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WIREs Syst Biol Med
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Understanding multimodal biological decisions from single cell and population dynamics

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Abstract Modern techniques on single‐cell and ‐molecule resolution reveal that gene and protein expressions between cells of an otherwise identical group are stochastic in time, and clonal population of cells display heterogeneity in the abundance of a given protein per cell at any measured time. Today, combinatorially, stochasticity and heterogeneity are considered as biological noise and are essential for generating phenotypic variations, cell fate decisions and amplification of molecular signals. Here, several works from experimental and theoretical aspects that show multimodal biological decisions at single cell and population level are reviewed. The emerging lessons from these studies suggest that, for yielding multimodal decisions, living systems are guided by well‐defined nonlinear deterministic processes which are sensitive to specific range of biological parameters. WIREs Syst Biol Med 2012 doi: 10.1002/wsbm.1175 This article is categorized under: Biological Mechanisms > Cell Fates

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Stochasticity and variability observed in single cells. (a) Time‐series schematic of green fluorescent proteins in Escherichia coli (Reprinted with permission from Ref 48. Copyright 2012 The American Association for the Advancement of Science). Synchronized (upper) and unsynchronized (lower) stochasticity or fluctuation in protein expression does not show and show color variation, respectively, in E. coli. (b) The variation (left) and stability in time (right) of Sca‐1 expression in multipotent mouse hematopoietic cell line (Reprinted with permission from Ref 56. Copyright 2008 Nature Publishing Group)

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Noise in nonlinear dynamical system aids multimodal phenomena. (A) Chaotic systems. Left: diverging endpoints of seven boarders' trajectories with minute (1 mm) changes in course maneuver at a ski slope with moguls (insert) (Reprinted with permission from Ref 89. Copyright 1995 University of Washington Press). Right: Schematic of mammalian cell differentiation process (Reprinted with permission from Ref 93. Copyright 2004 The Science Creative Quarterly). (B) Stochastic resonance. Consider a dynamical system governed by dx/dt = V(x) + Acos(ωt) + ξ(t), where V(x) is a generic nonlinear expression of x, Acos(ωt) is an oscillatory periodic force with frequency ω and ξ(t) represents noise function (such as Gaussian white noise97). Taking V(x) = αψψ3 and ξ(t) = σ1/2η(t) it can be shown for A = 0.023, 2π/ω = 1600 and the modulation of noise within a threshold range (0.005 < σ < 0.015) produce bistable states (left), which could statistically switch orientations between the two stable states (right). Note that P(ω) is the power spectrum of ω and see96 for details and for other multistable states (Reprinted with permission from Ref 96. Copyright 2009 IOP Publishing Ltd). (C) Schematic state‐space plots of stem cell differentiation (Reprinted with permission from Ref 100. Copyright 2011 Public Library of Science). Gene expressions variation in undifferentiated stem cells (left) compared with noise‐induced differentiation (right). Right panel shows the stabilization in gene expressions localization for each differentiated state, revealing attractor states.

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Chaos dynamics. Simulations of Lorenz atmospheric model. (a) Initial values of X = 1 and 1.00001 yield very different values over time demonstrating sensitivity to initial conditions. (b) Different initial value of X showing very different time‐series pattern. (c) The phase‐space plot (X(t + Δt)) vs X(t)) of Lorenz model (b) shows clear patterns despite being sensitive to initial conditions in time‐series plots. (Reprinted with permission from Ref 91. Copyright 2000 John Wiley and Sons)

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Stochasticity and threshold effects in cell fate decision. (a) Competence in Bacillus subtilis is determined by the concentration of comK protein, with threshold and noise switching between fates (Reprinted with permission from Ref 72. Copyright 2007 The American Association for the Advancement of Science). (b) Incomplete penetrance in Caenorhabditis elegans is also guided by noise in end‐1, threshold expression (left) and topology (right) contributing to the decision (Reprinted with permission from Ref 74. Copyright 2010 Nature Publishing Group)

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Chaotic dynamics and attractor states. (a) Schematic 3‐D landscape for cellular attractors. Each hole could represent a distinct attractor, such as cell type or cancer subtypes (Reprinted with permission from Ref 83. Copyright 2009 Elsevier Ltd). (b) The convergence of gene expression patterns, using clustering statistics, reflecting the same cell fate attractor to distinct stimulation of all‐trans‐retinoic acid (atRA) and dimethyl sulfoxide (DMSO) (Reprinted with permission from Ref 81. Copyright 2005 American Physical Society). (c) The emergence of distinct clustering patterns in lung tumor transcriptome data (Reprinted with permission from Ref 82. Copyright 2006 Hindawi Publishing Corporation). Despite variation between individual gene readouts, the global analysis reveals clear attractor pattern for each cancer subtype. (d) Scalable gene expression response (Reprinted with permission from Ref 84. Copyright 2009 Public Library of Science). Temporal Pearson (auto‐) correlations of whole genome (top left), random extractions of 100 genes (bottom), and 157 immune‐related (IR) genes (top right). In double knock‐out (DKO), the response in abolished for IR genes but not for random genes. The random extractions were repeated 30 times, yet, displayed similar structure with whole genome for all genotypes.84,85

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