Duke Probability Seminar
A seminar for the probability community at Duke, both in and outside of the Mathematics Department.
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Upcoming Seminars:
- Thursday, April 25, 2024, 3:15pm, Physics 119, Probability Seminar
KPZ equation from driven lattice gases
Kevin Yang (Harvard University)
- We will discuss a family of exclusion processes in one spatial dimension, where the random walk particles feel a speed-changed drift coming from an external “force field”. We show that their height functions have large-N limit given by the KPZ equation with homogenized transport operator coming from the speed-change. A similar result is shown for another type of driven lattice gas, where the particles are in contact with two external reservoirs. In this case, we derive an “open” KPZ equation limit and answer a question of Corwin ‘22.
- Friday, April 26, 2024, 12:00pm, Physics 119, Mathematical Biology Seminar
Spatial Jump Process Models for Estimating Antibody-Antigen Interactions
Samuel Isaacson (Boston University, Mathematics and Statistics)
- Surface Plasmon Resonance (SPR) assays are a standard approach for quantifying kinetic parameters in antibody-antigen binding reactions. Classical SPR approaches ignore the bivalent structure of antibodies, and use simplified ODE models to estimate effective reaction rates for such interactions. In this work we develop a new SPR protocol, coupling a model that explicitly accounts for the bivalent nature of such interactions and the limited spatial distance over which such interactions can occur, to a SPR assay that provides more features in the generated data. Our approach allows the estimation of bivalent binding kinetics and the spatial extent over which antibodies and antigens can interact, while also providing substantially more robust fits to experimental data compared to classical bivalent ODE models. I will present our new modeling and parameter estimation approach, and demonstrate how it is being used to study interactions between antibodies and spike protein. I will also explain how we make the overall parameter estimation problem computationally feasible via the construction of a surrogate approximation to the (computationally-expensive) particle model. The latter enables fitting of model parameters via standard optimization approaches.
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