A variational problem on Stiefel manifolds

In their paper on discrete analogues of some classical systems such as the rigid body and the geodesic flow on an ellipsoid, Moser and Veselov introduced their analysis in the general context of flows on Stiefel manifolds. We consider here a general class of continuous time, quadratic cost, optimal control problems on Stiefel manifolds, which in the extreme dimensions again yield these classical physical geodesic flows. We have already shown that this optimal control setting gives a new symmetric representation of the rigid body flow and in this paper we extend this representation to the geodesic flow on the ellipsoid and the more general Stiefel manifold case. The metric we choose on the Stiefel manifolds is the same as that used in the symmetric representation of the rigid body flow and that used by Moser and Veselov. In the extreme cases of the ellipsoid and the rigid body, the geodesic flows are known to be integrable. We obtain the extremal flows using both variational and optimal control approaches and elucidate the structure of the flows on general Stiefel manifolds.Comment: 30 page

An essential bifunctional enzyme in Mycobacterium tuberculosis for itaconate dissimilation and leucine catabolism

Mycobacterium tuberculosis (Mtb) is the etiological agent of tuberculosis. One-fourth of the global population is estimated to be infected with Mtb, accounting for ∼1.3 million deaths in 2017. As part of the immune response to Mtb infection, macrophages produce metabolites with the purpose of inhibiting or killing the bacterial cell. Itaconate is an abundant host metabolite thought to be both an antimicrobial agent and a modulator of the host inflammatory response. However, the exact mode of action of itaconate remains unclear. Here, we show that Mtb has an itaconate dissimilation pathway and that the last enzyme in this pathway, Rv2498c, also participates in L-leucine catabolism. Our results from phylogenetic analysis, in vitro enzymatic assays, X-ray crystallography, and in vivo Mtb experiments, identified Mtb Rv2498c as a bifunctional β-hydroxyacyl-CoA lyase and that deletion of the rv2498c gene from the Mtb genome resulted in attenuation in a mouse infection model. Altogether, this report describes an itaconate resistance mechanism in Mtb and an L-leucine catabolic pathway that proceeds via an unprecedented (R)-3-hydroxy-3-methylglutaryl-CoA (HMG-CoA) stereospecific route in nature

Conductivity of underdoped YBa2Cu3O7-d : evidence for incoherent pair correlations in the pseudogap regime

Conductivity due to superconducting fluctuations studied in optimally doped YBa2Cu3O7-d films displays a stronger decay law in temperature than explainable by theory. A formula is proposed, which fits the data very well with two superconductive parameters, Tc and the coherence length ksi_c0, and an energy scale Delta*. This is also valid in underdoped materials and enables to describe the conductivity up to 300 K with a single-particle excitations channel in parallel with a channel whose contribution is controlled by ksi_c0, Tc and Delta*. This allows to address the nature of the pseudogap in favour of incoherent pairing.Comment: 14 pages, 4 figures, 1 tabl

Catalysis by hen egg-white lysozyme proceeds via a covalent intermediate

Hen egg-white lysozyme (HEWL) was the first enzyme to have its three-dimensional structure determined by X-ray diffraction techniques(1). A catalytic mechanism, featuring a long-lived oxo-carbenium-ion intermediate, was proposed on the basis of model-building studies(2). The `Phillips' mechanism is widely held as the paradigm for the catalytic mechanism of beta -glycosidases that cleave glycosidic linkages with net retention of configuration of the anomeric centre. Studies with other retaining beta -glycosidases, however, provide strong evidence pointing to a common mechanism for these enzymes that involves a covalent glycosyl-enzyme intermediate, as previously postulated(3). Here we show, in three different cases using electrospray ionization mass spectrometry, a catalytically competent covalent glycosyl-enzyme intermediate during the catalytic cycle of HEWL. We also show the three-dimensional structure of this intermediate as determined by Xray diffraction. We formulate a general catalytic mechanism for all retaining beta -glycosidases that includes substrate distortion, formation of a covalent intermediate, and the electrophilic migration of C1 along the reaction coordinate

Lifetime of quasiparticles in the nearly free electron metal sodium

We report a high resolution angle resolved photoemission ARPES study of the prototypical nearly free electron metal sodium. The observed mass enhancement is slightly smaller than that derived in previous studies. The new results on the lifetime broadening increase the demand for theories beyond the random phase approximation. Our results do not support the proposed strong enhancement of the scattering rates of the charge carriers due to a coupling to spin fluctuations. Moreover, a comparison with earlier electron energy loss data on sodium yields a strong reduction of the mass enhancement of dipolar electron hole excitations compared to that of monopole hole excitations, measured by ARPE

A Model Study of Discrete Scale Invariance and Long-Range Interactions

We investigate the modification of discrete scale invariance in the bound state spectrum by long-range interactions. This problem is relevant for effective field theory descriptions of nuclear cluster states and manifestations of the Efimov effect in nuclei. As a model system, we choose a one dimensional inverse square potential supplemented with a long-range Coulomb interaction. We study the renormalization and bound-state spectrum of the system as a function of the Coulomb interaction strength. Our results indicate, that the counterterm required to renormalize the inverse square potential alone is sufficient to renormalize the full problem. However, the breaking of the discrete scale invariance through the Coulomb interaction leads to a modified bound state spectrum. The shallow bound states are strongly influenced by the Coulomb interaction while the deep bound states are dominated by the inverse square potential.Comment: 8 pages, 6 figures, EPJ style, published versio

The symmetric representation of the rigid body equations and their discretization

This paper analyses continuous and discrete versions of the generalized rigid body equations and the role of these equations in numerical analysis, optimal control and integrable Hamiltonian systems. In particular, we present a symmetric representation of the rigid body equations on the Cartesian product SO(n)×SO(n) and study its associated symplectic structure. We describe the relationship of these ideas with the Moser-Veselov theory of discrete integrable systems and with the theory of variational symplectic integrators. Preliminary work on the ideas discussed in this paper may be found in Bloch et al (Bloch A M, Crouch P, Marsden J E and Ratiu T S 1998 Proc. IEEE Conf. on Decision and Control 37 2249-54).Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/49076/2/no2416.pd

SARS-CoV-2 infects the human kidney and drives fibrosis in kidney organoids

Kidney failure is frequently observed during and after COVID-19, but it remains elusive whether this is a direct effect of the virus. Here, we report that SARS-CoV-2 directly infects kidney cells and is associated with increased tubule-interstitial kidney fibrosis in patient autopsy samples. To study direct effects of the virus on the kidney independent of systemic effects of COVID-19, we infected human-induced pluripotent stem-cell-derived kidney organoids with SARS-CoV-2. Single-cell RNA sequencing indicated injury and dedifferentiation of infected cells with activation of profibrotic signaling pathways. Importantly, SARS-CoV-2 infection also led to increased collagen 1 protein expression in organoids. A SARS-CoV-2 protease inhibitor was able to ameliorate the infection of kidney cells by SARS-CoV-2. Our results suggest that SARS-CoV-2 can directly infect kidney cells and induce cell injury with subsequent fibrosis. These data could explain both acute kidney injury in COVID-19 patients and the development of chronic kidney disease in long COVID