Holonomy and vortex structures in quantum hydrodynamics

In this paper we consider a new geometric approach to Madelung's quantum hydrodynamics (QHD) based on the theory of gauge connections. Unlike previous approaches, our treatment comprises a constant curvature thereby endowing QHD with intrinsic non-zero holonomy. In the hydrodynamic context, this leads to a fluid velocity which no longer is constrained to be irrotational and allows instead for vortex filaments solutions. After exploiting the Rasetti-Regge method to couple the Schr\"odinger equation to vortex filament dynamics, the latter is then considered as a source of geometric phase in the context of Born-Oppenheimer molecular dynamics. Similarly, we consider the Pauli equation for the motion of spin particles in electromagnetic fields and we exploit its underlying hydrodynamic picture to include vortex dynamics.Comment: 34 pages, no figures. To appear in Math. Sci. Res. Inst. Pub

Geometry of quantum hydrodynamics in theoretical chemistry

This thesis investigates geometric approaches to quantum hydrodynamics (QHD) in order to develop applications in theoretical quantum chemistry. Based upon the momentum map geometric structure of QHD and the associated Lie-Poisson and Euler-Poincar\'e equations, alternative geometric approaches to the classical limit in QHD are presented. These include a new regularised Lagrangian which allows for singular solutions called 'Bohmions' as well as a 'cold fluid' classical closure quantum mixed states. The momentum map approach to QHD is then applied to the nuclear dynamics in a chemistry model known as exact factorization. The geometric treatment extends existing approaches to include unitary electronic evolution in the frame of the nuclear flow, with the resulting dynamics carrying both Euler-Poincar\'e and Lie-Poisson structures. A new mixed quantum-classical model is then derived by considering a generalised factorisation ansatz at the level of the molecular density matrix. A new alternative geometric formulation of QHD is then constructed. Introducing a $\mathfrak{u}(1)$ connection as the new fundamental variable provides a new method for incorporating holonomy in QHD, which follows from its constant non-zero curvature. The fluid flow is no longer irrotational and carries a non-trivial circulation theorem, allowing for vortex filament solutions. Finally, non-Abelian connections are then considered in quantum mechanics. The dynamics of the spin vector in the Pauli equation allows for the introduction of an $\mathfrak{so}(3)$ connection whilst a more general $\mathfrak{u}(\mathscr{H})$ connection is introduced from the unitary evolution of a quantum system. This is used to provide a new geometric picture for the Berry connection and quantum geometric tensor, whilst relevant applications to quantum chemistry are then considered.Comment: 233 pages, 3 figures. Mathematics PhD thesis of Michael S. Foskett at the University of Surrey. Material includes results from the author's publications `Geometry of Nonadiabatic Quantum Hydrodynamics' link: http://link.springer.com/article/10.1007/s10440-019-00257-1 and 'Holonomy and vortex structures in quantum hydrodynamics' link: arXiv:2003.08664v

The mitochondrial Ca2+ channel MCU is critical for tumor growth by supporting cell cycle progression and proliferation

Introduction: The mitochondrial uniporter (MCU) Ca2+ ion channel represents the primary means for Ca2+ uptake by mitochondria. Mitochondrial matrix Ca2+ plays critical roles in mitochondrial bioenergetics by impinging upon respiration, energy production and flux of biochemical intermediates through the TCA cycle. Inhibition of MCU in oncogenic cell lines results in an energetic crisis and reduced cell proliferation unless media is supplemented with nucleosides, pyruvate or α-KG. Nevertheless, the roles of MCU-mediated Ca2+ influx in cancer cells remain unclear, in part because of a lack of genetic models.Methods: MCU was genetically deleted in transformed murine fibroblasts for study in vitro and in vivo. Tumor formation and growth were studied in murine xenograft models. Proliferation, cell invasion, spheroid formation and cell cycle progression were measured in vitro. The effects of MCU deletion on survival and cell-death were determined by probing for live/death markers. Mitochondrial bioenergetics were studied by measuring mitochondrial matrix Ca2+ concentration, membrane potential, global dehydrogenase activity, respiration, ROS production and inactivating-phosphorylation of pyruvate dehydrogenase. The effects of MCU rescue on metabolism were examined by tracing of glucose and glutamine utilization for fueling of mitochondrial respiration.Results: Transformation of primary fibroblasts in vitro was associated with increased MCU expression, enhanced MCU-mediated Ca2+ uptake, altered mitochondrial matrix Ca2+ concentration responses to agonist stimulation, suppression of inactivating-phosphorylation of pyruvate dehydrogenase and a modest increase of mitochondrial respiration. Genetic MCU deletion inhibited growth of HEK293T cells and transformed fibroblasts in mouse xenograft models, associated with reduced proliferation and delayed cell-cycle progression. MCU deletion inhibited cancer stem cell-like spheroid formation and cell invasion in vitro, both predictors of metastatic potential. Surprisingly, mitochondrial matrix [Ca2+], membrane potential, global dehydrogenase activity, respiration and ROS production were unaffected. In contrast, MCU deletion elevated glycolysis and glutaminolysis, strongly sensitized cell proliferation to glucose and glutamine limitation, and altered agonist-induced cytoplasmic Ca2+ signals.Conclusion: Our results reveal a dependence of tumorigenesis on MCU, mediated by a reliance on MCU for cell metabolism and Ca2+ dynamics necessary for cell-cycle progression and cell proliferation

Geometry of quantum hydrodynamics in theoretical chemistry

This thesis investigates geometric approaches to quantum hydrodynamics (QHD) in order to develop applications in theoretical quantum chemistry. Based upon the momentum map geometric structure of QHD and the associated Lie-Poisson and Euler-Poincaré equations, alternative geometric approaches to the classical limit in QHD are presented. Firstly, a new regularised Lagrangian is introduced, allowing for singular solutions called ‘Bohmions’ for which the associated trajectory equations are finite-dimensional and depend on a smoothened quantum potential. Secondly, the classical limit is considered for quantum mixed states. By applying a cold fluid closure to the density matrix the quantum potential term is eliminated from the Hamiltonian entirely. The momentum map approach to QHD is then applied to the nuclear dynamics in a chemistry model known as exact factorization. A variational derivation of the coupled electron-nuclear dynamics is presented, comprising an Euler-Poincaré structure for the nuclear motion. The QHD equations for the nuclei possess a Kelvin-Noether circulation theorem which returns a new equation for the evolution of the electronic Berry phase. The geometric treatment is then extended to include unitary electronic evolution in the frame of the nuclear flow, with the resulting dynamics carrying both Euler-Poincaré and Lie-Poisson structures. A new mixed quantum- classical model is then derived by applying both the QHD regularisation and cold fluid closure to a generalised factorisation ansatz at the level of the molecular density matrix. A new alternative geometric formulation of QHD is then constructed. Introducing a u(1) connection as the new fundamental variable provides a new method for incorporating holonomy in QHD, which follows from its constant non-zero curvature. The associated fluid flow is no longer constrained to be irrotational, thus possessing a non-trivial circulation theorem and allows for vortex filament solutions. This approach is naturally extended to include the coupling of vortex filament dynamics to the Schrödinger equation. This formulation of QHD is then applied to Born-Oppenheimer molecular dynamics suggesting new insights into the role of Berry phases in adiabatic phenomena. Finally, non-Abelian connections are then considered in quantum mechanics. The dynamics of the spin vector in the Pauli equation allows for the introduction of an so(3) connection whilst a more general u(H) connection can be introduced from the unitary evolution of a quantum system. This is used to provide a new picture for the Berry connection and quantum geometric tensor and well as derive more general systems of equations which feature explicit dependence on the curvature of the connection. Relevant applications to quantum chemistry are then considered

G Protein-Coupled Receptor Ca2+-Linked Mitochondrial Reactive Oxygen Species Are Essential for Endothelial/Leukocyte Adherence▿ †

Receptor-mediated signaling is commonly associated with multiple functions, including the production of reactive oxygen species. However, whether mitochondrion-derived superoxide (mROS) contributes directly to physiological signaling is controversial. Here we demonstrate a previously unknown mechanism in which physiologic Ca2+-evoked mROS production plays a pivotal role in endothelial cell (EC) activation and leukocyte firm adhesion. G protein-coupled receptor (GPCR) and tyrosine kinase-mediated inositol 1,4,5-trisphosphate-dependent mitochondrial Ca2+ uptake resulted in NADPH oxidase-independent mROS production. However, GPCR-linked mROS production did not alter mitochondrial function or trigger cell death but rather contributed to activation of NF-κΒ and leukocyte adhesion via the EC induction of intercellular adhesion molecule 1. Dismutation of mROS by manganese superoxide dismutase overexpression and a cell-permeative superoxide dismutase mimetic ablated NF-κΒ transcriptional activity and facilitated leukocyte detachment from the endothelium under simulated circulation following GPCR- but not cytokine-induced activation. These results demonstrate that mROS is the downstream effector molecule that translates receptor-mediated Ca2+ signals into proinflammatory signaling and leukocyte/EC firm adhesion

A recurrent missense variant in ITPR3 causes demyelinating Charcot-Marie-Tooth with variable severity

Charcot-Marie-Tooth (CMT) disease is a neuromuscular disorder affecting the peripheral nervous system. The diagnostic yield in demyelinating CMT (CMT1) is typically ∼80-95%, of which at least 60% is due to the PMP22 gene duplication. The remainder of CMT1 is more genetically heterogeneous. We used whole exome and whole genome sequencing data included in the GENESIS database to investigate novel causal genes and mutations in a cohort of ∼2,670 individuals with CMT neuropathy. A recurrent heterozygous missense variant p.Thr1424Met in the recently described CMT gene ITPR3, encoding IP3R3 (inositol 1,4,5-trisphosphate receptor 3) was identified. This previously reported p.Thr1424Met change was present in 33 affected individuals from nine unrelated families from multiple populations, representing an unusual recurrence rate at a mutational hotspot, strengthening the gene-disease relationship (GnomADv4 allele frequency 1.76e-6). Sanger sequencing confirmed the co-segregation of the CMT phenotype with the presence of the mutation in autosomal dominant and de novo inheritance patterns, including a four-generation family with multiple affected second-degree cousins. Probands from all families presented with slow nerve conduction velocities, matching the diagnostic category of CMT1. Remarkably, we observed a uniquely variable clinical phenotype for age at onset and phenotype severity in p.Thr1424Met carrying patients, even within families. Finally, we present data supportive of a dominant-negative effect of the p.Thr1424Met mutation with associated changes in protein expression in patient-derived cells.Charcot-Marie-Tooth (CMT) disease is a neuromuscular disorder affecting the peripheral nervous system. The diagnostic yield in demyelinating CMT (CMT1) is typically ∼80-95%, of which at least 60% is due to the PMP22 gene duplication. The remainder of CMT1 is more genetically heterogeneous. We used whole exome and whole genome sequencing data included in the GENESIS database to investigate novel causal genes and mutations in a cohort of ∼2,670 individuals with CMT neuropathy. A recurrent heterozygous missense variant p.Thr1424Met in the recently described CMT gene ITPR3, encoding IP3R3 (inositol 1,4,5-trisphosphate receptor 3) was identified. This previously reported p.Thr1424Met change was present in 33 affected individuals from nine unrelated families from multiple populations, representing an unusual recurrence rate at a mutational hotspot, strengthening the gene-disease relationship (GnomADv4 allele frequency 1.76e-6). Sanger sequencing confirmed the co-segregation of the CMT phenotype with the presence of the mutation in autosomal dominant and de novo inheritance patterns, including a four-generation family with multiple affected second-degree cousins. Probands from all families presented with slow nerve conduction velocities, matching the diagnostic category of CMT1. Remarkably, we observed a uniquely variable clinical phenotype for age at onset and phenotype severity in p.Thr1424Met carrying patients, even within families. Finally, we present data supportive of a dominant-negative effect of the p.Thr1424Met mutation with associated changes in protein expression in patient-derived cells