UBC Math Bio Seminar: Yu-Chen Cheng

Cells within a population often differ in their genetic and phenotypic states, leading to variable behaviors and treatment responses—a phenomenon known as cellular heterogeneity. Understanding how these differences shape therapeutic outcomes is crucial for improving treatment strategies in cancer and other complex diseases.

In this talk, I will present two complementary perspectives on cellular heterogeneity. The first focuses on genetic heterogeneity. I will discuss a mathematical model that incorporates cell-cycle dynamics to predict differential responses of wild-type and mutant estrogen receptor-positive breast cancer cells to combination therapy with fulvestrant and palbociclib. By integrating pharmacokinetic and pharmacodynamic data from clinical studies, the model enables in silico trials that reveal continuous dosing of palbociclib as more effective than the standard intermittent regimen for reducing overall tumor burden.

The second perspective addresses phenotypic heterogeneity, where genetically identical cells exhibit divergent fates under the same treatment. Using single-cell RNA sequencing data, I will show how optimal transport analysis captures heterogeneous epithelial-to-mesenchymal transitions (EMT) in breast epithelial cells. Building upon this, we developed PROFET (Particle-based Reconstruction Of generative Force-matched Expression Trajectories), a computational framework that integrates gradient-flow theory with neural force-matching to reconstruct continuous, nonlinear cellular trajectories from static and sparse data. By recovering temporal information from snapshot measurements, PROFET provides a powerful tool for inferring dynamic gene-expression trajectories and identifying cell subpopulations that drive treatment resistance.

Together, these studies illustrate how quantitative modeling bridges mathematics and cell biology, advancing our understanding of cellular diversification and enabling data-driven strategies to predict and optimize treatment responses.