Projects QB4

A variety of group projects will be proposed and discussed in the first few days of class. Students are also encouraged to bring their own project ideas. It is noteworthy that often these projects will continue beyond the time of the school itself, and it is hoped that in some cases the project results will be published in the peer-reviewed literature.

Here we describe potential projects that school faculty are interested in.

1. Moment closure as an approximation to solving stochastic systems

Moment closure techniques are an appealing approximation of stochastic systems to avoid time consuming stochastic simulations, as they are ordinary differential equations that approximate the mean and an arbitrary number of higher order moments. One of the key ingredients in those techniques is the choice of an accurate underlying distribution that helps to perform the closure of the equations. In this project, it is proposed the quantification of such distribution numerically (using stochastic simulations) in the case of a SIR model when the basic reproduction number close to unity (as in the case of influenza epidemics).

[1] Van Kampen, N. G. (1992). Stochastic processes in physics and chemistry(Vol. 1). Access Online via Elsevier.

[2] Gillespie, C. S. (2009). Moment-closure approximations for mass-action models. IET systems biology, 3(1), 52-58.

[3] Pearson, J. E., Krapivsky, P., & Perelson, A. S. (2011). Stochastic theory of early viral infection: Continuous versus burst production of virions. PLoS computational biology, 7(2), e1001058.

[4] Allen, L. J., & Burgin, A. M. (2000). Comparison of deterministic and stochastic SIS and SIR models in discrete time. Mathematical biosciences,163(1), 1-33.

[5] Currie, J., Castro, M., Lythe, G., Palmer, E., & Molina-París, C. (2012). A stochastic T cell response criterion. Journal of The Royal Society Interface,9(76), 2856-2870.

2. Stochastic models of T cell division and death

Quantitative understanding of the kinetics of lymphocyte proliferation and death upon activation with an antigen is crucial for elucidating factors determining the magnitude, duration and efficiency of the immune response. Recent advances in quantitative experimental techniques, in particular intracellular labeling and multi-channel flow cytometry, allow one to measure the population structure of proliferating and dying lymphocytes for several generations with high precision. These new experimental techniques require novel quantitative methods of analysis. In Zilman et al [1] a rigorous mathematical framework is used to analyze cellular proliferation, using theories of age-structured cell populations and of branching processes.

In this project, we would like to develop a user friendly (interactive) application to run the stochastic models proposed in [1], such that different hypothesis of T-cell proliferation can be easily explored and compared with data.

[1] Zilman A, Ganusov, VV, Perelson AS (2010) Stochastic Models of Lymphocyte Proliferation and Death. PLoS ONE 5(9): e12775. doi:10.1371/journal.pone.0012775

3. Broadly neutralizing antibody problem

Several research teams have presented results on the construction of broadly neutralizing antibodies. However, the theory of the role of broadly neutralizing antibody remains underdeveloped, obscuring the best paths forward for vaccine design. Some authors have proposed a theoretical model predicting that interference from strain-specific antibody responses could prevent a broadly-neutralizing antibody response from clearing HIV infection, even though such a response would clear an infection in isolation. An alternative hypothesis is that the regulation of antibody responses is such that the efficacy of broadly neutralizing antibody is unaffected (independent) of strain-specific responses. This project is to theoretically explore the predicted hurdles to vaccine development and possible ways around these hurdles.

Vaccines:

[1] doi:10.1126/science.1187659 DOI finder

[2] doi:10.1126/science.1194693 DOI finder

[3] doi:10.1126/science.1192819 DOI finder

[4] doi:10.1126/science.1207227 DOI finder

[5] doi:10.1126/science.1211919 DOI finder

Theory:

[1] doi:10.1016/j.jtbi.2011.01.050 DOI finder

[2] doi:10.1098/rspb.2012.0005 DOI finder

4. Models of HCV replication in primary infection

Hepatitis C virus (HCV) is present in the host as a quasi-species with multiple variants generated by its error prone RNA-dependent RNA polymerase. Little is known about the initial viral diversification and the viral life cycle processes that influence diversity. We have recently developed a new stochastic model of the HCV life cycle, and now would like to explore different variants and processes that may contribute to HCV diversification during acute infection.

The model was originally coded in R and will need to be converted to C++ so that it can run faster and that alternative processes can be efficiently explored. The relevant questions include the role of target cell limitation, effects of immune responses, variation in parameter values in the dynamics of virus growth and viral diversification.

[1] Ribeiro RM, et al. (2012) Quantifying the Diversification of Hepatitis C Virus (HCV) during Primary Infection: Estimates of the In Vivo Mutation Rate. PLoS Pathog 8(8): e1002881. doi:10.1371/journal.ppat.1002881

5. Pharmocokinetics for PrEP

PrEP (pre-exposure prophylaxis) is can be used to help prevent HIV infection in situations where risk of infection is elevated. But we don't yet know how the time-window of PrEP should be chosen in response to a known window of risk. How soon before travelling should one start PrEP, and how long after returning should one continue it? Let's figure out what the right recommendations should be.

[1] Conway J et al. Stochastic analysis of pre- and postexposure prophylaxis against HIV infection. SIAM J. Appl. Math. 73: 904.