From molecular networks to qualitative cell behavior

Adaptation and behavior are characteristics of life which are fundamentally dynamic. If we want to model the living cell we have to describe it as a dynamic system. Typical dynamic models are based on quantitative differential equations requiring very detailed kinetic knowledge. Alternative modeling techniques for less fine-grained information are better suited to available functional genomics data. As such, constraint-based techniques and qualitative modeling have proven themselves to be valid approaches in cell biology. These approaches offer formal support to check the consistency of molecular networks against phenotypic observations in the light of dynamic systems.     

Incorporating mating preferences into a host-parasite model

Mating preferences are incorporated into a host-macroparasite system. Mating preferences of the host and/or parasite can affect the outcome of the host-parasite relationship if certain genotypes of the host are more (or less) affected by the parasite induced death rate than others. Several examples illustrate the situations that can occur.     

Simulation modeling of ligand receptor interactions at non-equilibrium conditions: processing of noisy inputs by ionotropic receptors

The first event in signal transduction at a synapse is the binding of transmitters to receptors. Because of rapidly changing transmitter levels this binding is unlikely to occur at equilibrium. We describe a mathematical approach that models complex receptor interactions in which the timing and amplitude of transmitter release are noisy. We show that exact solutions for simple bimolecular interactions and receptor transitions can be used to model complex reaction schemes by expressing them in sets of difference equations. Results from the difference equation method to describe binding and channel opening at extended time points compare well with standard solutions using ordinary differential equations. Because it is applicable to noisy systems we used the difference method to investigate the information processing capabilities of GABA receptors and predict how pharmacological agents may modify these properties. As previously demonstrated, the response to a single pulse of GABA is prolonged through entry into a desensitized state. During trains of stimuli the signal to noise ratio can change, and even increase progressively, but the overall transmitted fidelity of the signal decreases with increased driving frequency. The GABA modulator chlorpromazine (primarily affects agonist on and off rates) is predicated to increase receptor signal to noise ratio at all frequencies whereas pregnenolone sulfate (affects receptor desensitization) completely inhibits information transfer.     

Tracking genes of ecological relevance using a genome scan in two independent regional population samples of Arabis alpina

Understanding the genetic basis of adaptation in response to environmental variation is fundamental as adaptation plays a key role in the extension of ecological niches to marginal habitats and in ecological speciation. Based on the assumption that some genomic markers are correlated to environmental variables, we aimed to detect loci of ecological relevance in the alpine plant Arabis alpina L. sampled in two regions, the French (99 locations) and the Swiss (109 locations) Alps. We used an unusually large genome scan [825 amplified fragment length polymorphism loci (AFLPs)] and four environmental variables related to temperature, precipitation and topography. We detected linkage disequilibrium among only 3.5% of the considered AFLP loci. A population structure analysis identified no admixture in the study regions, and the French and Swiss Alps were differentiated and therefore could be considered as two independent regions. We applied generalized estimating equations (GEE) to detect ecologically relevant loci separately in the French and Swiss Alps. We identified 78 loci of ecological relevance (9%), which were mainly related to mean annual minimum temperature. Only four of these loci were common across the French and Swiss Alps. Finally, we discuss that the genomic characterization of these ecologically relevant loci, as identified in this study, opens up new perspectives for studying functional ecology in A. alpina, its relatives and other alpine plant species.     

非线性高阶阻尼时滞微分方程的振动定理

研究具有阻尼项的非线性时滞微分方程,给出了使得方程的一切解振动的两个充分条件.一些实例说明,本文的结果在判定非线性阻尼方程的振动性时较文献中的结果更为有效.     

Non-local models for the formation of hepatocyte-stellate cell aggregates

Liver cell aggregates may be grown in vitro by co-culturing hepatocytes with stellate cells. This method results in more rapid aggregation than hepatocyte-only culture, and appears to enhance cell viability and the expression of markers of liver-specific functions. We consider the early stages of aggregate formation, and develop a new mathematical model to investigate two alternative hypotheses (based on evidence in the experimental literature) for the role of stellate cells in promoting aggregate formation. Under Hypothesis 1, each population produces a chemical signal which affects the other, and enhanced aggregation is due to chemotaxis. Hypothesis 2 asserts that the interaction between the two cell types is by direct physical contact: the stellates extend long cellular processes which pull the hepatocytes into the aggregates. Under both hypotheses, hepatocytes are attracted to a chemical they themselves produce, and the cells can experience repulsive forces due to overcrowding. We formulate non-local (integro-partial differential) equations to describe the densities of cells, which are coupled to reaction-diffusion equations for the chemical concentrations. The behaviour of the model under each hypothesis is studied using a combination of linear stability analysis and numerical simulations. Our results show how the initial rate of aggregation depends upon the cell seeding ratio, and how the distribution of cells within aggregates depends on the relative strengths of attraction and repulsion between the cell types. Guided by our results, we suggest experiments which could be performed to distinguish between the two hypotheses.     

A note on robust inference from a conditional Poisson model

A randomised controlled trial to evaluate a training programme for physician-patient communication required the analysis of paired count data. The impact of departures from the Poisson assumption when paired count data are analysed through use of a conditional likelihood is illustrated. A simple approach to providing robust inference is outlined and illustrated.     

The weighted generalized estimating equations approach for the evaluation of medical diagnostic test at subunit level

Sensitivity and specificity are common measures used to evaluate the performance of a diagnostic test. A diagnostic test is often administrated at a subunit level, e.g. at the level of vessel, ear or eye of a patient so that the treatment can be targeted at the specific subunit. Therefore, it is essential to evaluate the diagnostic test at the subunit level. Often patients with more negative subunit test results are less likely to receive the gold standard tests than patients with more positive subunit test results. To account for this type of missing data and correlation between subunit test results, we proposed a weighted generalized estimating equations (WGEE) approach to evaluate subunit sensitivities and specificities. A simulation study was conducted to evaluate the performance of the WGEE estimators and the weighted least squares (WLS) estimators (Barnhart and Kosinski, 2003) under a missing at random assumption. The results suggested that WGEE estimator is consistent under various scenarios of percentage of missing data and sample size, while the WLS approach could yield biased estimators due to a misspecified missing data mechanism. We illustrate the methodology with a cardiology example.     

Relations between biochemical thermodynamics and biochemical kinetics

The parameters in steady-state or rapid-equilibrium rate equations for enzyme-catalyzed reactions depend on the temperature, pH, and ionic strength, and may depend on the concentrations of specific species in the buffer. When the complete rate equation (i.e. the equation with parameters for the reverse reaction as well as the forward reaction) is determined, there are one or more Haldane relations between some of the kinetic parameters and the apparent equilibrium constant for the reaction that is catalyzed. When the apparent equilibrium constant can be calculated from the kinetic parameters, the equilibrium composition can be calculated. This is remarkable because the kinetic parameters all depend on the properties of the enzymatic site, but the apparent equilibrium constant and the equilibrium composition do not. The effects of ionic strength and pH on the unoccupied enzymatic site and the occupied enzymatic site have to cancel in the Haldane relation or in the calculation of the apparent equilibrium constant using the rate constants for the steps in the mechanism. Several simple enzymatic mechanisms and their complete rate equations are discussed.