Multistationarity in mass action networks with applications to ERK activation

Ordinary Differential Equations (ODEs) are an important tool in many areas of Quantitative Biology. For many ODE systems multistationarity (i.e. the existence of at least two positive steady states) is a desired feature. In general establishing multistationarity is a difficult task as realistic biological models are large in terms of states and (unknown) parameters and in most cases poorly parameterized (because of noisy measurement data of few components, a very small number of data points and only a limited number of repetitions). For mass action networks establishing multistationarity hence is equivalent to establishing the existence of at least two positive solutions of a large polynomial system with unknown coefficients. For mass action networks with certain structural properties, expressed in terms of the stoichiometric matrix and the reaction rate-exponent matrix, we present necessary and sufficient conditions for multistationarity that take the form of linear inequality systems. Solutions of these inequality systems define pairs of steady states and parameter values. We also present a sufficient condition to identify networks where the aforementioned conditions hold. To show the applicability of our results we analyse an ODE system that is defined by the mass action network describing the extracellular signal-regulated kinase (ERK) cascade (i.e. ERK-activation).     

A Novel Protein Elicitor (PaNie) from Pythium aphanidermatum Induces Multiple Defense Responses in Carrot, Arabidopsis, and Tobacco

A novel protein elicitor (PaNie(234)) from Pythium aphanidermatum (Edson) Fitzp. was purified, microsequenced, and the corresponding cDNA was cloned. The deduced amino acid sequence contains a putative eukaryotic secretion signal with a proteinase cleavage site. The heterologously expressed elicitor protein without the secretion signal of 21 amino acids (PaNie(213)) triggered programmed cell death and de novo formation of 4-hydroxybenzoic acid in cultured cells of carrot (Daucus carota). Programmed cell death was determined using the tetrazolium assay and DNA laddering. Infiltration of PaNie(213) into the intercellular space of leaves of Arabidopsis (Columbia-0, wild type) resulted in necroses and deposition of callose on the cell walls of spongy parenchyma cells surrounding the necrotic mesophyll cells. Necroses were also formed in tobacco (Nicotiana tabacum cv Wisconsin W38, wild type) and tomato (Lycopersicon esculentum Mill.) but not in maize (Zea mays), oat (Avena sativa), and Tradescantia zebrina (Bosse), indicating that monocotyledonous plants are unable to perceive the signal. The reactions observed after treatment with the purified PaNie(213) were identical to responses measured after treatment with a crude elicitor preparation from the culture medium of P. aphanidermatum, described previously. The availability of the pure protein offers the possibility to isolate the corresponding receptor and its connection to downstream signaling-inducing defense reactions.