Digital clocks: simple Boolean models can quantitatively describe circadian systems

Copyright © 2012 The Royal Society This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.The gene networks that comprise the circadian clock modulate biological function across a range of scales, from gene expression to performance and adaptive behaviour. The clock functions by generating endogenous rhythms that can be entrained to the external 24-h day-night cycle, enabling organisms to optimally time biochemical processes relative to dawn and dusk. In recent years, computational models based on differential equations have become useful tools for dissecting and quantifying the complex regulatory relationships underlying the clock's oscillatory dynamics. However, optimizing the large parameter sets characteristic of these models places intense demands on both computational and experimental resources, limiting the scope of in silico studies. Here, we develop an approach based on Boolean logic that dramatically reduces the parametrization, making the state and parameter spaces finite and tractable. We introduce efficient methods for fitting Boolean models to molecular data, successfully demonstrating their application to synthetic time courses generated by a number of established clock models, as well as experimental expression levels measured using luciferase imaging. Our results indicate that despite their relative simplicity, logic models can (i) simulate circadian oscillations with the correct, experimentally observed phase relationships among genes and (ii) flexibly entrain to light stimuli, reproducing the complex responses to variations in daylength generated by more detailed differential equation formulations. Our work also demonstrates that logic models have sufficient predictive power to identify optimal regulatory structures from experimental data. By presenting the first Boolean models of circadian circuits together with general techniques for their optimization, we hope to establish a new framework for the systematic modelling of more complex clocks, as well as other circuits with different qualitative dynamics. In particular, we anticipate that the ability of logic models to provide a computationally efficient representation of system behaviour could greatly facilitate the reverse-engineering of large-scale biochemical networks

Inductive Pattern Formation

With the extended computational limits of algorithmic recursion, scientific investigation is transitioning away from computationally decidable problems and beginning to address computationally undecidable complexity. The analysis of deductive inference in structure-property models are yielding to the synthesis of inductive inference in process-structure simulations. Process-structure modeling has examined external order parameters of inductive pattern formation, but investigation of the internal order parameters of self-organization have been hampered by the lack of a mathematical formalism with the ability to quantitatively define a specific configuration of points. This investigation addressed this issue of quantitative synthesis. Local space was developed by the Poincare inflation of a set of points to construct neighborhood intersections, defining topological distance and introducing situated Boolean topology as a local replacement for point-set topology. Parallel development of the local semi-metric topological space, the local semi-metric probability space, and the local metric space of a set of points provides a triangulation of connectivity measures to define the quantitative architectural identity of a configuration and structure independent axes of a structural configuration space. The recursive sequence of intersections constructs a probabilistic discrete spacetime model of interacting fields to define the internal order parameters of self-organization, with order parameters external to the configuration modeled by adjusting the morphological parameters of individual neighborhoods and the interplay of excitatory and inhibitory point sets. The evolutionary trajectory of a configuration maps the development of specific hierarchical structure that is emergent from a specific set of initial conditions, with nested boundaries signaling the nonlinear properties of local causative configurations. This exploration of architectural configuration space concluded with initial process-structure-property models of deductive and inductive inference spaces. In the computationally undecidable problem of human niche construction, an adaptive-inductive pattern formation model with predictive control organized the bipartite recursion between an information structure and its physical expression as hierarchical ensembles of artificial neural network-like structures. The union of architectural identity and bipartite recursion generates a predictive structural model of an evolutionary design process, offering an alternative to the limitations of cognitive descriptive modeling. The low computational complexity of these models enable them to be embedded in physical constructions to create the artificial life forms of a real-time autonomously adaptive human habitat

CoGNaC: A Chaste Plugin for the Multiscale Simulation of Gene Regulatory Networks Driving the Spatial Dynamics of Tissues and Cancer

We introduce a Chaste plugin for the generation and the simulation of Gene Regulatory Networks (GRNs) in multiscale models of multicellular systems. Chaste is a widely used and versatile computational framework for the multiscale modeling and simulation of mul- ticellular biological systems. The plugin, named CoGNaC (Chaste and Gene Networks for Cancer), allows the linking of the regulatory dynamics to key properties of the cell cycle and of the differentiation process in populations of cells, which can subsequently be modeled us- ing different spatial modeling scenarios. The approach of CoGNaC focuses on the emergent dynamical behaviour of gene networks, in terms of gene activation patterns characterizing the different cellular phenotypes of real cells and, especially, on the overall robustness to perturbations and biological noise. The integration of this approach within Chaste\u2019s modu- lar simulation framework provides a powerful tool to model multicellular systems, possibly allowing for the formulation of novel hypotheses on gene regulation, cell differentiation and, in particular, cancer emergence and development. In order to demonstrate the usefulness of CoGNaC over a range of modelling paradigms, two example applications are presented. The first of these concerns the characterization of the gene activation patterns of human T-helper cells. The second example is a multiscale simulation of a simplified intestinal crypt, in which, given certain conditions, tumor cells can emerge and colonize the tissue

Harnessing function from form: towards bio-inspired artificial intelligence in neuronal substrates

Despite the recent success of deep learning, the mammalian brain is still unrivaled when it comes to interpreting complex, high-dimensional data streams like visual, auditory and somatosensory stimuli. However, the underlying computational principles allowing the brain to deal with unreliable, high-dimensional and often incomplete data while having a power consumption on the order of a few watt are still mostly unknown. In this work, we investigate how specific functionalities emerge from simple structures observed in the mammalian cortex, and how these might be utilized in non-von Neumann devices like “neuromorphic hardware”. Firstly, we show that an ensemble of deterministic, spiking neural networks can be shaped by a simple, local learning rule to perform sampling-based Bayesian inference. This suggests a coding scheme where spikes (or “action potentials”) represent samples of a posterior distribution, constrained by sensory input, without the need for any source of stochasticity. Secondly, we introduce a top-down framework where neuronal and synaptic dynamics are derived using a least action principle and gradient-based minimization. Combined, neurosynaptic dynamics approximate real-time error backpropagation, mappable to mechanistic components of cortical networks, whose dynamics can again be described within the proposed framework. The presented models narrow the gap between well-defined, functional algorithms and their biophysical implementation, improving our understanding of the computational principles the brain might employ. Furthermore, such models are naturally translated to hardware mimicking the vastly parallel neural structure of the brain, promising a strongly accelerated and energy-efficient implementation of powerful learning and inference algorithms, which we demonstrate for the physical model system “BrainScaleS–1”