Developing Itô stochastic differential equation models for neuronal signal transduction pathways

Mathematical modeling and simulation of dynamic biochemical systems are receiving considerable attention due to the increasing availability of experimental knowledge of complex intracellular functions. In addition to deterministic approaches, several stochastic approaches have been developed for simulating the time-series behavior of biochemical systems. The problem with stochastic approaches, however, is the larger computational time compared to deterministic approaches. It is therefore necessary to study alternative ways to incorporate stochasticity and to seek approaches that reduce the computational time needed for simulations, yet preserve the characteristic behavior of the system in question. In this work, we develop a computational framework based on the It? stochastic differential equations for neuronal signal transduction networks. There are several different ways to incorporate stochasticity into deterministic differential equation models and to obtain It? stochastic differential equations. Two of the developed models are found most suitable for stochastic modeling of neuronal signal transduction. The best models give stable responses which means that the variances of the responses with time are not increasing and negative concentrations are avoided. We also make a comparative analysis of different kinds of stochastic approaches, that is the It? stochastic differential equations, the chemical Langevin equation, and the Gillespie stochastic simulation algorithm. Different kinds of stochastic approaches can be used to produce similar responses for the neuronal protein kinase C signal transduction pathway. The fine details of the responses vary slightly, depending on the approach and the parameter values. However, when simulating great numbers of chemical species, the Gillespie algorithm is computationally several orders of magnitude slower than the It? stochastic differential equations and the chemical Langevin equation. Furthermore, the chemical Langevin equation produces negative concentrations. The It? stochastic differential equations developed in this work are shown to overcome the problem of obtaining negative values.     

Regulation between nitric oxide and MAPK signal transduction in mammals

Nitric oxide (NO) is an important biological messenger in the regulation of tissue homeostasis. It exhibits a wide range of effects during physiological and pathophysiological processes. Typical beneficial properties of NO include the regulation of vascular tone,the protection of cells against apoptosis, the modulation of immune responses, and the killing of microbial pathogens. On the other hand,NO may cause severe vasodilation and myocardial depression during bacterial sepsis or act as a cytotoxic and tissue-damaging molecule in autoimmune diseases. Mitogen-activated protein kinase (MAPK) is a family of serine/threonine protein kinases that are widely distributed in mammalian cells. MAPK cascade plays pivotal roles in gene expression, cell proliferation, differentiation, neuronal survival and programmed cell death under a variety of experimental conditions. MAPKs transduce the signal for the cellular response to extracellular stresses or stimuli. The relation between them, however, has never been reviewed. Based on our researches and other reports in the field, we review their reciprocal regulatory functions.     

Nitric oxide involved in signal transduction of Jasmonic acid-induced stomatal closure of Vicia faba L.

Nitric oxide (NO) and Jasmonic acid (JA) are two key signaling molecules involved in many and diverse biological pathways in plants. Growing evidence suggested that NO signaling interacts with JA signaling. In this work, Our experiment showed that NO exists in guard cell of Vicia faba L., and NO is involved in signal transduction of JAinduced stomata closuring: ( i ) JA enhances NO synthesis in guard cell; ( ii ) both JA and NO induced stomatal closure, and had dose response to their effects; ( iU ) there are synergetic correlation between JA and lower NO concentration in regulation of stomatal movement; (iV) JA-induced stomatal closure was largely prevented by 2-phenyl-4,4,5,5-tetramethylimidazoline-l-oxyl-3-oxide (PTIO), a specific NO scavenger. An inhibitor of NO synthase (NOS) in mammalian cells, N^G-nitro-L-Arg-methyl eater (L-NAME) also inhibits plant NOS, repressing JA-induced NO generation and JA-induced stomatal closure. We presumed that NO mainly comes from NOS after JA treatment.     

植物抗病性的分子机制和信号传导

植物抗病性的分子机制一直是植物病理学关注的焦点.近年来,国内外不少学者和实验室正在大量分离和培养与抗病有关的突变体,并且寻找和研究与抗病有关的基因和抗病机制.研究表明,在病原物与植物的相互作用、病原信号的传导和抗病性激发的过程中存在着一系列的调节因子和基因,并形成复杂的调控网络.综述了近年来国内外植物抗病性的分子研究进展,阐述了植物抗病性分子机制和信号传导.     

Homogenization and concentrated capacity for the heat equation with non-linear variational data in reticular almost disconnected structures and applications to visual transduction

Out of a right, circular cylinder of height H and cross-section a disc of radius R+ one removes a stack of nH/ parallel, equi-spaced cylinders C_j,j=1,2,...,n, each of radius R and height . Here , are fixed positive numbers and is a positive parameter to be allowed to go to zero. The union of the C_j almost fills in the sense that any two contiguous cylinders C_j are at a mutual distance of the order of and that the outer shell, i.e., the gap S=-_o has thickness of the order of (_o is obtained from by formally setting =0). The cylinder from which the C_j are removed, is an almost disconnected structure, it is denoted by , and it arises in the mathematical theory of phototransduction.For each >0 we consider the heat equation in the almost disconnected structure , for the unknown function u, with variational boundary data on the faces of the removed cylinders C_j. The limit of this family of problems as 0 is computed by concentrating heat capacity and diffusivity on the outer shell, and by homogenizing the u within the limiting cylinder _o.It is shown that the limiting problem consists of an interior diffusion in _o and a boundary diffusion on the lateral boundary S of _o. The interior diffusion is governed by the 2-dimensional heat equation in _o, for an interior limiting function u. The boundary diffusion is governed by the Laplace–Beltrami heat equation on S, for a boundary limiting function u_S. Moreover the exterior flux of the interior limit u provides the source term for the boundary diffusion on S. Finally the interior limit u, computed on S in the sense of the traces, coincides with the boundary limit u_S. As a consequence of the geometry of , local arguments do not suffice to prove convergence in _o, and also we have to take into account the behavior of the solution in S. A key, novel idea consists in extending equi-bounded and equi-Hölder continuous functions in -dependent domains, into equi-bounded and equi-Hölder continuous functions in the whole ^N, by means of the Kirzbraun–Pucci extension technique.The biological origin of this problem is traced, and its application to signal transduction in the retina rod cells of vertebrates is discussed. Mathematics Subject Classification (2000) 35B27, 35K50, 92C37     

蓝藻真核型蛋白质激酶与信号传导

对最近10年在蓝藻中找到大量编码Ser／Thr基因的研究结果进行了综述,并对这些蛋白质激酶在信号传导中的作用模式做了讨论．