Phenotypic plasticity is associated with non-genetic drug tolerance in several cancers. Such plasticity can arise from chromatin remodeling, transcriptomic reprogramming, and/or protein signaling rewiring, and is characterized as a cell state transition in response to molecular or physical perturbations. This, in turn, can confound interpretations of drug responses and resistance development. Using BRAF- mutant melanoma cell lines as the prototype, we report on a joint theoretical and experimental investigation of the cell-state transition dynamics associated with BRAF inhibitor drug tolerance. Thermodynamically motivated surprisal analysis of transcriptome data was used to treat the cell population as an entropy maximizing system under the influence of time-dependent constraints. This permits the extraction of an epigenetic potential landscape for drug-induced phenotypic evolution. Single-cell flow cytometry data of the same system were modeled with a modified Fokker-Planck-type kinetic model. The two approaches yield a consistent picture that accounts for the phenotypic heterogeneity observed over the course of drug tolerance development. The results reveal that, in certain plastic cancers, the population heterogeneity and evolution of cell phenotypes may be understood by accounting for the competing interactions of the epigenetic potential landscape and state-dependent cell proliferation. Accounting for such competition permits accurate, experimentally verifiable predictions that can potentially guide the design of effective treatment strategies.

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Spontaneous symmetry breaking underlies much of our classification of phases of matter and their associated transitions [1][2][3]. It provides an example of the power of many-body interactions, enabling a collection of individual degrees of freedom to align its behavior across large spatial and temporal scales. Crucially, the nature of the underlying symmetry being broken determines many of the qualitative properties of the phase; this is illustrated by the case of discrete versus continuous symmetry breaking. Indeed, in contrast to the discrete case, the breaking of a continuous symmetry is governed by Goldstone's theorem, which predicts the existence of gapless modes that mediate power-law correlations [4,5]. In this work, we realize a two-dimensional dipolar XY model -which exhibits a continuous spin-rotational symmetry -utilizing a Rydberg quantum simulator. We demonstrate the adiabatic preparation of correlated low-temperature states of both the XY ferromagnet and the XY antiferromagnet. In the ferromagnetic case, we characterize the presence of long-range XY order, a feature prohibited in absence of the long-range dipolar interaction. Complementing recent works utilizing the Rydberg-blockade mechanism to realize Ising-type interactions (with a discrete spin rotation symmetry) [6-9], our work opens the door to exploring the many-body physics of XY interactions in a programmable quantum simulator.