Partial symmetry breaking and heteroclinic tangencies

We study some global aspects of the bifurcation of an equivariant family of volume-contracting vector fields on the three-dimensional sphere. When part of the symmetry is broken, the vector fields exhibit Bykov cycles. Close to the symmetry, we investigate the mechanism of the emergence of heteroclinic tangencies coexisting with transverse connections. We find persistent suspended horseshoes accompanied by attracting periodic trajectories with long periods

Involvement of a metalloprotease in the shedding of human neutrophil FcγRIIIB

AbstractFcγRIIIb is a glycosylphosphatidylinositol(GPI)-anchored, low-affinity IgG receptor, expressed exclusively on human neutrophils. Upon activation or apoptosis of neutrophils, FcγRIIIb is shed from the cell surface, but the enzyme(s) responsible for this process is (are) still unknown. Recently, metalloproteases have been suggested to mediate the shedding of cell surface proteins such as l-selectin and TNF-α. Using hydroxamic acid-based inhibitors of this class of proteases (BB-3103, Ro31-9790), we have observed a clear inhibitory effect on FcγRIIIb shedding after PMA stimulation of neutrophils or induction of apoptosis. These inhibitors did not affect PMA-induced degranulation or superoxide generation

Dynamics of coupled cell networks: synchrony, heteroclinic cycles and inflation

Copyright © 2011 Springer. The final publication is available at www.springerlink.comWe consider the dynamics of small networks of coupled cells. We usually assume asymmetric inputs and no global or local symmetries in the network and consider equivalence of networks in this setting; that is, when two networks with different architectures give rise to the same set of possible dynamics. Focussing on transitive (strongly connected) networks that have only one type of cell (identical cell networks) we address three questions relating the network structure to dynamics. The first question is how the structure of the network may force the existence of invariant subspaces (synchrony subspaces). The second question is how these invariant subspaces can support robust heteroclinic attractors. Finally, we investigate how the dynamics of coupled cell networks with different structures and numbers of cells can be related; in particular we consider the sets of possible “inflations” of a coupled cell network that are obtained by replacing one cell by many of the same type, in such a way that the original network dynamics is still present within a synchrony subspace. We illustrate the results with a number of examples of networks of up to six cells