Analytical solution to the initial-value problem for traveling bands of chemotactic bacteria

The governing parabolic partial differential equations for the diffusion and chemotactic transport of a distribution of bacteria and for the diffusion and bacterial degradation of a distribution of chemotactic agent are supplemented with boundary and initial conditions that model the recent capillary tube experiments on the formation and propagation of traveling bands of chemotactic bacteria. An iteration procedure that takes the exact solution to the “diffusionless” problem as a first approximation is applied to solve the equations of the complete theoretical model. It is shown that satisfactory agreement with experiment obtains for the analytical results of the first approximation which relate the velocity of propagation and total number of bacteria cells per unit cross-sectional area in a traveling band to the constant parameters in the governing equations and supplementary conditions. The second approximation is shown to yield approximate analytical expressions for the solution functions which are in close correspondence with previously derived traveling band solutions for values of time after the initial period of formation.     

Some stochastic features of bacterial constant growth apparatus

Stochastic models for bacterial constant growth apparatus such as the chemostat are posed and studied. Approximations are given for the mean and variance of the size of the bacterial population when the population is in steady state. Procedures for stimulating a chemostat are developed and the approximate moments are compared with simulated values. The distribution is derived for the waiting time until the occurrence of a population change-over to a faster growing strain. Research supported by National Institutes of Health Grant 5-R01-GM21214.     

Contribution to the mathematical biophysics of automobile driving

Traffic in one direction on a multilane highway is considered, and a general expression for the number of cars which pass a car travelling at a given velocity, as well as the number of cars which the given car passes, is derived for the case when the speeds of different cars are distributed in some arbitrary manner. Closed expressions are derived and discussed for a rectangular distribution. Each passing by another car or of another car is considered as a distracting stimulus which affects the reaction times of the driver. Using previously derived expressions for the safe speed as a function of reaction times, expressions for the safe average speed are derived, in terms of the volume of traffic and of the spread of the distribution of speeds.     

Dynamic mathematical model to predict microbial growth and inactivation during food processing.

Many sigmoidal functions to describe a bacterial growth curve as an explicit function of time have been reported in the literature. Furthermore, several expressions have been proposed to model the influence of temperature on the main characteristics of this growth curve: maximum specific growth rate, lag time, and asymptotic level. However, as the predictive value of such explicit models is most often guaranteed only at a constant temperature within the temperature range of microbial growth, they are less appropriate in optimization studies of a whole production and distribution chain. In this paper a dynamic mathematical model--a first-order differential equation--has been derived, describing the bacterial population as a function of both time and temperature. Furthermore, the inactivation of the population at temperatures above the maximum temperature for growth has been incorporated. In the special case of a constant temperature, the solution coincides exactly with the corresponding Gompertz model, which has been validated in several recent reports. However, the main advantage of this dynamic model is its ability to deal with time-varying temperatures, over the whole temperature range of growth and inactivation. As such, it is an essential building block in (time-saving) simulation studies to design, e.g., optimal temperature-time profiles with respect to microbial safety of a production and distribution chain of chilled foods.     

Inhibitory Effects and Mechanism of the Combined Use of α-Helical Peptides HPRP-A1/HPRP-A2 and Chlorhexidine Acetate Against Bacterial and Fungal Biofilms

International Journal of Peptide Research and Therapeutics - Drug resistance is an increasing problem in the treatment of vaginitis bacterial vaginosis and vulvovaginal candidiasis caused by...     

Dynamic mathematical model to predict microbial growth and inactivation during food processing.

Many sigmoidal functions to describe a bacterial growth curve as an explicit function of time have been reported in the literature. Furthermore, several expressions have been proposed to model the influence of temperature on the main characteristics of this growth curve: maximum specific growth rate, lag time, and asymptotic level. However, as the predictive value of such explicit models is most often guaranteed only at a constant temperature within the temperature range of microbial growth, they are less appropriate in optimization studies of a whole production and distribution chain. In this paper a dynamic mathematical model--a first-order differential equation--has been derived, describing the bacterial population as a function of both time and temperature. Furthermore, the inactivation of the population at temperatures above the maximum temperature for growth has been incorporated. In the special case of a constant temperature, the solution coincides exactly with the corresponding Gompertz model, which has been validated in several recent reports. However, the main advantage of this dynamic model is its ability to deal with time-varying temperatures, over the whole temperature range of growth and inactivation. As such, it is an essential building block in (time-saving) simulation studies to design, e.g., optimal temperature-time profiles with respect to microbial safety of a production and distribution chain of chilled foods.     

Towards the neurobiology of emotional body language

People's faces show fear in many different circumstances. However, when people are terrified, as well as showing emotion, they run for cover. When we see a bodily expression of emotion, we immediately know what specific action is associated with a particular emotion, leaving little need for interpretation of the signal, as is the case for facial expressions. Research on emotional body language is rapidly emerging as a new field in cognitive and affective neuroscience. This article reviews how whole-body signals are automatically perceived and understood, and their role in emotional communication and decision-making.     

Ciguatera — Parameters of a tropical health problem

Ciguatera fish poisoning is a significant health and resource problem in the tropical world, largely because of its uneven and unpredictable distribution in space and through time. Here, the problem is reviewed with evidence from the Pacific Basin. The contemporary distribution of ciguatera and the species commonly perceived to be toxic are considered and a hypothesis relating the greater prevalence of ciguatera in the eastern Pacific to reduced species diversity is presented. The problem is also considered as a public health phenomenon (the mean reported incidence for the Pacific region as a whole in 1981 was 109/100,000) and attention is given to island dwellers' adaptation to the problem, their explanations of its etiology, as well as its detection, prophylaxis, and cure.The primary research was made possible by a Fulbright-Hays Research Aboard Grant (#.441Ah70055); subsequent research was supported by a University of Hawaii Research and Training Revolving Fund Award.     

Outline of a possible mathematical approach to the problem of the effects of environment upon the incidence of some psychoneuroses

In previous papers we have studied the distribution of the differences of two desires or inner drives in a group of individuals, with a view to developing a theory of mass behavior. The same concept is now applied to the problem of incidence of neuroses. It is natural to consider that the incidence of neuroses in a group of individuals, which is characterized by a near equality of two opposite drives, will be particularly high. Applying the results of a previous paper (Bull. Math. Biophysics,18, 323–36, 1956) in which the distribution of certain types of opposite drives has been connected with the distribution of incomes, expressions are now derived which give the relative incidences of some types of neuroses for different income groups. The expressions derived hold only for certain types of assumptions and cannot, therefore, be directly applied to actual data. They suggest, however, new possibilities in experimental and observational approaches to the problem.     

Absorption of light in photoreceptors: Transverse incidence

The time variation of the absorption rate (i.e., the number of photons absorbed per sec) in a photoreceptor when light is incident perpendicular to its axis has been studied for various species and different conditions. Due to the cylindrical geometry of the photoreceptor the expressions for the absorption rates become very complicated. Hence, simple approximate expressions for the absorption rates in the case of some of the species have been suggested. The present analysis will be useful in analysing the mechanism of the photoreceptor when light is incident perpendicular to the axis.Work partially supported by Council of Scientific and Industrial Research (India)     

Defining the requirements for immunological control of mycobacterial infections.

Tuberculosis remains a major public health problem throughout the world. Research into the immunological basis of the host-pathogen relationship has recently benefited from the fascinating convergence of genetic data from mouse models and from humans. Latency - the seemingly quiescent phase of bacterial persistence - is the central problem in controlling tuberculosis and will be the next frontier of research.     

A Wiener-type neuronal model in the presence of exponential refractoriness

An instantaneous return process in the presence of random refractoriness for Wiener model of single neuron activity is considered. The case of exponential distributed refractoriness is analyzed and expressions for output distributions and interspike intervals density are obtained in closed form. A computational study is performed to elucidate the role played by the model parameters in affecting the firing probabilities and the interspike distribution.     

Transport Phenomena in Zonal Centrifuge Rotors: I. Velocity and Shear-Stress Distributions of Fluid During Acceleration

An analysis is presented for the evaluation of velocity components and shear-stress distributions of fluid in zonal centrifuge rotors during acceleration. Analytical expressions for the distribution of tangential and radial velocity components and the tangential shear-stress and the radial shear-stress distributions of fluid are obtained for the transient case. Characteristics of each distribution for a typical density gradient liquid in a zonal centrifuge rotor are computed from the relations derived, and are presented as figures. An unusual phenomenon—the tangential velocity of the gradient exceeding the velocity of the rotor during a particular period of acceleration—is demonstrated.     

Effects of asymmetric division on a stochastic model of the cell division cycle

The stochastic model of cell division formulated by Alt and Tyson is generalized to the case of imprecise binary fission. Closed-form expressions are derived for the generation-time distribution, the birth-size and division-size distributions, the beta curve, and the correlation coefficient of generation times of sister cells. The theoretical results are compared to observations of cell division statistics in a culture of fission yeast.     

Heterogeneity and spatial distribution of bacterial background contamination in pulp and process water of a paper mill

Identifying the source and the distribution of bacterial contaminant communities in water circuits of industrial applications is critical even when the process may not show signs of acute biofouling. The endemic contamination of facilities can cause adverse effects on process runability but may be masked by the observed daily variability. The distribution of background communities of bacterial contaminants may therefore be critical in the development of new site-specific antifouling strategies. In a paper mill as one example for a full-scale production process, bacterial contaminants in process water and pulp suspensions were mapped using molecular fingerprints at representative locations throughout the plant. These ecological data were analyzed in the process–engineering context of pulp and water flow in the facilities. Dispersal limits within the plant environment led to the presence of distinct groups of contaminant communities in the primary units of the plant, despite high flows of water and paper pulp between units. In the paper machine circuit, community profiles were more homogeneous than in the other primary units. The variability between sampled communities in each primary unit was used to identify a possible point source of microbial contamination, in this case a storage silo for reused pulp. Part of the contamination problem in the paper mill is likely related to indirect effects of microbial activity under the local conditions in the silo rather than to the direct presence of accumulated microbial biomass.     

Hydrodynamics of a permeable patch in the fluid membrane.

A patch of cross-linked proteins in the fluid membrane is considered for the case in which the patch is permeable (porous) for the lipid flow in the membrane. The Bretscher flow field is studied quantitatively and the distribution of Brownian particles over the surface of the cell is given. This leads to a simple quantitative criterion for cap formation. Finally, explicit expressions for the rotational and translational diffusion coefficients of a permeable patch, as calculated from hydrodynamics, are given.     

A note on distributions of times to coalescence,under time-dependent population size

Expressions for marginal distributions of times in the time-varying coalescence process are derived. The proposed method allows also for computation of joint probability distribution for pairs, triples, etc. of coalescence times. The expressions derived are useful for (1) extending several statistics from time constant to time-varying case, (2) increasing efficiency and accuracy of simulations in time-varying evolution, and (3) debugging coalescence simulation software.     

Modelling microbial processes (phyto- and bacterioplankton) in the Schelde estuary

Since about 10 years, studies have been conducted at the University of Brussels in modelling the microbiological processes affecting biogenic substances in the Schelde estuary and its watershed.The first model, a one dimensional redox model, simulated the longitudinal distribution of oxygen, nitrate, iron and manganese in relation to the observed bacterial heterotrophic activity. A model allowing calculation of bacterial activity from data on organic discharge was coupled to this model. It was completed by a model of phytoplanktonic development within the estuary. Finally, an idealized model of the hydrographical network, based on Horton analysis, is being established in order to calculate the quality of the water at the downward boundary of the estuary.Together, all these sub-models form a general model of the ecological working of the Schelde estuary, able to predict at least the general trends of the redox state, the organic carbon, mineral nitrogen, and chlorophyll-a concentrations as a function of distance to the sea, from the knowledge of geomorphological and meteorological data, along with informations concerning the distribution of anthropogenic discharges. This model therefore provides a powerfull tool for the rational management of the Schelde estuary.Research Associate of the Belgian National Scientific Research Funds.     

Optimal temperature policy for immobilized enzyme packed bed reactor performing reversible Michaelis-Menten kinetics using the disjoint policy.

The optimal temperature policy that maximizes the time-averaged productivity of a continuous immobilized enzyme packed bed reactor is determined. This optimization study takes into consideration the enzyme thermal deactivation with substrate protection during the reactor operation. The general case of reversible Michaelis-Menten kinetics under constant reactor feed flow rate is assumed. The corresponding nonlinear optimization problem is solved using the calculus of variations by applying the disjoint policy. This policy reduces the optimization problem into a differential-algebraic system, DAE. This DAE system defines completely the optimal temperature-time profiles. These profiles depend on the kinetic parameters, feed substrate concentration, operating period, and the residence time and are characterized by increasing form with time. Also, general analytical expressions for the slopes of the temperature and residual enzyme activity profiles are derived. An efficient solution algorithm is developed to solve the DAE system, which results into a one-dimensional optimization problem with simple bounds on the initial feed temperature. The enzymatic isomerization of glucose into fructose is selected as a case study. The computed productivities are very close to that obtained by numerical nonlinear optimization with simpler problem to solve. Moreover, the computed conversion profiles are almost constant over 90% of the operating periods, thus producing a homogeneous product.     

Steady size distributions for cells in one-dimensional plant tissues

We consider a population of cells growing and dividing steadily without mortality, so that the total cell population is increasing, but the proportion of cells in any size class remains constant. The cell division process is non-deterministic in the sense that both the size at which a cell divides, and the proportions into which it divides, are described by probability density functions. We derive expressions for the steady size/birth-size distribution (and the corresponding size/age distribution) in terms of the cell birth-size distribution, in the particular case of one-dimensional growth in plant organs, where the relative growth rate is the same for all cells but may vary with time. This birth-size distribution is shown to be the principal eigenfunction of a Fredholm integral operator. Some special cases of the cell birth-size distribution are then solved using analytical techniques, and in more realistic examples, the eigen-function is found using a simple, generally applicable numerical iteration.