11:30 - 12:00 :
Thomas, Peter J. (Department of Mathematics, Department of Biology, Case Western Reserve University)
-Authors: Suparat Chuechote (1), Harihara Baskaran (2,3), Peter Thomas (1,4,5)
(Case Western Reserve University, Departments of (1) Mathematics, (2)Chemical Engineering, (4) Biomedical Engineering, (4) Biology, (5)Cognitive Science)
-Title: Effects of Fluctuations in a 2D Model of Gradient Sensing
Chemotaxis is the directed migration of cells guided by chemical gradients. This process plays a role in embryogenesis, immune response, wound healing and tumor metastasis. During chemotaxis, a cell detects extracellular chemoattractants and translates these signals into a complex cellular response resulting in morphological reorganization and motility. The accuracy with which a cell can determine an external chemical gradient is limited by fluctuations arising from the discrete nature of second messenger release and diffusion processes within the small volume of a living cell. These sources of intrinsic noise have the potential to attenuate or disperse gradient information transduced by the membrane bound receptors. At the same time, models of the intracellular signaling network have been devised that use a combination of local excitation and global inhibition to sharpen the intracellular gradient signal. In this study, we implement a stochastic version one such model, the "balanced inactivation" model (Levine et. al. 2006), in a two dimensional geometry. We develop a fixed timestep approach in which the probabilities of individual molecules making spatial or chemical transitions is treated as a system of multinomial random variables. With this numerical framework we investigate the relationship between the amplification of the gradient signal, the propagation of noise in the signaling pathway, and fundamental limits on the accuracy of the gradient sensing mechanism.
12:00 - 12:30 :
(Los Alamos National Laboratory, Dept of Mathematics, Oakland University)
-Title: Rapid emergence of hepatitis C virus protease inhibitor resistance
Telaprevir, a novel hepatitis C virus (HCV) protease inhibitor, has demonstrated substantial antiviral activity in patients with chronic HCV infection. However, drug-resistant variants emerge at frequencies of 5-20% as early as day 2 after treatment initiation. Using probabilistic and viral dynamic models, we show that such rapid emergence of drug resistance is expected. We calculate that all possible single and double mutants preexist, and that one additional mutation is expected to arise during therapy. Examining the case of telaprevir therapy in detail, we show the model fits observed dynamics of both drug-sensitive and resistant viruses, and argue that combination therapy of direct antivirals will require drug combinations that have a genetic barrier of 4 or more mutations.