DDA </it>had highest expression levels in liver, hindgut and spleen respectively, suggestive of distinctive functions in these tissues. Phylogenetic studies revealed more yet undescribed divergent expressed MHC class II molecules also in other teleosts.</p> <p>Conclusion</p> <p>We have characterised one genomic region containing expressed non-classical MHC class II genes in addition to four other genes not involved in immune function. Salmonids contain at least two expressed MHC class II beta genes and four expressed MHC class II alpha genes with properties suggestive of new functions for MHC class II in vertebrates. Collectively, our data suggest that the class II is worthy of more elaborate studies also in other teleost species.</p

Family of solvable generalized random-matrix ensembles with unitary symmetry

We construct a very general family of characteristic functions describing Random Matrix Ensembles (RME) having a global unitary invariance, and containing an arbitrary, one-variable probability measure which we characterize by a `spread function'. Various choices of the spread function lead to a variety of possible generalized RMEs, which show deviations from the well-known Gaussian RME originally proposed by Wigner. We obtain the correlation functions of such generalized ensembles exactly, and show examples of how particular choices of the spread function can describe ensembles with arbitrary eigenvalue densities as well as critical ensembles with multifractality.Comment: 4 pages, to be published in Phys. Rev. E, Rapid Com

Mod-Gaussian convergence and its applications for models of statistical mechanics

In this paper we complete our understanding of the role played by the limiting (or residue) function in the context of mod-Gaussian convergence. The question about the probabilistic interpretation of such functions was initially raised by Marc Yor. After recalling our recent result which interprets the limiting function as a measure of "breaking of symmetry" in the Gaussian approximation in the framework of general central limit theorems type results, we introduce the framework of $L^1$-mod-Gaussian convergence in which the residue function is obtained as (up to a normalizing factor) the probability density of some sequences of random variables converging in law after a change of probability measure. In particular we recover some celebrated results due to Ellis and Newman on the convergence in law of dependent random variables arising in statistical mechanics. We complete our results by giving an alternative approach to the Stein method to obtain the rate of convergence in the Ellis-Newman convergence theorem and by proving a new local limit theorem. More generally we illustrate our results with simple models from statistical mechanics.Comment: 49 pages, 21 figure

Eosinophil recruitment into sites of delayed‐type hypersensitivity reactions in mice

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/142239/1/jlb0353.pd