George R. Stibitz

Distribution of the apical dendritic spines of the layer V pyramidal cells of the hamster neocortex

Abstract The distribution of the spines along the apical dendrites of 45 layer V pyramidal cells of the neocortex of young hamsters has been investigated. All visible spines present along the apical dendrite from the cell body to the end of the dendrite were counted and represented graphically. This study has shown: (a) The distribution of the apical dendritic spines of the layer V pyramidal cells of the hamsters neocortex follows a characteristic pattern which is similar to those described for man and mouse. (b) The graphic representation of the spine distribution consists of a characteristically shaped curve with distinct components or deflections. There appears to be a relationship between the different spine density and the cortical layers crossed by the apical dendrite. (c) The first portion of the curve of the spine distribution can be represented as an exponential function. (d) A computer analysis of the shape of the entire curve of the spine distribution in the apical dendrites of the layer V pyramidal cells of the hamsters neocortex was carried out. This approach has suggested that the curve and its deflections may be the result of the superposition of 4 distinct populations of spines. Each of these populations of spines has a distinct cortical depth, roughly corresponding to layers V, IV, III-II and I, and a distinct Gaussian distribution. The significance of this phenomenon and the possible application of this method are discussed.

Spine distribution of the layer V pyramidal cell in man: a cortical model

Abstract The specific aims of this study were to examine with an appropriate experimental design the main and interaction effects of the tranquilizer haloperidol (HPD) and electric shock on head and limb tremors in relation to changes in dopamine (DA) and norepinephrine (NE) concentrations in the caudate nuclei of 36 squirrel monkeys. Head and limb tremors were not observed in 6 control, 6 stress, or monkeys injected (i.m.) with 0.1 mg/kg HPD during 30 days of testing. Transient head and limb tremors lasting from 2 to 4 h after drug injection were observed in 30% of the monkeys of the higher 1.0 mg/kg HPD group. These tremors increased significantly in total incidence from 30 to 50%, and in the extent of the number of extremities affected from 2.8% to 11.1% in the drug-stress interaction group. Thirty days of HPD did not affect DA or NE concentrations in the caudate. Daily electric shock for 30 days decreaed DA but not NE concentrations. Although the 1.0 mg/kg HPD-stress interaction resulted in a higher incidence and extent of tremors, it did not produce a greater decrease in DA than electric shock alone. Since DA concentrations were very high and NE concentrations were low and not affected by drugs or stress, it was concluded that DA may play the more significant role in the caudate of the corpus striatum in primates.

Studies of Impedance in Cardiac Tissue using Sucrose Gap and Computer Techniques: II. Circuit Simulation of Passive Electrical Properties and Cell-to-Cell Transmission

The impedance measured in a strip of heart tissue from the moth Hyalophora cecropia is fitted by circuit models of several configurations. The circuits include: (a) a single R-C circuit (b) a double R-C circuit (c) terminated transmission lines, and (d) a pattern of cells with cell-to-cell transmission paths. The last of these is found to give the best fit. Calculation of the model impedances and optimization of element values are performed by a computer. The possibility that the mechanism of cell-to-cell transmission may be capacitative rather than conductive is explored using values of capacitance derived from the circuit models to calculate the effect of capacitative coupling alone on signal transmission. The calculations show that sufficient voltage can be transmitted from the excited cell to an adjacent cell to effect excitation.

Calculating diffusion in biological systems by random walks with special reference to gaseous diffusion in the lung

Abstract Diffusion may be visualized as the drift of particles of a diffusate moving randomly within a medium; this concept is made quantitative and taken as the basis for the calculation of flows and concentrations of a diffusate in biological systems. In the calculation we trace the paths of individual particles by successive steps, each of which is selected by a random process with appropriate probabilities. The simple-minded view is adopted that this is what is “really” happening in diffusion, and that physically measurable quantities like flux or concentration of diffusate are really averages over many walks, whether those walks be taken by physical molecules or be calculated by a computer. Since we are dealing with random processes in the walks, it is an easy step to introduce randomly selected regions in which the diffusion takes place. The biomedical investigator is often concerned, not with a completely determined system, but with a population of similar systems over which his measurements are averaged. Thus, in the lung there are myriads of alveoli of similar but not identical shapes and sizes, connected by paths that are likewise variable from one part of the lung to another, and it is the average diffusion in many regions that is of vital concern to the investigator. Such phenomena are naturally amenable to random calculations. In contrast with the “classical” or determinate methods of solution, the random walk method is limited by economic considerations rather than by the availability of mathematical procedures. Once the probabilities are assigned to the walks on the basis of local diffusion relations, a solution by random walks is assured; the accuracy and reliability of the solution are determined by the cost of computing a sufficiently large number of walks. The present paper deals with methods for setting up walks for a very general class of diffusion phenomena and with computer programs for tracing and evaluating such walks. Several examples are given, including a probabilistic “tree” model for portions of the lung.

A computer method for the acquisition and analysis of patch-clamp single-channel currents

The method we present instructs the computer to deliver sets of programmed membrane voltages and allows the acquisition of large amounts of digitized data, compact storage, ready identification of records and rapid, interactive analysis of channel current data. A typical cycle of analysis including amplitude determination and kinetic measurements for 10 s of continuous data digitized at 5 kHz requires 5-20 min depending on the complexity of the observed channel activity. This procedure is compatible with such storage protocols as that described by Bezanilla [Biophys. J., 47 (1985) 437-441], although there are obvious benefits to using standard computer storage devices such as hard disks, floppy disks, and Bernoulli Boxes. The programs described in this report are available from the authors.

Studies of Impedance in Cardiac Tissue Using Sucrose Gap and Computer Techniques: I. The Influence of Sucrose and Oil as Insulating Media

Impedances of cardiac cells of an insect were determined as a function of time to test the effects of sucrose and oil as insulating media in a gap arrangement. Impedance values are shown to increase markedly with time when sucrose is used as the insulating agent. Although impedance values are steady when oil is used, it is suggested that a layer of trapped electrolyte provides a shunt pathway and seriously impairs the validity of the measurements. A quick wash with sucrose followed by oil does not alleviate the situation but leaves a layer of sucrose trapped at the tissue-medium interface into which ions diffuse. The hypotheses (a) that the diffusion of intracellular K(+) into the sucrose would result in an increase in tissue impedance and (b) that a layer of trapped electrolyte under the oil film provides a shunt pathway are examined by computer analyses of a simple model.

A mathematical model of the urethra

Models having the form of surfaces of revolution may be used to represent the urethra under pre-voiding pressure. From such models are derived formulas for calculating muscle tension from the shape of a urethragram.

A model of diffusion in the respiratory unit

Abstract Diffusion between the bronchiole and the exchange surfaces of a typical respiratory unit is simulated by that in a simple model having the shape of a figure of revolution. The model is constructed so as to have the same distributions of surface and volume with distance from the port as does the respiratory unit sketched by Miller. Calculated diffusions in the Miller sketch of a unit and in the model are compared.

Bistable mathematical and mechanical models related to the urethra

Normal micturition is controlled primarily by a neural system. Certain physical effects become evident when neural control is destroyed, and the automatic or autonomous bladder phenomena occur. It is shown in this paper that a physical system simulating the alternating periods of continence and voiding of the automatic bladder may comprise only passive elastic components, and that periodic voiding does not per se imply neural control.

Substance uptake in variable systems with special reference to the use of the Fick equation

Abstract The Fick Principle expresses the indestructibility of a given substance in a fluid system wherein the rates of flow of the fluid, the concentration of the substance at each point in the system and the uptake rate are constant. It is not applicable to systems in which these parameters vary with time. An expression of conversation is derived here which is exactly valid in systems wherein the rates of flow, concentrations and uptake rate, as well as the paths of fluid flow in the system may vary. From the exact expression simpler expressions are derived which are exact in somewhat less general systems and are approximations in others. Limits for the error in the latter case are derived.