ABSTRACT
Scope is the response of Lagrangian flow topologies of three-dimensional time-periodic flows consisting of spheroidal invariant surfaces to perturbation. Such invariant surfaces generically accommodate nonintegrable Hamiltonian dynamics and, in consequence, intrasurface topologies composed of islands and chaotic seas. Computational studies predict a response to arbitrary perturbation that is dramatically different from the classical case of toroidal invariant surfaces: said islands and chaotic seas evolve into tubes and shells, respectively, that merge into "tube-and-shell" structures consisting of two shells connected via (a) tube(s) by a mechanism termed "resonance-induced merger" (RIM). This paper provides conclusive experimental proof of RIM and advances the corresponding structures as the physical topology of realistic flows with spheroidal invariant surfaces; the underlying unperturbed state is a singular limit that exists only for ideal conditions and cannot be achieved in a physical experiment. This paper furthermore expands existing theory on certain instances of RIM to a comprehensive theory (supported by experiments) that explains all observed instances of this phenomenon. This theory reveals that RIM ensues from perturbed periodic lines via three possible scenarios: truncation of tubes by (i) manifolds of isolated periodic points emerging near elliptic lines or by either (ii) local or (iii) global segmentation of periodic lines into elliptic and hyperbolic parts. The RIM scenario for local segmentation includes a perturbation-induced change from elliptic to hyperbolic dynamics near degenerate points on entirely elliptic lines (denoted "virtual local segmentation"). This theory furthermore demonstrates that RIM indeed accomplishes tube-shell merger by exposing the existence of invariant surfaces that smoothly extend from the tubes into the chaotic shells. These phenomena set the response to perturbation-and physical topology-of flows with spheroidal invariant surfaces fundamentally apart from flows with toroidal invariant surfaces. Its entirely kinematic nature and reliance solely on continuity and solenoidality of the velocity field render the comprehensive theory and its findings universal and generically applicable for (arbitrary perturbation of) basically any incompressible flow-in fact any smooth solenoidal vector field-accommodating spheroidal invariant surfaces.
ABSTRACT
BACKGROUND: Niemann-Pick type C (NPC) disease is characterized by lysosomal accumulation of cholesterol. Interestingly, NPC patients' brains also show increased levels of amyloid-ß (Aß) peptide, a key protein in Alzheimer's disease pathogenesis. We previously reported that the c-Abl tyrosine kinase is active in NPC neurons and in AD animal models and that Imatinib, a specific c-Abl inhibitor, decreased the amyloid burden in brains of the AD mouse model. Active c-Abl was shown to interact with the APP cytosolic domain, but the relevance of this interaction to APP processing has yet to be defined. RESULTS: In this work we show that c-Abl inhibition reduces APP amyloidogenic cleavage in NPC cells overexpressing APP. Indeed, we found that levels of the Aß oligomers and the carboxy-terminal fragment ßCTF were decreased when the cells were treated with Imatinib and upon shRNA-mediated c-Abl knockdown. Moreover, Imatinib decreased APP amyloidogenic processing in the brain of an NPC mouse model. In addition, we found decreased levels of ßCTF in neuronal cultures from c-Abl null mice. We demonstrate that c-Abl directly interacts with APP, that c-Abl inhibition prevents this interaction, and that Tyr682 in the APP cytoplasmic tail is essential for this interaction. More importantly, we found that c-Abl inhibition by Imatinib significantly inhibits the interaction between APP and BACE1. CONCLUSION: We conclude that c-Abl activity facilitates the APP-BACE1 interaction, thereby promoting amyloidogenic processing of APP. Thus, inhibition of c-Abl could be a pharmacological target for preventing the injurious effects of increased Aß levels in NPC disease.