HW01

Introduction to Systems Biology

(10 points) Find a paper in the literature in which a mechanistic mathematical or computational model of a biological system was used in conjunction with experimental approaches to make new discoveries. Write a paragraph presenting the following the following: (1) the system being studied, (2) the assumptions of the model, (3) the machinery used to analyze the model and draw conclusions, and (4) the key findings that arose from the study. Did the model contribute to the key findings of the study - why or why not? Please provide the complete reference to the paper you choose and a link, e.g.

[1] H. Mukhopadhyay, S.-P. Cordoba, P. K. Maini, P. A. van der Merwe, and O. Dushek, “Systems model of T cell receptor proximal signaling reveals emergent ultrasensitivity.,” PLoS Comput. Biol., 9, e1003004. (link)

Here is an example from a previous year (your writeup need not be quite this detailed):

Bar-Or, Ruth Lev, et al. ”Generation of oscillations by the p53-Mdm2 feedback loop: a theoretical and experimental study.” Proceedings of the National Academy of Sciences 97.21 (2000): 11250-11255.

The model consists of a series of ordinary differential equations describing the feedback loop between p53 and Mdm2, in which p53 positively induces Mdm2 (through transcription enhancement of the gene mdm2) after a delay, which in turn negatively influences p53 production as well as p53-dependent Mdm2 up-regulation. Stress conditions are assumed to lead to an increase in p53 activation and decrease in Mdm2-mediated p53 degradation. It is also assumed that these stress conditions (such as DNA damage) are relieved at a specific rate. The delay in up-regulation of Mdm2 by p53 is included in the model by a hypothetical intermediate state I between the two. In addition the model includes synthesis rates for both p53 and Mdm2, independent of their effects on one another. Numerically solving this series of differential equations under certain conditions leads to damped, coordinated oscillations of p53 and Mdm2. After an initial pulse of stress, p53 levels increase to a peak, at which time Mdm2 levels begin to increase and p53 drops. The local maximums of Mdm2 are approximately aligned with the local minimums of p53, and vice versa. These damped oscillations eventually disappear and the proteins return to their basal levels. Experimental results confirmed the model predictions by displaying the coordinated p53 and Mdm2 oscillations in wild-type cells which have experienced DNA damage. The model also demonstrated that the delay in p53-mediated Mdm2 up-regulation and an intermediate range for the parameters which dictate the interactions between p53 and Mdm2 are both critical to the production of the oscillations. A study of the dependence of the oscillations on the parameters, specifically the delay time, suggests a reason for the oscillatory behavior in cells. The authors suggest that the oscillations allow for repeated repair efforts by the cell without constitutive overexpression of p53, which leads to apoptosis. The oscillations therefore keep p53 within an intermediate range, and allow for short bursts of repair attempts, until the stress signal has subsided. Further, the authors posit that the exact quantitative parameters are likely dependent on cell type and species, though the general oscillatory mechanism is conserved across these different cases.

Introduction to Modeling

The modeling problem is in this pdf. It is worth 10 points.

BioNumbers

The two problems for this lecture are in this pdf. Each of the two problems is worth 5 points.