Inertial waves in rapidly rotating flows: a dynamical systems perspective

An overview of recent developments in a wide variety of enclosed rapidly rotating flows is presented. Highlighted is the interplay between inertial waves, which have been predicted from linear inviscid considerations, and the viscous boundary layer dynamics which result from instabilities as the nonlinearities in the systems are increased. Further, even in the absence of boundary layer instabilities, nonlinearity in the system often leads to complicated interior flows due to subcritical instabilities, Eckhaus bands and heteroclinic dynamics. The ensuing spatio-temporally complex dynamics is analysed in terms of equivariant dynamical systems, providing a general perspective for the wide range of dynamics involved.Postprint (author's final draft

Nonlinear and detuning effects of the nutation angle in precessionally-forced rotating cylinder flow

The flow in a rapidly rotating cylinder forced to precess through a nutation angle a is investigated numerically, keeping all parameters constant except a, and tuned to a triadic resonance at a = 1º. When increasing a, the flow undergoes a sequence of well- characterized bifurcations associated with triadic resonance, involving heteroclinic and homoclinic cycles, for a up to about 4º. For larger a, we identify two chaotic regimes. In the first regime, with a between about 4º and 27º, the bulk flow retains remnants of the helical structures associated with the triadic resonance, but there are strong nonlinear interactions between the various azimuthal Fourier components of the flow. For the larger a regime, large detuning effects lead to the triadic resonance dynamics being completely swamped by boundary layer eruptions. The azimuthal mean flow at large angles results in a large mean deviation from solid-body rotation and the flow is characterized by strong shear at the boundary layers with temporally chaotic eruptions.Postprint (author's final draft

Small aspect ratio Taylor-Couette flow: onset of a very-low-frequency three-torus state

The nonlinear dynamics of Taylor-Couette flow in a small aspect ratio annulus (where the length of the cylinders is half of the annular gap between them) is investigated by numerically solving the full three-dimensional Navier-Stokes equations. The system is invariant to arbitrary rotations about the annulus axis and to a reflection about the annulus half-height, so that the symmetry group is SO(2)×Z2. In this paper, we systematically investigate primary and subsequent bifurcations of the basic state, concentrating on a parameter regime where the basic state becomes unstable via Hopf bifurcations. We derive the four distinct cases for the symmetries of the bifurcated orbit, and numerically find two of these. In the parameter regime considered, we also locate the codimension-two double Hopf bifurcation where these two Hopf bifurcations coincide. Secondary Hopf bifurcations (Neimark-Sacker bifurcations), leading to modulated rotating waves, are subsequently found and a saddle-node-infinite-period bifurcation between a stable (node) and an unstable (saddle) modulated rotating wave is located, which gives rise to a very-low-frequency three-torus. This paper provides the computed example of such a state, along with a comprehensive bifurcation sequence leading to its onset.Postprint (published version

Structural Mechanism for the Specific Assembly and Activation of the Extracellular Signal Regulated Kinase 5 (ERK5) Module

Mitogen-activated protein kinase (MAPK) activation depends on a linear binding motif found in all MAPK kinases (MKK). In addition, the PB1 (Phox and Bem1) domain of MKK5 is required for extracellular signal regulated kinase 5 (ERK5) activation. We present the crystal structure of ERK5 in complex with an MKK5 construct comprised of the PB1 domain and the linear binding motif. We show that ERK5 has distinct protein-protein interaction surfaces compared with ERK2, which is the closest ERK5 paralog. The two MAPKs have characteristically different physiological functions and their distinct protein-protein interaction surface topography enables them to bind different sets of activators and substrates. Structural and biochemical characterization revealed that the MKK5 PB1 domain cooperates with the MAPK binding linear motif to achieve substrate specific binding, and it also enables co-recruitment of the upstream activating enzyme and the downstream substrate into one signaling competent complex. Studies on present day MAPKs and MKKs hint on the way protein kinase networks may evolve. In particular, they suggest how paralogous enzymes with similar catalytic properties could acquire novel signaling roles by merely changing the way they make physical links to other proteins

Th1/Th2 Differentiation and B Cell Function by the Atypical PKCs and Their Regulators

The members of the atypical Protein Kinase Cs (aPKC) kinase subfamily, PKCζ and PKCλ/ɩ, as well as their adapters, p62 and Par-6, form part of the PB1-domain-containing group of signaling regulators. Both adapters serve to locate through heterotypic interactions the aPKCs into the NF-κB and cell polarity pathways, respectively. Both signaling cascades have been critically implicated in T cell function in vitro and in vivo. The analysis of gene-knockout (KO) mice deficient in the different PB1 molecules is providing more definitive information on the actual role that the aPKCs and other PB1-containing molecules play in B cell biology and T cell polarity, survival, and differentiation toward the different effector lineages in vivo and at the cellular ex vivo level. Here we discuss recent data generated from the analysis of KO mice linking the control of cell polarity by PKCλ/ɩ and PKCζ, their adapter p62, and the Par-4 inhibitor, in the control of B and T cell signaling and differentiation. Altogether, these genetic and biochemical evidences reveal the existence of a PB1-orchestrated signaling network that acts to control Th2 differentiation in vitro and in vivo, and the gene transcriptional programs that are essential during the B cell maturation and function and Th2 differentiation.This work was funded by grants SAF2011-27330 and INDISNET 01592006 from the Spanish Ministry of Economy and Competitiveness, and Comunidad de Madrid, respectively, to Pilar Martín, and R01AI072581 from the National Institutes of Health to Jorge Moscat.S

Sestrin2 promotes Unc‐51‐like kinase 1 mediated phosphorylation of p62/sequestosome‐1

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/108630/1/febs12905.pd

P62/SQSTM1 is a novel leucine-rich repeat kinase 2 (LRRK2) substrate that enhances neuronal toxicity

Autosomal-dominant, missense mutations in the leucine-rich repeat protein kinase 2 (LRRK2) gene are the most common genetic predisposition to develop Parkinson’s disease (PD). LRRK2 kinase activity is increased in several pathogenic mutations (N1437H, R1441C/G/H, Y1699C, G2019S), implicating hyperphosphorylation of a substrate in the pathogenesis of the disease. Identification of the downstream targets of LRRK2 is a crucial endeavor in the field to understand LRRK2 pathway dysfunction in the disease. We have identified the signaling adapter protein p62/SQSTM1 as a novel endogenous interacting partner and a substrate of LRRK2. Using mass spectrometry and phospho-specific antibodies, we found that LRRK2 phosphorylates p62 on Thr138 in vitro and in cells. We found that the pathogenic LRRK2 PD-associated mutations (N1437H, R1441C/G/H, Y1699C, G2019S) increase phosphorylation of p62 similar to previously reported substrate Rab proteins. Notably, we found that the pathogenic I2020T mutation and the risk factor mutation G2385R displayed decreased phosphorylation of p62. p62 phosphorylation by LRRK2 is blocked by treatment with selective LRRK2 inhibitors in cells. We also found that the amino-terminus of LRRK2 is crucial for optimal phosphorylation of Rab7L1 and p62 in cells. LRRK2 phosphorylation of Thr138 is dependent on a p62 functional ubiquitin-binding domain at its carboxy-terminus. Co-expression of p62 with LRRK2 G2019S increases the neurotoxicity of this mutation in a manner dependent on Thr138. p62 is an additional novel substrate of LRRK2 that regulates its toxic biology, reveals novel signaling nodes and can be used as a pharmacodynamic marker for LRRK2 kinase activity.</p

Rapidly rotating cylinder flow with an oscillating sidewall

We present numerical simulations of a flow in a rapidly rotating cylinder subjected to a time-periodic forcing via axial oscillations of the sidewall. When the axial oscillation frequency is less than twice the rotation frequency, inertial waves in the form of shear layers are present. For very fast rotations, these waves approach the form of the characteristics predicted from the linearized inviscid problem first studied by Lord Kelvin. The driving mechanism for the inertial waves is the oscillating Stokes layer on the sidewall and the corner discontinuities where the sidewall meets the top and bottom end walls. A detailed numerical and theoretical analysis of the internal shear layers is presented. The system is physically realizable, and attractive because of the robustness of the Stokes layer that drives the inertial waves but beyond that does not interfere with them. We show that the system loses stability to complicated three-dimensional flow when the sidewall oscillation displacement amplitude is very large (of the order of the cylinder radius), but this is far removed from the displacement amplitudes of interest, and there is a large range of governing parameters which are physically realizable in experiments in which the inertial waves are robust. This is in contrast to many other physical realizations of inertial waves where the driving mechanisms tend to lead to instabilities and complicate the study of the waves. We have computed the response diagram of the system for a large range of forcing frequencies and compared the results with inviscid eigenmodes and ray tracing techniques.Postprint (published version

Vacuolating cytotoxin and variants in Atg16L1 that disrupt autophagy promote Helicobacter pylori infection in humans

Peer reviewedPreprin