Intratumoral heterogeneity in cancers arises from genomic instability and epigenomic plasticity and is associated with resistance to cytotoxic and targeted therapies. We show here that cell-state heterogeneity, defined by differentiation-state marker expression, is high in triple-negative and basal-like breast cancer subtypes, and that drug tolerant persister (DTP) cell populations with altered marker expression emerge during treatment with a wide range of pathway-targeted therapeutic compounds. We show that MEK and PI3K/mTOR inhibitor-driven DTP states arise through distinct cell-state transitions rather than by Darwinian selection of preexisting subpopulations, and that these transitions involve dynamic remodeling of open chromatin architecture. Increased activity of many chromatin modifier enzymes, including BRD4, is observed in DTP cells. Co-treatment with the PI3K/mTOR inhibitor BEZ235 and the BET inhibitor JQ1 prevents changes to the open chromatin architecture, inhibits the acquisition of a DTP state, and results in robust cell death in vitro and xenograft regression in vivo.

A classic reachability problem for safety of dynamic systems is to compute the set of initial states from which the state trajectory is guaranteed to stay inside a given constraint set over a given time horizon. In this paper, we leverage existing theory of reachability analysis and risk measures to devise a risk-sensitive reachability approach for safety of stochastic dynamic systems under non-adversarial disturbances over a finite time horizon. Specifically, we first introduce the notion of a risk-sensitive safe set as a set of initial states from which the risk of large constraint violations can be reduced to a required level via a control policy, where risk is quantified using the Conditional Value-at-Risk (CVaR) measure. Second, we show how the computation of a risk-sensitive safe set can be reduced to the solution to a Markov Decision Process (MDP), where cost is assessed according to CVaR. Third, leveraging this reduction, we devise a tractable algorithm to approximate a risk-sensitive safe set and provide arguments about its correctness. Finally, we present a realistic example inspired from stormwater catchment design to demonstrate the utility of risk-sensitive reachability analysis. In particular, our approach allows a practitioner to tune the level of risk sensitivity from worst-case (which is typical for Hamilton-Jacobi reachability analysis) to risk-neutral (which is the case for stochastic reachability analysis).

Drug resistance in breast cancer cell populations has been shown to arise through phenotypic transition of cancer cells to a drug-tolerant state, for example through epithelial-to-mesenchymal transition or transition to a cancer stem cell state. However, many breast tumors are a heterogeneous mixture of cell types with numerous epigenetic states in addition to stem-like and mesenchymal phenotypes, and the dynamic behavior of this heterogeneous mixture in response to drug treatment is not well-understood. Recently, we showed that plasticity between differentiation states, as identified with intracellular markers such as cytokeratins, is linked to resistance to specific targeted therapeutics. Understanding the dynamics of differentiation-state transitions in this context could facilitate the development of more effective treatments for cancers that exhibit phenotypic heterogeneity and plasticity. In this work, we develop computational models of a drug-treated, phenotypically heterogeneous triple-negative breast cancer (TNBC) cell line to elucidate the feasibility of differentiation-state transition as a mechanism for therapeutic escape in this tumor subtype. Specifically, we use modeling to predict the changes in differentiation-state transitions that underlie specific therapy-induced changes in differentiation-state marker expression that we recently observed in the HCC1143 cell line. We report several statistically significant therapy-induced changes in transition rates between basal, luminal, mesenchymal, and non-basal/non-luminal/non-mesenchymal differentiation states in HCC1143 cell populations. Moreover, we validate model predictions on cell division and cell death empirically, and we test our models on an independent data set. Overall, we demonstrate that changes in differentiation-state transition rates induced by targeted therapy can provoke distinct differentiation-state aggregations of drug-resistant cells, which may be fundamental to the design of improved therapeutic regimens for cancers with phenotypic heterogeneity.

This paper develops a safety analysis method for stochastic systems that is sensitive to the possibility and severity of rare harmful outcomes. We define risksensitive safe sets as sub-level sets of the solution to a non-standard optimal control problem, where a random maximum cost is assessed using the Conditional Value-at-Risk (CVaR) functional. The solution to the control problem represents the maximum extent of constraint violation of the state trajectory, averaged over the α • 100% worst cases, where α ∈ (0, 1]. This problem is well-motivated but difficult to solve in a tractable fashion because temporal decompositions for risk functionals generally depend on the history of the system's behavior. Our primary theoretical contribution is to derive under-approximations to risksensitive safe sets, which are computationally tractable. Our method provides a novel, theoretically guaranteed, parameter-dependent upper bound to the CVaR of a maximum cost without the need to augment the state space. For a fixed parameter value, the solution to only one Markov decision process problem is required to obtain the underapproximations for any family of risk-sensitivity levels. In addition, we propose a second definition for risk-sensitive safe sets and provide a tractable method for their estimation without using a parameter-dependent upper bound. The second definition is expressed in terms of a new coher-