Oxygen transport and consumption in germinating seeds

Three mathematical models were formulated to describe the oxygen con-sumption of seeds during germination. These models were fitted to measure-ment data of oxygen consumption curves for individual germinating seeds of Savoy cabbage, barley and sugar beet provided by Fytagoras. The first model builds on a logistic growth model for the increasing population of mitochondria in the embryo during growth. The other two take the anatomy and physiologi-cal properties of the seed into account. One describes the oxygen uptake during the germination phase only. An extension of this model is capable of fitting the complete oxygen consumption curve, including the initial ‘repair’ phase in which the embryonic cells recover from their dormant state before extensive cell division and growth commences. Keywords: Modelling, seed germination, cellular respiration, oxygen transpor

Fractional diffusion modeling of ion channel gating

An anomalous diffusion model for ion channel gating is put forward. This scheme is able to describe non-exponential, power-law like distributions of residence time intervals in several types of ion channels. Our method presents a generalization of the discrete diffusion model by Millhauser, Salpeter and Oswald [Proc. Natl. Acad. Sci. USA 85, 1503 (1988)] to the case of a continuous, anomalous slow conformational diffusion. The corresponding generalization is derived from a continuous time random walk composed of nearest neighbor jumps which in the scaling limit results in a fractional diffusion equation. The studied model contains three parameters only: the mean residence time, a characteristic time of conformational diffusion, and the index of subdiffusion. A tractable analytical expression for the characteristic function of the residence time distribution is obtained. In the limiting case of normal diffusion, our prior findings [Proc. Natl. Acad. Sci. USA 99, 3552 (2002)] are reproduced. Depending on the chosen parameters, the fractional diffusion model exhibits a very rich behavior of the residence time distribution with different characteristic time-regimes. Moreover, the corresponding autocorrelation function of conductance fluctuations displays nontrivial features. Our theoretical model is in good agreement with experimental data for large conductance potassium ion channels

Polar auxin transport: an early invention.

Plant science

Non-commutative desingularization of determinantal varieties, I

We show that determinantal varieties defined by maximal minors of a generic matrix have a non-commutative desingularization, in that we construct a maximal Cohen-Macaulay module over such a variety whose endomorphism ring is Cohen-Macaulay and has finite global dimension. In the case of the determinant of a square matrix, this gives a non-commutative crepant resolution.Comment: 52 pages, 3 figures, all comments welcom

Lattice formulation of the Fokker-Planck equation

A lattice version of the Fokker-Planck equation (FPE), accounting for dissipative interactions, not resolved on the molecular scale, is introduced. The lattice FPE is applied to the study of electrorheological transport of a one-dimensional charged fluid, and found to yield quantitative agreement with a recent analytical solution. Future extensions, including inelastic ion-ion collisions, are also outlined.Comment: 23 pages, 4 figure

A Simple Kinetic Model Describes the Processivity of Myosin-V

Myosin-V is a motor protein responsible for organelle and vesicle transport in cells. Recent single-molecule experiments have shown that it is an efficient processive motor that walks along actin filaments taking steps of mean size close to 36 nm. A theoretical study of myosin-V motility is presented following an approach used successfully to analyze the dynamics of conventional kinesin but also taking some account of step-size variations. Much of the present experimental data for myosin-V can be well described by a two-state chemical kinetic model with three load-dependent rates. In addition, the analysis predicts the variation of the mean velocity and of the randomness -- a quantitative measure of the stochastic deviations from uniform, constant-speed motion -- with ATP concentration under both resisting and assisting loads, and indicates a {\it sub}step of size $d_{0} \simeq$ 13-14 nm (from the ATP-binding site) that appears to accord with independent observations.Comment: 20 pages, 7 figures, to be published in Biophys. J. in 200

Onset of negative interspike interval correlations in adapting neurons

Negative serial correlations in single spike trains are an effective method to reduce the variability of spike counts. One of the factors contributing to the development of negative correlations between successive interspike intervals is the presence of adaptation currents. In this work, based on a hidden Markov model and a proper statistical description of conditional responses, we obtain analytically these correlations in an adequate dynamical neuron model resembling adaptation. We derive the serial correlation coefficients for arbitrary lags, under a small adaptation scenario. In this case, the behavior of correlations is universal and depends on the first-order statistical description of an exponentially driven time-inhomogeneous stochastic process.Comment: 12 pages (10 pages in the journal version), 6 figures, published in Phys. Rev. E; http://link.aps.org/doi/10.1103/PhysRevE.84.04190

Plant-inducible virulence promoter of the Agrobacterium tumefaciens Ti plasmid

Agrobacterium tumefaciens is the causative agent of crown gall, a plant tumour that can arise on most species of dicotyledonous plants. The tumour-inducing capacity of the bacterium requires the presence of a large plasmid, designated the Ti plasmid, which itself contains two regions essential for tumour formation-the T(umour)-region and the Vir(ulence)-region. The T-region is transferred to plant cells by an unknown mechanism, and becomes stably integrated into the plant genome. The Vir-region has been identified by transposon mutagenesis, but the DNA of this region has never been detected in tumour lines. However, trans-complementation of Vir mutants indicates that genes of the Vir-region are functional in the bacterium. Moreover, the Vir- and T-regions can be physically separated in A. tumefaciens without loss of tumour-inducing capacity. Seven loci, designated virA-F and virO, have been identified in the Vir-region of the octopine Ti plasmid, but their functions are unknown. As virC mutants in the octopine-type plasmid pTiB6 are invariably avirulent in tests on various plant species, this gene seems to be essential for virulence and we are studying it in detail. We report here that the promoter of virC shows no detectable activity in A. tumefaciens and Escherichia coli K-12 grown in standard medium, but that its activity is induced by a plant product.

Path probability density functions for semi-Markovian random walks

In random walks, the path representation of the Green's function is an infinite sum over the length of path probability density functions (PDFs). Here we derive and solve, in Laplace space, the recursion relation for the n order path PDF for any arbitrarily inhomogeneous semi-Markovian random walk in a one-dimensional (1D) chain of L states. The recursion relation relates the n order path PDF to L/2 (round towards zero for an odd L) shorter path PDFs, and has n independent coefficients that obey a universal formula. The z transform of the recursion relation straightforwardly gives the generating function for path PDFs, from which we obtain the Green's function of the random walk, and derive an explicit expression for any path PDF of the random walk. These expressions give the most detailed description of arbitrarily inhomogeneous semi-Markovian random walks in 1D