Boolean analysis of lateral inhibition

Journal of Mathematical Biology - We study Boolean networks which are simple spatial models of the highly conserved Delta–Notch system. The models assume the inhibition of Delta in each cell...     

A lateral look at olfactory bulb lateral inhibition

Contrast enhancement in sensory systems often relies on spatial filters implemented by lateral inhibition. However, in this issue of Neuron, Fantana et al. provide evidence that lateral inhibition in the olfactory bulb selectively acts between sparse populations of principal neurons without regard to spatial relations.     

Computer simulation of temperature autostabilization: an analysis of the phenomenon

A mathematical model of the temperature autostabilization by microorganism populations in batch and continuous operation has been developed. It adequately describes the process of temperature autostabilization by Candida tropicalis yeast microorganisms on H-alkanes. The model analysis has permitted determination of the conditions for the existence of the phenomenon and an explanation of its basic factors, such as linear biomass growth and dependence of microorganisms growth velocity on heat transfer through reactor walls. The industrial application of this interesting phenomenon is discussed. Correspondence to: M. Kristapsons     

On the theory of lateral inhibition

Zusammenfassung Das mathematische Modell für das Prinzip der lateralen Inhibition in der Theorie der optischen Perzeption führt auf ein System nichtlinearer Gleichungen für n reelle Variable. Dieses System wird auf Lösbarkeit und eindeutige Lösbarkeit untersucht. Es zeigt sich, daß die Gleichung als Bedingung für die stationären Zustände eines geeigneten zeitabhängigen Systems zu deuten ist. Hier kann man ein diskretes und ein kontinuierliches Modell einführen. In beiden Fällen kann die Frage der Existenz der Lösungen und der Stabilität einigermaßen vollständig geklärt werden. Eine Verallgemeinerung auf kontinuierlich viele Raumvariable ist möglich.     

Computer simulation of mutagenesis

A FORTRAN program is described which simulates point-substitution mutations in the DNA strands of typical organisms. Its objective is to help students to understand the significance and structure of the genetic code, and the mechanisms and effects of mutagenesis. The program is intended to be used as part of an elementary course in genetics at degree level.     

Two-stage lateral inhibition for auditory selectivity

It is shown that the narrow selectivity of the auditory system can be explained by neural processing that yields 20y−d ² y/dz ², wherey is the normalized single-tone response of the basilar membrane andz is the natural logarithm of normalized stapes distance. The desired response is synthesized via a two-stage lateral inhibition process. Stage 1 is the result of interaction between inner and outer hair cells; stage 2 takes place in the auditory cortex.     

Computer simulation of DNA supercoiling

We treat supercoiled DNA within a wormlike model with excluded volume. A modified Monte Carlo approach has been used, which allowed computer statistical-mechanical simulations of moderately and highly supercoiled DNA molecules. Even highly supercoiled molecules do not have a regular shape, though with an increase in writhing the chains look more and more like branched interwound helixes. The averaged writhing (Wr) approximately 0.7 delta Lk. The superhelical free energy F is calculated as a function of the linking number. Lk. The calculations have shown that the generally accepted quadratic dependence of F on Lk is valid for a variety of conditions, though it is by no means universal. Significant deviations from the quadratic dependence are expected at high superhelical density under ionic conditions where the effective diameter of DNA is small. The results are compared with the available experimental data.     

Computer simulation of ribosome editing

A stochastic model of protein synthesis was modified by including the process of dissociating peptidyl-tRNA from ribosomes. To simulate ribosome editing, the probability of dissociation was assumed to be high if the peptidyl-tRNA was erroneous; that is, if it resulted from transfer of a peptide to an aminoacyl-tRNA that was inappropriate relative to the mRNA codon. The effects of amino acid starvation on protein synthesis were simulated both by increasing the probability of such erring at and by reducing the conditional probability of elongation at “hungry” codons, those whose correct amino acid was in short supply. These probabilities were varied systematically to simulate tryptophan limitation during synthesis of coat protein from bacteriophage MS2.Significant reduction, during starvation, in the synthesis of complete coat protein required large reductions in the probability of elongation at hungry codons but only small increases in the probability of erring. Enhanced dissociation of peptidyl-tRNA during starvation, followed rapidly by dissociation of ribosomes from mRNA, led to reductions in mean polysome size, a result that had been interpreted by others as due to some effect of starvation on the initiation of protein synthesis.Results from experiments by Goldman (1982) on the cell-free synthesis of MS2 coat protein during tryptophan starvation could be mimicked in detail by the computer simulations. A simple competition between correct and erroneous amino acids was sufficient to explain the tryptophan dependence of complete coat protein and internal peptide syntheses. Values for the Michaelis constants were derived from the computer simulations.     

Computer simulation of calcium-induced myotonia

Summary In an extensive research project on myotonia, the ionic mechanisms which are at the basis of the phenomenon of calcium-induced myotonia have been taken into consideration. A mathematical model of a muscle fibre was constructed to demonstrate the possibility that anomalous values of the membrane permeability to Calcium ions have an active part in the genesis of myotonia. This work was in great part supported by Grant of Muscular Dystrophy Assoc. Inc. and by CNR, Rome.     

Computer simulation of biological systems

The current status of mathematical models of biological systems is reviewed. Advances in supercomputer hardware allows more complex models to be constructed. The new generation of microcomputers are quite adequate for many computer simulations of biological systems. A theory of modeling is being developed to improve the relationship between the real biological system and the model. Deterministic models, stochastic models and applications of control theory and optimization methods are discussed. Examples given include models of molecular structure, of experimental techniques, and of biochemical reactions. It is recommended that experimental biologists consider the use of microcomputers to model the system under study as a part of their research program.     

Computer simulation of purine metabolism

A computer model of purine metabolism, including catabolism, salvage pathways and interconversion among nucleotides, is given. Steady-state rate equations corresponding to metabolic enzymes are written based on information from the literature about their kinetic behaviour. Numerical integration of this set of equations is performed employing selected parameters taken from the literature. After stabilization of purine compound concentrations is reached, simulation of enzyme deficit and enzyme overproduction is carried out. The latter is calculated by varying specified maximum velocities in the numerical integration. A pattern of intermediate metabolite concentrations is found. These results form a basis for the comparison of normal patterns or patterns reflecting the effects of inborn errors of metabolism. The aim of this paper is to demonstrate the usefulness of this computer simulation method in complex metabolism pathways.     

Computer simulation of introductory neurophysiology

A computer-assisted learning (CAL) package, NeuroLab, developed for use by first-year university students undertaking professional programs in the health area, is described and evaluated. NeuroLab is a simulation of a laboratory, in which students are able to impale neurons to measure resting membrane potentials and subsequently undertake experiments including measuring resting membrane potentials, determining threshold potentials, measuring refractory periods, and examining effects on membrane potential through altering the membrane permeability to sodium and potassium ions. Students find the package to be a worthwhile learning experience, with 81 +/- 2.2% reporting the package increased their understanding of neuron function, and 78 +/- 2.5% expressing a desire for more CAL packages. Exposure to the package resulted in significantly higher mean scores in a multiple-choice question test on measuring neuron membrane potentials compared with those who were not exposed (mean scores out of 4 of 2.42 and 2.02, respectively, P < 0.001).     

Computer simulation of single-file transport

A stochastic model of single-file transport was developed as the Markov process in continuous time technique. The model was constructed using an EC-1060 computer. Unidirectional fluxes were investigated and populations of channels were correlated with flux fluctuations. The profiles of channel populations were shown to have nonlinear shapes even with the transport of nonelectrolyte (the classical diffusion approach gives linear profiles). The relationship between the paired correlation function F(AB) and the concentration of transported particles was examined. The F(AB) profile was shown to become flattened (or exponential for asymmetrical cases) at high concentrations. The concentration dependence jA/jA0 ratio were analyzed, where jA is a single-file unidirectional flux, jA0 is unidirectional flux for the case of free diffusion. An interesting "stack" phenomenon was observed for abnormal time correlations of single-file fluxes.     

Ptf1a-mediated control of Dll1 reveals an alternative to the lateral inhibition mechanism

Neurog3-induced Dll1 expression in pancreatic endocrine progenitors ostensibly activates Hes1 expression via Notch and thereby represses Neurog3 and endocrine differentiation in neighboring cells by lateral inhibition. Here we show in mouse that Dll1 and Hes1 expression deviate during regionalization of early endoderm, and later during early pancreas morphogenesis. At that time, Ptf1a activates Dll1 in multipotent pancreatic progenitor cells (MPCs), and Hes1 expression becomes Dll1 dependent over a brief time window. Moreover, Dll1, Hes1 and Dll1/Hes1 mutant phenotypes diverge during organ regionalization, become congruent at early bud stages, and then diverge again at late bud stages. Persistent pancreatic hypoplasia in Dll1 mutants after eliminating Neurog3 expression and endocrine development, together with reduced proliferation of MPCs in both Dll1 and Hes1 mutants, reveals that the hypoplasia is caused by a growth defect rather than by progenitor depletion. Unexpectedly, we find that Hes1 is required to sustain Ptf1a expression, and in turn Dll1 expression in early MPCs. Our results show that Ptf1a-induced Dll1 expression stimulates MPC proliferation and pancreatic growth by maintaining Hes1 expression and Ptf1a protein levels.     

Computer simulation of cellular movements: cell-sorting, cellular migration through a mass of cells and contact inhibition

The motility rules for cellular movement proposed earlier by Goel &; Rogers for engulfment of two or more intact embryonic tissues have been used to simulate on a computer the phenomena of cell-sorting, migration of individual cells through a mass of cells and contact inhibition of overlapping. These simulations in the most part are found to be consistent with the observations with real cells.     

Specificity of serotoninergic inhibition in Limulus lateral eye

The receptor specificity for synaptically mediated lateral inhibition in Limulus lateral eye retina was studied by structure-activity correlations of the action of the putative indoleaminergic neurotransmitter, serotonin (5-HT), and its isomers and structural analogs, tryptamine (TRYP), 6-hydroxytryptamine (6HT), 5,6-dihydroxytryptamine (5,6-DHT), 5-hydroxydimethyltryptamine (5-HDMT), and 5-hydroxytryptophan (5-HTP). The 5-HT blockers, lysergic acid diethylamide (LSD), bromo-LSD (BOL), and cinanserin, were also tested. The inhibitory action of the indoleaminergic agonists is highly structure-specific. An hydroxyl group in the 5 position of the indole nucleus, sterically unencumbered by hydroxyls in neighboing positions, is essential. In order of decreasing potency, 5-HT, 5-HDMT, and 5-HTP are active agonists; TRYP, 6-HT, and 5,6-DHT are inactive. Configuration and mobility of the side chains of the active agonists also affect the interaction, and these side-chain characteristics correlate with agonist potency. The receptors for inhibitory action and for transmembranal transport in reuptake are different. Both active agonists and inactive analogs appear to be taken up (Adolph and Ehinger, 1975. Cell Tissue Res. 163:1-14). LSD and BOL have bimodal actions: direct inhibition and agonist blockade. These actions may be mediated via low-specificity presynaptic uptake receptor sites rather than highly specific, postsynaptic, agonist receptor sites.