Predicting rates of cell state change caused by stochastic fluctuations using a data-driven landscape model

Abstract

We develop a potential landscape approach to quantitatively describe experimental data from a fibroblast cell line that exhibits a wide range of GFP expression levels under the control of the promoter for tenascin-C. Time-lapse live-cell microscopy provides data about short-term fluctuations in promoter activity, and flow cytometry measurements provide data about the long-term kinetics, because isolated subpopulations of cells relax from a relatively narrow distribution of GFP expression back to the original broad distribution of responses. The landscape is obtained from the steady state distribution of GFP expression and connected to a potentiallike function using a stochastic differential equation description (Langevin/Fokker-Planck). The range of cell states is constrained by a force that is proportional to the gradient of the potential, and biochemical noise causes movement of cells within the landscape. Analyzing the mean square displacement of GFP intensity changes in live cells indicates that these fluctuations are described by a single diffusion constant in log GFP space. This finding allows application of the Kramers' model to calculate rates of switching between two attractor states and enables an accurate simulation of the dynamics of relaxation back to the steady state with no adjustable parameters. With this approach, it is possible to use the steady state distribution of phenotypes and a quantitative description of the shortterm fluctuations in individual cells to accurately predict the rates at which different phenotypes will arise from an isolated subpopulation of cells.population distribution | dynamical systems | stochastic protein expression | biological noise G enetically identical cells do not respond identically when exposed to nominally identical environmental conditions. Such nongenetic phenotypic variability has been widely observed in bacteria (1, 2), yeast (3), and mammalian cells (4-8). Population heterogeneity is thought to result from the inherently stochastic nature of intracellular events, which are subject to statistical fluctuations caused by small copy numbers of the constituent molecules, such as transcription factors (9). Many investigations into the origins and effects of stochastic gene expression have used engineered organisms and stochastic gene network models to determine the sources and magnitude of variability (10-12). These fluctuations, although causing continual change at the single-cell level, can lead to stable distributions of phenotypes within a population.The idea of a stable distribution of states in the presence of random fluctuations is reminiscent of statistical physics, where randomness results from thermal fluctuations and the stable distribution of states reflects a potential energy function. The popular concept of the epigenetic landscape suggested in the work by Waddington (13) (i.e., a surface of branching valleys and ridges on which cells explore phenotypic states) can be thought of as a series of potential energy functions. The epigenetic landscape,...

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“…Multiplex protein expression (4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37) …”