Measurement of membrane potential inBacillus subtilis: A comparison of lipophilic cations,rubidium ion,and a cyanine dye as probes

Summary Two of the commonly used probes for measuring membrane potential—lipophilic cations and the cyanine dye diS-C₃(5)—indicated nominally opposite results when tetraphenylarsonium ion was added as a drug to suspensions of metabolizingBacillus subtilis cells. [³H]-Triphenylmethylphosphonium uptake was enhanced by the addition, indicating hyperpolarization, yet fluorescence of diS-C₃(5) was also enhanced, indicating depolarization. Evidence is presented that both effects are artifactual, and can occur without any change in membrane potential, as estimated by⁸⁶Rb⁺ uptake in the presence of valinomycin. The fluorescence studies suggest that tetraphenylarsonium ion displaces the cyanine dye from the cell envelope, or other binding site, into the aqueous phase.The uptake characteristics of the radiolabeled lipophilic cations were quite unusual: At low concentrations (e.g., less than 10 m for triphenylmethylphosphonium) there was potential-dependent uptake of the label to a stable level, but subsequent addition of nonradioactive lipophilic cation caused further uptake of label to a new stable level. Labeled triphenylmethylphosphonium ion taken up to the first stable level could be displaced by 10mm magnesium ion, whereas⁸⁶Rb⁺ uptake was unperturbed. Association of the lipophilic cations with the surface of de-energized cells was concentration-dependent, but there was no evidence for cooperative binding. This phenomenon of stimulated uptake inB. subtilis (which was not seen inEscherichia coli cells or vesicles) is consistent with a two-compartment model with access to the second compartment only being possible above a critical cation concentration. We tentatively propose such a model, in which these compartments are the cell surface and the cytoplasm, respectively.Triphenylmethylphosphonium up to 0.5mm exhibited linear binding to de-energized cells; binding of tetraphenylphosphonium and tetraphenylarsonium was nonlinear but was not saturated at the highest concentration tested (1mm). The usual assumption, that association of the cation with cell surfaces is saturated and so can be estimated on de-energized cells, therefore leads to undercorrected estimates of cytoplasmic uptake inB. subtilis, and hence to overestimates of membrane potential. We describe a more realistic procedure, in which the estimate of extent of binding is based on a mean aqueous concentration related both to the external concentration and to the much higher internal concentration that exists in energized cells. Using this procedure we estimate the membrane potential inB. subtilis to be 120 mV, inside-negative. The procedure is of general applicability, and should yield more accurate estimates of membrane potential in any system where there is significant potential-dependent binding.Work performed while on sabbatical leave from Department of Biology, Ben-Gurion University of the Negev, Beer-Sheva, Israel.     

Integral equation models for endemic infectious diseases

Summary Endemic infectious diseases for which infection confers permanent immunity are described by a system of nonlinear Volterra integral equations of convolution type. These constant-parameter models include vital dynamics (births and deaths), immunization and distributed infectious period. The models are shown to be well posed, the threshold criteria are determined and the asymptotic behavior is analysed. It is concluded that distributed delays do not change the thresholds and the asymptotic behaviors of the models.This work was partially supported by NIH Grant AI 13233.     

A model for population regulation with density- and frequency-dependent selection

The life-cycle of a species with separate generations is divided into a reproduction phase and a growing-up phase. In the reproduction phase we assume random mating and selection due to genotype differences in fecundity of the parents and viability of the offspring. During the growing-up phase we assume a (deterministic) death process in continuous time with death rates for the genotypes which increase linearly with the genotype population sizes.In the absence of genotype differences the model gives logistic population regulation. With genotype differences the model generalizes the usual separate generations selection patterns. In addition to these we exhibit cases with three polymorphic equilibria or with a stable cycle.     

Parameter identification of the calvin photosynthesis cycle

Summary This article is concerned with the determination of kinetic parameters of the Calvin photosynthesis cycle which is described by seventeen nonlinear ordinary differential equations. It is shown that the task requires dynamic data for several sets of initial conditions. The numerical technique is based upon an algorithm for non-linear optimization and Gear's numerical integration scheme for stiff systems of differential equations. The sensitivity of the parameters to noise in the data is tested with a method adapted from Rosenbrook and Storey. A preliminary set of parameters has been obtained from a preliminary set of experimental data. The numerical methods are then tested with synthetic data derived from these parameters. The mathematical model and the results obtained in the simulation are used as an aid in designing new experiments.     

Macrophage function in tumor-bearing mice: dissociation of phagocytic and chemotactic responsiveness

Infusion of CBA mice with lymphoid cells from the H-2 compatible but Mls-antigen incompatible C3H × CBA hybrid results in a specifically reduced capacity of the recipients lymphocytes to react in the MLC against C3H-cells. Although this reduction is immunologically specific the results of this investigation have shown that such mice exhibit a strongly reduced capacity to produce humoral antibodies against heterologous erythrocytes and a T-cell independent antigen (PVP).     

Shapes and functions of species–area curves (II): a review of new models and parameterizations

This paper has extended and updated my earlier list and analysis of candidate models used in theoretical modelling and empirical examination of species–area relationships (SARs). I have also reviewed trivariate models that can be applied to include a second independent variable (in addition to area) and discussed extensively the justifications for fitting curves to SARs and the choice of model. There is also a summary of the characteristics of several new candidate models, especially extended power models, logarithmic models and parameterizations of the negative-exponential family and the logistic family. I have, moreover, examined the characteristics and shapes of trivariate linear, logarithmic and power models, including combination variables and interaction terms. The choice of models according to best fit may conflict with problems of non-normality or heteroscedasticity. The need to compare parameter estimates between data sets should also affect model choice. With few data points and large scatter, models with few parameters are often preferable. With narrow-scale windows, even inflexible models such as the power model and the logarithmic model may produce good fits, whereas with wider-scale windows where inflexible models do not fit well, more flexible models such as the second persistence (P2) model and the cumulative Weibull distribution may be preferable. When extrapolations and expected shapes are important, one should consider models with expected shapes, e.g. the power model for sample area curves and the P2 model for isolate curves. The choice of trivariate models poses special challenges, which one can more effectively evaluate by inspecting graphical plots.     

hw‐quickcheck: an easy‐to‐use computer program for checking genotypes for agreement with Hardy–Weinberg expectations

Deviations from Hardy–Weinberg expectations are frequently a sign of genotyping error. hw‐quickcheck is an easy‐to‐use computer program for detecting departures from Hardy–Weinberg equilibrium. hw‐quickcheck uses exact tests for all of its calculations. These tests include a global test for heterozygote excess/deficiency and genotype‐specific tests.