Biomedical subjects

R E Plant

Publications and source records attributed to R E Plant.

7 recordsLinked to original sources

PubMed1986

Models for age structured populations with distributed maturation rates.

In the use of age structured population models for agricultural applications such as the modeling of crop-pest interactions it is often essential that the model take into account the distribution in maturation rates present in some or all of the populations. The traditional method for incorporating distributed maturation rates into crop and pest models has been the so-called "distributed delay" method. In this paper we review the application of the distributed delay formalism to the McKendrick equation of an age structured population. We discuss the mathematical properties of the system of ordinary differential equations arising out of the distributed delay formalism. We then discuss an alternative method involving modification of the Leslie matrix.

Aging↗

PubMed1979

The efficient numerical solution of biological simulation problems.

A subroutine called DESOL for the numerical solution of ordinary differential equations of the type arising in biological simulation problems is described. DESOL is about as efficient as current high quality integrators, but because of its compactness it can be easily used on small computers. The subroutine has excellent stability properties and functions with very little required input from the user. In addition, it has features which aid in debugging associated programs. Several test and example problems are given, as is the derivation of the major formulae used in the package.

Computers↗

PubMed1978

Simulation of coupling between chemical reactions and ion transport in brown adipose tissue using network thermodynamics.

Several cellular events associated with energy turnover in the mitochondria and at the Na+/K+ plasma membrane pump have been formulated in terms of network thermodynamics. The calorigenic role of the Na+/K+ pump is examined in terms of the relationship between the movement of sodium and potassium ions and the chemical reactions involved. In addition, attention is centered on the potential thermogenic role of three mitochondrial pathways involving proton fluxes--namely, one in which protons are transported from the matrix to the intermembrane space; a second in which protons are transferred back into the matrix in conjunction with the synthesis of ATP; and a third wherein protons re-enter the matrix without being coupled to any chemical reaction. (This latter pathway has been delineated by studies on isolated mitochondria and may be unique to brown fat.) At both sites (plasma membrane and mitochondria) the conversion of chemical energy to heat is considered.

Adenosine Triphosphate↗

PubMed1978

The effects of calcium++ on bursting neurons. A modeling study.

Many observed effects of ionized calcium on bursting pacemaker neurons may be accounted for by assuming that calcium has multiple effects on the membrane conductance mechanisms. Two models are proposed that represent extreme cases of a set of possible models for these multiple effects. Both models are a priori designed to account for directly observed phenomena, and both are found to be able to simulate a posteriori certain observed phenomena, including persistent inactivation, increasing spike width, and decreasing after-polarization. Experimental tests are proposed for the decision of validity between the set of models discussed and the null hypothesis, and for the decision of validity between the two models themselves. Extensions of the models are discussed. One of these extensions leads to a simulation of the behavior of the cell when placed in a calcium-free bathing medium.

Animals↗

PubMed1978

Controlled cellular energy conversion in brown adipose tissue thermogenesis.

Brown adipose tissue serves as a model system for nonshivering thermogenesis (NST) since a) it has as a primary physiological function the conversion of chemical energy to heat; and b) preliminary data from other tissues involved in NST (e.g., muscle) indicate that parallel mechanisms may be involved. Now that biochemical pathways have been proposed for brown fat thermogenesis, cellular models consistent with a thermodynamic representation can be formulated. Stated concisely, the thermogenic mechanism in a brown fat cell can be considered as an energy converter involving a sequence of cellular events controlled by signals over the autonomic nervous system. A thermodynamic description for NST is developed in terms of a nonisothermal system under steady-state conditions using network thermodynamics. Pathways simulated include mitochondrial ATP synthesis, a Na+/K+ membrane pump, and ionic diffusion through the adipocyte membrane.

Adipose Tissue, Brown↗

PubMed1976

The geometry of the Hodgkin-Huxley Model.

The Hodgkin-Huxley model for the "space-clamped" (i.e., having variables independent of position) squid giant axon is described by a system of four coupled nonlinear ordinary differential equations. In this study, the behavior under various conditions of the solution vector of these equations is predicted qualitatively. This is done by studying the geometry of the phase space of an approximation to the four dimensional system obtained by assuming that the two "rapid" components of the system, V and m, are described by algebraic rather than differential equations. Using this method, known properties of the solution of the Hodgkin-Huxley equation, such as threshold, repeated oscillation under constant current stimulus, etc., are explained qualitatively. The direct relation between the Hodgkin-Huxley equations and simpler systems such as the Fitz Hugh equations, which have been used as an aid to the understanding of the Hodgkin-Huxley model, is examined. The roles of the various activation and inactivation components of the Hodgkin-Huxley model are clarified and the effect of modification of those components is studied.

Action Potentials↗

PubMed1976

Mathematical description of a bursting pacemaker neuron by a modification of the Hodgkin-Huxley equations.

Modifications based on experimental results reported in the literature are made to the Hodgkin-Huxley equations to describe the electrophysiological behavior of the Aplysia abdominal ganglion R15 cell. The system is then further modified to describe the effects with the application of the drug tetrodotoxin (TTX) to the cells' bathing medium. Methods of the qualitative theory of differential equations are used to determine the conditions necessary for such a system of equations to have an oscillatory solution. A model satisfying these conditions is shown to preduct many experimental observations of R15 cell behavior. Numerical solutions are obtained for differential equations satisfying the conditions of the model. These solutions are shown to have a form similar to that of the bursting which is characteristic of this cell, and to preduct many results of experiments conducted on this cell. The physiological implications of the model are discussed.

Animals↗