Quantitative description of ion transport via plasma membrane of yeast and small cells

Modeling of ion transport via plasma membrane needs identification and quantitative understanding of the involved processes. Brief characterization of main ion transport systems of a yeast cell (Pma1, Ena1, TOK1, Nha1, Trk1, Trk2, non-selective cation conductance) and determining the exact number of molecules of each transporter per a typical cell allow us to predict the corresponding ion flows. In this review a comparison of ion transport in small yeast cell and several animal cell types is provided. The importance of cell volume to surface ratio is emphasized. The role of cell wall and lipid rafts is discussed in respect to required increase in spatial and temporal resolution of measurements. Conclusions are formulated to describe specific features of ion transport in a yeast cell. Potential directions of future research are outlined based on the assumptions.Comment: 22 pages, 6 figures, 1 tabl

Queueing with neighbours

In this paper we study asymptotic behaviour of a growth process generated by a semi-deterministic variant of cooperative sequential adsorption model (CSA). This model can also be viewed as a particular queueing system with local interactions. We show that quite limited randomness of the model still generates a rich collection of possible limiting behaviours

Stability of a growth process generated by monomer filling with nearest-neighbour cooperative effects

We study stability of a growth process generated by sequential adsorption of particles on a one-dimensional lattice torus, that is, the process formed by the numbers of adsorbed particles at lattice sites, called heights. Here the stability of process, loosely speaking, means that its components grow at approximately the same rate. To assess stability quantitatively, we investigate the stochastic process formed by differences of heights. The model can be regarded as a variant of a Polya urn scheme with local geometric interaction

Salinity tolerance in plants. Quantitative approach to ion transport starting from halophytes and stepping to genetic and protein engineering for manipulating ion fluxes.

Ion transport is the fundamental factor determining salinity tolerance in plants. The Review starts from differences in ion transport between salt tolerant halophytes and salt-sensitive plants with an emphasis on transport of potassium and sodium via plasma membranes. The comparison provides introductory information for increasing salinity tolerance. Effects of salt stress on ion transport properties of membranes show huge opportunities for manipulating ion fluxes. Further steps require knowledge about mechanisms of ion transport and individual genes of ion transport proteins. Initially, the Review describes methods to measure ion fluxes, the independent set of techniques ensures robust and reliable basement for quantitative approach. The Review briefly summarizes current data concerning Na(+) and K(+) concentrations in cells, refers to primary thermodynamics of ion transport and gives special attention to individual ion channels and transporters. Simplified scheme of a plant cell with known transport systems at the plasma membrane and tonoplast helps to imagine the complexity of ion transport and allows choosing specific transporters for modulating ion transport. The complexity is enhanced by the influence of cell size and cell wall on ion transport. Special attention is given to ion transporters and to potassium and sodium transport by HKT, HAK, NHX, and SOS1 proteins. Comparison between non-selective cation channels and ion transporters reveals potential importance of ion transporters and the balance between the two pathways of ion transport. Further on the Review describes in detail several successful attempts to overexpress or knockout ion transporters for changing salinity tolerance. Future perspectives are questioned with more attention given to promising candidate ion channels and transporters for altered expression. Potential direction of increasing salinity tolerance by modifying ion channels and transporters using single point mutations is discussed and questioned. An alternative approach from synthetic biology is to create new regulation networks using novel transport proteins with desired properties for transforming agricultural crops. The approach had not been widely used earlier; it leads also to theoretical and pure scientific aspects of protein chemistry, structure-function relations of membrane proteins, systems biology and physiology of stress and ion homeostasis. Summarizing, several potential ways are aimed at required increase in salinity tolerance of plants of interest

Long Term Behaviour of Locally Interacting Birth-and-Death Processes

In this paper we study long-term evolution of a finite system of locally interacting birth-and-death processes labelled by vertices of a finite connected graph. A detailed description of the asymptotic behaviour is obtained in the case of both constant vertex degree graphs and star graphs. The model is motivated by modelling interactions between populations and is related to interacting particle systems, Gibbs models with unbounded spins, as well as urn models with interaction.Comment: 26 pages, 2 figure

Boundary effect in competition processes

This paper studies the long-term behaviour of a continuous time Markov chain formed by two non-negative integer valued components that evolve subject to a competitive interaction. In the absence of interaction the Markov chain is just a pair of independent linear birth processes with immigration. Interactions of interest include, as a special case, the famous Lotka-Volterra interaction. The Markov chain with another special case of interaction can be interpreted as an urn model with ball removals and is reminiscent, in a sense, of Friedman's urn model. We show that, with probability one, eventually one of the components of the process tends to infinity, while the other component oscillates between values $0$ and $1$ (between values $0$ and $2$ in a special case)

Linear competition processes and generalized Polya urns with removals

A competition process is a continuous time Markov chain that can be interpreted as a system of interacting birth-and-death processes, the components of which evolve subject to a competitive interaction. This paper is devoted to the study of the long-term behaviour of such a competition process, where a component of the process increases with a linear birth rate and decreases with a rate given by a linear function of other components. A zero is an absorbing state for each component, that is, when a component becomes zero, it stays zero forever (and we say that this component becomes extinct). We show that, with probability one, eventually only a random subset of non-interacting components of the process survives. A similar result also holds for the relevant generalized Polya urn model with removals

Phosphorylated silk fibroin matrix for methotrexate release

Silk-based matrix was produced for delivery of a model anticancer drug, methotrexate (MTX). The calculation of net charge of silk fibroin and MTX was performed to better understand the electrostatic interactions during matrix formation upon casting. Silk fibroin films were cast at pH 7.2 and pH 3.5. Protein kinase A was used to prepare phosphorylated silk fibroin. The phosphorylation content of matrix was controlled by mixing at specific ratios the phosphorylated and unphosphorylated solutions. In vitro release profiling data suggest that the observed interactions are mainly structural and not electrostatical. The release of MTX is facilitated by use of proteolytic enzymes and higher pHs. The elevated -sheet content and crystallinity of the acidified-cast fibroin solution seem not to favor drug retention. All the acquired data underline the prevalence of structural interactions over electrostatical interactions between methotrexate and silk fibroin.The authors would like to acknowledge the support, granted by European NOVO Project, Contract No. FP7-HEALTH 2011-two-stage 278402. This work was partially supported by FEDER through POFC-COMPETE and by national funds from FCT through the projects PEst-C/BIA/UI4050/2011 (CBMA). V.V. also wants to thank Dr. Claudia Botelho for her helpful discussion and comments made during the critical reading of the manuscript