Bulletin of Mathematical Biology

Poznanski, Roman R.

doi: 10.1007/BF02460658pmid: 1515871

Abstract A detailed morphometric analysis of a Lucifer yellow-filled Cb amacrine cell was undertaken to provide raw data for the construction of a neuronal cable model. The cable model was employed to determine whether distal input-output regions of dendrites were electrically isolated from the soma and each other. Calculations of steady state electrotonic current spread suggested reasonable electrical communication between cell body and dendrites. In particular, the centripetal voltage attenuation revealed that a synaptic signal introduced at the distal end of the equivalent dendrite could spread passively along the dendrite and reach the soma with little loss in amplitude. A functional interpretation of this results could favour a postsynaptic rather than a presynaptic scheme for the operation of directional selectivity in the rabbit retina. On the other hand, dendrites of starburst amacrine cells process information electrotonically with a bias towards the centrifugal direction and for a restricted range of membrane resistance values the voltage attenuation in the centripetal direction suggests that the action of these dendrites can be confined locally. A functional interpretation of this result favours a presynaptic version of Vaney's cotransmission model which attempts to explain how the neural network of starburst amacrine cells might account for directionally selective responses observed in the rabbit retina.

Ebaseh-Onofa, B. O.;Matis, J. H.

doi: 10.1007/BF02460659pmid: N/A

Abstract In this paper a stochastic model for a two-compartment system which incorporates Erlang residence time distributions (i.e. the residence times have the gamma distribution where the shape parameters assume integer values only) into each compartment is generalized to include random rate coefficients. Analytical forms of the model are derived for the case where the rate coefficients have gamma densities. A relationship is established between the new models and existing models that are in current practical usage.

Solé, Ricard V.;Valls, Joaquim

doi: 10.1007/BF02460660pmid: N/A

Abstract Oscillations and chaos can be modelled and observed in a realistic simulation model of interacting prey-predator populations based on Monte Carlo simulation methods. These nonlinear phenomena are linked with some biological and physical bifurcation parameters and mathematical tools from dynamical systems theory may be used in order to characterize this behaviour. Chaotic dynamics are therefore, in our simulation, more the rule than the exception, and are related to delays associated with spatial degrees of freedom.

Zonneveld, C.

doi: 10.1007/BF02460661pmid: N/A

Abstract Current models on protandry in butterflies assume that females mate only once, yet for many species this assumption is not realistic. In this paper a model is formulated to study how polyandry, i.e. repeated mating of females, affects protandry. Moreover, the model is elaborated to describe the probability distribution of the number of matings per female. Field data on this distribution are well described by the model, which supports the use of the law of mass action to describe the encounter rate between males and females. Finally, a weight factor is derived, taking into account the decline in oviposition rate with age, as well as the chance that a female is remated. In comparison with the situation that all matings contribute equally to a male's reproductive success, the application of the weight factor enhances protandry. This suggests that mate competition is not the sole cause of protandry.

Barry, S. I.;Aldis, G. K.

doi: 10.1007/BF02460662pmid: 1515872

Abstract The behaviour of a cavity during an injection of fluid into biological tissue is considered. High cavity pressure drives fluid into the neighbouring tissue where it is absorbed by capillaries and lymphatics. The tissue is modelled as a nonlinear deformable porous medium with the injected fluid absorbed by the tissue at a rate proportional to the local pressure. A model with a spherical cavity in an infinite medium is used to find the pressure and displacement of the tissue as a function of time and radial distance. Analytical and numerical solutions for a step change in cavity pressure show that the flow induces a radial compression in the medium together with an annular expansion, the net result being an overall expansion of the medium. Thus any flow induced deformation of the material will aid in the absorption of fluid.

Baake, Ellen;Schlöder, Johannes P.

doi: 10.1007/BF02460663pmid: N/A

Abstract We construct an ODE model for the fast fluorescence rise of photosynthesis by combining the current reaction scheme of the PS II two-electron-gate with a quasi steady-state description of the fast processes of excitation energy transfer and primary charge separation. The model is fitted to measured induction curves with a multiple shooting algorithm, and remarkably good approximations of the data are obtained. Model refinements are discussed focusing on PS II heterogeneity, and on PS I.

Michelson, Seth;Slate, Doris

doi: 10.1007/BF02460664pmid: 1355383

Abstract Cells displaying the classic multidrug resistant (MDR) phenotype possess a transmembrane protein (p170 or P-glycoprotein) which can actively extrude cytotoxic agents from the cytoplasm. A mathematical model of this drug efflux pump has been developed. Outward transport is modeled as a facilitated diffusion process. Since energy-dependent efflux of cytotoxic agents requires that ATP also bind to p170, the model includes a dynamic calculation for efflux rate which considers Michaelis-Menten kinetics for both the substrate agent and ATP. The final system consists of one partial differential equation (PDE) for the facilitated diffusion of substrate agents out of the cell a 2×2 ordinary differential equation (ODE) system for the dynamic calculation of the ATP-ADP pool, and a dynamic algebraic calculation of the efflux rate given substrate levels at the interior cell membrane interface and ATP levels in the cell. A stability analysis of the ATP-ADP pool distribution and a simplistic closed form solution of the linearized PDE are included. Numerical simulations are also provided.

Palmer, A.;Brindley, J.;Holden, A. V.

doi: 10.1007/BF02460665pmid: 1515869

Abstract Reentry in the heart is the repeated excitation of the same tissue by a single excitation wave; it is responsible for several types of cardiac arrhythmia. The simplest model which permits the phenomenon of reentry is two laterally coupled excitable fibers; in this paper we examine such a model in order to establish a basis for the understanding of the fundamental physical processes underlying the process of reentry. Two versions of the FitzHugh-Nagumo equations are used to develop complementary numerical and analytical results for the coupled fiber model. On the basis of numerical studies, regions of qualitatively different behaviour are mapped in the parameter space of excitation threshold and coupling strength between the fibers, and the effect of the rate of recovery is explored. Some of these regions are also obtained analytically, in good agreement with the numerical results. Finally, the results are discussed in the light of recent work on the role of the anisotropy of cardiac tissue in the initiation of reentrant activity in the heart.

Day, William H. E.;McMorris, F. R.

doi: 10.1007/BF02460666pmid: 1515870

Abstract We apply concepts of social choice theory, in particular those concerning median and plurality rules, to investigate the problem of finding a consensus of aligned molecular sequences. Our model of consensus permits consensus elements at each aligned position to denote ambiguity codes if several alternatives are equally-preferred candidates for consensus. Our results concern plurality rules which are median rules are characterized by the Condorcet properties, and are efficient to calculate. Our approach is axiomatic.

Morris, Anne Krislov;Silk, Wendy Kuhn

doi: 10.1007/BF02460667pmid: N/A

Abstract A sigmoid curve with three fitting parameters is proposed as a descriptive model for the spatial velocity field in one-dimensional growth of plant organs. Analytic expressions are derived for the relative elemental growth (REG) rate, the position and value of the REG rate maximum, the length of the growth zone, the inverse of the growth trajectory and cell length in the “elongation only” zone. The expressions are fit to published data to characterize the effects of environmental variation on growth of monocotyledonous roots. The simple expressions for growth may prove useful in mechanistic models. The fitted curves summarize more than a decade of observations and thus provide a challenge to theorists.