Diffusion influenced binary reactive processes in membranes involving identical particles: a Monte Carlo study

Simple random walk simulations on triangular lattices were performed in order to obtain a basic quantitative understanding of the kinetics of diffusion influenced binary reactive processes of membrane associated peptides or proteins within the two dimensionality of lipid bilayers. The results of the Monte Carlo simulations are compared with various formal approximate steady-state approaches, such as presented by Keizer [Acc. Chem. Res., 18 (1985) 235-241] in the context of statistical nonequilibrium thermodynamics or by Hardt [Biophys. Chem., 10 (1979) 239-243], based on the well known work of Delbrück and Adam. For diffusion controlled binary reactions of identical particles, nice agreement with the numerically simulated values is found in the low concentration limit for both Hardt's and Keizer's approach. For the latter a fluctuating steady-state particle source has to be considered. The dependence of the steady-state rate coefficient on system size is investigated, and the results are compared to the work of Swartz and Peacock-López [J. Chem. Phys., 95 (4) (1991) 2727-2731]. In order to elucidate the results, a practical application is considered. An application to a dimerization reaction on vesicles of typical experimental dimensions is given.     

An application of the central limit theorem to coalescence times in the structured coalescent model with strong migration

The structured coalescent describes the ancestral relationship among sampled genes from a geographically structured population. The aim of this article is to apply the central limit theorem to functionals of the migration process to study coalescence times and population structure. An application of the law of large numbers to the migration process leads to the strong migration limit for the distributions of coalescence times. The central limit theorem enables us to obtain approximate distributions of coalescence times for strong migration. We show that approximate distributions depend on the population structure. If migration is conservative and strong, we can define a kind of effective population size N _e ^*, with which the entire population approximately behaves like a panmictic population. On the other hand, the approximate distributions for nonconservative migration are qualitatively different from those for conservative migration. And the entire population behaves unlike a panmictic population even though migration is strong.     

Optimal pharmacokinetic delivery of infused drugs: application to the treatment of cardiac arrhythmias

A common clinical goal of infusing drugs is to attain therapeutic steady-state concentrations as rapidly as possible. The desire is to closely approximate a step function in plasma concentration of the therapeutic agent. We have developed a novel approach to achieve this goal by using the principles of systems and compartmental analyses. The approach is to build a pharmacokinetic model for the disposition of the drug and then calculate backwards from the desired output function to derive the optimal input infusion function. We applied this technique to the infusion of Lidocaine, an antiarrhythmic agent which is often difficult to control. An optimal infusion function, used to drive a servo-controlled infusion pump, was derived to closely approximate a step-function response of drug levels. The efficacy of this infusion function was verified experimentally in dogs.     

Suppression of insulin receptor binding by prolonged enteral or parenteral nutrient infusion in the rat: role of gastric inhibitory polypeptide

In the rat, prolonged enteral or parenteral alimentation with a high-carbohydrate diet results in hyperinsulinemia, which is substantially greater with the parenteral route. Supplementing the parenteral infusate with porcine gastric inhibitory polypeptide (GIP) to approximate plasma immunoreactive GIP levels achieved with enteral feeding further increases steady-state plasma insulin and glucose concentrations, suggesting insulin resistance. We examined the effects of sustained hyperinsulinemia elicited by continuous nutrient infusion on insulin binding to isolated rat adipocytes and the modification of this response by GIP. Compared with a baseline group, both enterally and parenterally alimented groups showed decreased insulin receptor binding affinity. However, despite substantially different steady-state plasma insulin levels, insulin binding was similar with either infusion route. Factors other than plasma insulin concentration alone therefore contribute to insulin receptor down-regulation during prolonged enteral alimentation. Supplementing the parenteral infusate with exogenous GIP resulted in a further reduction in insulin receptor affinity. Thus, adaptation to continuous nutrient infusion is characterized by insulin receptor down-regulation regardless of the route of nutrient delivery. An additional suppression of insulin receptor binding may in part be responsible for the insulin resistance elicited by prolonged exogenous GIP administration.     

Probability density functions useful for parametrization of heterogeneity in growth and allometry data

This paper addresses the problem of modelling heterogeneous individual characteristics in a population. A flexible unified approach for stochastic parametrization dynamics of the distribution in population data is proposed. To approximate data with multiple observations per individual, models based on Markov processes are constructed. The method can be applied to scalar or multivariate characteristics, and its application to growth and allometry data is considered. Different stochastic versions of known growth and allometry functions are developed, which enable wide applicability. Simple informative growth indices are calculated as the moments of distribution. The three-parameter Gompertz growth model for size-at-age data was reparametrized to a size-increment data model with two parameters. An erratum to this article is available at .     

A Mathematical Model of Leaf Carbon Metabolism

A dynamic mechanistic mathematical model of C₃ leaf carbon metabolism,incorporating the Calvin cycle with starch and sucrose synthesisand degradation, is proposed. The model consists of a systemof non-linear differential equations based on biochemical andphysiological assumptions. An analytical steady-state solution,with interesting mathematical properties that are interpretedbiologically, is presented and shown to be stable. The systemequations are integrated numerically, and an approximate analyticalsolution to the sucrose sub-system is derived. Some resultsof the model are compared with experimental data. Mathematical model, Calvin cycle, leaf carbon metabolism, photosynthesis, differential equations     

A Monte Carlo simulation model for studying evolution in age-structured populations

This model provides for any number of genotypes defined by age-specific survival and fecundity rates in a population with completely overlapping generations and growing under the control of density-governing functions affecting survival or fecundity. It is tested in situations involving two alleles at one locus. Nonselection populations at Hardy–Weinberg equilibrium obey the ecogenetic law; i.e., each genotype follows Lotka's law regarding rate of increase and stable age distribution as if it were an independent true-breeding population. Populations experiencing age- and density-independent selection approximate this situation, and the changes in gene frequency are predicted by relative fitnesses bases on λ, the finite rate of increase of the genotypes. Polymorphic gene equilibria occurring at steady-state population sizes are determined by fitnesses based on R, the net reproductive rate. In examples involving differences in generation time produced by age-dependent differences in fecundity, the allele associated with longer generation time may be favored or opposed by selection, depending on whether the density-governing factor controlling population size affects survival or fecundity. If such genotypes have similar R's, a genetic equilibrium may be established if the population is governed by a density function acting upon fecundity. Received: August 23, 1999 / Accepted: July 13, 2000     

An approximate method for optimum independent culling level selection for n stages of selection with explicit solutions

Summary An approximate method with explicit solutions to apply independent culling levels for multiple traits in n-stages of selection was developed. An approximate solution was found for sequentially selected traits. Two assumptions were necessary. The first was to assume that subsequent selection would not appreciably change the mean of traits already selected, and the second was to approximate the variance of a correlated trait in a selected population with an upward biased projection. The procedure was shown to give near optimal results regardless of selection intensity or genetic correlations if phenotypic correlations among traits were low. The procedure gave poor results only for certain sequences of selection when phenotypic correlations were high. However, in those cases good results were obtained using a different sequence of selection. With high correlations, the procedure is recommended only after comparing solutions and expected genetic gain for all sequences of selection. If the expected aggregate gain for the sequence of selection desired is less than that of another order, culling points associated with the optimal ordering must be determined. Genetic gain from use of culling points is independent of order of selection. The procedure is recommended for use with computer programs that attempt to find optimal culling points to reduce computational time and to check results.Journal Paper No. 12448 of the Purdue University Agricultural Experiment Station     

Continuous culture algal bioassays for organic pollutants in aquatic ecosystems

Short-term responses of phytoplankton to organic pollutants are highly transitory. Time-course studies of non-steady state cells in continuous culture showed varying growth or photosynthetic responses such as enchancement, inhibition, adaptation (or development of resistance) or rebound, depending on the direction of changes in the intracellular toxicant concentration and the duration of exposure. However, steady-state cells in a two-stage chemostat system exhibited an increased tolerance to toxicants and subtle physiological effects such as photosynthetic enhancement which was accompanied by a considerable leakage of photosynthesates. It is important to understand such steady-state responses for the prediction and assessment of ecological impact by organic pollution on phytoplankton, since the time scale of changes in the toxicant/biomass ratio in most natural waters is long enough to approximate an equilibrium state.     

Approximative kinetic formats used in metabolic network modeling

An overview is presented of the different approximative enzyme kinetic formats that have been proposed for use in metabolic modeling studies. It is considered that the following four general properties are relevant for approximative kinetics: the rate must be proportional to enzyme level; at high metabolite concentrations, there is downward concave behavior of rate versus concentration; the number of kinetic parameters should be as small as possible; analytical solutions of steady-state network balances are desirable. Six different approximative kinetic formats are evaluated (linear, logarithmic-linear, power law GMA, power law S-systems, thermokinetic, linear-logarithmic) and it is concluded that only the recently proposed linear-logarithmic approach combines all desired properties and therefore seems a most appropriate approximate kinetic format.     

A model with 'growth retardation' for the kinetic heterogeneity of tumour cell populations

In the present paper we propose a continuous cell population model based on Shackney's idea of growth retardation. Cells are characterized by two state variables: the cell maturity x, 0 < or = x < or = 1, and a state variable T that identifies the rate of maturation along cell cycle. During their life span, cells can change T at random by jump transitions to T values corresponding to slower maturation rates, while at each jump the maturity x is conserved. Both the time evolution of the population and the exponential stationary solution are numerically computed. The distribution of the cell cycle transit time in asynchronous exponential growth is investigated by Monte Carlo simulation. An approximated formula for the distribution of cell cycle time is also provided.     

Dynamic instability of native microtubules from squid axons is rare and independent of gliding and vesicle transport

Dynamic instability characterizes the steady-state behavior of microtubules in vitro whereby polymer mass remains constant, while individual microtubules in the population may either grow or shrink. Video-enhanced contrast light microscopy was used to directly observe dynamic length changes in native, MAP-containing microtubules from squid axoplasm. We wanted to determine whether dynamic instability characterizes the steady-state behavior of axoplasmic microtubules in vitro. The lengths of a representative population of over 400 microtubules were analyzed. "Dynamic" microtubules were found to represent about 2% of the population. This observation is different from that described for cultured cells or microtubules assembled from PC-purified tubulin where most microtubules were either growing or shrinking.     

Use of zoospore concentrations and life cycle parameters in determining the population of anaerobic fungi in the rumen ecosystem

An indirect approach to quantification of the fibrolytic anaerobic fungi in the rumen is described. A mathematical model of the life cycle of anaerobic fungi, based upon observations of the life histories and growth kinetics of these organisms in vitro and in vivo, is constructed and solved in the steady-state to determine the population of particle-attached (substrate-associated) fungal thalli from the concentration of free-swimming zoospores in rumen liquid. The values obtained are broadly consistent with ruminal observations and with observations on faecal populations, which assume that a significant proportion of fungi leaving the rumen (as cysts or spores) can ultimately be accounted for in the faeces.     

Allele age and a test for selection on rare alleles

An approximate expression for the probability distribution of the age of a neutral allele as a function of its frequency is derived for a population undergoing arbitrary changes in population size. A simple maximum-likelihood estimator of allele age based on frequency is also obtained. The distribution of allele age, combined with a model predicting the extent of intra-allelic variability generated by mutation and recombination, leads to a statistical test of whether a rare allele has experienced natural selection. The test is based on finding whether there is too little or too much intra-allelic variability to be consistent with the observed frequency. The test is applied to the locus, BRCA1, associated with early-onset breast cancer in humans and shows that two common disease-associated alleles (5382insC and 185delAG) appear to have been subject to natural selection.     

The strength of the selection barrier between populations

Genetic differences among populations exposed to selection form barriers against genetic exchange by mortality among hybrids. The strength of such a selection barrier, with which one (recipient) population reacts against immigration from another (donor) population, may be measured as the cumulative mean fitness of hybrids and their descendants relative to the fitness of the recipient population. Previous work analysed a case of weak selection with pairwise epistatic interactions by assuming small genetic distance between two populations in contact. The present study allows large genetic difference between the donor and recipient populations and considers weak multilocus selection with arbitrary epistatic interactions between two or more linked loci. An approximate analytical expression for the barrier strength is obtained as an expansion in which the strength of selection plays the role of a small parameter. It is shown that allele frequencies and gametic linkage disequilibria contribute in different ways to the strength of the selection barrier.     

Development of a photosynthesis model with an emphasis on ecological applications

Summary A physiologically based steady-state model of whole leaf photosynthesis (WHOLEPHOT) is used to describe net photosynthesis daily time courses in Prunus armeniaca. Net photosynthesis rates are calculated in response to incident light intensity, leaf temperature, air carbon dioxide concentration, and leaf diffusion resistance measured at five minute intervals. The steady-state calculations closely approximate the observed net photosynthesis rates for a broad range of weather conditions and leaf stomatal behavior.     

On microbial states of growth†

It is crucial to the reproducibility of results and their proper interpretation that the conditions under which experiments are carried out be defined with rigour and consistency, in this review we attempt to clarify the differences and interrelationships among steady, balanced and exponential states of culture growth. Basic thermodynamic concepts are used to introduce the idea of steady-state growth in open, biological systems. The classical, sometimes conflicting, definitions of steady-state and balanced growth are presented, and a consistent terminology is proposed. The conditions under which a culture in balanced growth is also in exponential growth and in steady-state growth are indicated. It is pointed out that steady-state growth always implies both balanced and exponential growth, and examples in which the converse does not hold are described. More complex situations are then characterized and the terminology extended accordingly. This leads to the notion of normal growth and growth that can be synchronous or otherwise unbalanced but still reproducible, and to the condition of approximate steady state manifested by growth in batch culture and by asymmetrically dividing cells, which is analysed in some detail.     

Influences of Various Amino Acids on Tryptophan-Mediated Control of the Tryptophan Biosynthetic Enzymes in Escherichia coli

Lysates of Escherichia coli Ymel obtained from cultures grown in the absence of tryptophan in minimal medium supplemented with 0.1% casein hydrolysate show an approximate fivefold increase in steady-state specific activity of both anthranilate synthetase and tryptophan synthetase A protein relative to cultures grown in nonsupplemented medium. In the presence of repressing levels of exogenous tryptophan, growth of cultures in casein hydrolysate-supplemented medium results in a noncoordinate enhancement of repression of 10-fold for anthranilate synthetase and twofold for tryptophan synthetase A protein. Similar, but less pronounced, effects are shown for strain W3110. Strains possessing tryptophan regulator gene mutations do not exhibit this first effect, but do yield an approximate twofold decrease in specific activity of both enzymes when grown in medium supplemented with tryptophan and casein hydrolysate. A stimulation of derepression of both enzymes in strain Ymel equivalent to that induced by casein hydrolysate can be reproduced by growth in minimal medium supplemented with threonine, phenylalanine, tyrosine, serine, glutamic acid, and glutamine. Doubling time in this medium is not significantly different from that in minimal medium. An enhancement of repression which partially mimics that observed on growth in medium supplemented with tryptophan plus casein hydrolysate is obtained when Ymel is grown on medium supplemented with tryptophan plus methionine. Threonine or phenylalanine plus tyrosine as separate medium supplements are independently capable of producing a 1.4-fold or 3.4-fold stimulation, respectively, but in combination only the phenylalanine plus tyrosine effect is manifested unless serine and glutamic acid or glutamine are included. Our data show that expression of the tryptophan biosynthetic enzymes can be significantly influenced in vivo as a result of growth in medium supplemented with a variety of amino acids.