Formal Methods for Hopfield-Like Networks

On Computing Structural and Behavioral Complexities of Threshold Boolean Networks : Application to Biological Networks

Various threshold Boolean networks (TBNs), a formalism used to model different types of biological networks (genes notably), can produce similar dynamics, i.e. share same behaviors. Among them, some are complex (according to Kolmogorov complexity), others not. By computing both structural and behavioral complexities, we show that most TBNs are structurally complex, even those having simple behaviors. For this purpose, we developed a new method to compute the structural complexity of a TBN based on estimates of the sizes of equivalence classes of the threshold Boolean functions composing the TBN.

Connectomics of Morphogenetically Engineered Neurons as a Predictor of Functional Integration in the Ischemic Brain

Recent advances in cell reprogramming technologies enable the in vitro generation of theoretically unlimited numbers of cells, including cells of neural lineage and specific neuronal subtypes from human, including patient-specific, somatic cells. Similarly, as demonstrated in recent animal studies, by applying morphogenetic neuroengineering principles in situ, it is possible to reprogram resident brain cells to the desired phenotype. These developments open new exciting possibilities for cell replacement therapy in stroke, albeit not without caveats. Main challenges include the successful integration of engineered cells in the ischemic brain to promote functional restoration as well as the fact that the underlying mechanisms of action are not fully understood. In this review, we aim to provide new insights to the above in the context of connectomics of morphogenetically engineered neural networks. Specifically, we discuss the relevance of combining advanced interdisciplinary approaches to: validate the functionality of engineered neurons by studying their self-organizing behavior into neural networks as well as responses to stroke-related pathology in vitro; derive structural and functional connectomes from these networks in healthy and perturbed conditions; and identify and extract key elements regulating neural network dynamics, which might predict the behavior of grafted engineered neurons post-transplantation in the stroke-injured brain.