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Canalization is a property of Boolean automata that characterizes the extent to which subsets of inputs determine (canalize) the output. Here, we investigate the role of canalization as a characteristic of perturbation-spreading in random Boolean networks (BN) with homogeneous connectivity via numerical simulations. We consider two different measures of canalization introduced by Marques-Pita and Rocha, namely 'effective connectivity' and 'input symmetry,' in a three-pronged approach. First, we show that the mean 'effective connectivity,' a measure of the true mean in-degree of a BN, is a better predictor of the dynamical regime (order or chaos) of the BN than the mean in-degree. Next, we combine effective connectivity and input symmetry in a single measure of 'unified canalization' by using a common yardstick of Boolean hypercube "dimension," a form of fractal dimension. We show that the unified measure is a better predictor of dynamical regime than effective connectivity alone for BNs with large in-degrees. When considered separately, the relative contributions of the two components of the unified measure changes systematically with the mean in-degree, where input symmetry becomes increasingly more dominant with larger in-degrees. As an application, we show that the said measures of canalization characterize the dynamical regimes of a suite of Systems biology models better than the in-degree. Finally, we introduce 'integrated effective connectivity' as an extension of effective connectivity that characterizes the canalization present in BNs with arbitrary timescales obtained by iteratively composing a BN with itself. We show that the integrated measure is a better predictor of long-term dynamical regime than just effective connectivity for a small class of BNs known as the elementary cellular automata. This dissertation will advance theoretical understanding of BNs, allowing us to more accurately predict their short-term and long-term dynamic character, based on canalization. As BNs are generic models of complex systems, combining interaction graphs with multivariate dynamics, these results contribute to the complex networks and systems field. Moreover, as BNs are important models of choice in Systems biology, our methods contribute to the burgeoning toolkit of the field. |
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