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Biomedical subjects

L A Segel

Publications and source records attributed to L A Segel.

At least 37 records · Page 2Linked to original sources
PubMed1992

Pattern formation in one- and two-dimensional shape-space models of the immune system.

A large-scale model of the immune network is analyzed, using the shape-space formalism. In this formalism, it is assumed that the immunoglobulin receptors on B cells can be characterized by their unique portions, or idiotypes, that have shapes that can be represented in a space of a small finite dimension. Two receptors are assumed to interact to the extent that the shapes of their idiotypes are complementary. This is modeled by assuming that shapes interact maximally whenever their coordinates in the space-space are equal and opposite, and that the strength of interaction falls off for less complementary shapes in a manner described by a Gaussian function of the Euclidean "distance" between the pair of interacting shapes. The degree of stimulation of a cell when confronted with complementary idiotypes is modeled using a log bell-shaped interaction function. This leads to three possible equilibrium states for each clone: a virgin, an immune, and a suppressed state. The stability properties of the three possible homogeneous steady states of the network are examined. For the parameters chosen, the homogeneous virgin state is stable to both uniform and sinusoidal perturbations of small amplitude. A sufficiently large perturbation will, however, destabilize the virgin state and lead to an immune reaction. Thus, the virgin system is both stable and responsive to perturbations. The homogeneous immune state is unstable to both uniform and sinusoidal perturbations, whereas the homogeneous suppressed state is stable to uniform, but unstable to sinusoidal, perturbations. The non-uniform patterns that arise from perturbations of the homogeneous states are examined numerically. These patterns represent the actual immune repertoire of an animal, according to the present model. The effect of varying the standard deviation sigma of the Gaussian is numerically analyzed in a one-dimensional model. If sigma is large compared to the size of the shape-space, the system attains a fixed non-uniform equilibrium. Conversely if sigma is small, the system attains one out of many possible non-uniform equilibria, with the final pattern depending on the initial conditions. This demonstrates the plasticity of the immune repertoire in this shape-space model. We describe how the repertoire organizes itself into large clusters of clones having similar behavior. These results are extended by analyzing pattern formation in a two-dimensional (2-D) shape-space.(ABSTRACT TRUNCATED AT 400 WORDS)

B-Lymphocytes↗
PubMed1989

Neurotransmitter release: development of a theory for total release based on kinetics.

According to the calcium-voltage hypothesis for the control of neurotransmitter release, a molecule (or molecular complex) must be activated by membrane depolarization, after which the activated molecule can bind calcium and initiate release. In this study, we have examined properties of the kinetics of phasic release resulting from a set of differential equations that characterize the calcium-voltage hypothesis. It was found that, in accord with experiments, an important feature is the approximate constancy of the shape of the graph for the kinetics of phasic release at various depolarizations and extracellular calcium concentrations. The shape constancy allowed us to obtain an explicit and relatively simple analytical formula for the total transmitter release (quantal content) by approximating the differential equations of the model. This formula shows a saturating sigmoidal dependence on both intracellular and extracellular calcium concentrations. The formula thus agrees with various experiments. Moreover, it agrees with, and provides meaning to, earlier phenomenological expressions for the dependence of release on calcium concentration. In particular, the formula provides an expression for the maximal release in terms of kinetic parameters from the calcium-voltage model, and thereby allows one to supplement earlier kinetic tests of the calcium-voltage hypothesis with further tests focused upon the dependence of total release on depolarization.

Animals↗
PubMed1989

Facilitation as a tool to study the entry of calcium and the mechanism of neurotransmitter release.

We have shown the usefulness of using facilitation as an indirect tool for measuring release-related processes that cannot be measured directly. Most of the findings obtained by measuring facilitation have been verified (by various groups) by direct measurements in systems where such measurements could be carried out. This provides reassurance that the methodology is sound. Using facilitation one can gain insight into numerous processes that together govern the dependence of release on the intracellular calcium concentration C. The physiological conclusions have been listed in the text. We reiterate some of these conclusions here, in order to emphasize certain additional matters. For 20 years it has been known that release is a saturating cooperative function of the extracellular Ca2+ concentration Ce (Dodge and Rahamimoff, 1967). Yet several questions remained open, such as whether this behavior in fact reflected the dependence of the release on the intracellular Ca2+ concentration C, of entry on Ce, or of a combination of these individual possibilities. We have found, using short-term facilitation as the investigatory tool, that release is a saturating cooperative function of C. It is obvious that saturation will eventually take place as C increases. What is important to emphasize is that the saturation occurs at physiological values of C. Such values typically correspond to the amount of Ca2+ that enters following only one or very few pulses. Various aspects of facilitation F can be used to characterize the processes responsible for the removal of the calcium that enters the nerve terminal. Here we emphasized the role of the duration of F, but information can also be obtained by examining other aspects of facilitation (Parnas and Segel, 1980; H. Parnas et al., 1982; I. Parnas et al., 1982a). The principal conclusion is that removal shows saturation kinetics.(ABSTRACT TRUNCATED AT 250 WORDS)

Animals↗
PubMed1986

A mechanism for exact sensory adaptation based on receptor modification.

We provide a theoretical explanation for the observation that in many sensory systems a step increase in stimulus triggers a response that goes through a maximum and then returns to the basal level. Considered here is a receptor molecule that in the absence of ligand can be found in either of two states R and D. Two more states, RL and DL, are formed upon the addition of ligand L. It is assumed that the receptor triggers activity in a sensory system, and that the activity is proportional to a weighted combination of the fractions of molecules that are in each of the four states. It is shown that judicious choice of the weights can provide both an adequate response and exact adaptation to step increases in stimuli. The interconversion between states may operate without energy expenditure or through covalent modification. In both cases, adaptation is associated with receptor modification that acts as a counterweight to changed external conditions. Application to cAMP secretion in Dictyostelium discoideum and to chemotaxis in bacteria is discussed.

Adaptation, Physiological↗
PubMed1986

On the quantal hypothesis of neurotransmitter release: an explanation for the calcium dependence of the binomial parameters.

Results for quantal neurotransmitter release can be explained by assuming a binomial distribution with a population of N elements each with a probability p to release a quantum in a given trial. The binomial parameter N was unexpectedly observed to depend on external calcium concentration and (to a lesser extent) on the frequency of stimulation. This observation is explained here by the hypothesis that the release population is not homogeneous. It is shown that the same hypothesis can also account for other experimental findings. A possible cause for this inhomogeneity is suggested.

Calcium↗
PubMed1986

A molecular mechanism for sensory adaptation based on ligand-induced receptor modification.

Physiological responses mediated by cell-surface receptors frequently adapt or "desensitize" (i.e., terminate despite persistent occupancy of receptors by ligand). Binding of ligands to the external domains of a wide variety of surface receptors induces covalent modification of their cytoplasmic domains. A mechanism is presented in which the variety of receptor states generated by ligand binding and covalent modification act together to regulate physiological responsiveness. The development of the model is guided by observations of adaptation for chemotaxis in Escherichia coli and adenylate cyclase activation in Dictyostelium. The general features of the marked response and eventual exact adaptation predicted by the model match those observed in the experimental systems.

Adaptation, Physiological↗
PubMed1985

On a model for the structure of circular mitochondrial genomes in higher plants.

The mitochondrial genome of some higher plants consists of a discrete set of circular molecules. The heterogeneity found in the number of circles and their size is puzzling. In some plants evidence exists that indicates that these circular DNA molecules undergo intermolecular and intramolecular recombination events. The result of these events is that two small circles can combine to give one large circle or one large circle can break up into two small circles. Here we pursue the idea that such recombination events are responsible for the variability in genome composition. Treating the recombination events as chemical reactions we derive the equilibrium size distribution of circles. In Brassica campestris there are two basic subunits, circles A and B, containing 135 and 83 kilobases, respectively. By restriction-enzyme mapping one can determine in a multimeric circle, the number of interfaces between A- and B-derived DNA. Using a combinatorial argument we predict the frequency of such interfaces and compare our predictions with published data. A number of suggestions are made for additional experimental tests of the recombinational theory of genomic diversity.

DNA, Circular↗
PubMed1984

A model for the establishment of pattern by positional differentiation with memory.

A new model for the establishment of a pattern in a developing organism by means of positional differentiation is proposed. The model is capable of regenerating pattern in an amputated organism. The model uses a short range inductor and a long range inhibitor as signal carriers, as in many earlier works, but the following properties are different from previous (explicit) models: the processes of establishment of chemical and differentiated patterns proceed simultaneously; memory is included; there is no direct interaction between morphogens. Formulation of the model is in terms of linear differential equations, which are ordinary in the one dimensional case. Application to the slime mold Dictyostelium discoideum is discussed.

Cell Differentiation↗
PubMed1984

Exhaustion of calcium does not terminate evoked neurotransmitter release.

Theories are considered which assume that termination of evoked release is caused by the exhaustion of intracellular Ca. It is shown that such theories predict, contrary to experiment, that total release is an unsaturated function of intracellular Ca whose duration depends strongly on extracellular Ca. These and other findings lead to the conclusion that termination must be due to the fast change of another parameter (not intracellular Ca).

Action Potentials↗
PubMed1984

A gradually slowing travelling band of chemotactic bacteria.

A model for describing the motion of chemotactic bacteria in a capillary tube containing substrate is treated. Chemotactic substrate threshold effects are included in the chemotactic response coefficient. The ratio of the substrate threshold, ST, to the substrate level far ahead of the travelling band, S infinity, is used as a small parameter in developing an asymptotic solution of "near travelling wave" form.

Bacterial Physiological Phenomena↗
PubMed1983

A case study of linear versus non-linear modelling.

Theories for the facilitation of neurotransmitter release are discussed in a case study of the properties of linear and non-linear models for a phenomenon whose time course can be represented by a sum of decaying exponentials. Particular attention is paid to the effects of a "key factor" on the slopes and amplitudes of the exponentials that can be derived from semilog plots of the data. It is shown that the presence of such effects can give strong evidence for the inappropriateness of linear models. A non-linear model is demonstrated to be capable of describing the changes with extracellular Ca concentration of straight line segments that fit data in semilog plots of facilitation as a function of time. The conclusion is reached that even if data seems to be representable by several independently alterable exponentials one must be cautious in drawing inferences concerning the number, linearity, or independence of the underlying processes.

Action Potentials↗
PubMed1983

On spatial periodicity in the formation of cell adhesions to a substrate.

Interference reflection microscopy reveals a fairly regular array of marginal focal contacts in early states of cell spreading. A theoretical explanation of the onset of patchiness is given, based on the positively cooperative binding to the substrate of laterally diffusing receptor molecules.

Animals↗