The availability of time- and disease-dependent single-cell gene expression data has opened new opportunities for integrating these datasets into mathematical models representing the evolution and switching between cellular states. In this talk, I will focus on Hopfield recurrent networks, a mathematical framework from statistical physics that captures the multi-stable dynamics inherent in complex cell signaling networks, interpreting gene expression patterns as associative memories. Hopfield recurrent networks can mathematically implement Waddington’s interpretation of normal and abnormal cell phenotypes as dynamical attractors within epigenetic landscapes. I will discuss applications of this framework in modeling the onset of angiogenesis, the dynamics of disease progression in Multiple Myeloma (MM), and the cell cycle. In our angiogenesis model, we use data to visualize the cellular transition from stalk-like to tip-like endothelial cells, corresponding to the formation of capillary sprouts in blood vessels. The MM model employs scRNA-seq data from bone marrow aspirates of MM patients and those diagnosed with two medical conditions that often progress to full MM.

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