Probabilistic approach of water residence time and connectivity using Markov Chains with application to tidal embayments

Markov Chain analysis was recently proposed to assess the time scales and preferential pathways into biological or physical networks by computing residence time, first passage time, rates of transfer between nodes and number of passages in a node. We propose to adapt an algorithm already published for simple systems to physical systems described with a high resolution hydrodynamic model. The method is applied to bays and estuaries on the Eastern Coast of Canada for their interest in shellfish aquaculture. Current velocities have been computed by using a 2 dimensional grid of elements and circulation patterns were summarized by averaging Eulerian flows between adjacent elements. Flows and volumes allow computing probabilities of transition between elements and to assess the average time needed by virtual particles to move from one element to another, the rate of transfer between two elements, and the average residence time of each system. We also combined transfer rates and times to assess the main pathways of virtual particles released in farmed areas and the potential influence of farmed areas on other areas. We suggest that Markov chain is complementary to other sets of ecological indicators proposed to analyse the interactions between farmed areas - e.g. depletion index, carrying capacity assessment. Markov Chain has several advantages with respect to the estimation of connectivity between pair of sites. It makes possible to estimate transfer rates and times at once in a very quick and efficient way, without the need to perform long term simulations of particle or tracer concentration.

Two novel COLVI long chains in zebrafish that are essential for muscle development

Collagen VI (COLVI), a protein ubiquitously expressed in connective tissues, is crucial for structural integrity, cellular adhesion, migration and survival. Six different genes are recognized in mammalians, encoding six COLVI-chains that assemble as two ‘short’ (α1, α2) and one ‘long’ chain (theoretically any one of α3–6). In humans, defects in the most widely expressed heterotrimer (α123), due to mutations in the COL6A1-3 genes, cause a heterogeneous group of neuromuscular disorders, collectively termed COLVI-related muscle disorders. Little is known about the function(s) of the recently described α4-6 chains and no mutations have been detected yet. In this study, we characterized two novel COLVI long chains in zebrafish that are most homologous to the mammalian α4 chain; therefore, we named the corresponding genes col6a4a and col6a4b. These orthologues represent ancestors of the mammalian Col6a4-6 genes. By in situ hybridization and RT-qPCR, we unveiled a distinctive expression kinetics for col6a4b, compared with the other col6a genes. Using morpholino antisense oligonucleotides targeting col6a4a, col6a4b and col6a2, we modelled partial and complete COLVI deficiency, respectively. All morphant embryos presented altered muscle structure and impaired motility. While apoptosis was not drastically increased, autophagy induction was defective in all morphants. Furthermore, motoneuron axon growth was abnormal in these morphants. Importantly, some phenotypical differences emerged between col6a4a and col6a4b morphants, suggesting only partial functional redundancy. Overall, our results further confirm the importance of COLVI in zebrafish muscle development and may provide important clues for potential human phenotypes associated with deficiency of the recently described COLVI-chains.