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Register a new userMorphogenesis by coupled regulatory networks: Reliable control of positional information and proportion regulation
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Based on a non-equilibrium mechanism for spatial pattern formation we study how position information can be controlled by locally coupled discrete dynamical networks, similar to gene regulation networks of cells in a developing multicellular organism. As an example we study the developmental problems of domain formation and proportion regulation in the presence of noise, as well as in the presence of cell flow. We find that networks that solve this task exhibit a hierarchical structure of information processing and are of similar complexity as developmental circuits of living cells. Proportion regulation is scalable with system size and leads to sharp, precisely localized boundaries of gene expression domains, even for large numbers of cells. A detailed analysis of noise-induced dynamics, using a mean-field approximation, shows that noise in gene expression states stabilizes (rather than disrupts) the spatial pattern in the presence of cell movements, both for stationary as well as growing systems. Finally, we discuss how this mechanism could be realized in the highly dynamic environment of growing tissues in multi-cellular organisms.
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Based on a recently proposed non-equilibrium mechanism for spatial pattern formation [cond-mat/0312366] we study how morphogenesis can be controlled by locally coupled discrete dynamical networks, similar to gene regulation networks of cells in a developing multicellular organism. As an example we study the developmental problem of domain formation and proportion regulation in the presence of noise and cell flow. We find that networks that solve this task exhibit a hierarchical structure of information processing and are of similar complexity as developmental circuits of living cells. A further focus of this paper is a detailed study of noise-induced dynamics, which is a major ingredient of the control dynamics in the developmental network model. A master equation for domain boundary readjustments is formulated and solved for the continuum limit. Evidence for a first order phase transition in equilibrium domain size at vanishing noise is given by finite size scaling. A second order phase transition at increased cell flow is studied in a mean field approximation. Finally, we discuss potential applications.
Genetic regulatory circuits universally cope with different sources of noise that limit their ability to coordinate input and output signals. In many cases, optimal regulatory performance can be thought to correspond to configurations of variables and parameters that maximize the mutual information between inputs and outputs. Such optima have been well characterized in several biologically relevant cases over the past decade. Here we use methods of statistical field theory to calculate the statistics of the maximal mutual information (the `capacity) achievable by tuning the input variable only in an ensemble of regulatory motifs, such that a single controller regulates N targets. Assuming (i) sufficiently large N, (ii) quenched random kinetic parameters, and (iii) small noise affecting the input-output channels, we can accurately reproduce numerical simulations both for the mean capacity and for the whole distribution. Our results provide insight into the inherent variability in effectiveness occurring in regulatory systems with heterogeneous kinetic parameters.
A crucial step in the early development of multicellular organisms involves the establishment of spatial patterns of gene expression which later direct proliferating cells to take on different cell fates. These patterns enable the cells to infer their global position within a tissue or an organism by reading out local gene expression levels. The patterning system is thus said to encode positional information, a concept that was formalized recently in the framework of information theory. Here we introduce a toy model of patterning in one spatial dimension, which can be seen as an extension of Wolperts paradigmatic French Flag model, to patterning by several interacting, spatially coupled genes subject to intrinsic and extrinsic noise. Our model, a variant of an Ising spin system, allows us to systematically explore expression patterns that optimally encode positional information. We find that optimal patterning systems use positional cues, as in the French Flag model, together with gene-gene interactions to generate combinatorial codes for position which we call Counter patterns. Counter patterns can also be stabilized against noise and variations in system size or morphogen dosage by longer-range spatial interactions of the type invoked in the Turing model. The simple setup proposed here qualitatively captures many of the experimentally observed properties of biological patterning systems and allows them to be studied in a single, theoretically consistent framework.
Genes and proteins regulate cellular functions through complex circuits of biochemical reactions. Fluctuations in the components of these regulatory networks result in noise that invariably corrupts the signal, possibly compromising function. Here, we create a practical formalism based on ideas introduced by Wiener and Kolmogorov (WK) for filtering noise in engineered communications systems to quantitatively assess the extent to which noise can be controlled in biological processes involving negative feedback. Application of the theory, which reproduces the previously proven scaling of the lower bound for noise suppression in terms of the number of signaling events, shows that a tetracycline repressor-based negative-regulatory gene circuit behaves as a WK filter. For the class of Hill-like nonlinear regulatory functions, this type of filter provides the optimal reduction in noise. Our theoretical approach can be readily combined with experimental measurements of response functions in a wide variety of genetic circuits, to elucidate the general principles by which biological networks minimize noise.
Cancer invasion and metastasis depend on angiogenesis. The cellular processes (growth, migration, and apoptosis) that occur during angiogenesis are tightly regulated by signaling molecules. Thus, understanding how cells synthesize multiple biochemical signals initiated by key external stimuli can lead to the development of novel therapeutic strategies to combat cancer. In the face of large amounts of disjoint experimental data generated from multitudes of laboratories using various assays, theoretical signal transduction models provide a framework to distill this vast amount of data. Such models offer an opportunity to formulate and test new hypotheses, and can be used to make experimentally verifiable predictions. This study is the first to propose a network model that highlights the cross-talk between the key receptors involved in angiogenesis, namely growth factor, integrin, and cadherin receptors. From available experimental data, we construct a stochastic Boolean network model of receptor cross-talk, and systematically analyze the dynamical stability of the network under continuous-time Boolean dynamics with a noisy production function. We find that the signal transduction network exhibits a robust and fast response to external signals, independent of the internal cell state. We derive an input-output table that maps external stimuli to cell phenotypes, which is extraordinarily stable against molecular noise with one important exception: an oscillatory feedback loop between the key signaling molecules RhoA and Rac1 is unstable under arbitrarily low noise, leading to erratic, dysfunctional cell motion. Finally, we show that the network exhibits an apoptotic response rate that increases with noise, suggesting that the probability of programmed cell death depends on cell health.
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