Peristaltic transport in a channel with a porous peripheral layer: model of a flow in gastrointestinal tract

Peristaltic transport in a two dimensional channel, filled with a porous medium in the peripheral region and a Newtonian fluid in the core region, is studied under the assumptions of long wavelength and low Reynolds number. The fluid flow is investigated in the waveframe of reference moving with the velocity of the peristaltic wave. Brinkman extended Darcy equation is utilized to model the flow in the porous layer. The interface is determined as a part of the solution using the conservation of mass in both the porous and fluid regions independently. A shear-stress jump boundary condition is used at the interface. The physical quantities of importance in peristaltic transport like pumping, trapping, reflux and axial velocity are discussed for various parameters of interest governing the flow like Darcy number, porosity, permeability, effective viscosity etc. It is observed that the peristalsis works as a pump against greater pressure in two-layered model with a porous medium compared with a viscous fluid in the peripheral layer. Increasing Darcy number Da decreases the pumping and increasing shear stress jump constant beta results in increasing the pumping. The limits on the time averaged flux Q for trapping in the core layer are obtained. The discussion on pumping, trapping and reflux may be helpful in understanding some of the fluid dynamic aspects of the transport of chyme in gastrointestinal tract.     

Viscous flow through slowly expanding or contracting porous walls with low seepage Reynolds number: a model for transport of biological fluids through vessels

In this article, the problem of laminar, isothermal, incompressible and viscous flow in a rectangular domain bounded by two moving porous walls, which enable the fluid to enter or exit during successive expansions or contractions, is investigated. The governing non-linear equations and their associated boundary conditions are transformed into a highly non-linear ordinary differential equation. The series solution of the problem is obtained by utilising the homotopy perturbation method. Graphical results are presented to investigate the influence of the non-dimensional wall dilation rate and seepage Reynolds number (Re) on the velocity, normal pressure distribution and wall shear stress. Since the transport of biological fluids through contracting or expanding vessels is characterised by low seepage Res, the current study focuses on the viscous flow driven by small wall contractions and expansions of two weakly permeable walls.     

Viscous flow through slowly expanding or contracting porous walls with low seepage Reynolds number: a model for transport of biological fluids through vessels

In this article, the problem of laminar, isothermal, incompressible and viscous flow in a rectangular domain bounded by two moving porous walls, which enable the fluid to enter or exit during successive expansions or contractions, is investigated. The governing non-linear equations and their associated boundary conditions are transformed into a highly non-linear ordinary differential equation. The series solution of the problem is obtained by utilising the homotopy perturbation method. Graphical results are presented to investigate the influence of the non-dimensional wall dilation rate and seepage Reynolds number (Re) on the velocity, normal pressure distribution and wall shear stress. Since the transport of biological fluids through contracting or expanding vessels is characterised by low seepage Res, the current study focuses on the viscous flow driven by small wall contractions and expansions of two weakly permeable walls.     

Estimating tsetse population parameters: application of a mathematical model with density-dependence

A density-dependent model is used to describe the dynamics of an open population of tsetse flies (Diptera: Glossinidae). Immigration (or emigration) takes place when the total population is below (or above) a biologically determined threshold value. The population is also subjected to birth and death rates, as well as to the risk of being trapped (continuously or intermittently). During trapping the population decreases toward a 'low' equilibrium population and when trapping ceases the population starts recovering and increases toward a 'high' equilibrium. The model is fitted using data collected on trapped flies in four experiments. The first one was conducted with 'intermittent trapping' (i.e. several trapping-recovery cycles) on Glossina fuscipes fuscipes Newstead in the Central African Republic (Bangui area). In the other experiments, trapping data on Glossina palpalis palpalis (Robineau-Desvoidy) was collected in 'aggregate' form over several days at a time. Two of these were in Congo-Brazzaville (Bouenza area) and one in the Ivory Coast (Vavoua focus). Estimates are derived for the low and high equilibrium values as well as the trapping rate. The estimated effect of sustained trapping is to reduce the population to low equilibrium values that are 85-87% lower than the levels without trapping. The effects of the natural intrinsic growth and of the migration flows cannot be estimated separately because in the model they are mathematically indistinguishable.     

Plant interspecies competition for sunlight: a mathematical model of canopy partitioning

We examine the influence of canopy partitioning on the outcome of competition between two plant species that interact only by mutually shading each other. This analysis is based on a Kolmogorov-type canopy partitioning model for plant species with clonal growth form and fixed vertical leaf profiles (Vance and Nevai in J. Theor. Biol., 2007, to appear). We show that canopy partitioning is necessary for the stable coexistence of the two competing plant species. We also use implicit methods to show that, under certain conditions, the species’ nullclines can intersect at most once. We use nullcline endpoint analysis to show that when the nullclines do intersect, and in such a way that they cross, then the resulting equilibrium point is always stable. We also construct surfaces that divide parameter space into regions within which the various outcomes of competition occur, and then study parameter dependence in the locations of these surfaces. The analysis presented here and in a companion paper (Nevai and Vance, The role of leaf height in plant competition for sunlight: analysis of a canopy partitioning model, in review) together shows that canopy partitioning is both necessary and, under appropriate parameter values, sufficient for the stable coexistence of two hypothetical plant species whose structure and growth are described by our model. A. L. Nevai was supported in part by the National Institutes of Health, National Research Service Award (T32-GM008185) from the National Institute of General Medical Sciences (NIGMS).     

Mechanism of inhibition defines CETP activity: a mathematical model for CETP in vitro

Because cholesteryl ester transfer protein (CETP) inhibition is a potential HDL-raising therapy, interest has been raised in the mechanisms and consequences of CETP activity. To explore these mechanisms and the dynamics of CETP in vitro, a mechanistic mathematical model was developed based upon the shuttle mechanism for lipid transfer. Model parameters were estimated from eight published experimental datasets, and the resulting model captures observed dynamics of CETP in vitro. Simulations suggest the shuttle mechanism yields behaviors consistent with experimental observations. Three key findings predicted from model simulations are: 1) net CE transfer activity from HDL to VLDL and LDL can be significantly altered by changing the balance of homoexchange versus heteroexchange of neutral lipids via CETP; 2) lipemia-induced increases in CETP activity are more likely caused by increases in lipoprotein particle size than particle number; and 3) the inhibition mechanisms of the CETP inhibitors torcetrapib and JTT-705 are significantly more potent than a classic competitive inhibition mechanism with the irreversible binding mechanism having the most robust response. In summary, the model provides a plausible representation of CETP activity in vitro, corroborates strong evidence for the shuttle hypothesis, and provides new insights into the consequences of CETP activity and inhibition on lipoproteins.     

The affinity of phlorizin-like compounds for a beta-glucosidase in intestinal brush borders: comparison with the glucose transport system

The ability of a series of phlorizin-like glycosides to interact with the active center of the β-glucosidase (phlorizin hydrolase) present in hamster intestinal brush border membranes has been estimated from K_m and K_i measurements. All of the glycosides except para-phlorizin, were cleaved at the same V although large differences in their apparent K_m values were found. The inhibitors of [³H]glucose-labeled phlorizin hydrolysis all acted competitively and their K_i values equaled their respective K_ms with two exceptions: (1) para-phlorizin, an isomer with its sugar residue in a different orientation than any of the other derivatives, is a better inhibitor than substrate and (2) phloretin 2′-galactoside appeared to be a better substrate than inhibitor: it was extensively hydrolyzed, more than would have been predicted from its apparent K_i value. This “extra” hydrolysis was probably due to lactase action. The affinities of these compounds for the glucose transport system and phlorizin hydrolase were compared. The relative inhibitory potency of all but two of the analogs was the same in either system suggesting that there are similarities in the architecture of the two receptors. However, there are differences which indicate that these two membrane components do not share a common site: (1) The K_i values of the glycosides as sugar carrier blockers are 100-fold smaller than their K_iS as hydrolase inhibitors, (2) 4-methoxyphlorizin has somewhat greater affinity for the β-glucosidase than the transporter, and (3) para-phlorizin has essentially no affinity for the glucose carrier but is a good substrate and potent inhibitor of phlorizin hydrolase. Studies designed to isolate and affinity label the phlorizin-receptor component of the transport system must take into account that the intestinal brush border membrane possesses a β-glycosidase whose active site will probably also be labeled and at which phlorizin-like ligands could be inactivated.     

Analysis of a mathematical model for tuberculosis: What could be done to increase case detection

This paper presents qualitative and quantitative study of a TB mathematical model to test results from a survey carried out in Benin City, Nigeria. The purpose of the survey was to determine factors that could enhance the case detection rate of tuberculosis. Results from the survey identified four key factors that must be combined for an effective control of TB and increase the case detection rate: effective awareness programme, active cough identification, associated cost factor for treatment of identified cases and effective treatment. The overall effect of these factors on the basic reproduction number under treatment, R_T, of the TB model was considered. In all, a serious concentration on tuberculosis awareness programmes and active cough identification as a marker for someone having TB was shown to significantly reduce the value of the reproduction number, hereby reducing the severity of the disease in the presence of treatment.     

Analysis of a time-delayed mathematical model for tumour growth with an almost periodic supply of external nutrients

In this paper, the existence, uniqueness and exponential stability of almost periodic solutions for a mathematical model of tumour growth are studied. The establishment of the model is based on the reaction–diffusion dynamics and mass conservation law and is considered with a delay in the cell proliferation process. Using a fixed-point theorem in cones, the existence and uniqueness of almost periodic solutions for different parameter values of the model is proved. Moreover, by the Gronwall inequality, sufficient conditions are established for the exponential stability of the unique almost periodic solution. Results are illustrated by computer simulations.     

Validation of a mathematical model of the bovine estrous cycle for cows with different estrous cycle characteristics

A recently developed mechanistic mathematical model of the bovine estrous cycle was parameterized to fit empirical data sets collected during one estrous cycle of 31 individual cows, with the main objective to further validate the model. The a priori criteria for validation were (1) the resulting model can simulate the measured data correctly (i.e. goodness of fit), and (2) this is achieved without needing extreme, probably non-physiological parameter values. We used a least squares optimization procedure to identify parameter configurations for the mathematical model to fit the empirical in vivo measurements of follicle and corpus luteum sizes, and the plasma concentrations of progesterone, estradiol, FSH and LH for each cow. The model was capable of accommodating normal variation in estrous cycle characteristics of individual cows. With the parameter sets estimated for the individual cows, the model behavior changed for 21 cows, with improved fit of the simulated output curves for 18 of these 21 cows. Moreover, the number of follicular waves was predicted correctly for 18 of the 25 two-wave and three-wave cows, without extreme parameter value changes. Estimation of specific parameters confirmed results of previous model simulations indicating that parameters involved in luteolytic signaling are very important for regulation of general estrous cycle characteristics, and are likely responsible for differences in estrous cycle characteristics between cows.     

Co-culture of two MDCK strains with distinct junctional protein expression: a model for intercellular junction rearrangement and cell sorting

Distinct epithelial MDCK cell strains displaying extremes in transepithelial electrical resistance (paracellular permeability) have been established in co-culture and the subsequent cellular behaviour and formation of junctional complexes investigated. After high-density seeding, MDCK strain I and II cells in co-culture are initially randomly distributed but subsequently sort themselves out in a time-dependent manner to form separate homotypic aggregates. The final pattern of cell arrangement of homotypic aggregates depends on the relative seeding proportion of each cell type. Immunostaining of established marker proteins for junctional complexes has revealed that MDCK I and II cells differ in the degree of expression of the zonula-adherens-associated protein, E-cadherin, their cytoskeletal architecture and the junctional distribution of a desmosomal protein, and by showing subtle differences in tight junction staining for the zona-occludens-associated proteins, ZO-1 and occludin. The distinct pattern of junctional protein expression is maintained when the two MDCK strains are co-cultured; however, morphologically atypical intercellular junctions between heterotypic cells at the boundary of homotypic cell aggregates have been observed. It has been suggested that cell sorting, a phenomenon yet to be completely understood, is involved in important morphogenetic processes. We propose that co-culture of strains of the well-characterised MDCK cell line may be a novel but well-defined cell system for studying epithelial cell rearrangement and sorting in intact epithelial sheets.     

Gastrointestinal dysfunction in mice with a targeted mutation in the gene encoding vasoactive intestinal polypeptide: a model for the study of intestinal ileus and Hirschsprung's disease

In 1970, Drs. Said and Mutt isolated a novel peptide from porcine intestinal extracts with powerful vasoactive properties, and named it vasoactive intestinal peptide (VIP). Since then, the biological actions of VIP in the gut as well as its signal transduction pathways have been extensively studied. A variety of in vitro and in vivo studies have indicated that VIP, expressed in intrinsic non-adrenergic non-cholinergic (NANC) neurons, is a potent regulator of gastrointestinal (GI) motility, water absorption and ion flux, mucus secretion and immune homeostasis. These VIP actions are believed to be mediated mainly by interactions with highly expressed VPAC(1) receptors and the production of nitric oxide (NO). Furthermore, VIP has been implicated in numerous physiopathological conditions affecting the human gut, including pancreatic endocrine tumors secreting VIP (VIPomas), insulin-dependent diabetes, Hirschsprung's disease, and inflammatory bowel syndromes such as Crohn's disease and ulcerative colitis. To further understand the physiological roles of VIP on the GI tract, we have begun to analyze the anatomical and physiological phenotype of C57BL/6 mice lacking the VIP gene. Herein, we demonstrate that the overall intestinal morphology and light microscopic structure is significantly altered in VIP(-/-) mice. Macroscopically there is an overall increase in weight, and decrease in length of the bowel compared to wild type (WT) controls. Microscopically, the phenotype was characterized by thickening of smooth muscle layers, increased villi length, and higher abundance of goblet cells. Alcian blue staining indicated that the latter cells were deficient in mucus secretion in VIP(-/-) mice. The differences became more pronounced from the duodenum to the distal jejunum or ileum of the small bowel but, became much less apparent or absent in the colon with the exception of mucus secretion defects. Further examination of the small intestine revealed larger axonal trunks and unusual unstained patches in myenteric plexus. Physiologically, the VIP(-/-) mice showed an impairment in intestinal transit. Moreover, unlike WT C57BL/6 mice, a significant percentage of VIP(-/-) mice died in the first postnatal year with overt stenosis of the gut.     

Kinetics of the enzymatic hydrolysis of cellulose: 1. A mathematical model for a batch reactor process

A mathematical model for enzymatic cellulose hydrolysis, based on experimental kinetics of the process catalysed by a cellulase [see 1,4-(1,3;1,4)-β-d-glucan 4-glucanohydrolase, EC 3.2.1.4] preparation from Trichoderma longibrachiatum has been developed. The model takes into account the composition of the cellulase complex, the structural complexity of cellulose, the inhibition by reaction products, the inactivation of enzymes in the course of the enzymatic hydrolysis and describes the kinetics of d-glucose and cellobiose formation from cellulose. The rate of d-glucose formation decelerated through the hydrolysis due to a change in cellulose reactivity and inhibition by the reaction product, d-glucose. The rate of cellobiose formation decelerated due to inhibition by the product, cellobiose, and inactivation of enzymes adsorbed on the cellulose surface. Inactivation of the cellobiose-producing enzymes as a result of their adsorption was found to be reversible. The model satisfactorily predicts the kinetics of d-glucose and cellobiose accumulation in a batch reactor up to 70–80% substrate conversion on changing substrate concentration from 5 to 100 g l^?1and the concentration of the enzymic preparation from 5 to 60 g l^?1.     

The evolutionary dynamics of receptor binding avidity in influenza A: a mathematical model for a new antigenic drift hypothesis

The most salient feature of influenza evolution in humans is its antigenic drift. This process is characterized by structural changes in the virus''s B-cell epitopes and ultimately results in the ability of the virus to evade immune recognition and thereby reinfect previously infected hosts. Until recently, amino acid substitutions in epitope regions of the viral haemagglutinin were thought to be positively selected for their ability to reduce antibody binding and therefore were thought to be responsible for driving antigenic drift. However, a recent hypothesis put forward by Hensley and co-workers posits that cellular receptor binding avidity is the dominant phenotype under selection, with antigenic drift being a side effect of these binding avidity changes. Here, we present a mathematical formulation of this new antigenic drift model and use it to show how rates of antigenic drift depend on epidemiological parameters. We further use the model to evaluate how two different vaccination strategies can impact antigenic drift rates and ultimately disease incidence levels. Finally, we discuss the assumptions present in the model formulation, predictions of the model, and future work that needs to be done to determine the consistency of this hypothesis with known patterns of influenza''s genetic and antigenic evolution.     

A mathematical model of tumour growth with Beddington–DeAngelis functional response: a case of cancer without disease

A previously published mathematical model, governing tumour growth with mixed immunotherapy and chemotherapy treatments, is modified and studied. The search time, which is assumed to be neglectable in the previously published model, is incorporated into the functional response for tumour-cell lysis by effector cells. The model exhibits bistability where a tumour-cell population threshold exists. A tumour with an initial cell population below the threshold can be controlled by the immune system and remains microscopic and asymptomatic called cancer without disease while that above the threshold grows to lethal size. Bifurcation analysis shows that (a) the chemotherapy-induced damage may cause a microscopic tumour, which would never grow to become lethal if untreated, to grow to lethal size, (b) applying chemotherapy alone requires a large dosage to be successful, (c) immunotherapy is ineffective, and (d) a combination of chemotherapy and immunotherapy can produce a synergistic effect on the outcome of a treatment.     

Novel oxysterols observed in tissues and fluids of AY9944-treated rats: a model for Smith-Lemli-Opitz syndrome

Treatment of Sprague-Dawley rats with AY9944, an inhibitor of 3β-hydroxysterol-Δ(7)-reductase (Dhcr7), leads to elevated levels of 7-dehydrocholesterol (7-DHC) and reduced levels of cholesterol in all biological tissues, mimicking the key biochemical hallmark of Smith-Lemli-Opitz syndrome (SLOS). Fourteen 7-DHC-derived oxysterols previously have been identified as products of free radical oxidation in vitro; one of these oxysterols, 3β,5α-dihydroxycholest-7-en-6-one (DHCEO), was recently identified in Dhcr7-deficient cells and in brain tissues of Dhcr7-null mouse. We report here the isolation and characterization of three novel 7-DHC-derived oxysterols (4α- and 4β-hydroxy-7-DHC and 24-hydroxy-7-DHC) in addition to DHCEO and 7-ketocholesterol (7-kChol) from the brain tissues of AY9944-treated rats. The identities of these five oxysterols were elucidated by HPLC-ultraviolet (UV), HPLC-MS, and 1D- and 2D-NMR. Quantification of 4α- and 4β-hydroxy-7-DHC, DHCEO, and 7-kChol in rat brain, liver, and serum were carried out by HPLC-MS using d(7)-DHCEO as an internal standard. With the exception of 7-kChol, these oxysterols were present only in tissues of AY9944-treated, but not control rats, and 7-kChol levels were markedly (>10-fold) higher in treated versus control rats. These findings are discussed in the context of the potential involvement of 7-DHC-derived oxysterols in the pathogenesis of SLOS.     

Individual optimization efforts and population dynamics: a mathematical model for the evolution of resource allocation strategies, with applications to reproductive and mating systems

We develop a formal framework for the optimal allocation of limited resources that includes and clarifies the interplay between individual optimization and the resulting effects at the population level. As an example, in regard to the evolution of sexual recombination, the paradox of the twofold cost of sex is avoided by distinguishing between the evolution of recombination and the subsequent emergence and stability of different mating types as a result of individual optimization within a population that benefits from recombination.

A mathematical model for the temporal pattern of a population structure,with particular reference to the flour beetle: II. Competition between species

The effect of competition between species is considered in terms of a mathematical model. It is found that, except for special relations among the parameters, only one species should remain, as is found experimentally. It is also found that unless new factors arise in the competition, one can calculate an index to predict which of the two species is most likely to become extinct. The index involves quantities measured from isolated populations. A preliminary extimate yields satisfactory values when compared with the experimental results of competition.     

Kinetics of the enzymatic hydrolysis of cellulose: 2. A mathematical model for the process in a plug-flow column reactor

The kinetics of enzymatic cellulose hydrolysis in a plug-flow column reactor catalysed by cellulases [see 1,4-(1,3;1,4)-β-d-glucan 4-glucanohydrolase, EC 3.2.1.4] from Trichoderma longibrachiatum adsorbed on cellulose surface have been studied. The maximum substrate conversion achieved was 90–94%. The possibility of enzyme recovery for a reactor of this type is discussed. A mathematical model for enzymatic cellulose hydrolysis in a plug-flow column reactor has been developed. The model allows for the component composition of the cellulase complex, adsorption of cellulases on the substrate surface, inhibition by reaction products, changes in cellulose reactivity and the inactivation of enzymes in the course of hydrolysis. The model affords a reliable prediction of the kinetics of d-glucose and cellobiose formation from cellulose in a column reactor as well as the degree of substrate conversion and reactor productivity with various amounts of adsorbed enzymes and at various flow rates.