Model of HIV pathogenesis in HIV-infected individuals under very general conditions. In this model, we have considered five different types of CD4(+) T cells, two different types of HIV (M-tropic versus T-tropic) as well as infected and un-infected macrophage. This is a 9-dimensional stochastic process. For this process, we have developed stochastic differential equations for different types of cells. By using these stochastic equations, we have generated some Monte Carlo data to study the stochastic behavior of the HIV pathogenesis and the HIV progression.Through Monte Carlo studies, we have revealed an acute infection stage in the early stage of the HIV infection and have confirmed the basic role played by lymph nodes and some long-lived cells such as macrophage in serving as reservoirs of HIV to escape elimination by the immune system during the long asymptomatic stage of HIV infection. The Monte Carlo results have shown that the HIV heterogeneity and diversity may be a major factor to determine the time period since infection for uninfected T cells to drop to below 200/mm3 of blood. The numerical results have also confirmed our previous findings (see [1]) which concluded that the probability distributions of T cells and free HIV can be classified into three periods over time: The latent period, the transition period and the pseudo-steady period.

Wai-Yuan Tan

Zhengzheng Ye

Assessing Effects of HIV Heterogeneity and Macrophage on the HIV Pathogenesis in HIV-Infected Individuals

The proliferation of eukaryotic cells is driven by a process called the cell cycle. Proper regulation of this process, leading to orderly execution of sequential steps within the cycle, ensures normal development and homeostasis of the organism. On the other hand, perturbations of the cell cycle are frequently attributed to cancer cells. Mechanisms that ensure the order and fidelity of events in the cell cycle are called checkpoints. The checkpoints induced by damaged DNA delay the cell cycle progression, providing more time for repair of lesion before DNA replication and segregation. The DNA damage-induced checkpoints can be recognized as signal transduction pathways that communicate information between DNA lesion and components of the cell cycle. Proteins involved in the cell cycle, as well as components of the signal transduction pathways communicating with the cell cycle, are frequently products of oncogenes and tumor suppressor genes. Malfunction of these genes plays a critical role in the development of human cancers. The key component in the checkpoint machinery is tumor suppressor gene p53, involved in either regulation of the cell cycle progression (e.g. Gl arrest of cells treated with DNA damaging factor) or activation of programmed cell death (apoptosis). It is postulated that p53 protein is activated by DNA damage detectors. One of the candidates for this role is DNA-dependent protein kinase (DNA-PK) which recognizes DNA strand breaks and phosphorylates p53 protein.

Piotr Widlak

The DNA Damage-Induced Cell Cycle Checkpoints

Development in molecular biology have resulted in very significant increase in the volume of data available to scientists. Handling and modelling there data requires electronic tools, for which world-wide access via the internet is essential. This paper summarises contributions on this area to a summer school organiser in magdeling in September 1999.

Ralf Hofest&#xe4;dt

Summer School Bioinformatics &#8212; Information Systems and Network Analysis of Gene Regulation and Metabolism

B. D. Sleeman

Editorial

Dose response curves show that prolonged drug exposure at a low concentration may kill more cells than short exposures at higher drug concentrations, particularly for cell cycle phase specific drugs. Applying drugs at low concentrations for prolonged periods, however, allows cells with partial resistance to evolve higher levels of resistance through stepwise processes such as gene amplification. Models are developed for cell cycle specific (CS) and cell cycle nonspecific (CNS) drugs to identify the schedule of drug application that balances this tradeoff.The models predict that a CS drug may be applied most effectively by splitting the cumulative dose into many (&gt;40) fractions applied by long-term chemotherapy, while CNS drugs may be better applied in fewer than 10 fractions applied over a shorter term. The model suggests that administering each fraction by continuous infusion may be more effective than giving the drug as a bolus, whether the drug is CS or CNS. In addition, tumors with a low growth fraction or slow rate of cell division are predicted to be controlled more easily with CNS drugs, while those with a high proliferative fraction or fast cell division rate may respond better to CS drugs.

Shea N. Gardner

Scheduling Chemotherapy: Catch 22 between Cell Kill and Resistance Evolution

To contribute to the development of more effective aerosol therapy protocols in pediatric medicine, we examined airflow patterns in the lung of a four-year-old child. In particular, we addressed how the presence of tumors in airways affected the character of airflow patterns. To study the effects of tumors we employed a computational fluid dynamics package, FIDAP, to define flow conditions within a model lung. The results indicated that tumors have a pronounced affect on both (i) localized velocity profiles in airways and (ii) bulk flow distribution within the lung. By identifying the effects of physical factors on flow conditions the findings will lead to improved drug delivery regimens.

R. A. Segal

X. Guan

M. Shearer

T. B. Martonen

Mathematical Model of Airflow in the Lungs of Children I: Effects of Tumor Sizes and Locations

In this paper we present a simple mathematical model for angiogenesis in wound healing and then compare the results of theoretical predictions from computer simulations with actual experimental data. Numerical simulations of the model equations exhibit many of the characteristic features of wound healing in soft tissue. For example, the steady propagation of the wound healing unit through the wound space, the development of a dense band of capillaries near the leading edge of the unit, and the elevated vessel density associated with newly healed wounds, prior to vascular remodelling, are all discernible from the simulations. The qualitative accuracy of the initial model is assessed by comparing the numerical results with independent clinical measurements that show how the surface area of a range of wounds changes over time. The model is subsequently modified to include the effect of vascular remodelling and its impact on the spatio-temporal structure of the vascular network investigated. Predictions are made concerning the effect that changes in physical parameters have on the healing process and also regarding the manner in which remodelling is initiated.

H. M. Byrne

M. A. J. Chaplain

D. L. Evans

I. Hopkinson

Mathematical Modelling of Angiogenesis in Wound Healing: Comparison of Theory and Experiment

Earlier mathematical models of the authors which describe avascular tumour growth are extended to incorporate the process of cell shedding, a feature known to affect the growth of multicell spheroids. A continuum of live cells is assumed within which, depending on the concentration of a generic nutrient, movement (described by a velocity field) occurs due to volume changes caused by cell birth and death. The necrotic material is assumed to contain a mixture of basic cellular material (assumed necessary for creating new cells) and a non-utilisable material which may inhibit mitosis. The rate of cell shedding is taken to be proportional to the mitotic rate, with constant of proportionality θ. Numerical solutions of the resulting system of partial differential equations indicate that, depending on θ and the initial conditions, the solution may either tend to the trivial state in finite time (by which we mean complete death of the tumour), or to one of two non-trivial states, namely a steady-state (indicating growth saturation) or a travelling wave (indicating continual linear growth). These long time outcomes are explored by deriving the travelling wave and steady-state limits of the model. Numerical solutions demonstrate that there are two branches of solutions, which we have termed the ′Major′ and ′Minor′ branches, consisting of both travelling waves and steady-states. The behaviour of the solutions along each branch is discussed, with those of the Major branch expected to be stable. Beyond some critical θ,where the Major and Minor branches merge, the spheroid ultimately vanishes whatever the initial tumour size due to the effects of cell shedding being too strong for it to survive. The regions of existence of the two long time outcomes are investigated in parameter space, cell shedding being shown to expand significantly the parameter ranges within which growth saturation occurs.

J. P. Ward

J. R. King

Modelling the Effect of Cell Shedding on Avascular Tumour Growth

In this paper we present two types of mathematical model which describe the invasion of host tissue by tumour cells. In the models, we focus on three key variables implicated in the invasion process, namely, tumour cells, host tissue (extracellular matrix) and matrix-degradative enzymes associated with the tumour cells. The first model focusses on the macro-scale structure (cell population level) and considers the tumour as a single mass. The mathematical model consists of a system of partial differential equations describing the production and/or activation of degradative enzymes by the tumour cells, the degradation of the matrix and the migratory response of the tumour cells. Numerical simulations are presented in one and two space dimensions and compared qualitatively with experimental and clinical observations. The second type of model focusses on the micro-scale (individual cell) level and uses a discrete technique developed in previous models of angiogenesis. This technique enables one to model migration and invasion at the level of individual cells and hence it is possible to examine the implications of metastatic spread. Finally, the results of the models are compared with actual clinical observations and the implications of the model for improved surgical treatment of patients are considered.

A. R. A. Anderson

E. L. Newman

R. J. C. Steele

A. M. Thompson

Mathematical Modelling of Tumour Invasion and Metastasis

Patients with Insulin-Dependent Diabetes are continuously involved in a clinical optimization process: to maintain strict glycemic control without increasing their risk for hypoglycemia. This study offers quantitative tools for on-line assessment of the quality of this optimization, based on self-monitoring of blood glucose (SMBG). Ninety-six adults with Insulin Dependent Diabetes Mellitus (IDDM), age 35 ± 8 yrs., duration of diabetes 16 ± 10 yrs., HbAlc 8.6 ± 1.8%, 43 of whom had a recent history of severe hypoglycemia (SH), while 53 did not, used Lifescan One Touch II meters for 135 ± 53 SMBG readings over a month. For the following six months the subjects recorded occurrence of SH. The two patient groups, with and without a history of SH, did not differ in age, duration of diabetes, HbAlc, insulin units/day, average BG or BG variability. We suggest a computational procedure based on a symmetrization of the BG measurement scale and on a superimposed BG risk function, that allows for computation of two glycemic control markers: the Low BG Index (LBGI) and the High BG Index (HBGI). The LBGI is associated with SH: the LBGI and the rate of change of the BG risk, classified correctly 77% of the subjects with vs. without a history of SH and accounted for 46% of the variance of future SH. The HBGI, in combination with age, duration of diabetes and daily insulin dose, accounted for 57% of the variance of patients' glycosylated hemoglobin. We conclude that the LBGI and the HBGI are accurate on-line SMBG measures for patients' glycemic control.

Boris P. Kovatchev

Martin Straume

Daniel J. Cox

Leon S. Farhy

Risk Analysis of Blood Glucose Data: A Quantitative Approach to Optimizing the Control of Insulin Dependent Diabetes

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Computational and Mathematical Methods in Medicine