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 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.     

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 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 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.     

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 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 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.     

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 antibody binding specificity

A Monte Carlo algorithm that searches for the optimal docking configuration of hen egg white lysozyme to an antibody is developed. Both the lysozyme and the antibody are kept rigid. Unlike the work of other authors, our algorithm does not attempt to explicitly maximize surface contact, but minimizes the energy computed using coarse-grained pair potentials. The final refinement of our best solutions using all-atom OPLS potentials (Jorgensen and Tirado-Rives⁸) consistently yields the native conformation as the preferred solution for three different antibodies. We find that the use of an exponential distance-dependent dielectric function is an improvement over the more commonly used linear form. © 1993 Wiley-Liss, Inc.     

Computer simulation of movement-generating cross-bridges.

A stochastic computational method was developed to study properties of cross-bridge models for muscle contraction, by following the time history of individual cross-bridge model of Andrew Huxley (1957) and a modified two-state model with more realistic behavior during steady stretching are used as examples. The method can readily compute steady-state force during shortening and stretching and force-transients following rapid changes in length. Computations of velocity with a steady load and of velocity transients are more sensitive to the randomness inherent in the stochastic method.     

Computer simulation of renal countercurrent systems

The history of mathematical modeling of renal countercurrent systems is briefly outlined. Several examples are cited and discussed. These include efforts at parameter estimation and experimental design with models. The goal of this work was the evaluation of hypotheses of hypertonic urine formation. The argument is made that computer simulation with reasonably isomorphic models can be used in a variety of ways, but that one indispensable role for this approach is to provide a test of the quantitative sufficiency of hypotheses. Hypotheses of hypertonic urine formation that do not consider active transport in thin ascending limbs do not pass this test. A new proposal is suggested in which the energy for NaCl reabsorption from thin ascending limbs is derived from dissipation of a urea gradient via an antiport.     

Computer simulation of human body dynamics

Understanding human body dynamics is important in many situations, such as automobile and aircraft crashes, aircraft ejections, falls, and other acceleration environments. The design of automobile interiors, cockpits, and safety equipment requires knowledge of the forces and accelerations encountered during an emergency. Because of the limited information available from actual events and the various constraints in testing, computer simulations are often the only means of obtaining detailed information. The Armstrong Laboratory (AL) developed the Articulated Total Body (ATB) model to predict the human body dynamics in many of these environments. This model is a three-dimensional rigid body dynamics program in which the human body is modeled as a series of segments. Forces on the body segments are calculated based on their interaction with the surroundings including seat and cockpit surfaces. The model also calculates the internal joint resistive and constraint forces. Because of this capability to predict both internal and external forces acting on the body, the ATB model can be used in investigating injuries. It is also a valuable design tool for evaluating safety of proposed systems before prototypes are built or costly tests conducted. When testing is conducted, the model provides data that cannot be measured, such as forces within the body, and supplementing test data with parameter variation simulations. To validate the model, tests such as those conducted on the AL impact sled are simulated. Test films and instrumentation data are compared with simulation graphics and quantitative output to gain confidence in the simulation results.     

Computer simulation of protein molecular dynamics

A review of the works on the computer simulation of the globular protein dynamics is given. Methodological aspects of the simulation procedure are outlined briefly. Main peculiarities of protein dynamics revealed in the course of simulation of pancreatic trypsin inhibitor and cytochrome c are presented. The causes of "anomalous" processes, inherent in the simulated behaviour of model proteins are discussed. These "anomalous" processes are: continuous drift of the structure and its deviation from the experimental one, determined by X-ray analysis. Both processes are supposed to be the consequence of the reduced conformational rigidity of the model protein in comparison to the real one. Among the possible reasons for this reduced rigidity absence of the water molecules, hydrating peptide groups in the real protein, may be mentioned. Analogy between "anomalous" processes in the simulated protein dynamics and some phenomena observed in the real proteins during their functioning is drawn.     

Computer simulation of Paramecium chemokinesis behavior

A computer program was designed to simulate the distribution of paramecia in a T-maze assay for chemo-accumulation and dispersal. Simulated values of chemokinesis are compared to experimental values for normal and mutant paramecia. The roles of components of swimming behavior (turning frequency and swimming speed), adaptation, and reaction at the border of solutions are examined.     

Computer simulation of diffusely-connected neuronal populations

This paper describes computer simulations of diffusely-connected neuronal populations. Main findings are that diffuse monosynaptic linkages between populations are selectively sensitive to synchronized clusters of action potentials in the pre-synaptic population; that diffusely-connected excitatory recurrent collaterals tend to produce rhythmic series of synchronized clusters; and that diffusely-connected inhibition (both recurrent and afferent) tend to reduce the number of cells participating in a given synchronized cluster and thereby the overall transfer rate. However, recurrent inhibition tends to increase the rate at which synchronized clusters are produced by recurrent excitation. These results suggest the speculation that diffusely connected neuronal populations are particularly prone to deal with synchronized clusters of action potentials.This work has been supported by Grant GB 33687 of the National Science Foundation, Grant 1-R01-NS-10781-01 COM of the National Institutes of Health, and by a fellowship from Zonta, International