Development of drug resistance, the prime cause of failure in cancer therapy, is commonly explained by the selection of resistant mutant cancer cells. However, dynamic non-genetic heterogeneity of clonal cell populations continuously produces meta-stable phenotypic variants (persisters), some of which represent stem-like states that confer resistance. Even without genetic mutations, Darwinian selection can expand these resistant variants, which would explain the invariably rapid emergence of stem-like resistant cells. Here, using quantitative measurements and modeling we show that appearance of multi-drug resistance in HL60 leukemic cells following treatment with vincristine is not explained by Darwinian selection but by Lamarckian induction. Single-cell longitudinal monitoring confirms the induction of multi-drug resistance in individual cells. Associated transcriptome changes indicate a lasting stress-response consistent with a drug-induced switch between high-dimensional cancer attractors. Resistance-induction correlates with Wnt-pathway up-regulation and is suppressed by β-catenin knock-down, revealing a new opportunity for early therapeutic intervention against resistance development.

Cell fate choice and commitment of multipotent progenitor cells to a differentiated lineage requires broad changes of their gene expression profile. But how progenitor cells overcome the stability of their gene expression configuration (attractor) to exit the attractor in one direction remains elusive. Here we show that commitment of blood progenitor cells to the erythroid or myeloid lineage is preceded by the destabilization of their high-dimensional attractor state, such that differentiating cells undergo a critical state transition. Single-cell resolution analysis of gene expression in populations of differentiating cells affords a new quantitative index for predicting critical transitions in a high-dimensional state space based on decrease of correlation between cells and concomitant increase of correlation between genes as cells approach a tipping point. The detection of “rebellious cells” that enter the fate opposite to the one intended corroborates the model of preceding destabilization of a progenitor attractor. Thus, early warning signals associated with critical transitions can be detected in statistical ensembles of high-dimensional systems, offering a formal theory-based approach for analyzing single-cell molecular profiles that goes beyond current computational pattern recognition, does not require knowledge of specific pathways, and could be used to predict impending major shifts in development and disease.

The developmental dynamics of multicellular organisms is a process that takes place in a multistable system in which each attractor state represents a cell type, and attractor transitions correspond to cell differentiation paths. This new understanding has revived the idea of a quasipotential landscape, first proposed by Waddington as a metaphor. To describe development, one is interested in the 'relative stabilities' of N attractors (N . 2). Existing theories of state transition between local minima on some potential landscape deal with the exit part in the transition between two attractors in pair-attractor systems but do not offer the notion of a global potential function that relates more than two attractors to each other. Several ad hoc methods have been used in systems biology to compute a landscape in non-gradient systems, such as gene regulatory networks. Here we present an overview of currently available methods, discuss their limitations and propose a new decomposition of vector fields that permits the computation of a quasi-potential function that is equivalent to the Freidlin-Wentzell potential but is not limited to two attractors. Several examples of decomposition are given, and the significance of such a quasi-potential function is discussed.