Conformal Coordinates Research Articles

Metal Induced Conformational Changes of Alpha‐Synuclein and the Role of Ambient Oxygen

Hypotheses surrounding the native conformational states of α‐synuclein (αS), which is known to be a key player in Parkinson's Disease (PD) pathology, have evolved in recent years to adopt both a monomeric and tetrameric form. Traditionally, the conformation of αS was described as an intrinsically disordered monomer that aggregates to form β‐sheet fibrils, potentially through oligomeric intermediates. Upon interaction with membranes, this monomeric conformation of αS is known to shift from its dynamic unfolded state to α‐helical. Tetrameric αS has been characterized as both α‐helical and aggregation resistant, likely a passive storage form of the protein. The pathological conformation of αS remains controversial but each functional fold and dysfunctional misfold must originate from the monomeric protein. Membrane‐protein interactions are thought to facilitate the transition of monomeric αS to the α‐helical tetramer due to the similarity in folding patterns.Physiological levels of cerebral biometals, such as copper and iron, change in various regions of the brain with aging and with advanced disease states. Metal dyshomeostasis has long been linked to PD but most of the work predated the discovery of the tetramer and the acceptance of αS as being post‐translationally acetylated at the N‐terminus. The latter has shown biophysical variation in regards to both αS conformational dynamics and metal coordination. The presented research will highlight metal‐induced changes in the folding pattern of αS and the distinguishable differences observed between various metal oxidation states. Unique changes are observed in the protein secondary structure and the hydrodynamic radius upon the introduction of stoichiometric quantities of individual metal ions based on circular dichroism and dynamic light scattering analyses respectively. Under oxidatively stressed conditions, metal‐bound αS can promote the generation of reactive oxygen species. Immunoblotting techniques have revealed that metal‐bound αS can follow distinct pathways towards toxic oligomers or β‐sheet fibrils depending on the metal. Furthermore, a clear involvement of ambient oxygen in the production of post‐translational modifications has been observed. Such metal‐induced conformational changes result in altered membrane interactions, which could have physiological implications. Taken together, these results contribute to the ongoing conversation within the field about the role of metals and αS in PD progression.Support or Funding InformationSupported by Virginia Commonwealth University, College of Humanities & Sciences

Transformation of 3D object into flat ribbon for RPS additive manufacturing technology

PurposeThis study aims to give a description of conformal transformation Cartesian coordinates into spiral coordinates using the example of roll powder sintering (RPS) additive manufacturing (AM) technology. RPS has several advantages over dominant AM processes currently available in the market. RPS allows accomplishing designs, which are impossible, very expensive and difficult to create by other methods. The technology requires slicing a 3D object with spiral scanning.Design/methodology/approachThe paper describes the possibility of accurate 3D object transformation into a flat ribbon by spiral coordinate system. Parameters of conformal transformation are calculated according to the equation of equivalence between (x, y, z) and (l, z) coordinates.FindingsAs numerical examples show, it is possible to convert three-dimensional space to two-dimensional one if you know the thickness of the spatial layer. The proposed methodology can be used for the transformation of 3D computer-aided design models into 2D strip models.Originality/valueIn this paper, the author proposes a method of converting Cartesian coordinates into spiral coordinates. Conformal transformation of three-dimensional space to two-dimensional one by use of spiral coordinate system is demonstrated by RPS AM technology, which allows to produce objects with high accuracy.

Optimal convection cooling flows in general 2D geometries

We generalize a recent method for computing optimal 2D convection cooling flows in a horizontal layer to a wide range of geometries, including those relevant for technological applications. We write the problem in a conformal pair of coordinates which are the pure conduction temperature and its harmonic conjugate. We find optimal flows for cooling a cylinder in an annular domain, a hot plate embedded in a cold surface, and a channel with a hot interior and cold exterior. With a constraint of fixed kinetic energy, the optimal flows are all essentially the same in the conformal coordinates. In the physical coordinates, they consist of vortices ranging in size from the length of the hot surface to a small cutoff length at the interface of the hot and cold surfaces. With the constraint of fixed enstrophy (or fixed rate of viscous dissipation), a geometry-dependent metric factor appears in the equations. The conformal coordinates are useful here because they map the problems to a rectangular domain, facilitating numerical solutions. With a small enstrophy budget, the optimal flows are dominated by vortices that have the same size as the flow domain.

Metastabilities in the Human Prion Protein N-Terminal Beta-Sheet are Dictated by the 129 Polymorphism

We study the thermodynamic stability of the native state of the human prion protein using a new free-energy method, replica-exchange on-the-fly paramaterization. This method is designed to overcome hidden-variable sampling limitations to yield nearly error-free free-energy profiles along a conformational coordinate. We confirm that all four (M129V,D178N) polymorphs have a ground-state conformation with three intact beta-sheet hydrogen bonds. Additionally, they are observed to have distinct metastabilities determined by the side-chain at position 129. We rationalize these findings with reference to the prion “strain” hypothesis, which links the variety of transmissible spongiform encephalopathy phenotypes to conformationally distinct infectious prion forms and classifies distinct phenotypes of sporadic Creutzfeldt-Jakob disease based solely on the 129 polymorphism. Because such metastable structures are not easily observed in structural experiments, our approach could potentially provide new insights into the conformational origins of prion diseases and other pathologies arising from protein misfolding and aggregation.

Два подхода к интерпретации диаграммы Хаббла

Supernovae of type Ia are used as standard candles in modern cosmology, they serve to testcosmological models. Interpretation of the Hubble diagram based on the standard cosmologicalmodel led cosmologists to conclusion that the Universe is filled mostly with cosmic dust andmysterious dark energy.In this paper we present exact solutions of the Friedmann equation in standard cosmologyand conformal cosmology. The theoretical curves interpolating the Hubble diagram for thelatest supernova data are expressed in an analytical form. The functions belong to the classof meromorphic Weierstrass functions. Both approaches describe the modern Hubble diagramwith the same accuracy. Physical interpretation from the standpoint of conformal cosmologyis preferable, since supernova data are described without using a Λ-term. In the standardcosmology, the Hubble diagram is described by some characteristics: a Hubble parameter (),a deceleration (), and a jerk (). As calculations show, the deceleration parameter changesits sign during the evolution of the Universe, the -parameter remains constant. In the modernera, the Universe expands with acceleration, and in the past its acceleration was negative. Thechange in the sign of acceleration, without a clear physical reason, puzzles cosmologists.It seems obvious to us that to study objects dislocated from us at distances of billions oflight years, we should not use the coordinate time customary for work in laboratories, butthe conformal time. In conformal coordinates, the behavior of photons is described as in theMinkowski space. The time intervals d and d are different, they are related by the scale factor:d = d. The conformal luminosity distance is longer than the standard luminosity distance,which is manifested when observing distant stellar objects. As a result, the effective magnitudevalue - the redshift relationship, on which the Hubble diagram is constructed, will be different.Using the conformal Friedmann equation, we introduce the conformal parameters (), (),(). All parameters remain positive during the evolution of the Universe. The scale factorgrows with deceleration. The Universe does not experience a jerk.

Polymorphism at 129 dictates metastable conformations of the human prion protein N-terminal β-sheet.

We study the thermodynamic stability of the native state of the human prion protein using a new free-energy method, replica-exchange on-the-fly parameterization. This method is designed to overcome hidden-variable sampling limitations to yield nearly error-free free-energy profiles along a conformational coordinate. We confirm that all four (M129V, D178N) polymorphs have a ground-state conformation with three intact β-sheet hydrogen bonds. Additionally, they are observed to have distinct metastabilities determined by the side-chain at position 129. We rationalize these findings with reference to the prion "strain" hypothesis, which links the variety of transmissible spongiform encephalopathy phenotypes to conformationally distinct infectious prion forms and classifies distinct phenotypes of sporadic Creutzfeldt-Jakob disease based solely on the 129 polymorphism. Because such metastable structures are not easily observed in structural experiments, our approach could potentially provide new insights into the conformational origins of prion diseases and other pathologies arising from protein misfolding and aggregation.

Heparin Isomeric Oligosaccharide Separation Using Volatile Salt Strong Anion Exchange Chromatography.

The complexity of heparin and heparan sulfate saccharides makes their purification, including many isomeric structures, very challenging and is a bottleneck for structure-activity studies. High-resolution separations have been achieved by strong anion exchange (SAX) chromatography on Propac PA1 and cetyltrimethylammonium (CTA)-C18 silica columns; however, these entail subsequent desalting methodologies and consequent sample losses and are incompatible with orthogonal chromatography methodologies and, in particular, mass spectrometry. Here, we present the CTA-SAX purification of heparin oligosaccharides using volatile salt (VS) buffer. In VSCTA-SAX, the use of ammonium bicarbonate buffer for elution improves resolution through both weaker dissociation and conformational coordination of the ammonium across the sulfate groups. Using ion mobility mass spectrometry, we demonstrate that isomeric structures have different structural conformations, which makes chromatographic separation achievable. Resolution of such structures is improved compared to standard SAX methods, and in addition, VSCTA-SAX provides an orthogonal method to isolate saccharides with higher purity. Because ammonium bicarbonate is used, the samples can be evaporated rather than desalted, preventing substantial sample loss and allowing more effective subsequent analysis by electrospray mass spectrometry. We conclude that VSCTA-SAX is a powerful new tool that helps address the difficult challenge of heparin/heparan sulfate saccharide separation and will enhance structure-activity studies.

Parametric instability of classical Yang-Mills fields in an expanding geometry

We investigate the instability of classical Yang-Mills field in an expanding geometry under a color magnetic background field within the linear regime. We consider homogeneous, boost-invariant and time-dependent color magnetic fields simulating the glasma configuration. We introduce the conformal coordinates which enable us to map an expanding problem approximately into a nonexpanding problem. We find that the fluctuations with finite longitudinal momenta can grow exponentially due to parametric instability. Fluctuations with finite transverse momenta can also show parametric instability, but their momenta are restricted to be small. The most unstable modes start to grow exponentially in the early stage of the dynamics and they may affect the thermalization in heavy-ion collisions.

Spatial regression models over two-dimensional manifolds

We propose a regression model for data spatially distributed over general two-dimensional Riemannian manifolds. This is a generalized additive model with a roughness penalty term involving a differential operator computed over the non-planar domain. By virtue of a semiparametric framework, the model allows inclusion of space-varying covariate information. Estimation can be performed by conformally parameterizing the non-planar domain and then generalizing existing models for penalized spatial regression over planar domains. The conformal coordinates and the estimation problem are both computed with a finite element approach.

Resolving Conformational Switches in the Protease Ftsh using Single-Molecule FRET

FtsH is a homohexameric AAA+ protease embedded in the prokaryote membrane, where it recognizes, unfolds, translocates and lyses protein substrates. Previous crystal structural data of Thermotoga maritima FtsH in an ADP-bound and an apo-state showed an ATPase and a protease domain linked by a flexible unresolved hinge, facilitating a large conformational change upon ADP binding. The current model of the chemo-mechanical cycle was inferred from these two crystal structures and describes FtsH with a power stroke mechanism, whereby the energy released by ATP hydrolysis is converted into a conformational switch. To date, this mechanism could not be observed experimentally. Here, we use single-molecule Förster Resonance Energy Transfer (smFRET) to study FtsH in real time. Our assay involved the vesicle encapsulation of unlabeled and double-labeled monomers to promote self-assembled FtsH hexamers. Total Internal Reflection Fluorescence (TIRF) microscopy of the immobilized molecules allowed us to collect kinetic information of conformational changes. Data analysis based on hidden Markov modeling resolved distinct conformational states, transition coordinates and transition rates. Surprisingly, without nucleotide, an FtsH monomer adopted four distinct conformational states, undergoing highly dynamic interconversion on the second timescale. Thus, FtsH performed stochastic transitions independently of an energy source, but rather using thermal activation. Upon binding of ATP, the number of conformational states remained identical, however, presence of ATP reduced some barriers of the free energy landscape. A homolog mutation in FtsH, A359V, of the pathogenic mutation A510V in paraplegin displayed an additional further closed conformational state, which was highly populated in the presence of ATP. We propose that this highly populated state could reflect the malfunctioning of the pathogenic mutation in paraplegin.

Efficient Stabilization of Advection Terms Involved in Separated Representations of Boltzmann and Fokker-Planck Equations

AbstractThe fine description of complex fluids can be carried out by describing the evolution of each individual constituent (e.g. each particle, each macromolecule, etc.). This procedure, despite its conceptual simplicity, involves many numerical issues, the most challenging one being that related to the computing time required to update the system configuration by describing all the interactions between the different individuals. Coarse grained approaches allow alleviating the just referred issue: the system is described by a distribution function providing the fraction of entities that at certain time and position have a particular conformation. Thus, mesoscale models involve many different coordinates, standard space and time, and different conformational coordinates whose number and nature depend on the particular system considered. Balance equation describing the evolution of such distribution function consists of an advection-diffusion partial differential equation defined in a high dimensional space. Standard mesh-based discretization techniques fail at solving high-dimensional models because of the curse of dimensionality. Recently the authors proposed an alternative route based on the use of separated representations. However, until now these approaches were unable to address the case of advection dominated models due to stabilization issues. In this paper this issue is revisited and efficient procedures for stabilizing the advection operators involved in the Boltzmann and Fokker-Planck equation within the PGD framework are proposed.

A note on the nonperturbative nature of the Schwinger effect in the expanding de Sitter space

We reconsider a recent perturbative calculation [M. A. Băloi, Mod. Phys. Lett. A29, 1450138 (2014)] of particle production in the expanding de Sitter space in an external electromagnetic field and apply it to the case of a constant uniform electric field in two dimensions. We show that perturbative number of created particles significantly differs from the existing nonperturbative result based on the Bogoliubov transformation method. We also point out that for a physically meaningful perturbative amplitude one should restrict to external potentials Aμ which in conformal coordinates vanish at infinite times. Potentials which do not respect this condition lead to gauge-dependent amplitudes, which also show close similarities with amplitudes in flat space in the unphysical case when the external potential suddenly vanishes. These problems are intimately linked with the finite upper limit of the conformal time in the de Sitter space and most probably a similar restriction should be imposed in perturbative calculations in FRW spacetimes with the same property.

Optical cavity resonator in an expanding universe

We study evolution of frequency of a standing electromagnetic (EM) wave in a resonant optical cavity placed to the expanding manifold described by the Robertson-Walker metric. One builds a local coordinate system in which spacetime is locally Minkowskian. However, due to the conformal nature of the Robertson-Walker metric the conventional transformation to the local inertial coordinates introduces ambiguity in the physical interpretation of the local time coordinate. Therefore, contrary to a common-sense expectation, a straightforward implementation of EEP alone does not allow us to decide whether atomic clocks ticks at the same rate as the clocks based on EM modes of a cavity. To resolve the ambiguity we analyzed the cavity rigidity and the oscillation of its EM modes in an expanding universe by employing the Maxwell equations. We found out that both the size of the cavity and the EM frequency experience an adiabatic drift in conformal coordinates as the universe expands. We set up the oscillation equation for the EM modes, solve it by the WKB approximation, and reduce the coordinate-dependent quantities to their counterparts measured by a local observer who counts time with atomic clock. The solution shows that there is a perfect cancellation of the adiabatic drift of cavity's frequency by the transformation to local coordinates, and the time counted by the clocks based on EM modes of cavity has the same rate as that of atomic clocks. We conclude that there should be no cosmological drift of frequency of a standing EM wave oscillating in the cavity resonator as compared to the frequency of atomic clocks. Continuous comparison of the frequency of the optical cavity resonator against that of atomic clock yields a powerful null test of the local isotropy of the Hubble expansion and the Einstein equivalence principle in cosmology.

Resolving Conformational Switching of AAA+ Protease FtsH using Single-Molecule FRET

FtsH is a homohexameric AAA+ protease embedded in the prokaryote membrane, where it recognizes, unfolds, translocates and lyses protein substrates. Previous crystal structural data of Thermotoga maritima FtsH in an ADP-bound and an apo-state showed an ATPase and a protease domain linked by a flexible unresolved hinge, facilitating a large conformational change upon ADP binding. The current model of the chemo-mechanical cycle was inferred from these two crystal structures and describes FtsH with a power stroke mechanism, whereby the energy released by ATP hydrolysis is converted into a conformational switch. To date, this mechanism could not be observed experimentally.Here, we use single-molecule Forster Resonance Energy Transfer (smFRET) to study FtsH in real time. Our assay involved the vesicle encapsulation of unlabeled and double-labeled monomers to promote self-assembled FtsH hexamers. Total Internal Reflection Fluorescence (TIRF) microscopy of the immobilized molecules allowed us to collect kinetic information of conformational changes. Data analysis based on hidden Markov modeling resolved distinct conformational states, transition coordinates and transition rates.Surprisingly, without nucleotide, an FtsH monomer adopted four distinct conformational states, undergoing highly dynamic interconversion on the second timescale. Thus, FtsH performed stochastic transitions independently of an energy source, but rather using thermal activation. Upon binding of ATP, the number of conformational states remained identical, however, presence of ATP reduced some barriers of the free energy landscape. A homolog mutation in FtsH, A359V, of the pathogenic mutation A510V in paraplegin displayed an additional further closed conformational state, which was highly populated in the presence of ATP. We propose that this highly populated state could reflect the malfunctioning of the pathogenic mutation in paraplegin.

Muon anomalous magnetic moment and penguin loops in warped extra dimensions

We describe the computation of the one-loop muon anomalous magnetic moment and radiative penguin transitions in the minimal and custodially protected Randall–Sundrum model. A fully five-dimensional (5D) framework is employed to match the 5D theory onto the Standard Model extended by dimension-six operators. The additional contribution to the anomalous magnetic moment from the gauge-boson exchange contributions is [Formula: see text] where the first (second) number refers to the minimal (custodially-protected) model. Here 1/T denotes the location of the TeV brane in conformal coordinates, and is related to the mass of the lowest gauge-boson KK excitation by M KK ≈2.35T. We also determine the Higgs-exchange contribution, which depends on the 5D Yukawa structure and the precise interpretation of the localization of the Higgs field near or at the TeV brane.

Frozen in Beta

Frozen in Beta

Bondi Mass Cannot Become Negative in Higher Dimensions

We prove that the Bondi mass of an asymptotically flat, vacuum spacetime cannot become negative in any even dimension \({d \geq 4}\) . The notion of Bondi mass is more subtle in d > 4 dimensions because radiating metrics have a slower decay than stationary ones, and those subtleties are reflected by a considerably more difficult proof of positivity. Our proof holds for the standard spherical infinities, but it also extends to infinities of more general type which are (d − 2)-dimensional manifolds admitting a real Killing spinor. Such manifolds typically have special holonomy and Sasakian structures. The main technical advance of the paper is an expansion technique based on “conformal Gaussian null coordinates”. This expansion helps us to understand the consequences imposed by Einstein’s equations on the asymptotic tail of the metric as well as auxiliary spinorial fields. As a by-product, we derive a coordinate expression for the geometrically invariant formula for the Bondi mass originally given by Hollands and Ishibashi.

Case study on temperature-accelerated molecular dynamics simulation of ligand dissociation: inducer dissociation from the Lac repressor protein.

We studied ligand dissociation from the inducer-binding domain of the Lac repressor protein using temperature-accelerated molecular dynamics (TAMD) simulations. With TAMD, ligand dissociation could be observed within relatively short simulation time. This allowed many dissociation trajectories to be sampled. Under the adiabatic approximation of TAMD, all but one degree of freedom of the system were sampled from usual canonical ensembles at room temperature. Thus, meaningful statistical analyses could be carried out on the trajectories. A systematic approach was proposed to analyze possible correlations between ligand dissociation and fluctuations of various protein conformational coordinates. These analyses employed relative entropies, allowing both linear and nonlinear correlations to be considered. Applying the simulation and analysis methods to the inducer binding domain of the Lac repressor protein, we found that ligand dissociation from this protein correlated mainly with fluctuations of side-chain conformations of a few residues that surround the binding pocket. In addition, the two binding sites of the dimeric protein were dynamically coupled: occupation of one site by an inducer molecule could significantly reduce or slow down conformational dynamics around the other binding pocket.

Double trace flows and holographic RG in dS/CFT correspondence

If there is a dS/CFT correspondence, time evolution in the bulk should translate to RG flows in the dual euclidean field theory. Consequently, although the dual field is expected to be non-unitary, its RG flows will carry an imprint of the unitary time evolution in the bulk. In this note we examine the prediction of holographic RG in de Sitter space for the flow of double and triple trace couplings in any proposed dual. We show quite generally that the correct form of the field theory beta functions for the double trace couplings is obtained from holography, provided one identifies the scale of the field theory with (i|T|) where T is the `time' in conformal coordinates. For dS(4), we find that with an appropriate choice of operator normalization, it is possible to have real n-point correlation functions as well as beta functions with real coefficients. This choice leads to an RG flow with an IR fixed point at negative coupling unlike in a unitary theory where the IR fixed point is at positive coupling. The proposed correspondence of Sp(N) vector models with de Sitter Vasiliev gravity provides a specific example of such a phenomenon. For dS(d+1) with even d, however, we find that no choice of operator normalization exists which ensures reality of coefficients of the beta-functions as well as absence of n-dependent phases for various n-point functions, as long as one assumes real coupling constants in the bulk Lagrangian.

The muon anomalous magnetic moment in the Randall-Sundrum model

We calculate the anomalous magnetic moment of the muon in the minimal Randall-Sundrum model with standard model fields in five-dimensional (5D) warped space and a brane-localized Higgs. We use a fully 5D framework to compute the one-loop matching coefficients of the effective theory at the electroweak scale. The extra contribution to the anomalous magnetic moment from the model-independent gauge-boson exchange contributions \Delta a_\mu is approximately 8.8*10^-11 (1TeV/T)^2, where 1/T denotes the location of the TeV brane in conformal coordinates, and is related to the mass of the lowest gauge boson KK excitation, which is roughly 2.5T. The result constitutes the first complete determination of the gauge-boson contribution to g-2 and is robust against the variation of the bulk fermion masses and 5D Yukawa coupling. We also determine the strongly model-parameter dependent effect of Higgs-exchange diagrams.