Quaternions in collective dynamics

We introduce a model of multi-agent dynamics for self-organised motion; individuals travel at a constant speed while trying to adopt the averaged body attitude of their neighbours. The body attitudes are represented through unitary quaternions. We prove the correspondance with the model presented in Ref. [16] where the body attitudes are represented by rotation matrices. Differently from this previous work, the individual based model (IBM) introduced here is based on nematic (rather than polar) alignment. From the IBM, the kinetic and macroscopic equations are derived. The benefit of this approach, in contrast to Ref. [16], is twofold: firstly, it allows for a better understanding of the macroscopic equations obtained and, secondly, these equations are prone to numerical studies, which is key for applications

Activation of cAMP signaling transiently inhibits apoptosis in vascular smooth muscle cells in a site upstream of caspase-3

Intracellular signaling pathways that are involved in protection of vascular smooth muscle cells (VSMC) from apoptosis remain poorly understood. This study examines the effect of activators of cAMP/cGMP signaling on apoptosis in non-transfected VSMC and in VSMC transfected with c-myc (VSMC-MYC) or with its functional analogue, E1A-adenoviral protein (VSMC-E1A). Serum-deprived VSMC-E1A exhibited the highest apoptosis measured as the content of chromatin and low molecular weight DNA fragments, phosphatidylserine content in the outer surface of plasma membrane and caspase-3 activity (ten-, five-, four- and tenfold increase after 6 h of serum withdrawal, respectively). In VSMC-E1A, the addition of an activator of adenylate cyclase, forskolin, abolished chromatin cleavage, DNA laddering, caspase-3 activation and the appearance of morphologically-defined apoptotic cells triggered by 6 h of serum deprivation. In non-transfected VSMC and in VSMC-MYC, 6 h serum deprivation led to approximately six- and threefold activation of chromatin cleavage, respectively, that was also blocked by forskolin. In VSMC-E1A, inhibition of apoptosis was observed with other activators of cAMP signaling (cholera toxin, isoproterenol, adenosine, 8-Br-cAMP), whereas 6 h incubation with modulators of cGMP signaling (8-Br-cGMP, nitroprusside, atrial natriuretic peptide, L-NAME) did not affect the development of apoptotic machinery. The antiapoptotic effect of forskolin was abolished in 24 h of serum deprivation that was accompanied by normalization of intracellular cAMP content and protein kinase A (PKA) activity. Protection of VSMC-E1A from apoptosis by forskolin was blunted by PKA inhibitors (H-89 and KT5720), whereas transfection of cells with PKA catalytic subunit attenuated apoptosis triggered by serum withdrawal. The protection of VSMC-E1A by forskolin from apoptosis was insensitive to modulators of cytoskeleton assembly (cytochalasin B, colchicine). Neither acute (30 min) nor chronic (24 h) exposure of VSMC to forskolin modified basal and serum-induced phosphorylation of the MAP kinase ERK1/2. Thus, our results show that activation of cAMP signaling delays the development of apoptosis in serum-deprived VSMC at a site upstream of caspase-3 via activation of PKA and independently of cAMP-induced reorganization of the cytoskeleton network and the ERK1/2-terminated MAPK signaling cascade

Hyperbolicity and non-conservativity of a hydrodynamic model of swarming rigid bodies

International audienceIn this paper, we study a nonlinear system of first order partial differential equations describing the macroscopic behavior of an ensemble of interacting selfpropelled rigid bodies. Such system may be relevant for the modelling of bird flocks, fish schools or fleets of drones. We show that the system is hyperbolic and can be approximated by a conservative system through relaxation. We also derive viscous corrections to the model from the hydrodynamic limit of a kinetic model. This analysis prepares the future development of numerical approximations of this system

Hyperbolicity and non-conservativity of a hydrodynamic model of swarming rigid bodies

In this paper, we study a nonlinear system of first order partial differential equations describing the macroscopic behavior of an ensemble of interacting selfpropelled rigid bodies. Such system may be relevant for the modelling of bird flocks, fish schools or fleets of drones. We show that the system is hyperbolic and can be approximated by a conservative system through relaxation. We also derive viscous corrections to the model from the hydrodynamic limit of a kinetic model. This analysis prepares the future development of numerical approximations of this system