A tropical geometric approach to exceptional points.

Non-Hermitian systems have been widely explored in platforms ranging from photonics to electric circuits. A defining feature of non-Hermitian systems is exceptional points (EPs), where both eigenvalues and eigenvectors coalesce. Tropical geometry is an emerging field of mathematics at the interface between algebraic geometry and polyhedral geometry, with diverse applications to science. Here, we introduce and develop a unified tropical geometric framework to characterize different facets of non-Hermitian systems. We illustrate the versatility of our approach using several examples and demonstrate that it can be used to select from a spectrum of higher-order EPs in gain and loss models, predict the skin effect in the non-Hermitian Su-Schrieffer-Heeger model, and extract universal properties in the presence of disorder in the Hatano-Nelson model. Our work puts forth a framework for studying non-Hermitian physics and unveils a connection of tropical geometry to this field.

Mechano-regulation by clathrin pit-formation and passive cholesterol-dependent tubules during de-adhesion.

Adherent cells ensure membrane homeostasis during de-adhesion by various mechanisms, including endocytosis. Although mechano-chemical feedbacks involved in this process have been studied, the step-by-step build-up and resolution of the mechanical changes by endocytosis are poorly understood. To investigate this, we studied the de-adhesion of HeLa cells using a combination of interference reflection microscopy, optical trapping and fluorescence experiments. We found that de-adhesion enhanced membrane height fluctuations of the basal membrane in the presence of an intact cortex. A reduction in the tether force was also noted at the apical side. However, membrane fluctuations reveal phases of an initial drop in effective tension followed by saturation. The area fractions of early (Rab5-labelled) and recycling (Rab4-labelled) endosomes, as well as transferrin-labelled pits close to the basal plasma membrane, also transiently increased. On blocking dynamin-dependent scission of endocytic pits, the regulation of fluctuations was not blocked, but knocking down AP2-dependent pit formation stopped the tension recovery. Interestingly, the regulation could not be suppressed by ATP or cholesterol depletion individually but was arrested by depleting both. The data strongly supports Clathrin and AP2-dependent pit-formation to be central to the reduction in fluctuations confirmed by super-resolution microscopy. Furthermore, we propose that cholesterol-dependent pits spontaneously regulate tension under ATP-depleted conditions.

Thickness-Dependent Magnetic Breakdown in ZrSiSe Nanoplates.

We report a study of thickness-dependent interband and intraband magnetic breakdown by thermoelectric quantum oscillations in ZrSiSe nanoplates. Under high magnetic fields of up to 30 T, quantum oscillations arising from degenerated hole pockets were observed in thick ZrSiSe nanoplates. However, when decreasing the thickness, plentiful multifrequency quantum oscillations originating from hole and electron pockets are captured. These multiple frequencies can be explained by the emergent interband magnetic breakdown enclosing individual hole and electron pockets and intraband magnetic breakdown within spin-orbit coupling (SOC) induced saddle-shaped electron pockets, resulting in the enhanced contribution to thermal transport in thin ZrSiSe nanoplates. These experimental frequencies agree well with theoretical calculations of the intriguing tunneling processes. Our results introduce a new member of magnetic breakdown to the field and open up a dimension for modulating magnetic breakdown, which holds fundamental significance for both low-dimensional topological materials and the physics of magnetic breakdown.

Biologically Active Micropatterns of Biomolecules and Living Matter Using Microbubble Lithography.

In situ patterning of biomolecules and living organisms while retaining their biological activity is extremely challenging, primarily because such patterning typically involves thermal stresses that could be substantially higher than the physiological thermal or stress tolerance level. Top-down patterning approaches are especially prone to these issues, while bottom-up approaches suffer from a lack of control in developing defined structures and the time required for patterning. A microbubble generated and manipulated by optical tweezers (microbubble lithography) is used to self-assemble and pattern living organisms in continuous microscopic structures in real-time, where the material thus patterned remains biologically active due to their ability to withstand elevated temperatures for short exposures. Successful patterns of microorganisms (Escherichia coli, Lactococcus. lactis and the Type A influenza virus) are demonstrated, as well as reporter proteins such as green fluorescent protein (GFP) on functionalized substrates with high signal-to-noise ratio and selectivity. Together, the data presented herein may open up fascinating possibilities in rapid in situ parallelized diagnostics of multiple pathogens and bioelectronics.

Nondegenerate Integer Quantum Hall Effect from Topological Surface States in Ag2Te Nanoplates.

The quantum Hall effect is one of the exclusive properties displayed by Dirac Fermions in topological insulators, which propagates along the chiral edge state and gives rise to quantized electron transport. However, the quantum Hall effect formed by the nondegenerate Dirac surface states has been elusive so far. Here, we demonstrate the nondegenerate integer quantum Hall effect from the topological surface states in three-dimensional (3D) topological insulator ß-Ag2Te nanostructures. Surface-state dominant conductance renders quantum Hall conductance plateaus with a step of e2/h, along with typical thermopower behaviors of two-dimensional (2D) massless Dirac electrons. The 2D nature of the topological surface states is proven by the electrical and thermal transport responses under tilted magnetic fields. Moreover, the degeneracy of the surface states is removed by structure inversion asymmetry (SIA). The evidenced SIA-induced nondegenerate integer quantum Hall effect in low-symmetry ß-Ag2Te has implications for both fundamental study and the realization of topological magneto-electric effects.

Spin-Direction-Spin Coupling of Quasiguided Modes in Plasmonic Crystals.

We report an unusual spin-direction-spin coupling phenomenon of light using the leaky quasiguided modes of a waveguided plasmonic crystal. This is demonstrated as simultaneous input spin-dependent directional guiding of waves (spin-direction coupling) and wave-vector-dependent spin acquisition (direction-spin coupling) of the scattered light. These effects, manifested as the forward and the inverse spin Hall effect of light in the far field, and other accompanying spin-orbit interaction effects are observed and analyzed using a momentum (k) domain polarization Mueller matrix. Resonance-enabled enhancement of these effects is also demonstrated by utilizing the spectral Fano resonance of the hybridized modes. The fundamental origin and the unconventional manifestation of the spin-direction-spin coupling phenomenon from a relatively simple system, ability to probe and interpret the resulting spin-orbit phenomena in the far field through momentum-domain polarization analysis, and their regulated control in plasmonic-photonic crystals open up exciting avenues in spin-orbit-photonic research.

A Search for Uniformity in Human Chorionic Gonadotropin (hCG) Reporting.

Varying reports across different laboratories or across different analysers in the same lab for the same sample is not an uncommon phenomena. Experts call this a lack of harmonization. A test that is harmonized provides the same results regardless of the manufacturer of reagents used or the laboratory where the test is performed. When laboratory tests are not harmonized, the entire continuum of patient care can be affected in a number of ways. Here, we present a case of varying reports for a single serum human chorionic gonadotropin (hCG) sample on two different immunoassay platforms for a young female presenting with an abdominopelvic mass. The lab reports for serum hCG for this particular patient showed inconsistent results with the same sample within the same lab. The phenomena behind this was lack of harmonization of test results. We introspect many of the factors responsible for lack of uniformity in hCG results amongst the major ones being with use of antibodies directed against different epitopes of hCG (analyte) and the heterogeneity of the hCG molecule itself. Harmonization is a process to ensure that different clinical testing procedures used by different laboratories give equivalent results. Harmonizing test results will enable healthcare providers to use clinical guidelines with greater confidence for diagnosing disease and managing patients.

Adaptive hyperspectral imaging using structured illumination in a spatial light modulator-based interferometer.

We develop a novel hyperspectral imaging system using structured illumination in an SLM-based Michelson interferometer. In our design, we use a reflective SLM as a mirror in one of the arms of a Michelson interferometer and scan the interferometer by varying the phase across the SLM display. For achieving the latter, we apply a checkerboard phase mask on the SLM display where the gray value varies between 0-255, thereby imparting a dynamic phase of up to 262° to the incident light beam. We couple a supercontinuum source into the interferometer in order to mimic an astronomical object such as the Sun and choose a central wavelength of 637.4 nm akin to the strong emission line of Fe X present in the solar spectrum. We use a bandwidth of 30 nm and extract fringes corresponding to a spectral resolution of 3.8 nm which is limited by the reflectivity of the SLM. We also demonstrate a maximum wavelength tunability of ∼8 nm by varying the phase over the phase mask with a spectral sampling of around 0.03 nm between intermediate fringes. The checkerboard phase mask can be adapted close to real time on time-scales of a few tens of milliseconds to obtain spectral information for other near-contiguous wavelengths. The compactness, potential low cost, low power requirements, real-time tunability and lack of moving mechanical parts in the setup implies that it can have very useful applications in settings that require near real-time, multi-wavelength spectroscopic applications and is especially relevant in space astronomy.

Directed Self-Assembly Driven Mesoscale Lithography Using Laser-Induced and Manipulated Microbubbles: Complex Architectures and Diverse Applications.

A microbubble nucleated due to the absorption of a tightly focused laser at the interface of a liquid-solid substrate enables directed and irreversible self-assembly of mesoscopic particles dispersed in the liquid at the bubble base. This phenomenon has facilitated a new microlithography technique which has grown rapidly over the past decade and can now reliably pattern a vast range of soft materials and colloids, ranging from polymers to metals to proteins. In this review, we discuss the science behind this technology and the present state-of-the-art. Thus, we describe the physics of the self-assembly driven by the bubble, the techniques for generating complex mesoarchitectures, both discrete and continuous, and their properties, and the various applications demonstrated in plastic electronics, site-specific catalysis, and biosensing. Finally, we describe a roadmap for the technique to achieve its potential of successfully patterning "everything" mesoscopic and the challenges that lie therein.

IgA Monoclonal Gammopathy with Pseudohyperphosphatemia.

Monoclonal gammopathies (MGs) reflect conditions in which abnormal amounts of immunoglobulins are produced by a clone that developed from a single pro-B germ cell. They range from asymptomatic, benign disorders such as monoclonal gammopathy of undetermined significance to malignant plasma cell and lymphoid disorders, including multiple myeloma and Waldenstorm macroglobulinemia. The identification of the particular subtype of immunoglobulin molecule is done by serum immunofixation by use of specific antisera directed against different subtypes of immunoglobulin classes. However depending upon the characteristic position taken up by migrating M band on protein electrophoresis due to its molecular weight and charge, serum protein electrophoresis can itself reveal the nature of the immunoglobulin without the need to do serum immunofixation. IgA mostly migrates to beta globulin region and may often be missed out for lack of a sharp, discrete M band in gamma globulin region. Systemic manifestations of MG can be attributed to the physicochemical properties of the monoclonal immunoglobulin, to its antibody activity or to other mechanisms. We describe a case of IgA MG with pseudohyperphosphatemia.

POEMS Syndrome: Clinical and Laboratory Approach Towards Diagnosis.

Polyneuropathy, organomegaly, endocrinopathy, M protein, skin changes (POEMS) syndrome is a rare multisystem paraneoplastic disorder. Here we describe a case of a 50 year old post-menopausal female who presented with chief complaints of difficulty in walking, getting up from squatting position and tingling sensation of bilateral lower limbs since 1 month. Additional unusual features in the patient included hepatosplenomegaly, endocrinal involvement in the form of hypothyroidism and elevated estradiol levels for her age. There were skin changes in the form of hyperpigmentation. M protein was not noted on serum electrophoresis but was visible on serum protein immunofixation (IgA lambda). She was investigated as a case of polyneuropathy and later a provisional clinical diagnosis of POEMS was made based on the presence of major and minor criteria. The patient was managed with methyl prednisolone, calcium carbonate and vit D3 and topical antibiotics for local infections.

Pseudohyperkalemia in Serum and Plasma: The Phenomena and Its Clinical Implications.

Hyperkalemia is a life threatening electrolyte derangement that must be recognized and treated quickly. Pseudohyperkalemia is defined as a difference between serum and plasma potassium concentration of more than 0.4 meq/L with serum values on the higher side when both the samples are obtained at the same time, remain at room temperature and are tested within 1 h of sample collection. Given the implication of basing medical decisions on falsely elevated potassium levels, timely identification of the entity of pseudohyperkalemia and differentiating it from true hyperkalemia becomes utmost important. Here we present a case report of a 36 year old female admitted with a provisional diagnosis of pyrexia of unknown origin with hepatosplenomegaly and anaemia under evaluation. During hospital stay her potassium levels in whole blood, serum and plasma reportedly differed significantly. An abnormal WBC count beyond assay range was reported and during subsequent investigations this lead to a peripheral smear being advised and diagnosis revealed chronic lymphoblastic leukaemia with blast crisis and 86% blast cells. In patients with leukocytosis and thrombocytosis, pseudohyperkalemia may exist in the absence of electrocardiogram changes or other clinical manifestations of true hyperkalemia thus leading to reevaluation of potassium values in serum, plasma and whole blood to arrive at the true picture.

Proteomic analysis reveals that wildtype and alanine-expanded nuclear poly(A)-binding protein exhibit differential interactions in skeletal muscle.

Oculopharyngeal muscular dystrophy (OPMD) is a late-onset, primarily autosomal dominant disease caused by a short GCN expansion in the PABPN1 (polyadenylate-binding protein nuclear 1) gene that results in an alanine expansion at the N terminus of the PABPN1 protein. Expression of alanine-expanded PABPN1 is linked to the formation of nuclear aggregates in tissues from individuals with OPMD. However, as with other nuclear aggregate-associated diseases, controversy exists over whether these aggregates are the direct cause of pathology. An emerging hypothesis is that a loss of PABPN1 function and/or aberrant protein interactions contribute to pathology in OPMD. Here, we present the first global proteomic analysis of the protein interactions of WT and alanine-expanded PABPN1 in skeletal muscle tissue. These data provide both insight into the function of PABPN1 in muscle and evidence that the alanine expansion alters the protein-protein interactions of PABPN1. We extended this analysis to demonstrate altered complex formation with and loss of function of TDP-43 (TAR DNA-binding protein 43), which we show interacts with alanine-expanded but not WT PABPN1. The results from our study support a model where altered protein interactions with alanine-expanded PABPN1 that lead to loss or gain of function could contribute to pathology in OPMD.

Post-transcriptional regulation of Pabpn1 by the RNA binding protein HuR.

RNA processing is critical for proper spatial and temporal control of gene expression. The ubiquitous nuclear polyadenosine RNA binding protein, PABPN1, post-transcriptionally regulates multiple steps of gene expression. Mutations in the PABPN1 gene expanding an N-terminal alanine tract in the PABPN1 protein from 10 alanines to 11-18 alanines cause the muscle-specific disease oculopharyngeal muscular dystrophy (OPMD), which affects eyelid, pharynx, and proximal limb muscles. Previous work revealed that the Pabpn1 transcript is unstable, contributing to low steady-state Pabpn1 mRNA and protein levels in vivo, specifically in skeletal muscle, with even lower levels in muscles affected in OPMD. Thus, low levels of PABPN1 protein could predispose specific tissues to pathology in OPMD. However, no studies have defined the mechanisms that regulate Pabpn1 expression. Here, we define multiple cis-regulatory elements and a trans-acting factor, HuR, which regulate Pabpn1 expression specifically in mature muscle in vitro and in vivo. We exploit multiple models including C2C12 myotubes, primary muscle cells, and mice to determine that HuR decreases Pabpn1 expression. Overall, we have uncovered a mechanism in mature muscle that negatively regulates Pabpn1 expression in vitro and in vivo, which could provide insight to future studies investigating therapeutic strategies for OPMD treatment.

Novel mouse models of oculopharyngeal muscular dystrophy (OPMD) reveal early onset mitochondrial defects and suggest loss of PABPN1 may contribute to pathology.

Oculopharyngeal muscular dystrophy (OPMD) is a late onset disease caused by polyalanine expansion in the poly(A) binding protein nuclear 1 (PABPN1). Several mouse models have been generated to study OPMD; however, most of these models have employed transgenic overexpression of alanine-expanded PABPN1. These models do not recapitulate the OPMD patient genotype and PABPN1 overexpression could confound molecular phenotypes. We have developed a knock-in mouse model of OPMD (Pabpn1+/A17) that contains one alanine-expanded Pabpn1 allele under the control of the native promoter and one wild-type Pabpn1 allele. This mouse is the closest available genocopy of OPMD patients. We show that Pabpn1+/A17 mice have a mild myopathic phenotype in adult and aged animals. We examined early molecular and biochemical phenotypes associated with expressing native levels of A17-PABPN1 and detected shorter poly(A) tails, modest changes in poly(A) signal (PAS) usage, and evidence of mitochondrial damage in these mice. Recent studies have suggested that a loss of PABPN1 function could contribute to muscle pathology in OPMD. To investigate a loss of function model of pathology, we generated a heterozygous Pabpn1 knock-out mouse model (Pabpn1+/Δ). Like the Pabpn1+/A17 mice, Pabpn1+/Δ mice have mild histologic defects, shorter poly(A) tails, and evidence of mitochondrial damage. However, the phenotypes detected in Pabpn1+/Δ mice only partially overlap with those detected in Pabpn1+/A17 mice. These results suggest that loss of PABPN1 function could contribute to but may not completely explain the pathology detected in Pabpn1+/A17 mice.

The RNA-binding protein, ZC3H14, is required for proper poly(A) tail length control, expression of synaptic proteins, and brain function in mice.

A number of mutations in genes that encode ubiquitously expressed RNA-binding proteins cause tissue specific disease. Many of these diseases are neurological in nature revealing critical roles for this class of proteins in the brain. We recently identified mutations in a gene that encodes a ubiquitously expressed polyadenosine RNA-binding protein, ZC3H14 (Zinc finger CysCysCysHis domain-containing protein 14), that cause a nonsyndromic, autosomal recessive form of intellectual disability. This finding reveals the molecular basis for disease and provides evidence that ZC3H14 is essential for proper brain function. To investigate the role of ZC3H14 in the mammalian brain, we generated a mouse in which the first common exon of the ZC3H14 gene, exon 13 is removed (Zc3h14Δex13/Δex13) leading to a truncated ZC3H14 protein. We report here that, as in the patients, Zc3h14 is not essential in mice. Utilizing these Zc3h14Δex13/Δex13mice, we provide the first in vivo functional characterization of ZC3H14 as a regulator of RNA poly(A) tail length. The Zc3h14Δex13/Δex13 mice show enlarged lateral ventricles in the brain as well as impaired working memory. Proteomic analysis comparing the hippocampi of Zc3h14+/+ and Zc3h14Δex13/Δex13 mice reveals dysregulation of several pathways that are important for proper brain function and thus sheds light onto which pathways are most affected by the loss of ZC3H14. Among the proteins increased in the hippocampi of Zc3h14Δex13/Δex13 mice compared to control are key synaptic proteins including CaMK2a. This newly generated mouse serves as a tool to study the function of ZC3H14 in vivo.

A quantitative analysis of memory effects in the viscously coupled dynamics of optically trapped Brownian particles.

We provide a quantitative description of the memory effects existing in the apparently random Markovian dynamics of a pair of optically trapped colloidal microparticles in water. The particles are trapped in very close proximity to each other such that the resultant hydrodynamic interactions lead to non-Markovian signatures manifested by the double exponential auto-correlation function for the Brownian motion of each particle. In connection with the memory effects, we quantify the storage of energy in terms of various system parameters and demonstrate that a pair of Markovian particles - confined in individual optical traps in a viscous fluid - can be described in the framework of a single Brownian particle in a viscoelastic medium. We define and quantify the equivalent storage and loss moduli of the two-particle system, and show experimentally that the memory effects are maximized at a certain trap stiffness ratio, and reduce with increasing particle separation. The technique can be generally used to determine the effective viscoelastic parameters of any such fluid-particle systems, and can thus help understand the interactions between active particles mediated by simple or complex fluids.

Self-assembly and complex manipulation of colloidal mesoscopic particles by active thermocapillary stress.

We demonstrate that the active thermocapillary stresses induced by multiple microbubbles offer simple routes to directed self-assembly and complex but controllable micromanipulation of mesoscopic colloidal particles embedded in a liquid. The microbubbles are nucleated on a liquid-glass interface using optical tweezers. The flow around a single bubble causes self-assembly of the particles in rings at the bubble-base, while an asymmetric temperature profile generated across the bubble interface breaks the azimuthal symmetry of the flow, and induces simultaneous accumulation and repulsion of particles at different axial planes with respect to the bubble. The flow due to two adjacent bubbles leads to more diverse effects including the sorting of particles, and to local vorticity that causes radial and axial rotation of the particles - the latter being obtained for the first time using optical tweezers. The sorting is enabled by nucleating the bubbles on spatially discrete temperature profiles, while the vorticity is generated by nucleating them in the presence of a temperature gradient which once again causes a strong symmetry-breaking in the azimuthal flow. The flow profiles obtained in the experiments are explained by analytical solutions or qualitative explanations of the associated thermocapillary problem employing the Stokes and heat equations.

Nuclear poly(A) binding protein 1 (PABPN1) and Matrin3 interact in muscle cells and regulate RNA processing.

The polyadenylate binding protein 1 (PABPN1) is a ubiquitously expressed RNA binding protein vital for multiple steps in RNA metabolism. Although PABPN1 plays a critical role in the regulation of RNA processing, mutation of the gene encoding this ubiquitously expressed RNA binding protein causes a specific form of muscular dystrophy termed oculopharyngeal muscular dystrophy (OPMD). Despite the tissue-specific pathology that occurs in this disease, only recently have studies of PABPN1 begun to explore the role of this protein in skeletal muscle. We have used co-immunoprecipitation and mass spectrometry to identify proteins that interact with PABPN1 in mouse skeletal muscles. Among the interacting proteins we identified Matrin 3 (MATR3) as a novel protein interactor of PABPN1. The MATR3 gene is mutated in a form of distal myopathy and amyotrophic lateral sclerosis (ALS). We demonstrate, that like PABPN1, MATR3 is critical for myogenesis. Furthermore, MATR3 controls critical aspects of RNA processing including alternative polyadenylation and intron retention. We provide evidence that MATR3 also binds and regulates the levels of long non-coding RNA (lncRNA) Neat1 and together with PABPN1 is required for normal paraspeckle function. We demonstrate that PABPN1 and MATR3 are required for paraspeckles, as well as for adenosine to inosine (A to I) RNA editing of Ctn RNA in muscle cells. We provide a functional link between PABPN1 and MATR3 through regulation of a common lncRNA target with downstream impact on paraspeckle morphology and function. We extend our analysis to a mouse model of OPMD and demonstrate altered paraspeckle morphology in the presence of endogenous levels of alanine-expanded PABPN1. In this study, we report protein-binding partners of PABPN1, which could provide insight into novel functions of PABPN1 in skeletal muscle and identify proteins that could be sequestered with alanine-expanded PABPN1 in the nuclear aggregates found in OPMD.

A conserved role for the zinc finger polyadenosine RNA binding protein, ZC3H14, in control of poly(A) tail length.

The ZC3H14 gene, which encodes a ubiquitously expressed, evolutionarily conserved, nuclear, zinc finger polyadenosine RNA-binding protein, was recently linked to autosomal recessive, nonsyndromic intellectual disability. Although studies have been carried out to examine the function of putative orthologs of ZC3H14 in Saccharomyces cerevisiae, where the protein is termed Nab2, and Drosophila, where the protein has been designated dNab2, little is known about the function of mammalian ZC3H14. Work from both budding yeast and flies implicates Nab2/dNab2 in poly(A) tail length control, while a role in poly(A) RNA export from the nucleus has been reported only for budding yeast. Here we provide the first functional characterization of ZC3H14. Analysis of ZC3H14 function in a neuronal cell line as well as in vivo complementation studies in a Drosophila model identify a role for ZC3H14 in proper control of poly(A) tail length in neuronal cells. Furthermore, we show here that human ZC3H14 can functionally substitute for dNab2 in fly neurons and can rescue defects in development and locomotion that are present in dNab2 null flies. These rescue experiments provide evidence that this zinc finger-containing class of nuclear polyadenosine RNA-binding proteins plays an evolutionarily conserved role in controlling the length of the poly(A) tail in neurons.