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H G Othmer

Publications and source records attributed to H G Othmer.

13 recordsLinked to original sources
PubMed1989

Cyclic AMP oscillations in suspensions of Dictyostelium discoideum.

A model developed previously for signal relay and adaptation in the cellular slime mould Dictyostelium discoideum is shown to account for the observed oscillations of calcium and cyclic AMP in cellular suspensions. A qualitative argument is given which explains how the oscillations arise, and numerical computations show how characteristics such as the period and amplitude of the periodic solutions depend on parameters in the model. Several extensions of the basic model are investigated, including the effect of cell aggregation and the effect of time delays in the activation and adaptation processes. The dynamics of mixed cell populations in which only a small fraction of the cells are capable of autonomous oscillation are also studied.

Adenylyl Cyclases↗
PubMed1988

Pacemakers in aggregation fields of Dictyostelium discoideum: does a single cell suffice?

In this paper we address the following question: can a single cell of the cellular slime mold Dictyostelium discoideum serve as a pacemaker for the aggregation phase? Whether or not this is possible is determined by the relative importance of cyclic AMP production due to self-stimulation as compared to diffusion of cyclic AMP away from the cell and extracellular degradation. We determine the conditions under which a single cell on an infinite place can emit periodic signals of cyclic AMP using a model developed previously for signal relay and adaptation in Dictyostelium. Elsewhere it has been shown that this model provides an accurate representation of the stimulus-response behavior of Dictyostelium for a variety of experimental conditions.

Cell Aggregation↗
PubMed1988

Models of dispersal in biological systems.

In order to provide a general framework within which the dispersal of cells or organisms can be studied, we introduce two stochastic processes that model the major modes of dispersal that are observed in nature. In the first type of movement, which we call the position jump or kangaroo process, the process comprises a sequence of alternating pauses and jumps. The duration of a pause is governed by a waiting time distribution, and the direction and distance traveled during a jump is fixed by the kernel of an integral operator that governs the spatial redistribution. Under certain assumptions concerning the existence of limits as the mean step size goes to zero and the frequency of stepping goes to infinity the process is governed by a diffusion equation, but other partial differential equations may result under different assumptions. The second major type of movement leads to what we call a velocity jump process. In this case the motion consists of a sequence of "runs" separated by reorientations, during which a new velocity is chosen. We show that under certain assumptions this process leads to a damped wave equation called the telegrapher's equation. We derive explicit expressions for the mean squared displacement and other experimentally observable quantities. Several generalizations, including the incorporation of a resting time between movements, are also studied. The available data on the motion of cells and other organisms is reviewed, and it is shown how the analysis of such data within the framework provided here can be carried out.

Cell Movement↗
PubMed1986

Differentiation, cell sorting and proportion regulation in the slug stage of Dictyostelium discoideum.

Recent experimental work suggests that under normal conditions cell sorting plays an important part in maintaining and re-establishing the axial pattern of cell types in the slug stage of the cellular slime mold Dictyostelium discoideum. Following removal of the anterior zone of the slug, anterior-like cells that are normally distributed throughout the posterior of the slug rapidly migrate to the anterior end of the transected slug, and new anterior-like cells appear in the posterior portion. These results provide evidence that the direct linkage between spatial location and differentiation hypothesized in positional information models of spatial pattern formation is not universal. In this paper we develop and analyze a class of mathematical models of the slug in which cell determination can be less rigidly tied to spatial location, and which involve chemotactic cell sorting to re-establish and maintain the spatial pattern of cell types. We show that these models can reproduce the qualitative aspects of the experimental observations and that sorting takes place on the observed time scale when reasonable values of the parameters are used.

Cell Differentiation↗
PubMed1984

Applications of a model for scale-invariant pattern formation in developing systems.

A fundamental problem in developmental biology concerns the proportioning of the developing tissue of a morphallactic system into different cell types in a way that is independent of the overall size of the tissue. The two main models for positional information in pattern formation, the source-sink models and the Turing reaction-diffusion models, have shortcomings that limit their applicability. In a previous paper, we described a model that can produce perfectly scale-invariant spatial patterns and analyzed some of its mathematical properties. In the present paper, we demonstrate some of the shortcomings of the standard reaction-diffusion models and discuss the applicability of our model to developmental systems.

Animals↗
PubMed1983

A continuum model for coupled cells.

A continuum model of diffusion-coupled cells that more accurately reflects the presence of low-permeability gap junctions between cells is analyzed. It is shown by a multi-scale analysis that to lowest order the slow evolution of the mean concentration is described by the usual ordinary differential equations for a discrete model. Furthermore, stable non-uniform steady solutions are shown to exist in the continuum model of a one component system, whereas this is impossible for the standard reaction-diffusion model of this system. It is also shown how to average the equations in this continuum model to obtain a system of reaction-diffusion equations with constant coefficients.

Animals↗
PubMed1980

Scale-invariance in reaction-diffusion models of spatial pattern formation.

We propose a reaction-diffusion model of spatial pattern formation whose solutions can exhibit scale-invariance over any desired range for suitable choices of parameters in the model. The model does not invoke preset polarity or any other ad hoc distinction between cells and provides a solution to the French flag problem without sources at the boundary. Furthermore, patterns other than the polar pattern that usually arises first in a growing one-dimensional system described by Turing's model can be obtained. Evidence is given that suggests that the model may apply in the slug stage of Dictyostelium discoideum.

Cell Differentiation↗
PubMed1978

The effects of cell density and metabolite flux on cellular dynamics.

Density-dependent regulation of cell growth in tissue culture is a well-known phenomenon but the mechanism of regulation remains obscure. Here we explore the effects of cell density and metabolite flux on the collective dynamics of a cell population. The intracellular dynamics are modelled by positive feedback kinetic mechanisms of the kind known to apply to yeast cells. Several experimental observations related to glycolytic oscillations are predicted and it is suggested that the general conclusions may be applicable in a broader context.

Cells↗
PubMed1976

The qualitative dynamics of a class of biochemical control circuits.

The dynamical behavior of a class of biochemical control circuits that regulate enzyme or protein synthesis by end-product feedback is analyzed. Both inducible and repressible systems are studied and it is proven that in the former unique steady states are globally asymptotically stable. This precludes periodic solutions in these systems. A similar result holds for repressible systems under certain constraints on kinetic parameters and binding contants. However, when the reaction sequence is sufficiently long, or when a large enough number of effector molecules bind to each repressor molecule, repressible systems can show zero-amplitude ("soft") bifurcations: these are predicted by Hopf's bifurcation theorem.

Allosteric Regulation↗