Minimal Developmental Computation: A Causal Network Approach to Understand Morphogenetic Pattern Formation

What information-processing strategies and general principles are sufficient to enable self-organized morphogenesis in embryogenesis and regeneration? We designed and analyzed a minimal model of self-scaling axial patterning consisting of a cellular network that develops activity patterns within implicitly set bounds. The properties of the cells are determined by internal ‘genetic’ networks with an architecture shared across all cells. We used machine-learning to identify models that enable this virtual mini-embryo to pattern a typical axial gradient while simultaneously sensing the set boundaries within which to develop it from homogeneous conditions—a setting that captures the essence of early embryogenesis. Interestingly, the model revealed several features (such as planar polarity and regenerative re-scaling capacity) for which it was not directly selected, showing how these common biological design principles can emerge as a consequence of simple patterning modes. A novel “causal network” analysis of the best model furthermore revealed that the originally symmetric model dynamically integrates into intercellular causal networks characterized by broken-symmetry, long-range influence and modularity, offering an interpretable macroscale-circuit-based explanation for phenotypic patterning. This work shows how computation could occur in biological development and how machine learning approaches can generate hypotheses and deepen our understanding of how featureless tissues might develop sophisticated patterns—an essential step towards predictive control of morphogenesis in regenerative medicine or synthetic bioengineering contexts. The tools developed here also have the potential to benefit machine learning via new forms of backpropagation and by leveraging the novel distributed self-representation mechanisms to improve robustness and generalization

The Role of Canalization in the Spreading of Perturbations in Boolean Networks

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

Psychoanalysis of a minimal agent

The Secretary problem is studied with minimal cognitive agents, being a problem that needs memory and judgment. A sequence of values, drawn from an unknown range, is presented; the agent has only one chance to pick a single value as they are presented, and should try to maximize the value chosen. In extension of previous work (Tuci et al. 2002), Continuous Time Recurrent Neural Networks (CTRNN) are evolved to solve the problem, and then their strategies are analyzed by relating mechanisms to behavior. Strategies similar to the known optimal strategy are observed, and it is noted that significantly different strategies can be generated by very different mechanisms that perform equally well

The nonlinearity of regulation in biological networks

Abstract The extent to which the components of a biological system are (non)linearly regulated determines how amenable they are to therapy and control. To better understand this property termed “regulatory nonlinearity”, we analyzed a suite of 137 published Boolean network models, containing a variety of complex nonlinear regulatory interactions, using a probabilistic generalization of Boolean logic that George Boole himself had proposed. Leveraging the continuous-nature of this formulation, we used Taylor decomposition to approximate the models with various levels of regulatory nonlinearity. A comparison of the resulting series of approximations of the biological models with appropriate random ensembles revealed that biological regulation tends to be less nonlinear than expected, meaning that higher-order interactions among the regulatory inputs tend to be less pronounced. A further categorical analysis of the biological models revealed that the regulatory nonlinearity of cancer and disease networks could not only be sometimes higher than expected but also be relatively more variable. We show that this variation is caused by differences in the apportioning of information among the various orders of regulatory nonlinearity. Our results suggest that there may have been a weak but discernible selection pressure for biological systems to evolve linear regulation on average, but for certain systems such as cancer, on the other hand, to simultaneously evolve more nonlinear rules

Biological underpinnings for lifelong learning machines

Biological organisms learn from interactions with their environment throughout their lifetime. For artificial systems to successfully act and adapt in the real world, it is desirable to similarly be able to learn on a continual basis. This challenge is known as lifelong learning, and remains to a large extent unsolved. In this Perspective article, we identify a set of key capabilities that artificial systems will need to achieve lifelong learning. We describe a number of biological mechanisms, both neuronal and non-neuronal, that help explain how organisms solve these challenges, and present examples of biologically inspired models and biologically plausible mechanisms that have been applied to artificial systems in the quest towards development of lifelong learning machines. We discuss opportunities to further our understanding and advance the state of the art in lifelong learning, aiming to bridge the gap between natural and artificial intelligence