A permutation method for network assembly.

We present a method for assembling directed networks given a prescribed bi-degree (in- and out-degree) sequence. This method utilises permutations of initial adjacency matrix assemblies that conform to the prescribed in-degree sequence, yet violate the given out-degree sequence. It combines directed edge-swapping and constrained Monte-Carlo edge-mixing for improving approximations to the given out-degree sequence until it is exactly matched. Our method permits inclusion or exclusion of 'multi-edges', allowing assembly of weighted or binary networks. It further allows prescribing the overall percentage of such multiple connections-permitting exploration of a weighted synthetic network space unlike any other method currently available for comparison of real-world networks with controlled multi-edge proportion null spaces. The graph space is sampled by the method non-uniformly, yet the algorithm provides weightings for the sample space across all possible realisations allowing computation of statistical averages of network metrics as if they were sampled uniformly. Given a sequence of in- and out- degrees, the method can also produce simple graphs for sequences that satisfy conditions of graphicality. Our method successfully builds networks with order O(107) edges on the scale of minutes with a laptop running Matlab. We provide our implementation of the method on the GitHub repository for immediate use by the research community, and demonstrate its application to three real-world networks for null-space comparisons as well as the study of dynamics of neuronal networks

A single-cell atlas of de novo β-cell regeneration reveals the contribution of hybrid β/δ cells to diabetes recovery in zebrafish

Regeneration-competent species possess the ability to reverse the progression of severe diseases by restoring the function of the damaged tissue. However, the cellular dynamics underlying this capability remain unexplored. Here, we use single-cell transcriptomics to map the cellular dynamics underlying de novo β-cell regeneration during induction and recovery from diabetes in zebrafish. We show that the zebrafish has evolved two distinct types of somatostatin-producing δ-cells, which we term δ1- and δ2-cells. Moreover, we characterize a small population of glucose-responsive islet cells, which share the hormones and fate-determinants of both β- and δ1-cells. The transcriptomic analysis of β-cell regeneration reveals that the development of β/δ hybrid cells constitutes a prominent source of insulin-expression during diabetes recovery. Using in vivo calcium imaging and cell tracking, we further show that the hybrid cells form de novo upon β-cell loss and acquire glucose-responsiveness in the course of regeneration. The overexpression of dkk3, a gene enriched in hybrid cells, increases their formation in the absence of β-cell injury. Our data provide an atlas of β-cell regeneration and indicate that the rapid formation of glucose-responsive hybrid cells contributes to the resolution of diabetes in zebrafish