Second q-bio Summer School: Other Topics in Biological Modeling

Lecture 1

Scope

Modeling Viral Dynamics, Part I: How to model HIV Infection

Lecturer

Alan Perelson

Abstract

Mathematical modeling of HIV infection has lead to asignificant dvances in our knowledge about HIV and its treatment. This lecture will provide a tutorial about how one goes from data to developing models that have practical utility. Modeling will involve ordinary differential equations. The basic biology of HIV will be reviewed as well as the action of drugs used in therapy. If you have questions about HIV/AIDS this would be good venue to ask them.

References

Perelson, A. S. and Nelson, P. (1999). Mathematical analysis of HIV-1 dynamics in vivo. SIAM Rev. 41, 3-44.

Callaway, D. S. and Perelson, A. S. (2002). HIV-1 infection and low steady-state viral loads. Bull. Math. Biol. 64, 29–64.

Perelson, A. S. (2002). Modelling viral and immune system dynamics. Nature Rev. Immunol. 2, 28-36.

Rong, L., Feng, Z. and Perelson, A. S. (2007). Mathematical analysis of age-structured HIV-1 dynamics with combination therapy. SIAM J. Appl. Math. 67, 731-756.

Lecture 2

Scope

Modeling Viral Dynamics, Part II: Dynamics of CD4+ T cells in HIV-1 Infection

Lecturer

Ruy Ribeiro

Abstract

Mathematical modeling is becoming established in the immunologist’s toolbox as a method to gain insight into the dynamics of the immune response and its components. No more so than in the case of the study of human immunodeficiency virus (HIV) infection, where earlier work on the viral dynamics brought significant advances in our understanding of HIV replication and evolution. Here, I review different areas of the study of the dynamics of CD4+ T-cells in the setting of HIV, where modeling played important and diverse roles in helping us understand CD4+ T-cell homeostasis and the effect of HIV infection. Modeling has been applied to understand experiments labeling dividing cells with the objective of quantifying the turnover of CD4+ T-cells in health and infection; as well, models of thymic production have been crucial to define rigorously the de novo production of T-cells in primates. As the experimental techniques become more accurate and quantitative, modeling should play a more important part in both experimental design and data analysis.

References

1. Ribeiro RM “Dynamics of CD4+ T-cells in HIV-1 infection”, Immunology and Cell Biology 85: 287 (2007)

2. Ribeiro RM & Perelson AS “Determining thymic output quantitatively: using models to interpret experimental T-cell receptor excision circle (TREC) data”, Immunological Reviews 216: 21 (2007)

3. Asquith B et al. “Lymphocyte kinetics: the interpretation of labelling data”, Trends in Immunology 23: 596 (2002)

Problem

In T-cell labeling experiments, performed to infer the turnover of these cells, the contribution of new production from the thymus is often not included. In this case, the dynamics of T-cells in the periphery is modeled by a simple set of differential equations (such as those presented in reference 1 above). Assume that the thymus behaves as a conveyor belt, corresponding to the maturation of T-cells, where some proliferation occurs. Thus, during maturation some cells will pick up label. Write a model or a simulation for the fraction of labeled cells in the periphery that takes into account both peripheral division and input from a conveyor-belt type thymus. Discuss any differences observed in the label profiles in relation to the simple periphery-only model.

Lecture 3

Scope

Modeling Cancer Development, Part I Experimental models

Lecturer

[ James Freyer]

Abstract

A solid tumor in a human is arguably one of the most unique, complex and chaotic biological systems in existence. Contributing greatly to this complexity is the highly heterogeneous tumor microenvironment, which has both spatial and temporal variations in an unaccountably large number of parameters (extracellular chemistry, cellular physiology, metabolism, gene expression and protein composition, to name a few). Unfortunately, this unique microenvironment has numerous adverse effects on the response of a tumor to essentially every therapy that has been devised to date. Thus, improving our understanding of this extremely complex biological system will have benefits for cancer therapy as well as for basic biology. An increasingly important tool in this field is the use of model systems, both experimental and theoretical. This lecture will start with a basic description of the tumor microenvironment, including mechanisms behind the heterogeneity, recent advances in assaying the microenvironment, and impacts on cancer therapy. This will be followed by a description of three-dimensional (3-D) experimental tumor models, focusing on the multicellular spheroid that we use in our laboratory. Two examples of our recent experimental work with spheroids will demonstrate how this system can be used to answer basic questions on the regulation of the cell cycle and protein expression. A new application for spheroids will be presented, along with a new experimental model system we have under development. The lecture will conclude with a description of theoretical models used to describe tumor growth and the tumor microenvironment, including an introduction to a multiscale model developed at Los Alamos that will be presented in much more detail in a subsequent lecture in this series.

Lecture 4

Scope

Modeling Cancer Development, Part II Multiscale cell-based models

Lecturer

Yi Jiang

Abstract

Cancer has become the leading cause of disease death for middle aged Americans. At the same time, after a quarter century of rapid advances, cancer research has generated a rich and complex body of knowledge. We have developed a cell-based, multiscale modeling framework to model cancer development based on this body of knowledge. Our model includes a cellular model for cell dynamics (cell growth, division, death, migration and adhesion), an intracellular protein regulatory network for cell cycle control and a signaling network for cell decision-making, and extracellular reaction-diffusion chemical dynamics. This model has produced avascular tumor growth dynamics that agree with tumor spheroid experiments; it has generated realistic sprout patterns in tumor-induced angiogenesis; it has also shown potential for investigating chemotherapeutic strategies for tumor. Given the biological flexibility of the model, we believe that it can facilitate a deeper understanding of the cellular and molecular interactions associated with cancer progression and treatment, and potentially guide experimental design and interpretation.

References

1.Yi Jiang, Jelena Pjesivac, Charles Cantrell and James Freyer, "A Multiscale Model for Avascular Tumor Growth ", Biophysical Journal , vol. 89, pp. 3873--3883, 2005

2.Amy Bauer, Trachette Jackson and Yi Jiang, "A Cell-Based Model Exhibiting Branching and Anastomosis During Tumor-Induced Angiogenesis", Biophysical Journal , vol. 92, pp. 3105--3121, 2007

Lecture 5

Scope

Protein dynamics

Lecturer

Hans Frauenfelder

Abstract

Proteins are involved in essentially every biological reaction. In texts they are usually shown just as X-ray diffraction reveals them, namely rigid, without hydration shell and bulk solvent. Proteins are, however, dynamic systems that continuously fluctuate and the fluctuations are essential for functions. The lecture will discuss two concepts that are the basis for understanding the dynamics, namely the existence of an energy landscape and the influence of the hydration shell and the bulk solvent.

Lecture 6

Scope

Random Walk Techniques in Quantitative Biology: Molecules to Mice

Lecturer

Nitant Kenkre

Abstract

Random Walk techniques, equivalently Master equation methods, will be introduced and applied to a quantitative description of biological systems on a wide variety of scales: transmembrane molecules diffusing in cells, bacteria moving in Petri dishes, and rodents traversing the landscape in the context of the Hantavirus epidemic. A brief exposition to effective medium theories and nonlinearities in diffusion equations will be included in the lecture.

Lecture 7

Scope

 ??

Lecturer

[Cliff Unkefer]

Lecture 8

Scope

Lecturer

[Pat Unkefer]

Lecture 9

Scope

Molecular Simulation Techniques: Kinetic Monte Carlo, Accelerated Molecular Dynamics

Lecturer

Art Voter

Lecture 10

Scope

Manipulation of biological systems in controlled environments

Lecturer

Robert H. Austin