Compact 3-manifolds via 4-colored graphs

We introduce a representation of compact 3-manifolds without spherical boundary components via (regular) 4-colored graphs, which turns out to be very convenient for computer aided study and tabulation. Our construction is a direct generalization of the one given in the eighties by S. Lins for closed 3-manifolds, which is in turn dual to the earlier construction introduced by Pezzana's school in Modena. In this context we establish some results concerning fundamental groups, connected sums, moves between graphs representing the same manifold, Heegaard genus and complexity, as well as an enumeration and classification of compact 3-manifolds representable by graphs with few vertices ($\le 6$ in the non-orientable case and $\le 8$ in the orientable one).Comment: 25 pages, 11 figures; changes suggested by referee: references added, figure 2 modified, results about classification of the manifolds in Proposition 17 announced at the end of section 9. Accepted for publication in RACSAM. The final publication is available at Springer (see DOI

Impaired Sprouting and Axonal Atrophy in Cerebellar Climbing Fibres following In Vivo Silencing of the Growth-Associated Protein GAP-43

The adult mammalian central nervous system has a limited ability to establish new connections and to recover from traumatic or degenerative events. The olivo-cerebellar network represents an excellent model to investigate neuroprotection and repair in the brain during adulthood, due to its high plasticity and ordered synaptic organization. To shed light on the molecular mechanisms involved in these events, we focused on the growth-associated protein GAP-43 (also known as B-50 or neuromodulin). During development, this protein plays a crucial role in growth and in branch formation of neurites, while in the adult it is only expressed in a few brain regions, including the inferior olive (IO) where climbing fibres (CFs) originate. Following axotomy GAP-43 is usually up-regulated in association with regeneration. Here we describe an in vivo lentiviral-mediated gene silencing approach, used for the first time in the olivo-cerebellar system, to efficiently and specifically downregulate GAP-43 in rodents CFs. We show that lack of GAP-43 causes an atrophy of the CF in non-traumatic conditions, consisting in a decrease of its length, branching and number of synaptic boutons. We also investigated CF regenerative ability by inducing a subtotal lesion of the IO. Noteworthy, surviving CFs lacking GAP-43 were largely unable to sprout on surrounding Purkinje cells. Collectively, our results demonstrate that GAP-43 is essential both to maintain CFs structure in non-traumatic condition and to promote sprouting after partial lesion of the IO