On the Topology and Dynamics of Breast Cancer Cell Morphologies

A prerequisite to understanding a dynamical system is to understand the underlying topology. In past research our lab has extracted a wide variety of morphological metrics for many in vitro spheroid cells. Since we are dealing with biological systems, these morphological realizations are governed by the expression of phenotypes, which will endow the phase space with a particular topology. To better understand this natural topology, we employed the use of an adversarial autoencoder, a neural network, to reduce the dimensionality and better understand the phase space's topology. In our work, we were able to reduce this morphological phase space to two dimensions while still being able to reconstruct the encoded vectors back to their corresponding morphological metrics. We then characterize the similar topologies and probe different questions about the space: What do individual cell trajectories look like, i.e. what do the dynamics look like in this phase space? Are there regions where the 4 main morphological phenotypes are characterized? How strongly are the embedded vectors bound to their neighbors? Do different priors significantly affect the topology?