Rapid self-organized criticality: Fractal evolution in extreme environments

Information generating, sharing, and manipulating Source-Reservoir-Sink model of self-organizing dissipative structures

The evolution of self-organizing ensembles of fullerenes and the emergence of the Buckyball are described by information generating, sharing, and manipulating Source-Reservoir-Sink model. Shannon's information-theoretic model of signal transmitter, channel, and receiver that preserves and retains the original signal is extended to our model that maps the transformations of chemical and physical components of the self-organizing dissipative structures into Source, Reservoir, and Sink. The information generated by Source is manipulated by controlling the flow of information to Reservoir before being transmitted to Sink. It is demonstrated in a Box-model. The role of Reservoir in building up the manipulative capacity for information storage and selective sharing is illustrated by the asymmetric exchange of material and information. The number of boxes and the flow rates are varied to evaluate the information-theoretic diagnostic tools of Shannon entropy, complexity, fractal dimension, relative entropy, and the entropic cost of the emerging dissipative structures.

A conceptual and computational framework for modelling and understanding the non-equilibrium gene regulatory networks of mouse embryonic stem cells

The capacity of pluripotent embryonic stem cells to differentiate into any cell type in the body makes them invaluable in the field of regenerative medicine. However, because of the complexity of both the core pluripotency network and the process of cell fate computation it is not yet possible to control the fate of stem cells. We present a theoretical model of stem cell fate computation that is based on Halley and Winkler’s Branching Process Theory (BPT) and on Greaves et al.’s agent-based computer simulation derived from that theoretical model. BPT abstracts the complex production and action of a Transcription Factor (TF) into a single critical branching process that may dissipate, maintain, or become supercritical. Here we take the single TF model and extend it to multiple interacting TFs, and build an agent-based simulation of multiple TFs to investigate the dynamics of such coupled systems. We have developed the simulation and the theoretical model together, in an iterative manner, with the aim of obtaining a deeper understanding of stem cell fate computation, in order to influence experimental efforts, which may in turn influence the outcome of cellular differentiation. The model used is an example of self-organization and could be more widely applicable to the modelling of other complex systems. The simulation based on this model, though currently limited in scope in terms of the biology it represents, supports the utility of the Halley and Winkler branching process model in describing the behaviour of stem cell gene regulatory networks. Our simulation demonstrates three key features: (i) the existence of a critical value of the branching process parameter, dependent on the details of the cistrome in question; (ii) the ability of an active cistrome to “ignite” an otherwise fully dissipated cistrome, and drive it to criticality; (iii) how coupling cistromes together can reduce their critical branching parameter values needed to drive them to criticality.

Pluripotent stem cells possess the capacity both to renew themselves indefinitely and to differentiate to any cell type in the body. Thus the ability to direct stem cell differentiation would have immense potential in regenerative medicine. There is a massive amount of biological data relevant to stem cells; here we exploit data relating to stem cell differentiation to help understand cell behaviour and complexity. These cells contain a dynamic, non-equilibrium network of genes regulated in part by transcription factors expressed by the network itself. Here we take an existing theoretical framework, Transcription Factor Branching Processes, which explains how these genetic networks can have critical behaviour, and can tip between low and full expression. We use this theory as the basis for the design and implementation of a computational simulation platform, which we then use to run a variety of simulation experiments, to gain a better understanding how these various transcription factors can combine, interact, and influence each other. The simulation parameters are derived from experimental data relating to the core factors in pluripotent stem cell differentiation. The simulation results determine the critical values of branching process parameters, and how these are modulated by the various interacting transcription factors.

Self-organizing circuitry and emergent computation in mouse embryonic stem cells

Pluripotency is a cellular state of multiple options. Here, we highlight the potential for self-organization to contribute to stem cell fate computation. A new way of considering regulatory circuitry is presented that describes the expression of each transcription factor (TF) as a branching process that propagates through time, interacting and competing with others. In a single cell, the interactions between multiple branching processes generate a collective process called 'critical-like self-organization'. We explain how this phenomenon provides a valid description of whole genome regulatory circuit dynamics. The hypothesis of exploratory stem cell decision-making proposes that critical-like self-organization (also called rapid self-organized criticality) provides the backbone for cell fate computation in regulative embryos and pluripotent stem cells. Unspecific amplification of TF expression is predicted to initiate this self-organizing circuitry, where cascades of gene expression propagate and may interact either synergistically or antagonistically. The emergent and highly dynamic circuitry is affected by various sources of selection pressure, such as the expression of TFs with disproportionate influence over other genes, and extrinsic biological and physical stimuli that differentially modulate particular gene expression cascades. Extrinsic conditions continuously trigger waves of transcription that ripple throughout regulatory networks on multiple spatiotemporal scales, providing the context within which circuitry self-organizes. In this framework, a distinction between instructive and selective mechanisms of fate determination is misleading because it is the 'interference pattern', rather than any single instructing or selecting factor, that is ultimately responsible for computing and directing cell fate. Using this framework, we consider whether the idea of a naïve ground state of pluripotency and that of a fluctuating transcriptome are compatible, and whether a ground state like that captured in vitro could exist in vivo.