Type III secretion contact-dependent model for the intracellular development of Chlamydia

The medically significant genus Chlamydia is a class of obligate intracellular bacterial pathogens that replicate within vacuoles in host eukaryotic cells termed inclusions. Chlamydia's developmental cycle involves two forms; an infectious extracellular form, known as an elementary body (EB), and a non-infectious form, known as the reticulate body (RB), that replicates inside the vacuoles of the host cells. The RB surface is covered in projections that are in intimate contact with the inclusion membrane. Late in the developmental cycle, these reticulate bodies differentiate into the elementary body form. In this paper, we present a hypothesis for the modulation of these developmental events involving the contact-dependent type III secretion (TTS) system. TTS surface projections mediate intimate contact between the RB and the inclusion membrane. Below a certain number of projections, detachment of the RB provides a signal for late differentiation of RB into EB. We use data and develop a mathematical model investigating this hypothesis. If the hypothesis proves to be accurate, then we have shown that increasing the number of inclusions per host cell will increase the number of infectious progeny EB until some optimal number of inclusions. For more inclusions than this optimum, the infectious yield is reduced because of spatial restrictions. We also predict that a reduction in the number of projections on the surface of the RB (and as early as possible during development) will significantly reduce the burst size of infectious EB particles. Many of the results predicted by the model can be tested experimentally and may lead to the identification of potential targets for drug design. © Society for Mathematical Biology 2006.

Hysteresis and phase transitions in a single partially internally wetted catalyst pellet: Thermogravimetric studies

The hydrogenation of cyclohexene over palladium supported in a microporous gamma-alumina pellet is studied thermogravimetrically with a view to measuring the extent of partial internal wetting associated with the different steady state branches. As many as three steady state branches having significantly different degrees of internal wetting and reaction rates, with transitions between them, are confirmed from observations of catalyst weight change. It is seen that with reduction in catalyst activity the middle branch, obtained by condensation from a vapor filled pellet, is much more prominent without showing an evaporative transition for the range of hydrogen partial pressures used here. The catalyst activity is therefore an important parameter affecting the structure of the steady state branches. Hysteresis effects are found to occur, and the thermogravimetric results also confirm the importance of history in determining the catalyst state. The measured degree of wetting is in accordance with that estimated from a mathematical model incorporating capillary condensation effects in addition to reaction-diffusion phenomena. The same model also satisfactorily interprets the reaction rate variations and transitions seen in the present work.

Modeling ex vivo hematopoiesis using chemical engineering metaphors

Ex vivo hematopoiesis is increasingly used for clinical applications. Models of ex vivo hematopoiesis are required to better understand the complex dynamics and to optimize hematopoietic culture processes. A general mathematical modeling framework is developed which uses traditional chemical engineering metaphors to describe the complex hematopoietic dynamics. Tanks and tubular reactors are used to describe the (pseudo-) stochastic and deterministic elements of hematopoiesis, respectively. Cells at any point in the differentiation process can belong to either an immobilized, inert phase (quiescent cells) or a mobile, active phase (cycling cells). The model describes five processes: (1) flow (differentiation), (2) autocatalytic formation (growth),(3) degradation (death), (4) phase transition from immobilized to mobile phase (quiescent to cycling transition), and (5) phase transition from mobile to immobilized phase (cycling to quiescent transition). The modeling framework is illustrated with an example concerning the effect of TGF-beta 1 on erythropoiesis. (C) 1998 Published by Elsevier Science Ltd. All rights reserved.

Kinetic analysis of vascular marker distribution in perfused rat livers after regeneration following partial hepatectomy

Background/Aims: Liver clearance models are based on information (or assumptions) on solute distribution kinetics within the microvasculatory system, The aim was to study albumin distribution kinetics in regenerated livers and in livers of normal adult rats, Methods: A novel mathematical model was used to evaluate the distribution space and the transit time dispersion of albumin in livers following regeneration after a two-thirds hepatectomy compared to livers of normal adult rats. Outflow curves of albumin measured after bolus injection in single-pass perfused rat livers were analyzed by correcting for the influence of catheters and fitting a long-tailed function to the data. Results: The curves were well described by the proposed model. The distribution volume and the transit time dispersion of albumin observed in the partial hepatectomy group were not significantly different from livers of normal adult rats. Conclusions: These findings suggest that the distribution space and the transit time dispersion of albumin (CV2) is relatively constant irrespective of the presence of rapid and extensive repair. This invariance of CV2 implies, as a first approximation, a similar degree of intrasinusoidal mixing, The finding that a sum of two (instead of one) inverse Gaussian densities is an appropriate empirical function to describe the outflow curve of vascular indicators has consequences for an improved prediction of hepatic solute extraction.

Anthocyanin synthesis, growth and nutrient uptake in suspension cultures of strawberry cells

Strawberry (Fragaria ananassa cv. Shikinari) cell suspension cultures carried out in shake flasks for 18 d were closely examined for cell growth, anthocyanin synthesis and the development of pigmented cells in relation to the uptake of carbohydrate, extracellular PO4, NO3, NH4, and calcium. Cell viability, extracellular anthocyanin content, pH and electrical conductivity of the broth were also monitored. The specific growth rate of strawberry cells at exponential phase was 0.27 and 0.28 d(-1) based on fresh and dry weight, respectively. Anthocyanin synthesis was observed to increase continuously to a maximum value of 0.86 mg/g fresh cell weight (FCW) at day 6, and was partially growth-associated. Anthocyanin synthesis was linearly related to the increase in pigmented cell ratio, which increased with time and reached a maximum value of ca. 70% at day 6 due to reduction in cell viability and depletion of substrate. Total carbohydrate uptake was closely associated with increase in cell growth, and glucose was utilized in preference to fructose. Nitrate and ammonia were consumed until 9 d of culture, but phosphate was completely absorbed within 4 d. Calcium was assimilated throughout the growth cycle. After 9 d, cell lysis was observed which resulted in the leakage of intracellular substances and a concomitant pH rise. Anthocyanin was never detected in the broth although the broth became darkly pigmented during the lysis period. This suggests that anthocyanin was synthesized only by viable pigmented cells, and degraded rapidly upon cell death and lysis. Based on the results of kinetic analysis, a model was developed by incorporating governing equations for the ratio of pigmented cells into a Bailey and Nicholson's model. This was verified by comparison with the experimental data. The results suggest Bat the model satisfactorily describes the strawberry cell culture process, and may thus be used for process optimization.

Grazers and diggers: Exploitation competition and coexistence among foragers with different feeding strategies on a single resource

A mathematical model is presented that describes a system where two consumer species compete exploitatively for a single renewable resource. The resource is distributed in a patchy but homogeneous environment; that is, all patches are intrinsically identical. The two consumer species are referred to as diggers and grazers, where diggers deplete the resource within a patch to lower densities than grazers. We show that the two distinct feeding strategies can produce a heterogeneous resource distribution that enables their coexistence. Coexistence requires that grazers must either move faster than diggers between patches or convert the resources to population growth much more efficiently than diggers. The model shows that the functional form of resource renewal within a patch is also important for coexistence. These results contrast with theory that considers exploitation competition for a single resource when the resource is assumed to be well mixed throughout the system.

The mechanical properties of Saccharomyces cerevisiae

Cell-wall mechanical properties play an integral part in the growth and form of Saccharomyces cerevisiae, In contrast to the tremendous knowledge on the genetics of S. cerevisiae, almost nothing is known about its mechanical properties. We have developed a micromanipulation technique to measure the force required to burst single cells and have recently established a mathematical model to extract the mechanical properties of the cell wall from such data, Here we determine the average surface modulus of the S, cerevisiae cell wall to be 11.1 +/- 0.6 N/m and 12.9 +/- 0.7 N/m in exponential and stationary phases, respectively, giving corresponding Young's moduli of 112 +/- 6 MPa and 107 +/- 6 MPa, This result demonstrates that yeast cell populations strengthen as they enter stationary phase by increasing wall thickness and hence the surface modulus, without altering the average elastic properties of the cell-wall material. We also determined the average breaking strain of the cell wall to be 82% +/- 3% in exponential phase and 80% +/- 3% in stationary phase, This finding provides a failure criterion that can be used to predict when applied stresses (e,g,, because of fluid flow) will lead to wall rupture, This work analyzes yeast compression experiments in different growth phases by using engineering methodology.

Structured modeling of recombinant protein production in batch and fed-batch culture of baculovirus-infected insect cells

The infection of insect cells with baculovirus was described in a mathematical model as a part of the structured dynamic model describing whole animal cell metabolism. The model presented here is capable of simulating cell population dynamics, the concentrations of extracellular and intracellular viral components, and the heterologous product titers. The model describes the whole processes of viral infection and the effect of the infection on the host cell metabolism. Dynamic simulation of the model in batch and fed-batch mode gave good agreement between model predictions and experimental data. Optimum conditions for insect cell culture and viral infection in batch and fed-batch culture were studied using the model.

Finite element modelling of heat transfer through permeable cracks in hydrothermal systems with upward throughflow

We use the finite element method to model the heat transfer phenomenon through permeable cracks in hydrothermal systems with upward throughflow. Since the finite element method is an approximate numerical method, the method must be validated before it is used to soh,e any new, kind of problem. However, the analytical solution, which can be used to validate the finite element method and other numerical methods, is rather limited in the literature, especially, for the problem considered here. Keeping this in mind, we have derived analytical solutions for the temperature distribution along the vertical axis of a crack in a fluid-saturated porous layer. After the finite element method is validated by comparing the numerical solution with the analytical solution for the same benchmark problem, it is used to investigate the pore-fluid flow and heat transfer in layered hydrothermal systems with vertical permeable cracks. The related analytical and numerical results have demonstrated that vertical cracks are effective and efficient members to transfer heat energy from the bottom section to the top section in hydrothermal systems with upward throughflow.

Diel vertical migration: Modelling light-mediated mechanisms

Light is generally regarded as the most likely cue used by zooplankton to regulate their vertical movements through the water column. However, the way in which light is used by zooplankton as a cue is not well understood. In this paper we present a mathematical model of diel vertical migration which produces vertical distributions of zooplankton that vary in space and time. The model is used to predict the patterns of vertical distribution which result when animals are assumed to adopt one of three commonly proposed mechanisms for vertical swimming. First, we assume zooplankton tend to swim towards a preferred intensity of light. We then assume zooplankton swim in response to either the rate of change in light intensity or the relative rate of change in light intensity. The model predicts that for all three mechanisms movement is fastest at sunset and sunrise and populations are primarily influenced by eddy diffusion at night in the absence of a light stimulus. Daytime patterns of vertical distribution differ between the three mechanisms and the reasons for the predicted differences are discussed. Swimming responses to properties of the light field are shown to be adequate for describing diel vertical migration where animals congregate in near surface waters during the evening and reside at deeper depths during the day. However, the model is unable to explain how some populations halt their ascent before reaching surface waters or how populations re-congregate in surface waters a few hours before sunrise, a phenomenon which is sometimes observed in the held. The model results indicate that other exogenous or endogenous factors besides light may play important roles in regulating vertical movement.

The kinetics of baculovirus adsorption to insect cells in suspension culture

The influence of various culture parameters on the attachment of a recombinant baculovirus to suspended insect cells was examined under normal culture conditions. These parameters included cell density, multiplicity of infection, and composition of the cell growth medium. It was found that the fractional rate of virus attachment was independent of the multiplicity of infection but dependent on the cell density. A first order mathematical model was used to simulate the adsorption kinetics and predict the efficiency of virus attachment under the various culture conditions. This calculated efficiency of virus attachment was observed to decrease at high cell densities, which was attributed to cell clumping. It was also observed that virus attachment was more efficient in Sf900II serum free medium than it was in IPL-41 serum-supplemented medium. This effect was attributed to the protein in serum which may coat the cells and so inhibit adsorption. A general discussion relating the observations made in-these experiments to the kinetics of recombinant baculovirus adsorption to suspended insect cells is presented.

Odorant-induced currents in intact patches from rat olfactory receptor neurons: Theory and experiment

Odorant-induced currents in mammalian olfactory receptor neurons have proved difficult to obtain reliably using conventional whole-cell recording. By using a mathematical model of the electrical circuit of the patch and rest-of-cell, we demonstrate how cell-attached patch measurements can be used to quantitatively analyze responses to odorants or a high (100 mM) K+ solution. High K+ induced an immediate current flux from cell to pipette, which was modeled as a depolarization of similar to 52 mV, close to that expected from the Nernst equation (56 mV), and no change in the patch conductance. By contrast, a cocktail of cAMP-stimulating odorants induced a current flux from pipette into cell following a significant (4-10 s) delay. This was modeled as an average patch conductance increase of 36 pS and a depolarization of 13 mV, Odorant-induced single channels had a conductance of 16 pS. In cells bathed with no Mg2+ and 0.25 mM Ca2+, odorants induced a current flow from cell to pipette, which was modeled as a patch conductance increase of similar to 115 pS and depolarization of similar to 32 mV, All these results are consistent with cAMP-gated cation channels dominating the odorant response, This approach, which provides useful estimates of odorant-induced voltage and conductance changes, is applicable to similar measurements in any small cells.

Host selection in phytophagous insects: a new explanation for learning in adults

Insect learning can change the preferences an egg laying female displays towards different host plant species. Current hypotheses propose that learning may be advantageous in adult host selection behaviour through improved recognition, accuracy or selectivity in foraging. In this paper, we present a hypothesis for when learning can be advantageous without such improvements in adult host foraging. Specifically, that learning can be an advantageous strategy for egg laying females when larvae must feed on more than one plant in order to complete development, if the fitness of larvae is reduced when they switch to a different host species. Here, larvae benefit from developing on the most abundant host species, which is the most likely choice of host for an adult insect which increases its preference for a host species through learning. The hypothesis is formalised with a mathematical model and we provide evidence from studies on the behavioural ecology, of a number of insect species which demonstrate that the assumptions of this hypothesis may frequently be fulfilled in nature. We discuss how multiple mechanisms may convey advantages in insect learning and that benefits to larval development, which have so far been overlooked, should be considered in explanations for the widespread occurrence of learning.

Time of treatment influences the appearance of drug-resistant parasites in Plasmodium falciparum infections

A deterministic mathematical model which predicts the probability of developing a new drug-resistant parasite population within the human host is reported, The model incorporates the host's specific antibody response to PfEMP1, and also investigates the influence of chemotherapy on the probability of developing a viable drug-resistant parasite population within the host. Results indicate that early, treatment, and a high antibody threshold coupled with a long lag time between antibody stimulation and activity, are risk factors which increase the likelihood of developing a viable drug-resistant parasite population. High parasite mutation rates and fast PfEMP1 var gene switching are also identified as risk factors. The model output allows the relative importance of the various risk factors as well as the relationships between them to be established, thereby increasing the understanding of the conditions which favour the development of a new drug-resistant parasite population.

The effect of latent heat of fusion on heat transfer in fluidized-bed coating of thin plates

This paper presents a numerical study of fluidized-bed coating on thin plates using an orthogonal collocation technique. Inclusion of the latent heat of fusion term in the boundary conditions of the mathematical model accounts for the fact that some polymer powders used in coating may be partially crystalline. Predictions of coating thickness on flat plates were made with actual polymers used in fluidized-bed coating. Reasonably good agreement between numerical predictions of the coating thickness and experimental coating data of Richart was obtained for steel panels preheated to 316 degreesC. A good agreement was also obtained between numerical predictions and our coating thickness data for nylon-11 and polyethylene powders. Predicted coating thickness for polyethylene powder on flat plates were obtained with values of heat transfer coefficient closer to those obtained from our experiments. (C) 2002 Elsevier Science B.V. All rights reserved.