Stochastic Methods in Oncology and Population Dynamics

Heyrim Cho

University of California Riverside (Mathematics)

"Modeling of CAR T-cell and neural stem cell therapy for brain cancer"

Recent advances in cell and gene engineering technologies enabled a variety of cell based treatments to be used as part of a treatment for a variety of diseases and conditions. Many different types of cells are available to be transplanted to replace or repair damaged tissue and/or cells. In this talk, I will discuss chimeric antigen receptor (CAR) T-cell therapy and neural stem cell (NSC) therapy for brain diseases, and the potential of how mathematical models can help increase the treatment efficacy. A hybrid stochastic agent based and partial differential equation model of CAR T-cell therapy is developed to understand the effect of timing in a combination treatment for heterogeneous brain cancer. Similarly, a hybrid model of NSC treatment is developed to study the effect of injection location and to predict its migration path. I will also present results using ordinary differential equation models on better understanding of the cellular dynamics in a population level.
Additional authors: Runpeng Li (University of California Riverside); Austin Hansen (University of California Riverside); Vikram Adhikarla (City of Hope); Margarita Gutova (City of Hope); Christine E. Brown (City of Hope) Russell C. Rockne (City of Hope);

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Alexandru Hening

Texas A&M (Mathematics)

"Population dynamics under random switching"

An important question in ecology is the relationship between the coexistence of species and environmental fluctuations. A natural way to model environmental fluctuations is to use stochastic differential equations (SDE) or piecewise deterministic Markov processes (PDMP). In a PDMP, the environment switches between a fixed finite number of states to each of which we associate an ordinary differential equation (ODE). In each state the dynamics is given by the flow of its associated ODE. After a random time, the environment switches to a different state, and the dynamics is governed by the ODE associated to the new state. I will look at two and three species examples of SDE and PDMP and explain how the randomness can lead to some very interesting and counterintuitive behavior.
Additional authors: Dang Nguyen, University of Alabama Nhu Nguyen, University of Rhode Island Harrison Watts, University of Alabama

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Khanh Ngoc Dinh

Columbia University (Irving Institute for Cancer Dynamics)

"Modeling and simulation of cancer evolution in bulk and single-cell DNA-sequencing data"

We explain how models of population genetics can be used to provide quantitative inference of clonal evolution of cancer. The talk has two parts. Part 1 is devoted to the definition and mathematical properties of the Site Frequency Spectrum (SFS), one of the commonly used characteristics of cell populations undergoing growth and mutation. We explore the basic consistency of the approaches based on Wright-Fisher or Moran coalescents versus those based on birth-death processes. This provides building blocks for Part 2, which introduces the heuristic estimation equations, which employ the observable characteristics of the SFS, and allow an exact solution providing estimates of the growth and mutation rates and origin times of the clones. Examples based on simulations and available tumor data are presented. Accuracy of the estimates and their possible applications are discussed. Contributions of Emmanuel Asante, Khanh Dinh, Roman Jaksik, Andrew Koval, Paweł Kuś, and Simon Tavaré are acknowledged.
Additional authors: Marek Kimmel

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James MacLaurin

New Jersey Institute of Technology (Mathematics)

"From blips to puffs: estimating the probability of noise-induced calcium waves"

Intracellular calcium signalling is widely hypothesized to be a stochastic phenomenon that bridges scales. Microscopic calcium channels open and close stochastically, producing small blips in the local calcium concentration. If enough of them open, then the local elevation in calcium concentration can be sufficient to initiate a cell-wide calcium wave or 'puff'. We estimate the probability / frequency of calcium puffs using the theory of Large Deviations: this theory facilitates accurate estimates for the most probable way that numerous microscopic channels (coupled by the concentration of calcium and other signalling molecules) can organize to produce a cell-wide puff.
Additional authors: Moshe Silverstein NJIT; Gaetan Barbet Robert Wood Johnson Medical School (New Brunswick) and Child Health Institute of New Jersey

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