Robustness of mathematical models for biological systems

The robustness of mathematical models for biological systems is studied by sensitivity analysis and stochastic simulations. Using a neural network model with three genes as the test problem, we study robustness properties of synthesis and degradation processes. For single parameter robustness, sensitivity analysis techniques are applied for studying parameter variations and stochastic simulations are used for investigating the impact of external noise. Results of sensitivity analysis are consistent with those obtained by stochastic simulations. Stochastic models with external noise can be used for studying the robustness not only to external noise but also to parameter variations. For external noise we also use stochastic models to study the robustness of the function of each gene and that of the system.

Modelling cell lifespan and proliferation: is likelihood to die or to divide independent of age?

In cell lifespan studies the exponential nature of cell survival curves is often interpreted as showing the rate of death is independent of the age of the cells within the population. Here we present an alternative model where cells that die are replaced and the age and lifespan of the population pool is monitored until a, steady state is reached. In our model newly generated individual cells are given a determined lifespan drawn from a number of known distributions including the lognormal, which is frequently found in nature. For lognormal lifespans the analytic steady-state survival curve obtained can be well-fit by a single or double exponential, depending on the mean and standard deviation. Thus, experimental evidence for exponential lifespans of one and/or two populations cannot be taken as definitive evidence for time and age independence of cell survival. A related model for a dividing population in steady state is also developed. We propose that the common adoption of age-independent, constant rates of change in biological modelling may be responsible for significant errors, both of interpretation and of mathematical deduction. We suggest that additional mathematical and experimental methods must be used to resolve the relationship between time and behavioural changes by cells that are predominantly unsynchronized.

A mathematical model of integrin-mediated haptotactic cell migration

Haptotactic cell migration, a directed response to gradients of cell—extracellular matrix adhesion, is an important process in a number of biological phenomena such as wound healing and tumour cell invasion. Previously, mathematical models of haptotaxis have been developed on the premise that cells migrate in response to gradients in the density of the extracellular matrix. In this paper, we develop a novel mathematical model of haptotaxis which includes the adhesion receptors known as integrins and a description of their functional activation, local recruitment and protrusion as part of lamellipodia. Through the inclusion of integrins, the modelled cell matter is able to respond to a true gradient of cell–matrix adhesion, represented by functionally active integrins. We also show that previous matrix-mediated models are in fact a subset of the novel integrin-mediated models, characterised by specific choices of diffusion and haptotaxis coefficients in their model equations. Numerical solutions suggest the existence of travelling waves of cell migration that are confirmed via a phase plane analysis of a simplified model.

Modelling of froth transportation in industrial flotation cells: Part I. Development of froth transportation models for attached particles

Modelling of froth transportation, as part of modelling of froth recovery, provides a scale-up procedure for flotation cell design. It can also assist in improving control of flotation operation. Mathematical models of froth velocity on the surface and froth residence time distribution in a cylindrical tank flotation cell are proposed, based on mass balance principle of the air entering the froth. The models take into account factors such as cell size, concentrate launder configuration, use of a froth crowder, cell operating conditions including froth height and air rate, and bubble bursting on the surface. (C) 2004 Elsevier Ltd. All rights reserved.

Modelling solute transport in structured soils: Performance evaluation of the ADR and TRM models

The movement of chemicals through the soil to the groundwater or discharged to surface waters represents a degradation of these resources. In many cases, serious human and stock health implications are associated with this form of pollution. The chemicals of interest include nutrients, pesticides, salts, and industrial wastes. Recent studies have shown that current models and methods do not adequately describe the leaching of nutrients through soil, often underestimating the risk of groundwater contamination by surface-applied chemicals, and overestimating the concentration of resident solutes. This inaccuracy results primarily from ignoring soil structure and nonequilibrium between soil constituents, water, and solutes. A multiple sample percolation system (MSPS), consisting of 25 individual collection wells, was constructed to study the effects of localized soil heterogeneities on the transport of nutrients (NO3-, Cl-, PO43-) in the vadose zone of an agricultural soil predominantly dominated by clay. Very significant variations in drainage patterns across a small spatial scale were observed tone-way ANOVA, p < 0.001) indicating considerable heterogeneity in water flow patterns and nutrient leaching. Using data collected from the multiple sample percolation experiments, this paper compares the performance of two mathematical models for predicting solute transport, the advective-dispersion model with a reaction term (ADR), and a two-region preferential flow model (TRM) suitable for modelling nonequilibrium transport. These results have implications for modelling solute transport and predicting nutrient loading on a larger scale. (C) 2001 Elsevier Science Ltd. All rights reserved.

Computational immunology: The coming of age

The explosive growth in biotechnology combined with major advancesin information technology has the potential to radically transformimmunology in the postgenomics era. Not only do we now have readyaccess to vast quantities of existing data, but new data with relevanceto immunology are being accumulated at an exponential rate. Resourcesfor computational immunology include biological databases and methodsfor data extraction, comparison, analysis and interpretation. Publiclyaccessible biological databases of relevance to immunologists numberin the hundreds and are growing daily. The ability to efficientlyextract and analyse information from these databases is vital forefficient immunology research. Most importantly, a new generationof computational immunology tools enables modelling of peptide transportby the transporter associated with antigen processing (TAP), modellingof antibody binding sites, identification of allergenic motifs andmodelling of T-cell receptor serial triggering.

Analysis of dynamic process models for structural insight and model reduction .1. Structural identification measures

An important consideration in the development of mathematical models for dynamic simulation, is the identification of the appropriate mathematical structure. By building models with an efficient structure which is devoid of redundancy, it is possible to create simple, accurate and functional models. This leads not only to efficient simulation, but to a deeper understanding of the important dynamic relationships within the process. In this paper, a method is proposed for systematic model development for startup and shutdown simulation which is based on the identification of the essential process structure. The key tool in this analysis is the method of nonlinear perturbations for structural identification and model reduction. Starting from a detailed mathematical process description both singular and regular structural perturbations are detected. These techniques are then used to give insight into the system structure and where appropriate to eliminate superfluous model equations or reduce them to other forms. This process retains the ability to interpret the reduced order model in terms of the physico-chemical phenomena. Using this model reduction technique it is possible to attribute observable dynamics to particular unit operations within the process. This relationship then highlights the unit operations which must be accurately modelled in order to develop a robust plant model. The technique generates detailed insight into the dynamic structure of the models providing a basis for system re-design and dynamic analysis. The technique is illustrated on the modelling for an evaporator startup. Copyright (C) 1996 Elsevier Science Ltd

Proliferation, apoptosis, and survival in high-level microsatellite instability sporadic colorectal cancer

Sporadic colorectal cancer (CRC) characterized by high-level DNA microsatellite instability (MSI-H) has a favorable prognosis. The reason for this MSI-H survival advantage is not known. The aim of this study was to correlate proliferation, apoptosis, and prognosis in CRC stratified by MSI status. The proliferative index (PI) was measured by immunohistochemical staining with the Ki-67 antibody in a selected series of 100 sporadic colorectal cancers classified according to the level of MSI as 31 MSI-H, 29 MSI-Low (MSI-L), and 40 microsatellite stable (MISS). The Ki-67 index was significantly higher in MSI-H cancers (P < 0.0001) in which the PI was 90.1 1.2% (mean +/- SE) compared with 69.5 +/- 3.1 % and 69.5 +/- 2.3 % in MSI-L and MSS subgroups, respectively. There was a positive linear correlation between the apoptotic index (AI) and PI (r = 0.51; P < 0.001), with MSI-H cancers demonstrating an increased AI:PI ratio indicative of a lower index of cell production. A high PI showed a trend toward predicting improved survival within MSI-H cancers (P = 0.09) but did not predict survival in MSI-L or MSS cancers. The Al was not associated with survival in any MSI subgroup. In conclusion, this is the first study to show that sporadic MSI-H cancers are characterized by a higher AL:PI ratio and increased proliferative activity compared with MSI-L and MSS cancers, and that an elevated PI may confer a survival advantage within the MSI-H subset.

Apoptosis and Expression of Bcl-2, Bcl-XL, and Bax in Renal Cell Carcinomas

There are at present disparate published results with regard to the relevance of the Bcl-2 gene family, levels of apoptosis, and cell proliferation in the development and progression of renal cell carcinoma (RCC). The present study v analyses the interrelationship between the expression of representatives of the anti-apoptotic (Bcl-2, Bcl-X-L) or pro-apoptotic (Bax) Bcl-2 proteins, incidence of apoptosis, and mitosis in a selected small group of 22 graded RCCs that had paired normal renal tissue, or non-neoplastic tissue in the renal biopsy specimen. The cases were chosen to determine the feasibility of measuring these parameters as potential surrogate markers of progression or treatment failure of the cancers. The results showed that in approximately 50% of the RCCs, where Bcl-2 and/or Bcl-X-L expression was high, apoptosis it-as not detected, and when expression of these proteins was low or not found, increased levels of apoptosis were seen. In most of the remaining 50% of samples, high levels of Bcl-X-L but not Bcl-2 were negatively correlated with low levels of apoptosis (Bcl-X-L: r = -0.437, P = 0.07 and Bcl-2: r = + 0.560, P = 0.02). For the same group of samples, high Bax expression was found in association with apoptosis (r = + 0.578, P = 0,02). A novel finding was an association between low expression of Bcl-2 an/or Bcl-X-L in normal tissue and the level of expression of these proteins in the RCCs, an intrinsic variation that may be an individual patient factor. The results indicate that, in RCCs with increased expression of Bcl-2 and/or Bcl-X-L, levels of apoptosis are minimal and these combined factors may assist in progression of the cancers and resistance to treatments.

Identification of T cell epitopes on the 33-kDa fragment of Plasmodium yoelii merozoite surface protein 1 and their antibody-independent protective role in immunity to blood stage malarial

Merozoite surface protein 1 (MSP1) of malaria parasites undergoes proteolytic processing at least twice before invasion into a new RBC. The 42-kDa fragment, a product of primary processing, is cleaved by proteolytic enzymes giving rise to MSP1(33), which is shed from the merozoite surface, and MSP1(19), which is the only fragment carried into a new RBC. In this study, we have identified T cell epitopes on MSP1(33) of Plasmodium yoelii and have examined their function in immunity to blood stage malaria. Peptides 20 aa in length, spanning the length of MSP1(33) and overlapping each other by 10 aa, were analyzed for their ability to induce T cell proliferation in immunized BALB/c and C57BL/6 mice. Multiple epitopes were recognized by these two strains of mice. Effector functions of the dominant epitopes were then investigated. Peptides Cm15 and Cm21 were of particular interest as they were able to induce effector T cells capable of delaying growth of lethal P. yoelii YM following adoptive transfer into immuno-deficient mice without inducing detectable Ab responses. Homologs of these epitopes could be candidates for inclusion in a subunit vaccine.

Establishment and characterization of a new epithelial cell line, KC-1, from koala (Phascolarctos cinereus) conjunctiva

A novel, untransformed koala cell line (KC-1) was established by culturing koala conjunctival tissue in growth medium, which has permitted the study of the cell biology of this unique system. After the establishment of the KC-1 cell line, the cells were characterized by light microscopy, doubling time, and Western blot analysis. Light microscopy revealed that the cells have an epithelial morphology. Doubling times were significantly different (P < 0.015) depending on fetal calf serum (FCS) concentration (16.5 h in 10% FCS and 26.5 h in 2% FCS). Cells constricted while in suspension but were shown to attach to the coverslip (or flask) and flatten rapidly, less than 1 h after seeding. To confirm the epithelial nature of the cells, protein was extracted and Western blot analysis was performed. Subsequent probing with primary and secondary antibodies (monoclonal anticytokeratin clone C-11 IgG1 and anti-mouse IgG) revealed two bands at 45 and 52 kDa (compared against a protein molecular weight marker) that correspond to primary type I keratin and major type II keratin, respectively, expressed in simple epithelial cells. The koala cell line was adapted to grow continuously in Dulbecco modified Eagle medium containing 10% FCS for at least 30 passages. This unique cell line is an ideal toot for further investigation on koala cell biology and cytogenetics and for exploration of the pathophysiological mechanism of eye infections caused by different pathogens in koalas.

Erythropoietin protects against ischaemic acute renal injury

Erythropoietin (EPO) has recently been shown to exert important cytoprotective and anti-apoptotic effects in experimental brain injury and cisplatin-induced nephrotoxicity. The aim of the present study was to determine whether EPO administration is also renoprotectivein both in vitro and in vivo models ofischaemic acute renal failure Methods. Primary cultures of human proximal tubule cells (PTCs) were exposed to either vehicle or EPO (6.25–400 IU/ml) in the presence of hypoxia (1% O2), normoxia (21% O2) or hypoxia followed by normoxia for up to 24 h. The end-points evaluated included cell apoptosis (morphology and in situ end labelling [ISEL], viability [lactate dehydrogenase (LDH release)], cell proliferation [proliferating cell nuclear antigen (PCNA)] and DNA synthesis (thymidine incorporation). The effects of EPO pre-treatment (5000 U/kg) on renal morphology and function were also studied in rat models of unilateral and bilateral ischaemia–reperfusion (IR) injury. Results. In the in vitro model, hypoxia (1% O2) induced a significant degree of PTC apoptosis, which was substantially reduced by co-incubation with EPO at 24 h (vehicle 2.5±0.5% vs 25 IU/ml EPO 1.8±0.4% vs 200 IU/ml EPO 0.9±0.2%, n = 9, P

An in vivo comparative study of sonic, desert and Indian hedgehog reveals that hedgehog pathway activity regulates epidermal stem cell homeostasis

Despite the well-characterised role of sonic hedgehog (Shh) in promoting interfollicular basal cell proliferation and hair follicle downgrowth, the role of hedgehog signalling during epidermal stem cell fate remains largely uncharacterised. In order to determine whether the three vertebrate hedgehog molecules play a role in regulating epidermal renewal we overexpressed sonic (Shh), desert (Dhh) and Indian (Ihh) hedgehog in the basal cells of mouse skin under the control of the human keratin 14 promoter. We observed no overt epidermal morphogenesis phenotype in response to Ihh overexpression, however Dhh overexpression resulted in a range of embryonic and adult skin manifestations indistinguishable from Shh overexpression. Two distinct novel phenotypes were observed amongst Shh and Dhh transgenics, one exhibiting epidermal progenitor cell hyperplasia with the other displaying a complete loss of epidermal tissue renewal indicating deregulation of stem cell activity. These data suggest that correct temporal regulation of hedgehog activity is a key factor in ensuring epidermal stem cell maintenance. In addition, we observed Shh and Dhh transgenic skin from both phenotypes developed lesions reminiscent of human basal cell carcinoma (BCC), indicating that BCCs can be generated despite the loss of much of the proliferative (basal) compartment. These data suggest the intriguing possibility that BCC can arise outside the stem cell population. Thus the elucidation of Shh (and Dhh) target gene activation in the skin will likely identify those genes responsible for increasing the proliferative potential of epidermal basal cells and the mechanisms involved in regulating epidermal stem cell fate.