The meaning of the Weber-Fechner law and description of scenes: III. Description of the visual space

The Weber-Fechner fraction was measured in experiments where a subject was presented with a pair of lines, the length of one (reference) line being constant and the length of the other (test) one varying. The subject had to say whether the longer line was above or below the shorter one. The subject was trained to distinguish the positions of lines in areas limited in the number of reference lines located at different degrees of eccentricity. The fraction curve for each area proved to be of the same shape as the curve obtained for the entire range and reflecting the Weber-Fechner law. The fraction was originally maximum and only slightly decreased afterwards. On the basis of these data, a neural construction is suggested that serves for describing the visual space and explains the shape of the curve reflecting the Weber-Fechner law.     

A method for comparing DNA replication programmes at the level of the chromosome bands

During DNA synthesis, each pair of homologous chromosomes replicates its bands in a precise order and at a specific time. When using asynchronous cell populations, this replication programme has to be reconstructed from a series of "stills"--serial samples taken at intervals through S-transit. Obviously, the result obtained is dependent upon the kinetic progression of cells through the cycle, and any perturbation of the cycle. A difficulty arises when we wish to compare the replication programme of a chromosome in two different cultures (e.g. cells from different origins, or after different treatments). Kinetic differences between cultures make it almost impossible to obtain two samples for analysis containing the same "mixture" of cells. Thus, a false programme difference could be introduced, or a real one masked. In this paper, we present a method of comparison that overcomes this problem. It is based upon the observation that with serial sampling of steady-state cell populations through S-phase, band appearance curves are sigmoidal and are very well approximated by cumulative Normal distributions with very similar standard deviations. If a family of such curves, closely spaced in time, is sampled twice, the two observed frequencies for each curve are related, their probits all lying on a single straight line. This line has a slope of 45 degrees and its displacement from the origin is a function of the time interval between the two samples. Given two identical families of such curves, exactly the same relationship will hold if one sample is drawn from each. If, however, the two families differ (in order, spacing, standard deviation etc.), the probit/probit plot will deviate in various ways from a straight line with 45 degrees slope. Any two subsets of chromosome replication-band frequencies can be regarded as derived from a family of cumulative Normal curves and probit/probit comparisons used to test the similarity of their replication programmes.     

Nematode growth patterns and the moulting cycle: the population growth profile

Population growth profiles of Caenorhabditis elegans and Panagrellus redivivus constructed from length frequencies have a number of steps in them coinciding with the number of extrauterine moults. Each step has a constant size relationship with that of one of the midmoults measured directly.
The profiles could only have the shape they do if there are corresponding steps in the true growth curve of individual worms: the fact that previous workers have been unable to detect these steps being due to the limitations of techniques available for the study of synchronous and individual growth curves. Nevertheless, a synchronous system with Trichostrongylus retortaeformis gives qualitative support to the findings from population profiles.
The population growth profile is a new tool in the study of environmental effects on moulting, though there are theoretical reasons why the true growth curve cannot be derived from it.
Abandonment of the "continuous growth" model for post-embryonic development simplifies the framing of hypotheses to explain ecdysis in nematodes.     

A Symmetric Extended Logistic Model with Applications to Experimental Toxicity Data

The fit of the logit and probit models for quantal response data can be improved by embedding these classical models within a richer parametric family indexed by one or two shape parameters. In this paper, a symmetric extended logistic model indexed by a shape parameter λ is discussed with application to dose response curves. The usual maximum likelihood method is employed to estimate the parameters of the model. The need to include the shape parameter λ is illustrated by analyzing a set of real experimental data and comparing the fit of the extended logistic model to those obtained by the standard logit and probit models.     

Kinetics of the light flash of the living firefly: a supramolecular process.

The light intensity vs. time curve of the light flash of the living firefly has been measured. Unlike the purified firefly enzyme system in aqueous solution, the living system does not show light decay conforming to a double exponential time curve, to simple first or second order decay, or to solid-state Elovich kinetics. Light decay of the living flash does show linearity in a probit vs. square root of time plot, which may indicate a reaction rate-limited by cooperative interactions of a biological phase transition. The observation that the kinetics of the firefly light system differ in the living cell from those in the purified system suggests that in the living system supramolecular factors control the rate of the reaction.     

Quantification of the dose-Mortality response of Trichoplusia ni,Helioithis, zea,and Spodoptera frugiperda to Nuclear polyhedrosis viruses: Applicability of an exponential model

In vivo assays of several nuclear polyhedrosis viruses were conducted in neonate Trichoplusia ni, Heliothis zea, and Spodoptera frugiperda larvae using a droplet feeding method. Characteristic deviations from the probit model were observed with several virus isolats that suggested the dose-reponse relation might be determined primarily by the chance of obtaining virus from the inoculum rather than by variabilityin host susceptibility. This was supported by comparisons of the slopes of the probit lines with the corresponding expected values based on the exponential relationship described by a one-hit Poissonian curve. Where applicable, the exponential model offers severl advantages over the probit model in describing and quantifying virus-host relations.     

Diagnostic uses of the Hill (Logit and Nernst) plots.

Analysis of the Hill plot for ligand-binding studies shows that it can adopt a variety of shapes other than a straight line. The shape of the curve can yield valuable information about the details of the binding process. In some cases it is possible to discriminate between models of co-operativity without the need for curve-fitting by computer.     

Initial rates. A new plot.

Excellent estimations of initial rates can be obtained from plots of delta P/t versus product formed (where P is the instantaneous concentration of the product). delta P/t is the chord from P0,t0 to P,t on an ordinary P-versus-t plot. When the chord is plotted as a function of product, the intercept at P0 of the resulting curve is necessarily dP/dt0. This curve approximates to a straight line extremely closely in all cases tested thus far. If delta P/t versus product is calculated from the integrated rate equation for a first-order reaction, and if a straight line is fitted through points representing the first 50% of the reaction, the discrepancy between the true initial rate and dP/dt0 estimated from the plot is 0.68%. For the most common form of the integrated rate equation for catalysed reactions the discrepancy varies between 0 and 0.90%. Because of the complexities of the integrated rate equations, catalysed second-order reactions have not been evaluated directly; uncatalysed reactions have been done instead. For a reaction with one reactant and two products, the discrepancy varies from 0.68 to 2.02%. For two reactants and one product, it varies from 0 to 0.68%; for two and two, 0 to 2.02%. The larger discrepancies occur only when unfavourable equilibrium constants are being overcome by the initial conditions.     

Susceptibility of irradiated B6D2F1/J mice to Klebsiella pneumoniae administered intratracheally: a pulmonary infection model in an immunocompromised host

Bacteria such as Klebsiella pneumoniae can invade and colonize an immunocompromised host and complicate clinical recovery. In the study reported here, an experimental model of induced pneumonia was developed in 60Co gamma-photon-irradiated mice for the purpose of evaluating efficacy of therapeutic agents. The model was characterized by use of probit analysis of bacterial dose, and microbiologic, and histopathologic results. Bacterial colony-forming-unit (CFU) values producing 50% mortality within 30 days (LD50/30) and their 95% confidence intervals were 4.0 x 10(4) [1.7 x 10(4) - 8.9 x 10(4)] for 0-Gray (Gy)-irradiated mice, 1.9 x 10(4) [7.0 x 10(3) - 4.8 x 10(4)] for 5-Gy-irradiated mice, and 1.0 x 10(3) [2.8 x 10(2) - 3.3 x 10(3)] for 7-Gy-irradiated mice. Probit regression line fits calculated by use of an iterative, weighted least-squares fit, were used to assess a dose-modifying factor (DMF). The DMFs for mortality, compared with that for the 0-Gy dose, with their 95% confidence intervals, were 2.2 [0.63 - 7.7] for the 5-Gy and 38.9 [9.6 -165.0] for 7-Gy doses. The 5-Gy probit line did not significantly differ (P = 0.21) from the 0-Gy probit line (dose ratios did not significantly differ from 1), whereas the 7-Gy probit line differed significantly from the 0-Gy probit line (P < 0.001). These results demonstrate that 7-Gy 60Co gamma-photon radiation in combination with intratracheal K. pneumoniae challenge induces a valid pulmonary infection model in immunocompromised female B6D2F1/J mice.     

Crenation and cupping of the red cell: A new theoretical approach. Part II. Cupping

Typical, axisymmetrical cup shaped cells have been carefully measured and the shapes analyzed mathematically. The results show that the strain energy of a cup shaped cell is always higher than that of a biconcave cell except when the two layers of the membrane involved in resistance to bending are free to slide over one another. This is true whether intrinsic curvature of the membrane is positive, negative or zero. If the two layers can slide over one another, the cup shape becomes the lower energy form. Shear resistance, if appreciable, must cause the cup cell to buckle. Photomicrographs of cup shaped cells show buckled configurations characteristic of those of a partly deflated thin-walled rubber ball, which is a similar object having a low ratio of bending/shear strength.In light of these findings, the cup shape of the red cell can no longer be considered as evidence of intrinsic membrane curvature of opposite sign to that of the crenated cell, but appears to indicate a phase change either in the hydrophobic interior of the bimolecular membrane or in some equivalent interface.     

Probability of response models and DNA repair: a statistical-biological approach

This paper develops a simple statistical model, the weighted hazard model, which incorporates the toxicological idea of DNA repair and its role in chemical carcinogenesis. We restrict attention to a small segment of DNA that migrates in and out of the high risk states; it is shown that random hazard functions play an important role in the distributional properties of the time to first detectable tumor. Included in the many shapes of the weighted hazard model is one that has a shape in the low dose region similar to that of the probit model, a model that many toxicologists favor. The analyses of two data sets are presented and interpreted, and suggestions for further research are given.     

The effect of interfering substances on the disinfection process: a mathematical model

AIMS: To gain a greater understanding of the effect of interfering substances on the efficacy of disinfection. METHODS AND RESULTS: Current kinetic disinfection models were augmented by a term designed to quantify the deleterious effect of soils such as milk on the disinfection process of suspended organisms. The model was based on the assumption that inactivation by added soil occurred at a much faster rate than microbial inactivation. The new model, the fat-soil model, was also able to quantify the effect of changing the initial inoculum size (1 x 10(7)-5 x 10(7) ml(-1) of Staphylococcus aureus) on the outcome of the suspension tests. Addition of catalase to the disinfection of Escherichia coli by hydrogen peroxide, resulted in changes to the shape of the log survivor/time plots. These changes were modelled on the basis of changing biocide concentration commensurate with microbial inactivation. CONCLUSIONS: The reduction in efficacy of a disinfectant in the presence of an interfering substance can be quantified through the use of adaptations to current disinfection models. SIGNIFICANCE AND IMPACT OF THE STUDY: Understanding the effect of soil on disinfection efficacy allows us to understand the limitations of disinfectants and disinfection procedures. It also gives us a mechanism with which to investigate the soil tolerance of new biocides and formulations.     

The Fe(2+)-His(F8) Raman band shape of deoxymyoglobin reveals taxonomic conformational substates of the proximal linkage

The band shape of the Raman line attributed to the Fe(2+)-N(epsilon)(His(F8)) stretching mode in deoxymyoglobin contains significant information on the nature of the Fe-His proximal linkage. Raman lines appearing close to it, however, obscure the true line profile. To isolate this from its accompanying lines we use its isotopic shift of approximately 1 cm(-1) when (56)Fe in natural-abundance deoxymyoglobin is substituted by (54)Fe. This enables us to isolate the true line shape. We have measured this line shape in sperm whale myoglobin dissolved in a 66% vol/vol glycerol/water solution for nine temperatures from 10 K to 300 K. The nu(Fe-His) band shows a complex temperature-dependent profile, with a shoulder on its high-frequency wing, which becomes more prominent with increasing temperature. Detailed analysis reveals that the band is composed of five distinct lines attributable to taxonomic conformational substates of the nu(Fe-His) linkage. These are in thermodynamic equilibrium above the glass transition temperature T(f) but freeze in into the thermodynamic distribution at T(f) for lower temperatures. Alternative models that try to explain the nu(Fe-His) band shape by either an anharmonic coupling of the nu(Fe-His) to a low-frequency heme doming mode or by conformational substates related to a Gaussian distribution of iron out-of-plane displacements are at variance with the distinct features observed experimentally.     

Nucleoprotein fusion. III. Causes and conditions for development of the multiphase character of the DNA--protein fusion curve

The influence of proteins reversibly and irreversibly bound to DNA on the shape of melting curve has been considered. It is shown that the melting curve becomes biphasic in two cases: (i) cooperative binding of proteins with DNA (II) STRONG DIFFERENCE IN THE BINDING CONSTANTS WITH HELICAL AND COILED REGIONS. Simple formulae permitting to determine which of two causes stipulate for biphasic profile of a given experimental melting curve are obtained. Melting curves of DNA-basic oligopeptides complexes have been investigated. It is shown that the oligopeptides, when their chain length does not exceed 10, are able to migrate along DNA and biphasic shape of the melting curve is stipulated by the cooperative manner of their binding with DNA.     

Mechanisms for the biomechanical destruction of L1210 leukemia cells: a rate regulator for metastasis.

Mechanical trauma appears to be one significant cause of the rapid intravascular death of cancer cells and, as such, could act as an important rate regulator for the metastatic process. Intravascular mechanical trauma to cancer cells is thought to be a consequence of shape transitions, occurring when they are deformed from spherical shape by entry into, and passage along, capillaries having smaller diameters than themselves. These transitions from spherical shape require increases in surface area; first, an apparent increase in surface area is accomplished by a reversible, nonlethal surface membrane unfolding. If this is insufficient to meet geometric demands, it is followed by a true increase in surface area, resulting in increased tension in the cancer cell surface membrane, leading to its lethal rupture.     

Microcomputer BASIC programs for rapid determination of lethal dosages of biocides using logit transformations

The probit analysis model is generally used for the deterininationof lethal dosages in bioassay applications. However, the logitmodels, which use the logistic curve instead of the integratednonnal curve, could also be effectively used for the determinationof lethal dosages and regression coefficients. In this paper,two lypes of logit models, namely minimum logit chi square andmaximum likelihood, have been described in detail for the estimationof the parameters. The results of these two models are alsocompared with those of the probit model.     

Dose-Response Analysis of Factors Involved in Germination and Secondary Dormancy of Seeds of Sisymbrium officinale: II. Nitrate

The role of nitrate as a promoter of germination of Sisymbrium officinale seeds was examined in optimal light conditions. It was shown that the requirement for nitrate was absolute. This was true for all seed lots used. The probit of germination in water was log-linearly related to the level of endogenous nitrate. Preincubation at 15°C resulted in an immediate decrease in germination, whereas in 25 millimolar KNO₃ the decrease was delayed. The decline of germination in water was strongly correlated with the rate at which nitrate leached from the seeds. The germination response to a range of KNO₃ concentrations was followed during preincubation at 24-hour intervals. During the entire 264-hour preincubation period increasingly higher nitrate concentrations were required to maintain a response. This resulted in a right-hand shift of the dose-response curve parallel to the x axis. After 120 hours the high maximum germination level started to decline. The dose-response curves could be simulated by an equation from the receptor-occupancy theory. It is proposed that induction of secondary dormancy is a result of a decrease of the number of nitrate receptors. After 24 and 48 hours of preincubation, the nitrate-response curves were biphasic. The biphasic character could be related to the level of endogenous nitrate and to a differential requirement for nitrate of two fractions of the seed population. Similarities with the behavior of fluence-response curves after prolonged dark incubation led to the hypothesis that phytochrome and nitrate share the same site of action.     

The Huxley-Simmons manoeuvre: is still lacking the experimental evidence that the quick release is a pure elastic phenomenon

The analysis of the quick release is usually made by fitting a straight line to the first few experimental points of the tension-length curve. The line is then extrapolated to zero force. The fact that the tension-length curve can be represented by a straight line does not grant, however, that the quick release is a pure elastic process. As a matter of fact the experimental precision is not such to exclude a small nonlinearity from the curve and thus to mistake a visco-elastic process for an elastic one. At least two are the consequences of such a mistake: (1) stiffness is overestimated; (2) energy balance is incorrect.     

Preferences for familiarity and novelty: a model for the simultaneous development of both

Many developing animals show an increasing preference for familiar companions and objects. They may also come to prefer things which are slightly different from the familiar. A model which shows how both processes can occur simultaneously is developed with particular reference to imprinting in birds. It shows how a biphasic curve would be obtained if preferences were measured in choice tests during the course of familiarization. The model predicts that shape of the preference curve will depend on the difference between the familiar and unfamiliar objects. It also predicts that the shape will be altered if inexperienced animals show a preference for one object over the other.