Methods for Building Network Models of Neural Circuits

Artificial recurrent neural networks (RNNs) are powerful models for understanding and modeling dynamic computation in neural circuits. As such, RNNs that have been constructed to perform tasks analogous to typical behaviors studied in systems neuroscience are useful tools for understanding the biophysical mechanisms that mediate those behaviors. There has been significant progress in recent years developing gradient-based learning methods to construct RNNs. However, the majority of this progress has been restricted to network models that transmit information through continuous state variables since these methods require the input-output function of individual neuronal units to be differentiable. Overwhelmingly, biological neurons transmit information by discrete action potentials. Spiking model neurons are not differentiable and thus gradient-based methods for training neural networks cannot be applied to them. This work focuses on the development of supervised learning methods for RNNs that do not require the computation of derivatives. Because the methods we develop do not rely on the differentiability of the neural units, we can use them to construct realistic RNNs of spiking model neurons that perform a variety of benchmark tasks, and also to build networks trained directly from experimental data. Surprisingly, spiking networks trained with these non-gradient methods do not require significantly more neural units to perform tasks than their continuous-variable model counterparts. The crux of the method draws a direct correspondence between the dynamical variables of more abstract continuous-variable RNNs and spiking network models. The relationship between these two commonly used model classes has historically been unclear and, by resolving many of these issues, we offer a perspective on the appropriate use and interpretation of continuous-variable models as they relate to understanding network computation in biological neural circuits. Although the main advantage of these methods is their ability to construct realistic spiking network models, they can equally well be applied to continuous-variable network models. An example is the construction of continuous-variable RNNs that perform tasks for which they provide performance and computational cost competitive with those of traditional methods that compute derivatives and outperform previous non-gradient-based network training approaches. Collectively, this thesis presents efficient methods for constructing realistic neural network models that can be used to understand computation in biological neural networks and provides a unified perspective on how the dynamic quantities in these models relate to each other and to quantities that can be observed and extracted from experimental recordings of neurons

Under-approximating Cut Sets for Reachability in Large Scale Automata Networks

In the scope of discrete finite-state models of interacting components, we present a novel algorithm for identifying sets of local states of components whose activity is necessary for the reachability of a given local state. If all the local states from such a set are disabled in the model, the concerned reachability is impossible. Those sets are referred to as cut sets and are computed from a particular abstract causality structure, so-called Graph of Local Causality, inspired from previous work and generalised here to finite automata networks. The extracted sets of local states form an under-approximation of the complete minimal cut sets of the dynamics: there may exist smaller or additional cut sets for the given reachability. Applied to qualitative models of biological systems, such cut sets provide potential therapeutic targets that are proven to prevent molecules of interest to become active, up to the correctness of the model. Our new method makes tractable the formal analysis of very large scale networks, as illustrated by the computation of cut sets within a Boolean model of biological pathways interactions gathering more than 9000 components

Representability of algebraic topology for biomolecules in machine learning based scoring and virtual screening

This work introduces a number of algebraic topology approaches, such as multicomponent persistent homology, multi-level persistent homology and electrostatic persistence for the representation, characterization, and description of small molecules and biomolecular complexes. Multicomponent persistent homology retains critical chemical and biological information during the topological simplification of biomolecular geometric complexity. Multi-level persistent homology enables a tailored topological description of inter- and/or intra-molecular interactions of interest. Electrostatic persistence incorporates partial charge information into topological invariants. These topological methods are paired with Wasserstein distance to characterize similarities between molecules and are further integrated with a variety of machine learning algorithms, including k-nearest neighbors, ensemble of trees, and deep convolutional neural networks, to manifest their descriptive and predictive powers for chemical and biological problems. Extensive numerical experiments involving more than 4,000 protein-ligand complexes from the PDBBind database and near 100,000 ligands and decoys in the DUD database are performed to test respectively the scoring power and the virtual screening power of the proposed topological approaches. It is demonstrated that the present approaches outperform the modern machine learning based methods in protein-ligand binding affinity predictions and ligand-decoy discrimination

Analysis of parametric biological models with non-linear dynamics

In this paper we present recent results on parametric analysis of biological models. The underlying method is based on the algorithms for computing trajectory sets of hybrid systems with polynomial dynamics. The method is then applied to two case studies of biological systems: one is a cardiac cell model for studying the conditions for cardiac abnormalities, and the second is a model of insect nest-site choice.Comment: In Proceedings HSB 2012, arXiv:1208.315

On combinatorial optimisation in analysis of protein-protein interaction and protein folding networks

Abstract: Protein-protein interaction networks and protein folding networks represent prominent research topics at the intersection of bioinformatics and network science. In this paper, we present a study of these networks from combinatorial optimisation point of view. Using a combination of classical heuristics and stochastic optimisation techniques, we were able to identify several interesting combinatorial properties of biological networks of the COSIN project. We obtained optimal or near-optimal solutions to maximum clique and chromatic number problems for these networks. We also explore patterns of both non-overlapping and overlapping cliques in these networks. Optimal or near-optimal solutions to partitioning of these networks into non-overlapping cliques and to maximum independent set problem were discovered. Maximal cliques are explored by enumerative techniques. Domination in these networks is briefly studied, too. Applications and extensions of our findings are discussed