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Biomedical subjects

M C Mackey

Publications and source records attributed to M C Mackey.

At least 55 records · Page 3Linked to original sources
PubMed1984

The dynamics of recurrent inhibition.

A heuristic model for the dynamics of recurrent inhibition, emphasizing non-linearities arising from the stoichiometry of transmitter-receptor interactions and time delays due to finite feedback pathway transmission times, is developed and analyzed. It is demonstrated that variation in model parameters may lead to the existence of multiple steady states, and the local stability of these are analyzed as well as the occurrence of switching behaviour between them. As an example of the applicability of this model, parameters are estimated for the hippocampal mossy fibre-CA3 pyramidal cell-basket cell complex. Numerically simulated responses of this system to alterations in presynaptic drive and titration of inhibitory transmitter receptors by penicillin are presented. Numerical simulations indicate the existence of multiple bifurcations between periodic solutions, as well as the existence of bifurcations to chaotic solutions, as presynaptic drive and receptor density are varied. It is hypothesized that the model offers insight into the sequences of events recorded in single CA3 pyramidal cells following the application of penicillin, a specific inhibitory receptor blocking agent.

Animals↗
PubMed1982

Continuous maturation of proliferating erythroid precursors.

This study examines published steady state cell kinetic (mitotic and DNA synthesis phase) data from the recognizable proliferating erythroid precursors in humans, rats, and guinea-pigs, and human neutrophilic precursors, for consistency with a continuous maturation-proliferation model of the cell cycle. We find that these data are completely consistent with the hypothesis that maturation between morphological compartment may take place at any point in the cell cycle. A number of compartmental parameters are derived under this assumption.

Animals↗
PubMed1981

Minimizing therapeutically induced anemia.

A model for erythroid production based on a continuous maturation-proliferation scheme is developed. The model includes a simple control mechanism operating at the proliferating cell level, and analytic solutions for the time dependent response of the model are derived. Using this model, the response of the erythron to a massive depletion of the proliferating cell compartment (due for example to cytostatic drugs or radiation) is calculated. It is demonstrated that a therapeutic measure designed to decrease the erythroid precursor maturation velocity may considerably ameliorated the deleterious effects of proliferating cell destruction. One way to decrease the erythroid cell maturation rate would be by having the patient breathe in an oxygen enriched atmosphere.

Anemia↗
PubMed1980

The extinction of slowly evolving dynamical systems.

The time evolution of slowly evolving discrete dynamical systems xi + 1 = T(ri, xi), defined on an interval [0, L], where a parameter ri changes slowly with respect to i is considered. For certain transformations T, once ri reaches a critical value the system faces a non-zero probability of extinction because some xj psi [0, L]. Recent ergodic theory results of Ruelle, Pianigiani, and Lasota and Yorke are used to derive a simple expression for the probability of survival of these systems. The extinction process is illustrated with two examples. One is the quadratic map, T (r, x) = rx (1 - x), and the second is a simple model for the growth of a cellular population. The survival statistics for chronic myelogenous leukemia patients are discussed in light of these extinction processes. Two other dynamical processes of biological importance, to which our results are applicable, are mentioned.

Biological Evolution↗
PubMed1979

A simple model for phase locking of biological oscillators.

A mathematical model is presented for phase locking of a biological oscillator to a sinusoidal stimulus. Analytical, numerical and topological considerations are used to discuss the patterns of phase locking as a function of amplitude of the sinusoidal stimulus and the relative frequencies of the osillator and the sinusoidal stimulus. The sorts of experimental data which are needed to make comparisons between theory and experiment are discussed.

Biological Clocks↗
PubMed1977

Oscillation and chaos in physiological control systems.

First-order nonlinear differential-delay equations describing physiological control systems are studied. The equations display a broad diversity of dynamical behavior including limit cycle oscillations, with a variety of wave forms, and apparently aperiodic or "chaotic" solutions. These results are discussed in relation to dynamical respiratory and hematopoietic diseases.

Cheyne-Stokes Respiration↗
PubMed1973

Determinants of time-dependent membrane conductance. The nonrole of classical ion-membrane molecule interactions.

We have examined the steady-state and time-dependent electrical properties of a model membrane system. The model assumes that the directed velocity and energy of ions moving through the membrane are determined by the applied electric field, ionic diffusion forces, and central elastic collisions between ions and membrane molecules. A simple analysis of the steady-state electrical properties of the model yields results identical with ones obtained previously using a more complex analysis procedure. The time-dependent conductance changes of the model in response to a step change in electric field strength when there is solution symmetry display three qualitative patterns dependent on the nature of the ion-membrane molecule interaction. One of the patterns of conductance change is quite similar to that observed in the sodium conductance system of a number of excitable tissues: an initial conductance rise to a maximum (activation) followed by a decay to a final steady-state value (inactivation). However, the correspondence between the time-dependent model behavior and known experimental behavior of excitable systems is only qualitative. We conclude that the classical ion-membrane molecule interactions we consider are not involved in determining time-dependent conductance processes in the excitable systems for which comparison is possible.

Biological Transport↗
PubMed1971

Kinetic theory model for ion movement through biological membranes. I. Field-dependent conductances in the presence of solution symmetry.

A model for ion movement through specialized sites in the plasma membrane is presented and analyzed using techniques from nonequilibrium kinetic theory. It is assumed that ions traversing these specialized regions interact with membrane molecules through central conservative forces. The membrane molecules are approximated as massive spherical scattering centers so that ionic fractional energy losses per collision are much less than one. Equations for steady-state membrane ionic currents and conductances as functions of externally applied electric field strength are derived and numerically analyzed, under the restriction of identical solutions on each size of the membrane and constant electric fields within the membrane. The analysis is carried through for a number of idealized ion-membrane molecule central force interactions. For any interaction leading to a velocity-dependent ion-membrane molecule collision frequency, the membrane chord conductance is a function of the externally applied electric field. Interactions leading to a collision frequency that is an increasing (decreasing) function of ionic velocity are characterized by chord conductances that are decreasing (increasing) functions of field strength. For ion-neutral molecule interactions, the conductance is such a rapidly decreasing function of field strength that the slope conductance becomes negative for all field strengths above a certain value.

Biological Transport↗
PubMed1971

Kinetic theory model for ion movement through biological membranes. II. Interionic selectivity.

The equation presented in the previous paper for steady-state membrane ionic current as a function of externally applied electric field strength is numerically analyzed to determine the influence of ionic and membrane molecule parameters on current densities. The model displays selectivity between different ions. A selectivity coefficient S(i), defined as the ratio of current carried by an ionic species i at a given field strength to the current carried by a reference species at the same field strength, has the following properties: (a) S(i) is a function of electric field strength except for ion-membrane molecule interactions yielding velocity independent collision frequencies; (b) for ion-membrane molecule interactions characterized by a collision frequency that is a decreasing (increasing) function of increasing ionic velocity, ions whose S(i) > 1 (<1) at zero field strength will show maxima (minima) (minima[maxima]) in their S(i) vs. electric field strength curves.

Ammonia↗
PubMed1971

Kinetic theory model for ion movement through biological membranes. 3. Steady-state electrical properties with solution asymmetry.

An electrodiffusion model for plasma membrane ion transport, which takes into account the influence of high electric field strengths and ion-membrane molecule interactions, is presented and analyzed. A generalized Nernst-Planck equation for steady-state situations is derived which has electric field-dependent mobility and diffusion coefficients. Under the assumption of a constant electric field within the membrane, this equation is integrated to give a more general form of the Goldman equation. Based on this equation numerical computations of ionic chord conductance as a function of applied electric field strength were carried out for several permeant ion concentration ratios. The model is capable of yielding significantly larger rectification ratios than is the Goldman equation. Further, high field asymptotes to the current vs. electric field strength curve do not generally intersect at the origin.

Biological Transport↗
PubMed1971

The independence principle. A reconsideration.

The electrodiffusion model presented in the previous paper, which specifically excludes ion-ion interactions, is analyzed for the ratio of one-way fluxes (flux ratio) as a function of the ionic driving force across the membrane. Significant deviations from the behavior expected on the basis of the Ussing relation are found. These are sufficient to explain the "nonindependent" ion movement noted in some biological flux ratio data. One-way fluxes are dependent on the ionic concentration on both sides of the membrane. The coupling of these fluxes to ionic concentrations comes from the dependence of ionic mobility and the diffusion coefficient on the equilibrium potential. It is concluded that nonindependent behavior in experimental data is not sufficient to implicate ion-ion interaction as the source of the discrepancy.

Biological Transport↗
PubMedDate not supplied

Age-structured and two-delay models for erythropoiesis.

An age-structured model is developed for erythropoiesis and is reduced to a system of threshold-type differential delay equations using the method of characteristics. Under certain assumptions, this model can be reduced to a system of delay differential equations with two delays. The parameters in the system are estimated from experimental data, and the model is simulated for a normal human subject following a loss of blood. The characteristic equation of the two-delay equation is analyzed and shown to exhibit Hopf bifurcations when the destruction rate of erythrocytes is increased. A numerical study for a rabbit with autoimmune hemolytic anemia is performed and compared with experimental data.

Aging↗