Michaëlle Mayalu, Jan 2017
Michaëlle Mayalu from MIT will visit on 23-24 January.
23 Jan (Mon)
24 Jan (Tue)
Reduced-order Systems Approach to Prediction of Emergent Behaviors
Michaëlle N. Mayalu
Massachusetts Institute of Technology
Monday, January 23, 2017
12-1 pm, 121 Annenberg
Increased understanding of the physical and chemical principles that drive a biological process has led to the development of mathematical formulations that are used to simulate a rich variety of responses. As a result, a vast amount of simulation data can be created for analyzing single cell behavior numerically. However complex and extensive mechanisms involved in emergent behavior of multiple interacting cells may become intractable due to mathematical and computational complexity. This talk will address how we can exploit simulation data describing the nonlinear dynamics of single cell behavior to create a reduced- order linear state equation in latent variable space. Furthermore, the linearity of the reduced-order latent variable state equation allows for the superposition of multiple solutions to predict emergent behaviors of interacting cells. The linear latent state equation describing the nonlinear dynamics of single cell is created in two steps. First the original independent state variables are augmented by adding auxiliary variables necessary to “sufficiently inform” the single cell nonlinear dynamics. This creates a high-dimensional state space where a linear description of the nonlinear system can be found. Second, latent variables extracted from the high-dimensional state space and used to create the reduced-order linear equation. While the resultant latent state equation is linear, complex nonlinearities are embedded in the compact model, leading to precise and global linearization of nonlinear dynamics. Furthermore, in order to predict multi-cell emergent behavior, the reduced-order linear models of single cells are used as agents in a comprehensive agent-based framework based on linear superposition of mutually shared variables. The approach is motivated by emergent behaviors in collective cell migration in order to gain insight for the study and control cancer metastasis and wound healing. However, the general approach may be applied to systems of interacting nonlinear agents, which would otherwise be prohibitively complex to compute.
Michaëlle N. Mayalu is a Ph.D. student at the Brit and Alex d’Arbeloff Laboratory for Information Systems and Technology in the Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge MA. She received the B.S., and M.S., degrees in Mechanical Engineering in 2010 and 2012 from Massachusetts Institute of Technology. Her thesis work is focused on modeling and predicting biological systems behavior by drawing on aspects of dynamic modeling and simulation, data analysis, statistical learning and control theory. Her thesis supervisor is Professor H. Harry Asada in the Department of Mechanical Engineering at MIT.