Identification of Phenotypic State Transition Probabilities in Living Cells

Abstract

Living cells stochastically switch their phenotypic states in response to environmental cues to maintain persistence and viability. Estimating the state transition probabilities from biological observations of cell populations gives valuable insight to the underlying processes, and gives insights as to how the transition statistics are influenced by external factors. In this work, we present two Bayesian estimation approaches. The first is applicable when individual cell state trajectories are observed. The second approach is applicable when only aggregate population statistics are available. Estimation of transition probabilities when individual cell state trajectories are available is a straightforward problem, whereas estimation from only aggregate statistics can be computationally expensive. In the latter case, we present an algorithm that relies on three key ideas to cut down computational time: i) approximating high-dimensional multinomial distributions with multi-variate Gaussians, ii) employing Monte-Carlo techniques to efficiently integrate over high dimensional spaces, and iii) explicitly incorporating sampling constraints by computing lower dimensional distributions over the constrained variable. Simulation results demonstrate the viability of the algorithm.

Estimation of state-transition probability matrices in asynchronous population Markov processes

“…In [7] we have shown that in order to satisfy equality constraint (12), we sample from a distribution characterized by…”

“…In [7], we developed Bayesian estimation schemes for addressing both estimation problems (using panel and longitudinal data). A tacit assumption was that, in both formulations, the state transitions are synchronous among the population members, and are also synchronous with the observations.…”

Time Lapse Observation Based Modeling and Identification of Cell Behaviors in Angiogenic Sprout Development

“…For simplicity, we ignore phenotypic state, except for the distinction between tip and stalk cells. For more details on modeling and identification of phenotypic state, see [5,9].…”

Stochastic modeling and identification of emergent behaviors of an Endothelial Cell population in angiogenic pattern formation

“…Computing transition probabilities is a rather straightforward problem if time lapse data of phenotype state transitions are available. Although migration states are easy to detect from time lapse trajectory data, differentiating the quiescent state from proliferative and apoptotic states is difficult, and has been a research issue (Farahat and Asada, 2009). In this paper we assume that such phenotype transition data are available.…”