br Acknowledgments br Introduction Mouse embryonic stem ES c

Acknowledgments
Introduction Mouse embryonic stem (ES) ppar pathway can give rise to all somatic cell types and germ cells in a regulative manner and are thereby defined as pluripotent. They are thought to have ‘no pre-determined programme’. However, whether or not an ES cell represents a ‘tabula rasa’ (Smith, 2009) depends upon the design principles that are intrinsic to its decision-making machinery. Is there a naïve ground state of pluripotency out of which altered activity of key transcription factors (via external factors and extracellular signalling) leads to a primed metastable state within which decisions must then be computed? (Silva and Smith, 2008). Alternatively, is the nature of pluripotency derived from intrinsic heterogeneity of cell states since the ES cell transcriptome fluctuates and interconverts among multiple metastable states? (Graf and Stadtfeld, 2008; Huang, 2009a; Kalmar et al., 2009). Here, we ask whether these views of pluripotency are compatible and consider whether a ground state like that captured in vitro could exist in vivo. We apply the hypothesis of exploratory behaviour in stem cell decision-making, which highlights the possible role of self-organization in cell fate computation (Halley et al., 2009). This coarse-grained approach reflects an underlying philosophy that resonates most strongly with the physical sciences, where explanations are sought in terms of general principles or laws that do not depend on specific, sometimes obscuring, details. Some models of stem or progenitor cell decision-making consider cell fates as attractors, and cell fate decisions as driven by bifurcations that destabilize the stem cell attractor (Huang, 2009b). Attractors are equilibrium states in the state space or attractor landscape of possible network configurations towards which a system evolves (Huang, 2009b; Milnor, 1985). Nonlinear dynamical systems theory, within which attractor states are typically discussed, simplifies the complexity of cellular decision-making using differential equations. For example, a description of a genetic switch may comprise a set of ordinary differential equations that prescribe how quantities of two TFs, x1 and x2, change through time. At any given time, t, the circuit state, S(t), is captured as a function of x1 and x2, linked by a formal understanding of how the transcription factors (TFs) influence each other\'s expression. This conceptualization gives the circuit state, S(t), position-like properties in state space, with x1 and x2 acting as coordinates (Huang, 2009b). The beauty of this formalization of decision-making circuitry is that known regulatory interactions translate directly into predicted trajectories of cellular behaviour. Starting with initial values for x1 and x2, the trajectory S(t) will move toward one of the system\'s attractors, unless it is already within one or balanced precariously on a separatrix between adjacent attractors. Hereafter S(t) will remain unless perturbed sufficiently by factors external to the described circuit or changes occur in regulatory interactions that underpin the attractor\'s stability. However, large nonlinear dynamical network models that involve thousands of regulatory genes require a greater number of coupled differential equations. While these models can be developed with modern computing resources, the parameterization and interpretation of such models is problematic. Finding appropriate values for the thousands of model parameters (decay rates, production rates, interaction strengths etc.) and interpreting complex model behaviour remains a challenge (Bornholdt, 2005). Furthermore, despite a wealth of some types of data (gene expression profiles, TF localization data), understanding of most regulatory mechanisms on the molecular level is incomplete. Given these problems with developing traditional dynamical systems network models for gene regulation, an alternative type of coarse-grained theoretical model better matched to available data and more readily interpretable is important. We argue that there exists another perspective in which the process of cell fate computation can be described by critical-like self-organization (also called rapid self-organized criticality) (Halley et al., 2004, 2009). This perspective offers insights not provided by dynamical systems theory and appears more natural to describe complex systems that are stable yet flexible, and able to compute solutions to complex problems, as epitomized by pluripotent stem cells. It also suggests a way to consider regulatory networks as whole integrated systems, which is important if gene expression is highly context dependent. A requirement of this perspective is that the decision-making system is considered as a dynamic self-organizing phenomenon comprising numerous semi-independent agents, rather than one that is static and fixed, like the common wiring diagram network representations imply. Hence, our framework describes a highly dynamic circuitry (in a more abstract sense) that shifts continuously in response to both intrinsic and extrinsic factors.