R and minor radius r is provided. Its streamfunction is represented by an exact solution to the modified Liouville equation, κ denote the Laplace–Beltrami operator and the Gauss curvature of the toroidal surface respectively, and c, d are real parameters with cd < 0. This is a generalization of the flows with smooth vorticity distributions owing to Stuart ) in the plane and Crowdy ) on the spherical surface. The flow consists of two point vortices at the innermost and the outermost points of the toroidal surface on the same line of a longitude, and a smooth vorticity distribution centred at their antipodal position. Since the surface of a torus has non-constant curvature and a handle structure that are different geometric features from the plane and the spherical surface, we focus on how these geometric properties of the torus affect the topological flow structures along with the change of the aspect ratio α = R/r. A comparison with the Stuart vortex on the flat torus is also made.A steady solution of the incompressible Euler equation on a toroidal surface  When the vorticity ω is defined by ω = ∂xv − ∂yu, these two functions are connected through the Poisson equation, ∇2ψ = ∂2xψ + ∂2yψ =  − ω. In the study of fluid dynamics, by assuming the functional form of the vorticity ω in this equation, one can consider various kinds of flows with vortex structures. For a point measure distribution at ω = δx0,y0), its corresponding vortex structure is called a point vortex. The constant vorticity distribution on a domain vortex patch, in which the non-zero vorticity region is enclosed by the boundary ∂D of the domain. More generally, when the vorticity is represented by a smooth function of the streamfunction, say −ω = F(ψ), the solution to the quasi-linear elliptic equation ∇2ψ = F(ψ) yields the steady solution to the two-dimensional Euler equation. Many steady solutions of the Euler equations with vortex structures are found in the monographs [For the velocity field  = c edψ for c, Stuart vortex. In connection with geophysical and astrophysical flows, Crowdy [Suppose now that the smooth function is specified by equation ,1.1∇2ψ=e papers –6 for kne papers  obtained, Crowdy  extendedN point vortices along the line of a latitude become point vortex equilibria.The purpose of the present study is constructing Stuart vortex on the surface of a torus, a compact surface having different geometric features from the plane and the sphere. Since vortex dynamics on the toroidal surface has recently been formulated with using the analytic representation of Green's function on the surface , a few svortex crystals, are obtained [More equilibrium states of point vortices whose relative configuration is unchanged throughout the evolution, called obtained . HoweverIn the meantime, naively speaking, there seem to be less relevant to real flow phenomena, since it is difficult to confine fluid flows on the surface of a torus unless we assume the existence of a certain special external forcing. On the other hand, it has been pointed out that the incompressible Euler flow on the toroidal surface is available as a theoretical model of superfluid helium on porous media –15. The 2ψ = σsinhψ, in a doubly periodic domain and showed the existence of an elongated ‘cat-eye’ pattern and a symmetric ‘diagonal’ configuration with smooth vorticity distributions. While no exact solutions to the Liouville equation on the flat torus have been provided explicitly to the best of our knowledge, we obtain the exact solution to the Liouville equation on the flat torus as a consequence of the present study. Not only that, Stuart vortex on the toroidal surface elucidates a difference from that on the flat torus with respect to the existence of curvature and the Gauss constraint, where the total vorticity over the closed surface vanishes.The flows on the toroidal surface should be periodic both in the latitudinal as well as the longitudinal directions. In this regard, it is useful to review some preceding results on the steady vortex structures on the doubly periodic flat torus. Stationary lattice structures of point vortices –19 and aThe paper is organized as follows. In §2.R and minor radius r. The Riemannian metric is introduced through the following three-dimensional Euclidean representation of the surface [α = R/r > 1, from which we define two real parameters Let  surface :2.1ι:(θrc(θ) is defined byrc(θ) is monotonically decreasing owing to r′c(θ) < 0 for α > 1, and it satisfies a quasi-periodicity in terms of θ as follows:The toroidal surface is endowed with a complex analytic structure through the stereographic projection,ψ in terms of the toroidal coordinates uθ, uϕ) as follows:ω is obtained by taking the curl of the velocity field. Then the streamfunction ψ and the vorticity ω satisfy the following equation:dσ denotes the area element of the toroidal surface. We refer to the constraint as the Gauss constraint.According to Green & Marshall , we intrc, d are arbitrary real parameters with cd < 0, and g is a function determined later. Substituting this relation into  in an appropriate manner, we review the preceding results on the Liouville equation. Stuart [2ψp = c edψp in the domain D of the complex plane f(ζ) is an analytic function on D. In its extension to the general solution on the spherical surface, Crowdy [d, he successfully derived an analytic formula of the exact solution ψs to this modified Liouville equation from the exact solution  so that the exact solution to 2 in the Laplace–Baltrami operator  is represented byg(θ) is inconsequential to the Gauss constraint since Gauss–Bonnet theorem assures the total curvature over the toroidal surface vanishes:χ(M) denotes the Euler characteristic of the manifold M. Hence, it is sufficient to find the exact solution satisfyingLet us provide the complex representation of the Laplace–Beltrami operator ojection . Owing tequation  on the aequation :2.7ψ. Crowdy [f(ζ) does not need to be analytic everywhere on Dζ. That is to say, even if f(ζ) has isolated pole singularities, the solution (f′(ζ) = 0 in the domain, the solution (We are constructing the exact solution  to the L. Crowdy  has discsolution  remains solution  acquiresf(ζ) must be chosen so that the streamfunction Dζ, since it is a function defined on the toroidal surface. To be specific, ζ↦ρnζ and ϕ↦ϕ + 2πm for any n, z = logζ = rc(θ) + iϕ for Dz is identified with the two-dimensional domain r′c(θ) < 0 for α > 1. Then the streamfunction ψ becomes invariant with respect to the transformations θ↦θ + 2πn and ϕ↦ϕ + 2πm for n, The analytic function f(z) = tan(z) = sin(z)/cos(z) to construct the solution (z) and cn(z) are the Jacobi elliptic functions with the quarter periods K′ = π. The definitions of those functions and their formulae used in the present paper are found in the handbook [ζ) and cn(logζ) are given byz) denotes the other Jacobi elliptic function, we haveDζ to the Liouville equation (z = logζ = rc(θ) + iϕ, it is represented byDz. Since R − rcosθ is periodic with respect to θ↦θ − 2π, i.e. rc(θ), it is sufficient to see that the functionz↦z + 2K and z↦z + 2iK′ with K′ = π. As a matter of fact, it follows fromK and 2iK′ on the fundamental domain Dz. It is now easy to check that the streamfunction Dζ, sinceζ = logζ + 2πi = logζ + 2iK′.Let us remember that Stuart  used thesolution  with thehandbook . Since tsolution  on the dequation  becomessolution  to the msolution  on the tf(z) = sn(z)/cn(z) into the general formula (Dz.z), cn(z) and dn(z) in the quarter of the fundamental domain Dz. We also remember that the order of the zeros and poles are all one. Hence, we find the function Dz. Accordingly, the streamfunction z = α1 and z = α2. However, this situation is not crucial, since they correspond to point vortices in the physical space. That is to say, according to [z = αi with the strength (circulation) Γi on the toroidal surface has the following asymptotic expansion:z = αi, since z = α1 and z = α2 as follows:z = α1 and α2 correspond to the innermost and the outermost points of the toroidal surface on the same line of a longitude ϕ = π around the handle. Moreover, they are an equilibrium configuration of point vortices as shown in [In the course of the construction stated above, we have already obtained the solution to the Liouville equation  on the f formula  yields tomparing , we clearding to , the strfunction  has the shown in . Hence, z = α1 and α2, and the contribution from the smooth vorticity distribution. Owing to Γ1 = Γ2 = − 4π/d, the total circulation induced by the two point vortices becomes −8π/d. The remaining part coming from the smooth vorticity distribution in dσ associated with the Euclidean representation (Dz asz) = dn(z)/cn(z). This function has simple poles at Dz due to the double periodicity. Let us confirm that the residue of u = 0:K, they also satisfyk′ is the complementary modulus of the Jacobi elliptic functions satisfying K′ = K(k′), where K(k) denotes the complete elliptic integral of the first kind. Using these formulae, we have the expansion of q(u + K) = − 1/u + O(u). Setting z = u + K, we haveWe finally confirm whether the solution entation  is given4.ψ and the vorticity ω in the fundamental domain c = 1 and d = − 2. We change the aspect ratio α = R/r. The Jacobi elliptic functions sn(z), cn(z) and dn(z) are computed numerically with using a software package for Matlab provided by Moiseev [Dz are K′ = 2πi, we set k of the Jacobi elliptic functions is determined byθ2 and θ3 are the Jacobi theta functions of modulus τ. We can approximate the modulus k accurately by using the following convergent series with respect to In order to examine the flow generated by the exact solution , we visu Moiseev . Since tψ, which are streamlines, in the fundamental domain for α = 1.2, 1.5, 2.0 and 3.0. For all panels, there are two point vortices at ∼ and  that correspond to the innermost and the outermost points of the toroidal surface on the longitudinal line ϕ = π. Their circulations Γ1 = Γ2 = − 4π/d = 2π are equivalent and independent on α, generating counter-clockwise rotational flows around the point vortices. We observe another rotational flow domain centred at the corner point  = ∼∼∼ of the fundamental domain. The corner point is antipodal to the positions of the two point vortices. There exist three saddle points: two of them are on the longitudinal line ϕ = π between the two point vortices and the other one is located at  = ∼ on the boundary of the fundamental domain. The streamlines except the point vortices, the corner point, the saddle points and their connecting orbits represent periodic orbits. Topologically, these periodic orbits are characterized into three categories in terms of the generators, say σ and μ, of the fundamental group associated with the toroidal surface.—null homotopic periodic orbits, which are homotopic to a point;—σ-homotopic periodic orbits, which are homotopic to a loop going around the handle of the torus in the θ-direction;—μ-homotopic periodic orbits, which are homotopic to a loop going around the hole of the torus in the ϕ-direction.α varies. When α = 1.2, the saddle points on the line ϕ = π are connected by a homoclinic and a heteroclinic orbits, whereas the saddle point on the boundary is self-connected. These connecting orbits divide the fundamental domain into small domains containing periodic orbits. There are three domains consisting of null homotopic periodic orbits around the point vortices and the corner point. We observe the other two domains filled with μ-homotopic periodic orbits between the separatrices. At α = 1.5, the reconnection of these separatrices occurs. As a result, the two saddle points on the longitudinal line ϕ = π are now connected by heteroclinic orbits, while the other saddle point at the boundary remains self-connected but its separatrices are running in the θ-direction. Consequently, there appear two domains consisting of σ homotopic periodic orbits between the homoclinic and the heteroclinic connections. The streamline topology remains the same qualitatively for α larger than 1.5. However, as the aspect ratio α increases, the three domains of null homotopic periodic orbits deform into thin band-like structures in the θ-direction and the two domains of σ homotopic periodic orbits fill the most part of the toroidal surface. See the contour plots of the streamfunction on the surface of the torus in The topological structure of separatrices connecting these saddle points changes as ω is the contribution from the streamfunction and the second term represents the effect of curvature of the toroidal surface θ, ϕ) = ∼ and  generate the positive circulations 2π, but no vorticity is created by them in the whole domain except at their locations where the vorticity diverges. On the other hand, the negative continuous vorticity distribution is observed at the corner of the fundamental domain. When α is small, the negative vorticity at the corner is strongly localized at the innermost part of the toroidal surface. On the contrary, as α gets larger, the localized vorticity distribution at this region gets weaker. Accordingly, the vorticity distribution in the middle of the fundamental domain tends to be dominated by the second term θ in the most part of the toroidal surface, as In c = 1 and d = − 2. In order to adjust the modulus of the fundamental domain for comparison, identifying the complex number z = x + iy with a point x and y from a given aspect ratio 0 < α < 1 as follows. Setting k and its complement k′ of the Jacobi elliptic functions,α = K(k′)/K(k) is given byWe now observe the Stuart vortex on the flat torus to understand the effect of curvature on the vortex structures. The parameters are the same as ψf on the flat torus in the fundamental domain Dfz with the aspect ratios α = 1.1, 1.3, 1.5 and 1.9. As we observe in π at  = )∼(2K(k), K(k′)) and (K(k), K(k′)) and two saddle points between them on y = K(k′). We also observe a saddle point on the boundary  = (K(k), 0)∼(K(k), 2K(k′)) and a domain consisting of null homotopic periodic orbits centred at the corner of the fundamental domain. As α varies, the topological structure of connecting orbits between three saddle points changes in the same manner as we observed in α≧1.3, the flow domains of null homotopic periodic orbits around the two point vortices is homogeneous. This is in contrast to the streamline patterns on the toroidal surface, where the domain of null homotopic periodic orbits around the point vortex at  =  is larger than that around the point vortex at  = . Accordingly, we could say that the inhomogeneity of the domain sizes is due to the effect of the curvature.ω = − c edψf in the fundamental domain Dfz derived from the streamfunctions in x-direction and forms a thin band-like distribution as the aspect ratio increases. Hence, the vorticity distribution tends to be uniform in the y-direction, whereas it still contains a thin vortex core in the centre of the band structure as 5.μ-homotopic for small α, but they change to null homotopic and σ-homotopic periodic orbits for large α. The qualitative change of the streamline patterns occurs due to the reconnection of separatrices of the saddle points.We obtain the analytic formula of an exact solution to the modified Liouville equation,d needs to be added to the Liouville equation to obtain the exact solution. He argued that it is not clear why the choice of the constant term is relevant, which remains an open problem. The present study strongly suggests that the modification term stems from the Gauss curvature of the surface. That is to say, since the curvature of the spherical surface with the unit radius is In the generalization of Stuart vortex to the spherical surface owing to Crowdy , the conN point vortices by specifying the other analytic functions f(ζ). Then, these analytic functions should be doubly periodic in the annular fundamental domain Dζ. It should also be verified whether the solution satisfies the Gauss condition for every choice of f(ζ). In addition, if there exist points satisfying f′(ζ) = 0 that correspond to point vortex singularities, we need to confirm if they are an equilibrium solution to the evolution equation of point vortices given in [N point vortices along the line of a latitude whose linear stability has been investigated in detail [In the present paper, we have obtained the exact solution to the modified Liouville equation  with Stugiven in . We notegiven in . One of n detail . This wi


Proteins containing Ly6/uPAR (LU) domains exhibit very diverse biological functions and have broad taxonomic distributions in eukaryotes. In general, they adopt a characteristic three-fingered folding topology with three long loops projecting from a disulfide-rich globular core. The majority of the members of this protein domain family contain only a single LU domain, which can be secreted, glycolipid anchored, or constitute the extracellular ligand binding domain of type-I membrane proteins. Nonetheless, a few proteins contain multiple LU domains, for example, the urokinase receptor uPAR, C4.4A, and Haldisin. In the current review, we will discuss evolutionary aspects of this protein domain family with special emphasis on variations in their consensus disulfide bond patterns. Furthermore, we will present selected cases where missense mutations in LU domain−containing proteins leads to dysfunctional proteins that are causally linked to genesis of human disease. Protein domains are autonomous folding units that may function alone or as building blocks in the context of multidomain proteins. When such protein domains are encoded by exons flanked by introns of identical phases, they may become genetically mobile and prone to exon shuffling, resulting in the insertion of a domain into a non-homologous protein environment. This process is facilitated by intronic recombination . Highly LY6G6C, LY6G6D, LY6G6F, LY6G5C, and LY6G5B), 8q24 , 11q24.2 , and 19q13 ; the latter gene cluster includes all proteins in the human genome known to contain multiple LU domains [LYPD1, LYPD6, LYPD6B, LYPD8, CD59, BAMBI, ACVR1, ACVR1A, ACVR1B, ACVR1C, ACVR2A, ACVR2B, ACVRL1, BMPR1A, BMPR1B, BMPR2, TGFBR1, and TGFBR2).Genes encoding LU domain proteins typically contain three exons: One for the N-terminal signal sequence followed by a set of two exons for the mature LU domain—generally flaked by phase-1 introns—thus facilitating genetic mobility A. ConsisThe consensus sequence defining the primordial LU domain comprises 60−90 residues with 10 plesiotypic cysteine residues engaged in a stereotypical disulfide-bonded network: 1–5, 2–3, 4–6, 7–8, and 9–10, as depicted by the sequence alignment of LU domains from different metazoan classes in Another salient feature of all LU domains is their unique protein-folding topology, where a cysteine-rich core projects three long β-hairpins  that assemble into a slightly curved central β-sheet, thus forming the dominating secondary structure of the characteristic three-fingered fold C. The siEchiodermata [Although genes encoding LU-domain proteins are recognized in almost all phyla of the metazoan kingdom  and protodermata , we willToxins from venomous snakes provide a rich source of information on the evolution of LU-domain containing proteins, in particular with a view to sequence diversification and neo-functionalization of α-neurotoxins. The co-evolutionary “arms race” between snake venom α-neurotoxins and their specific target proteins within the cholinergic system of their agile prey which they need to subdue provides a unique setting dominated by gene duplications and sequence evolution under positive Darwinian selection . ExtensiBoiga in the family Colubridae). These toxins are often misclassified as “weak neurotoxins” due to their low toxicity towards synapsid targets . This is clearly a misnomer, since they are potent inhibitors of the cholinergic system of diapsids, which makes sense as these snakes feed primarily on birds, reptiles, and amphibians. Basal-type α-neurotoxin is, thus, a more appropriate terminology for these toxins, referring to their primordial phylogenetic origin. Within the framework for LU domains, an atypical covalently linked heterodimeric toxin, irditoxin [Boiga irregularis as an invasive species in the Pacific island of Guam [Three-fingered toxins with the ancestral 10-cysteine LU-domain signature are the main constituent in venom from the advanced non-front fanged snake lineages  have attracted considerable interest. These single LU-domain proteins play non-redundant roles in establishing the epithelial septate junctions in Drosophilae, which function as anatomical diffusion barriers equivalent to tight junctions in vertebrate epithelia [From a functional perspective, four pithelia ,35,36. TDrosophila brain contains another GPI-anchored, single LU-domain protein resembling an endogenous prototoxin. This LU-domain protein, encoded by quiver/sleepless, possesses a remarkable dual functionality. It both antagonizes the nAChR encoded by redeye [shaker [Drosophila [LYNX1) and Insecta (sleepless).Interestingly, the y redeye  and stim [shaker . These posophila . This obFrom the standpoint of evolution, the wholesale genome duplication that occurred at the base of the teleost radiation provides another interesting case involving diversification of two paralogous genes. The fate of duplicated genes may entail neo-functionalization, functional conservation, or drift into a silenced pseudogene . Althougbouncer, is expressed on zebrafish oocytes and is required for fertilization, as it mediates the contact between the oocyte and the spermatocyte. The closest human homolog of bouncer is SPACA4/SAMP14 . Herberg et al. proposed that bouncer is one of the key components governing species-specific fertilization in teleosts. This conclusion is based mainly on cross-fertilization experiments after swapping the endogenous expression of bouncer in zebrafish oocytes with that of medaka. This swapping strategy allowed the entry of medaka sperm into zebrafish oocytes, albeit at a low efficiency. As illustrated in bouncer occurs in two paralogous forms (A and B) in medaka, due to the early gene duplication. One variant contains the 10-cysteine LU-domain signature (B), whereas the other (A) has lost the 2–3 plesiotypic disulfide bond that in snakes induced rapid diversification and neo-functionalization of the α-neurotoxins (bouncer with the 8-cysteine LU-domain variant from medaka (A) may therefore have lowered the efficacy by which cross-fertilization occurred. It is possible that the B-form of medaka bouncer does not produce a correctly folded protein, as it contains an unpaired eleventh cysteine residue  encoding a GPI-anchored LU-domain protein on early zebrafish development is also clearly documented [lypd6, it was shown that this protein regulates embryonic mesoderm and neuroectoderm patterning by enhancing Wnt/β-catenin signaling via binding to Lrp6 in lipid rafts [Lypd6 contains an additional apotypic disulfide bond stabilizing its third loop .The importance of another gene . These secreted proteins retain the genetic and structural hallmarks of LU domains. Among the secreted LU-domain proteins, SLURP-1 has received the most attention, since missense mutations in that gene cause a rare autosomal-recessive skin disease, e Meleda . Patientpidermis . SeveralCys99Tyr ). These  pathway ,50,51. S pathway , while S pathway . WhetherThe majority of LU-domain proteins encoded in the human genome are GPI-anchored single-domain proteins with the 10-cysteine signature. Although protein structures and biological functions of a few of these proteins are well-characterized , molecular and functional insights into the majority of these family members are at best rudimentary.Cavia porcellus (guinea pig), where the CD59 gene has been transformed into a pseudogene [One of the best-characterized proteins within this group is the complement regulatory protein CD59 . CD59 preudogene . A few reudogene ,55,56,57eudogene . One of Lynx1 reveal that this prototoxin limits neuronal plasticity in the adult visual cortex by attenuating the cholinergic response of α4β2 and α7 nAChRs [Lynx1 is widely expressed in a variety of neuronal subtypes in the brain where it colocalizes with α4β2 and α7 nAChRs [Lynx1 expression in the visual cortex neurons of the developing brain thus gradually impair visual acuity after monocular deprivation (amblyopia) in adults versus juveniles, but importantly this limitation of adult mice is rescued by increased neuronal plasticity in Lynx1 deficient mice [Lynx1 on the complex regulation of cholinergic output is nonetheless not restricted to the visual cortex, but includes additional functions, such as motor learning and associative learning [Studies on mice with genetic ablation of 7 nAChRs ,59. Lynx7 nAChRs ,60. The ent mice . Pharmacent mice . The implearning ,61. The learning , which ilearning . A more learning .Monodelfis domestica; XP_016287565.1). The evolutionary origin of the additional exon-2 in the GPIHBP1 gene remains unclear, but it was speculated to have arisen from integration of a segment of the BCL11A gene [From an evolutionary perspective, the inclusion of GPIHBP1 in the LU-domain protein superfamily represents a recent event, as this protein occurs exclusively in the class Mammalia . GPIHBP111A gene .onk) between LPL and GPIHBP1 is thus >250-fold greater for full-length GPIHBP1 than for a mutant lacking the acidic N-terminal extension [The acidic extension, which is intrinsically disordered, endows GPIHBP1 with several unique functional properties. First, it dramatically increases the encounter rate with LPL due to electrostatic steering; the association rate constant —a condition associated with life-threatening bouts of acute pancreatitis. Chylomicronemia is lifelong in the setting of homozygosity or compound heterozygosity for loss-of-function mutations in GPIHBP1 or LPL ,75. SeveAcquired forms of chylomicronemia can occasionally occur in children or adults as a result of autoantibodies against GPIHBP1 ,79. ThesLY6E and PSCA) have adverse pathogenic effects, as they enhance the susceptibility of certain cell types to a subset of viral infections. Host entry of Flaviviridae, such as Zika virus, dengue virus, and yellow fever virus, occurs via clathrin-mediated endocytosis, but the size of these virion particles requires the active engagement of a non-canonical endocytosis pathway, which includes the GPI-anchored LU domain protein LY6E [LY6E for promoting disassembly of the viral capsid (uncoating) after endosomal escape of the internalized virus. How LY6E aids disassembly of the capsid proteins remains nevertheless unclear, but the base of loop 1 in the LU domain of LY6E seems to play an essential role in this process. Possible mechanistic insights into the LY6E-facilitated entry of viruses may perhaps be gleaned upon from studies on the biological function of LY6E in normal physiology. Ly6e-deficient mice show mid-gestational embryonic lethality (E15.5) due to placental malfunction with impaired labyrinth morphogenesis and imperfect syncytiotrophoblast fusion [Syna, an ancient retroviral envelope gene that was co-opted in Mammalia to mediate fusion of distinct placental cells into functional syncytiotrophoblasts [Two interferon inducible LU genes . Several of these genes encode GPI-anchored proteins with two or more LU domains with the generic intron−exon structure preserved for each added LU domain. As a completely unexpected and unique feature, the N-terminal LU domain in all these multi-LU-domain proteins lack the 7−8 plesiotypic disulfide bond [PLAUR) with three consecutive LU domains and the two LU domain-containing proteins, C4.4A (LYPD3) and Haldisin (LYDP5).The human genome contains a small locus on chromosome 19q13 that encodes atypical LU domain-containing proteins  receptor (uPAR), which is also the founding member of the LU domain superfamily. In a functional context, uPAR serves to focus uPA-mediated plasminogen activation on the cell surface though high-affinity interaction with the growth factor-like domain of uPA D. One imD’s for uPA and vitronectin are 0.02 nM and 4 µM, respectively). A dynamic assembly of all three LU domains in uPAR creates a large hydrophobic uPA-binding cavity involving the concave faces of all of the central β-sheets of its LU domains [The two key physiological binding partners for uPAR, uPA and vitronectin, bind uPAR with markedly different affinities , it probably cannot be considered a bona fide mobile protein module, as it is found predominantly as single LU-domain proteins or as repetitive units in multidomain proteins containing only this domain. However, it would be entirely reasonable to propose the LU domain as a “proto-module”, given that it is found in the context of a non-homologous protein environment in a few proteins, for example, GPIHBP1, SP-10 and the ECD of TGF-β receptors.


At the same time, such a layer facilitates the possibility to switch domain wall helicity by an external electric field or even to completely change the characteristic structure of a ferroelectric Bloch wall passing through it. Thus, ferroelectric Bloch domain walls are shown to be ideal nanoscale objects with switchable properties. The reported results hint towards the possibility to exploit ferroelectric domain wall interaction with simple nanoscale devices.The phase-field simulations of ferroelectric Bloch domain walls in BaTiO In other words, a sufficiently thin paraelectric layer is effectively polarized by the neighboring ferroelectric material. However, little is known about robustness of the inner polarization, present within the nanoscale thickness of ferroelectric Bloch walls [Nanometer-scale mixtures of paraelectric and ferroelectric materials in disordered solid solutions or in very fine artificial crystalline superlattices often show qualitatively similar domain phenomena as the parent ferroelectric materials. For example, in the case of BaTiOterfaces –5. In gech walls –7. For e3–SrTiO3 crystalline superlattice, formed by thin SrTiO3 paraelectric layers of 0.5–3 nm thickness, separated by about 13 nm thick BaTiO3 ferroelectric slabs . Phase-field simulations for pure BaTiO3 single crystal and for the BaTiO3–SrTiO3 crystalline superlattice at stress-free mechanical conditions were performed using the phase-field simulation code ferrodo [Pt values, as in Pt values in the two domain states had the same magnitude and sign.The BaTiOthose of , except  ferrodo . The app ferrodo . The ini


VPS34 phosphorylates phosphatidylinositol to produce PtdIns3P and is the progenitor of the phosphoinositide 3-kinase (PI3K) family. VPS34 has a simpler domain organization than class I PI3Ks, which belies the complexity of its quaternary organization, with the enzyme always functioning within larger assemblies. PtdIns3P recruits specific recognition modules that are common in protein-sorting pathways, such as autophagy and endocytic sorting. It is best characterized in two heterotetramers, complexes I and II. Complex I is composed of VPS34, VPS15, Beclin 1, and autophagy-related gene (ATG)14L, whereas complex II replaces ATG14L with UVRAG. Because VPS34 can form a component of several distinct complexes, it enables independent regulation of various pathways that are controlled by PtdIns3P. Complexes I and II are critical for early events in autophagy and endocytic sorting, respectively. Autophagy has a complex association with cancer. In early stages, it inhibits tumorigenesis, but in later stages, it acts as a survival factor for tumors. Recently, various disease-associated somatic mutations were found in genes encoding complex I and II subunits. Lipid kinase activities of the complexes are also influenced by posttranslational modifications (PTMs). Mapping PTMs and somatic mutations on three-dimensional models of the complexes suggests mechanisms for how these affect VPS34 activity. The phosphoinositide 3-kinases (PI3Ks) are a family of intracellular lipid kinases that are unique to eukaryotic cells. The enzymes all phosphorylate the 3-OH of inositol lipids, but they can be grouped into three classes based on their domain organization. The class I PI3Ks evolved in metazoa and use phosphatidylinositol 4,5-bisphosphate [PtdInsP2] to produce PtdInsP3, which has a role as a membrane-resident second messenger. The class II PI3Ks have a C-terminal PX-C2 domain extension to the class I-like core, and they have an N-terminal region unrelated to the adaptor-binding domains of the class I enzymes. While there are four class I and three class II PI3Ks in mammalian cells, there is only one class III enzyme, VPS34, and given that it is present in all eukaryotes, it represents the primordial PI3K. VPS34 has a three-domain architecture consisting of an N-terminal C2 domain, a helical domain, and a C-terminal kinase domain that is homologous with other members of the PI3K family , and thiVPS34 uses phosphatidylinositol (PtdIns) as a substrate to produce PtdIns3P. The PtdIns3P recruits effectors bearing domains evolved to recognize the lipid headgroup. Among the common PtdIns3P-recognizing domains are the FYVE, PX, and PROPPINS. However, VPS34 produces PtdIns3P on many distinct compartments, with varying temporal changes in PtdIns3P concentration. For example, during amino-acid starvation that promotes autophagy, complex I activity is stimulated, whereas the majority of other VPS34 complexes are inhibited, because Unc-51-like autophagy activating kinase 1 (Ulk1) recruits autophagy-related gene (ATG)14L, enabling the kinase to phosphorylate Beclin 1 and enhance autophagy . This raIn mammalian cells, VPS34 forms two heterotetrameric core complexes known as complexes I and II. Complex I is composed of VPS34 (PIK3C3), VPS15 , Beclin 1, and ATG14L, whereas complex II has UV irradiation resistance-associated gene (UVRAG) instead of ATG14L . This diAlthough complexes I and II are the best characterized, quantitative immunoprecipitation suggests that subcomplexes of complexes I and II also exist in cells (VPS34/VPS15 and VPS34/VPS15/Beclin 1) . Upon glComplexes I and II are 1:1:1:1 heterotetramers, as shown by multi-angle light scattering, the X-ray crystal structure of complex II, and the cryo-EM structures of complexes I and II , 17, 18.Caenorhabditis elegans) are poly-ubiquitinated by the UBC-13/UEV-1/CHN-1 complex. This stabilizes VPS34 and increases autophagosome maturation and clearance of cytoplasmic debris ..25). SigAutophagy can prevent tumor formation by removing superfluous or damaged proteins and organelles and thereby maintain cellular homeostasis . In contUVRAG-containing VPS34 complexes associate with the insulin receptor, and insulin stimulates VPS34 activity. A conditional deletion of Vps15 in mouse livers resulted in a positive influence on the metabolic effects in mouse models of obesity and type II diabetes . This haDrosophila melanogaster have been found in the WD40 domain   . These m V1337I) .BECN1) was originally found in a transcription mapping study of the BRCA1 locus ..BECN1) wagy gene  discoveragy gene , 66. Allagy gene . The BARagy gene , 68. It agy gene  (66).ATG14L is the defining component for VPS34 complex I. It consists of an N-terminal domain (residues 1–72), a short coiled-coil (CC1) (residues 73–107), two longer coiled-coils (CC2 and CC3) , a C-terminal domain (residues 233–412), and a Barkor/Atg14L autophagosome targeting sequence (BATS) domain (residues 412–493). The N-terminal part of ATG14L contains a pair of CXXC motifs  that are the most conserved regions through evolution . These regions are important for ATG14L localization to the ER . For comComplex I activity is inhibited by multiple phosphorylations on ATG14L in its C-terminal domain by mTOR  72). AT. AT72). UVRAG is the fourth subunit of the VPS34 complex II. The UVRAG gene was first identified in a genetic screen in 1997 in which it was shown to partially rescue UV sensitivity in xeroderma pigmentosum cells . XeroderUVRAG consists of five distinct regions: a proline-rich domain (residues 1–52), a lipid-binding C2 domain (residues 53–164), a short CC1 (residues 195–226), a longer CC2 (residues 240–333), a BARA2 domain (residues 364–464), and a C-terminal domain (residues 464–699). The C2 domain was shown to bind to PtdIns3P, PtdIns4P, and PtdIns5P with residues K78 and R82, although the C2 domain is distant from the putative membrane plane facing the VPS15 helical domain , 2 84)..84). IntThe C-terminal region of UVRAG is considered to be unstructured and significantly longer than the C terminus of Vps38 (UVRAG ortholog). Sequence alignment showed that the amino acid stretch of 465 to 699 is unique to its mammalian counterpart . IntriguIn addition to the core subunits of complexes I and II, accessory subunits have been characterized that control the activities and localization of the complexes. Four such components that have been extensively characterized are the proteins, NRBF2, Rubicon, PAQR3, and AMBRA1. NRBF2 and Rubicon associate to form stable associations with complexes I and II, respectively. In contrast, AMBRA1 only weakly associates with complexes I and II .NRBF2 is a fifth component of human complex I, although there is disagreement as to the nature of its regulation of kinase activity –93. StruComplex I localizes to the phagophore/isolation membrane, autophagosome, and ER, and can associate with AMBRA1. AMBRA1 is a 1,300 residue protein that has an N-terminal WD40 domain and a vast region that is thought to be intrinsically disordered . AMBRA1 While complex I upregulates autophagy at an early step, a UVRAG-containing complex (presumably complex II) forms a stable interaction with Rubicon through an interaction with Beclin 1, localizes on late endosomes/lysosomes, and negatively regulates later events in both autophagy and the endocytic pathway , 62, 99.The VPS34 complexes are activated in unique contexts and the mechanisms of their spatiotemporal regulation are now emerging. Structures of the complexes are beginning to clarify the organization of the complexes and the accessory subunits with which they associate. This has begun to offer interpretations to the sometimes bewildering range of interactions that have been reported for these complexes. The PTMs of the VPS34 complex subunits have a wide range of complex-specific influences, and suggest that it may be possible to devise approaches to inhibit specific VPS34 pathways.


A comprehensive resource identifying positions within domains that tend to interact with nucleic acids, small molecules and other ligands would expand our knowledge of domain functionality as well as aid in detecting ligand-binding sites within structurally uncharacterized proteins. Here, we introduce an approach to identify per-domain-position interaction ‘frequencies’ by aggregating protein co-complex structures by domain and ascertaining how often residues mapping to each domain position interact with ligands. We perform this domain-based analysis on ∼91000 co-complex structures, and infer positions involved in binding DNA, RNA, peptides, ions or small molecules across 4128 domains, which we refer to collectively as the InteracDome. Cross-validation testing reveals that ligand-binding positions for 2152 domains are highly consistent and can be used to identify residues facilitating interactions in ∼63–69% of human genes. Our resource of domain-inferred ligand-binding sites should be a great aid in understanding disease etiology: whereas these sites are enriched in Mendelian-associated and cancer somatic mutations, they are depleted in polymorphisms observed across healthy populations. The InteracDome is available at  The rate at which new genomes are sequenced has long since outpaced our ability to experimentally characterize the biological functions of the encoded genes and their protein products. Leveraging the fact that similar protein sequences or subsequences tend to share similar functions, computational approaches have been developed to mitigate this sequence-to-function discrepancy by rapidly detecting and modeling the sequence similarity between proteins . Such hoIndividual protein domains are associated with specific functionalities, among the most important of which are mediating the interactions proteins make with nucleic acids, other proteins and various other molecules in the cell. Indeed, protein–DNA and protein–RNA interactions have been found to occur via domain interfaces so frequently that factors associated with transcriptional and post-transcriptional activity are regularly classified according to their incorporation of particular nucleic acid-binding domains ,7. Moreowithin these domains would enable a more precise analysis of the many thousands of sequenced proteins across species that contain domain instances but lack further biological characterizations. Indeed, more comprehensive knowledge of protein interaction interfaces will have considerable implications for investigating the evolution and natural variation of interaction network connectivities  domain are required for proper domain folding and thus are highly conserved—other binding positions are not: amino acids within DNA-contacting positions in these same C2H2-ZF domains, for example, vary dramatically across domain instances to confer diverse binding specificities, and thus cannot be identified by conservation-based analyses ) . Furtherpositions within these domains that mediate interactions  structures on 12 September 2018 from BioLiP , a curatWe classify BioLiP ligands into biologically relevant groups. Protein residues responsible for determining DNA- and RNA-binding specificity often contact nucleic acid bases, whereas residues that primarily contact the backbones of nucleic acid molecules may be more important for the stability and affinity of the binding complex ,26. As Bin vivo) from non-cognate ligands. To highlight domain positions whose residues comprise metabolically relevant and/or potentially druggable binding pockets, we further categorize small molecules as follows. Any small molecule ligand with a Tanimoto coefficient ≥ 0.9   ,28 betwe v2.4.1)  is respe v2.4.1) ; furtherrepresentable set of domain–ligand interactions as those with at least one corresponding domain–ligand co-complex structure in BioLiP. We require that these structures give coordinates for residue side-chain atoms—as opposed to just backbone carbon atoms—but do not otherwise consider structural resolution. For each domain in the representable set, we assess the ligand-binding frequencies of individual domain positions by aggregating protein–ligand atom proximity information across their corresponding co-complex structures . We finrepresentable-NR set. For each domain–ligand pair in the representable-NR set, we evaluate both the consistency of its structural interface as well as the accuracy of our aggregation approach in identifying ligand-binding positions in cross-validation.We refer to each domain–ligand type pair with at least three distinct (i.e. non-redundant) sequences across separate PDB entries as belonging to the First, to evaluate consistencies of domain–ligand structural interfaces, for each domain–ligand pair in the representable-NR set, we first randomly split its structural instances into two folds. We next compute, across all instances within each fold, the average minimum residue-to-ligand distance at each domain position. Finally, we compute the Pearson’s correlation coefficient (PCC) between the two resulting domain-length vectors. We report the average PCC achieved across ten repetitions of this process as the consistency of the domain–ligand structural interface.i in each hold-out fold in turn, we examine the structure to assign a binary vector where 1 and 0 respectively indicate domain positions whose residues are or are not in contact with the ligand (i.e. as annotated by BioLiP). Binding frequencies are then calculated as before from instances in the remaining folds. For each position in each instance in the hold-out fold, we use the corresponding positional binding frequency, computed from the other folds, as its ‘score.’ We then rank in descending order all positions within the hold-out fold by score, with higher ranking positions corresponding to the more confident predictions of binding. As we iteratively decrease the score threshold used to predict whether a position is binding, we compute precision and recall with respect to the known binding (true positive) and non-binding (true negative) positions inferred from the actual structures in the held-out set. This allows us to compute a precision-recall curve (PRC) for each domain–ligand interaction. We refer to the set of domain–ligand interactions that achieved a cross-validated precision of at least 0.5 at some threshold as the confident set. We also compute the area under under the PRC (AUPRC), and compare it to an average baseline AUPRC corresponding to the fraction of binding positions in the held-out set.Second, to test the power of our approach in identifying binding positions across previously unseen domain instances, for each domain–ligand type pair in the representable-NR set, we randomly divide its structural instances into up to 10 folds. For each domain instance We note that instances of the same domain family have by definition clearly identifiable sequence similarity and thus can have highly similar amino acid sequences. Nevertheless, as an alternate cross-validation test, for each domain–ligand type pair in the representable-NR set, we also try to divide all its instances within BioLiP into groups such that the amino acid sequence identity between instances in different groups is <90%. We repeat the steps above to determine domain–ligand structural consistencies and cross-validated precisions and recalls by dividing these groups of BioLiP instances with sequence identity ≥90%—rather than individual instances—into folds as before; these results are reported in the ‘Protein sequences, corresponding cDNA sequences and corresponding genomic coordinates for 104 295 known and predicted human protein isoforms encoded by 23043 genes were downloaded from Ensembl (build GRCh38.p10). We consider the subset of 89024 protein isoforms from 22712 human genes where the genomic DNA sequence matched the cDNA sequence, the cDNA sequence translated to the protein sequence with ≤5% sequence mismatch, and the protein transcript was not annotated with ‘decay’ nor ‘pseudogene.’ We functionally classify single nucleotide variants (SNVs) with respect to the longest protein isoform for each gene by mapping SNVs onto Ensembl cDNA sequences and translating to proteins.http://www.bioinf.org.uk/omim/).Naturally occurring exonic SNVs from 123 136 healthy humans were downloaded from the Genome Aggregation database  . We restWe also downloaded all open-access TCGA somatic SNV data and RNA-seq expression data from NCI’s Genomic Data Commons on 15 July 2017 ,37. We eWe query the longest protein isoform of each human gene and infer ligand-binding positions in these proteins in three ways. First, we extract human proteins from BioLiP, and obtain the residues identified in this database to interact with ligands. Next, we transfer structural binding information from BioLiP to human proteins with high sequence similarity, as described previously . FinallyN sites of interest across proteins are modeled as N independent Bernoulli trials, where the p1, ..., pN probabilities of ‘success’ (i.e. overlap with the putative binding sites) for each trial are non-uniform. Specifically, each success probability pi is equal to the proportion of putative binding sites in the protein where the site of interest i occurs; this way, sites of interest that occur in proteins with a large proportion of putative ligand-binding sites will not bias global trends. We determine if K—the number of sites of interest observed to overlap with the putative binding sites—is significantly greater than or less than we would expect by chance by respectively computing Pr(X ≥ K) and Pr(X ≤ K) using the Poisson binomial implemented in R’s poibin package  and a set of putative ligand-binding sites in human proteins, we determine whether the overlap between these two sets is significantly larger or smaller than what is expected by chance alone using the Poisson binomial distribution. Here, the  package . P-valueOur fully automated procedure to build the InteracDome resource identifies 4128 domain families that are representable . Of these, 2375 domain families have at least three non-redundant instances in complex with the same ligand type across distinct PDB structures; these domain–ligand interactions comprise the representable-NR set. Within the representable set of domain interactions, 564 domain families are co-complexed with DNA, 490 are co-complexed with RNA, 830 are co-complexed with other peptides, 2557 are co-complexed with ions and 2847 are co-complexed with one or more small molecules. In the representable-NR set, 257, 244, 299, 1204 and 1634 domain families are respectively co-complexed with DNA, RNA, peptides, ions and/or small molecules. Note that the same domain family can be found to interact with multiple ligand types (e.g. the RRM domain interacts with both DNA and RNA across instances).http://pawsonlab.mshri.on.ca). We find that our representable set of domain–ligand interactions includes all the DNA-binding domain families, all the RNA-binding domain families and ∼85% of postulated protein-binding domain families, many of which have been particularly difficult to structurally characterize due to the low affinity and transience of protein–protein interactions in signaling pathways  ; these fWe next examine InteracDome binding frequencies for two peptide-binding domains. In the WW domain, our highest peptide-binding frequencies are found at positions 17, 19, 21, 24, 26 and 28—all corresponding to known binding residues. The next highest peptide-binding frequencies identify positions 8, 10 and 11—all known to confer binding specificity differences between type I and IV domains Figure  44). Si. Si44). Finally, our approach also recapitulates ATP-binding positions in the kinase domain. Our high small molecule binding frequencies include several residues from subdomains I–VII that are responsible for interacting with and anchoring ATP’s adenine ring , α, β and γ phosphates , and ribose hydroxyl group (i.e. position 127) .We next show, in a systematic analysis, that structural interfaces between domains and their ligands in the representable-NR set tend to be conserved. Briefly, we compare the residue-to-ligand distances across different structural instances of a domain–ligand interaction type to each other see ‘’ sectionAs we have just shown, domains generally tend to interact with their ligands in a relatively consistent fashion. However, some interaction domains are also known to have multiple binding modes, where different combinations of domain positions are in contact with the ligand ,45; thesWe next evaluate how well the binding frequencies for a given domain–ligand type pair indicate positions involved in binding across previously unobserved structural instances. To measure this, we employ cross-validation to compute PR curves for each domain–ligand pair in the representable-NR set, and compare the AUPRCs to corresponding baseline AUPRCs see ‘’ sectionFor the remainder of our analysis, we consider a confident set of 12010 domain–ligand interactions from the representable-NR set (involving 2152 distinct domains) that achieve a cross-validated precision ≥0.5 at some binding threshold. Note that though many domain–ligand interactions are structurally consistent across domain instances, ∼25% of domain–ligand interactions in the representable-NR set are not included in the confident set due to the diversity with which they bind their ligands across structural instances. For example, the PAZ (Piwi/Argonaute/Zwille) domain binds RNA using a variety of positions across distinct instances and thus achieves a low cross-validated precision in identifying binding sites in held-out structures.We next use our InteracDome resource to infer sites in human proteins that may be involved in interactions with DNA, RNA, peptides, ions, metabolites and small molecules.As of September 2018, only 3099  human genes were associated with biologically relevant protein–ligand complex structures in BioLiP. Homology modeling as described in  13,46,4,446,47. Approximately 90% of human genes contain complete instances of ∼6000 Pfam domain families. Of course, not all of these domains have associated structural co-complex information, and thus neither their roles in mediating binding nor which positions within them are involved in ligand binding are known. However, 14335 (63.1%) genes contain InteracDome domain instances with confident interactions or homology-inferred binding interfaces. Including any domain with representable interactions across 5+ or 1+ instances in BioLiP, rather than only domains with confident interactions, respectively covers 64.4 and 69.2% of human genes. Our InteracDome resource thus represents a 2.3- to 2.5-fold increase in coverage over current state-of-the-art approaches to infer putative interaction sites across human genes. Furthermore, our approach covers a diverse range of interaction types, as substantial fractions of these genes contain instances of domains with confident interactions with DNA, RNA, peptides, ions, metabolites and other small molecules Figure . AltogetBecause the vast majority of proteins’ functions are carried out through specific interactions, even rare DNA variants or mutations that alter interaction-mediating protein residues can have critical impacts in human disease. As such, we expect inferred protein interaction sites to be relatively conserved across healthy human individuals, whereas we would expect these same sites to be perturbed across individuals with disease . To deteless than expected by random chance . Moreover, when we repeat our global, site-based analysis, considering all somatically mutated sites across >10000 tumor samples from 33 cancer types and using a much more comprehensive set of inferred binding sites than previous studies, we confirm the same trend. Sites harboring somatic missense mutations tend to coincide with inferred binding sites significantly more than expected by random chance  of inferred binding sites with mutated or varying sites is significant even when considering only specific types of ligand binding in turn Figure . SomaticWe have introduced here a fully automated approach for aggregating protein co-complex structural data in the context of domains to reveal how positions within these domains are generally involved in mediating interactions with DNA, RNA, ions, peptides, metabolites and other small molecules Figure . This coPreviously, interaction site information has been transferred from structurally modeled proteins to uncharacterized proteins with similar sequences or subsequences using various homology-based approaches ,46,47. SDetermining the binding positions within these domains represents a challenging task due to biases inherent in structural data: structures often harbor confounding experimental artifacts, are dominated by non-cognate drug interactions, and can have highly redundant sequences to each other . We showSome domains can bind different types of ligands, though one of these may be rare or nonstandard; for instance, the C2H2-ZF and HTH domains predominantly bind DNA but sometimes bind RNA or peptides. Other domains may bind the same ligand type via multiple, diverse binding modes; for example, though the PAZ domain primarily binds RNA, the positions within the domain mediating RNA interactions vary across structural instances. We mitigate these two concerns in our aggregation approach by conservatively restricting domain–ligand interactions to those with substantial structural representation that bind consistently across instances as demonstrated via cross-validation testing (i.e. ‘confident’ domain–ligand interactions).Substantial previous work has focused on detecting and characterizing the domain–domain interactions that mediate a number of protein–protein interactions across cellular interaction networks ,55–58. WOverall, we believe that our structural aggregation framework and resultant InteracDome resource lay the groundwork for many future domain-centric analyses and thus will be of broad use for the community. Not only can knowledge of domain binding positions be used to further group, subtype, subdivide or functionally annotate domain families themselves, but the putative interaction sites inferred across proteins using the InteracDome should be relevant in understanding disease etiology. Indeed, we find that these sites are globally conserved across healthy human individuals yet preferentially perturbed in tumor samples and disease populations. As such, we anticipate that future approaches that utilize InteracDome to detect interaction-altering protein coding variants will be a great aid in both prioritizing disease-associated mutations as well as reasoning about their molecular effects.Supplementary DataClick here for additional data file.


Ground-based synthetic aperture radar (GB-SAR) uses active microwave remote-sensing observation mode to achieve two-dimensional deformation measurement and deformation trend extraction, which shows great prospects in the field of deformation monitoring. However, in the process of GB-SAR deformation monitoring, the disturbances caused by atmospheric effect cannot be neglected, and the atmospheric phases will seriously affect the precision of deformation monitoring. In discontinuous GB-SAR deformation monitoring mode, the atmospheric phases are particularly affected by changes of time and space, so the traditional models of atmospheric phase correction are no longer applicable. In this paper, the interferometric phase signal model considering atmospheric phase is first established. Then, the time- and space-varying characteristics of the atmospheric phase are analyzed, and a novel time- and space-varying atmospheric phase correction algorithm, based on coherent scatterers analysis, is proposed. Finally, slope deformation monitoring experiments are carried out to verify the validity and robustness of the proposed algorithm. Natural disasters, such as landslides and mudslides, seriously threaten people’s personal and property safety. Ground-based synthetic aperture radar (GB-SAR) can extract the deformation value and the deformation trend of the overall monitoring area, which has become an important technical means for the deformation monitoring of slopes, dams, bridges, etc. ,5,6,7,8.Atmospheric disturbances, caused by the difference in the atmospheric temperature, pressure, and humidity in the electromagnetic wave propagation, are shown as the delay phases in radar images. The atmospheric delay phase has always been an important factor affecting the development of the InSAR application. Current InSAR atmospheric phase correction algorithms are mainly divided into two categories. One is based on the external auxiliary data, which mainly includes the ground meteorological data, GPS data, and space radiation measurement data ,13. HoweIn order to solve the above problem, a novel time- and space-varying atmospheric phase correction algorithm, based on coherent scatterers (CSs) analysis, is proposed. First, a GB-SAR interferometric phase model considering the atmospheric phase is established. Then, the CSs are extracted by the frequency interleaved sub-images entropy method and local spatial consistency analysis. Compared with the existing atmospheric phase correction algorithm, using permanent scatterers analysis methods to extract stable control points (SCPs), the proposed algorithm can complete stable control point extraction through a single GB-SAR pair ,19, whicThis paper is organized as follows. In i is the SAR image series number, cf is the radar center frequency, and c is the speed of electromagnetic wave. For ideal zero-baseline interferometric data, the interferometric processing and deformation retrieval model can be expressed as follows: S* is the conjugate of S, The observation geometry of GB-SAR is shown in k is the wrapped phase cycle value. However, in GB-SAR field measurement data processing, the interferometric phase includes not only the deformation phase, but also phases such as the atmospheric phase, the noise phase, and the wrapped phase. The GB-SAR interferometric processing is to extract the deformation phase from these phases, and realize the process of deformation retrieval. The interferometric phase model can be expressed as follows:k can be solved by the phase-unwrapping algorithm, and the related algorithms are sufficient [The noise phase election , which celection , and is fficient ,24,25,26N depends on the atmospheric pressure P, the temperature T, and the relative humidity H. N can be expressed asAtmospheric phases of GB-SAR are caused by the difference of atmospheric pressure, temperature, and humidity in different time and space . TherefoN is a vector related to the distance vector (r) and time (t), which can be expressed as follows:Therefore, the refractive index S of radar electromagnetic wave propagation [Then, the atmospheric phase can be obtained by integrating on the path pagation .(8)φatmK is an unknown constant and r is the distance from radar to observation point. According to the atmospheric physics model, Noferini built the atmospheric phase linear correction model based on the analysis of the permanent scatterers in , which aThe above model parameters can be calculated by using the phase value of the permanent scatterers in the scene, so the GB-SAR time series data is mandatory. The discontinuous GB-SAR has a long acquisition interval, so the dataset is small and the temporal decorrelation is serious. Therefore, the permanent scatterers analysis method is not suitable for atmospheric phase correction in discontinuous GB-SAR deformation monitoring.In this section, a novel time- and space-varying atmospheric phase correction algorithm for discontinuous GB-SAR deformation monitoring is proposed. Discontinuous deformation monitoring is different from that of the continuous mode, and is suitable for the scene with slow deformation and no continuous real-time monitoring. The GB-SAR data in the discontinuous deformation monitoring has the characteristics of little data and a long time baseline, so the frequency interleaved sub-images entropy method is used to extract the CSs as stable control point candidates. Then, according to the local consistency analysis of the atmospheric phases, the candidate points satisfying the requirements are selected as SCPs, which can be used for discontinuous GB-SAR time- and space-varying atmospheric phase correction.In the continuous deformation monitoring mode, GB-SAR can obtain time series data, so the SCPs can be extracted by using permanent scatterer (PS) methods . For disH between sub-images is defined by [i, j) is the pixel index, 2N is the total number of sub-images, and kP iskλ represents the eigenvalues of the covariance matrix C, and the covariance matrix is given byS represents the sub-image, and E{·} represents the expectation operation.Entropy is an alternative approach to estimate coherence in the spectral domain, which can make full use of the sub-image data information by calculating the covariance matrix. The entropy fined by (11)H of the whole monitoring scene. The spatial interpolation of a discrete point set is a classical problem in computational geometry. The Delaunay triangulation method is used for the spatial interpolation in this paper. Delaunay triangulation is an optimized spatial structure . There wThe realization of Delaunay triangulation first needs the construction of a super triangle , which iT0 is the fitting order and tA is the fitting coefficient. For the atmospheric phase values in the range direction, the polynomial fitting is performed after spatial interpolation. The objective function is to minimize the sum of distance squares from the atmospheric phase points However, the SCPs in the monitoring scene often cannot cover the whole scene, so the Delaunay triangulation algorithm can only estimate the atmospheric phases of the regions surrounded by the SCPs, so the APS of the whole scene cannot be obtained. According to Equation (8) in After polynomial fitting in the range direction, considering the space-varying characteristics of the atmospheric phases—and that polynomial fitting results also hardly completely cover the entire scene—the polynomial fitting in the azimuth direction is also performed. Then the APS of the monitoring scene is completely obtained, and the atmospheric phase can be corrected according to the interferometric phase model in Equation (4).The flowchart of the proposed GB-SAR time- and space-varying atmospheric phase correction algorithm is shown in In order to verify the effectiveness and robustness of the time- and space-varying atmospheric phase correction algorithm proposed in this paper, two slope deformation monitoring experiments in different scenes and atmospheric conditions were carried out. The experimental sites have different climates and height differences. The first experimental site is located in north China, and is a mine park in the suburb of Beijing. The height difference of the observation scene is small and the climate is dry. The second experimental site is located in a mine in Fujian province, in the southern part of China. This scene has large height difference, and the climate in south China is humid. All of the experimental conditions are beneficial for the validation of the proposed time- and space-varying atmospheric phase correction algorithm.The GB-SAR system used in the experiments is mainly composed of a horizontal rail, a radar transmitting/receiving (T/R) module, and a hardware and software control cabinet. The system uses a stepped frequency continuous wave signal. The maximum observation distance of the system is 5 km. The system parameters are shown in The first experimental scene is shown in The deformation monitoring experiment lasted for one month and the slope was monitored in real time, which was the continuous deformation measurement mode. However, the monitoring scene is a slow deformation scene for the GB-SAR, and the high-frequency data acquisition will increase unnecessary costs. Therefore, the discontinuous deformation monitoring mode is a cost-effective solution. We focus on the discontinuous deformation monitoring data in this case. With respect to the slow deformation scene, the time baseline is increased to achieve the discontinuous deformation monitoring of the scene. A long time baseline will trigger the time-varying characteristics of the environmental parameters. Moreover, the atmospheric refractive indexes are heterogeneous in the azimuth, so the atmospheric phases are space-varying. Therefore, the time- and space-varying atmospheric phase correction algorithm proposed in In the continuous deformation monitoring mode, the data acquisition time of one GB-SAR image is 20 min. In order to obtain the discontinuous deformation data in this experiment, the interferometric data with three-day intervals are selected for processing. In order to verify the robustness of the proposed algorithm, the atmospheric phase correction algorithm, based on a linear model, is performed for comparison. The monitoring scene of the second case is shown in The second experiment lasted 20 days, which realized the real-time deformation monitoring of the slope. The interferometric data with two-day intervals were selected as the discontinuous deformation monitoring data. Due to the great distance from the slope to the location of the GB-SAR system, the closest area is not the region of interest. Therefore, the monitoring range is limited to (400–1400 m) by software settings. The data processing results of the experiment are shown in Atmospheric phase correction plays an important part in GB-SAR deformation monitoring, which is directly related to the precision and reliability of deformation production. In the discontinuous GB-SAR deformation monitoring, the atmospheric phases have time- and space-varying characteristics, and the conventional linear atmospheric phase correction model is no longer applicable. Therefore, in this paper, a novel time- and space-varying atmospheric phase correction algorithm based on CSs analysis is proposed. First of all, the frequency interleaved sub-images entropy method is used to detect the CSs in the scene. Then the extraction of SCPs is completed through the spatial consistency analysis. Finally, the spatial interpolation based on Delaunay triangulation and the polynomial fitting are used to realize the correction of the atmospheric phases. The proposed algorithm can use only a single GB-SAR pair to correct the atmospheric phases in the discontinuous deformation monitoring mode. Two case study results are given for the qualitative and quantitative analysis. Through analyzing the experimental results, and comparing those results with those of the linear atmospheric phase correction model and total station, the validity and reliability of the proposed algorithm are verified.


Mammalian DNMT1 is mainly responsible for maintenance DNA methylation that is critical in maintaining stem cell pluripotency and controlling lineage specification during early embryonic development. A number of studies have demonstrated that DNMT1 is an auto-inhibited enzyme and its enzymatic activity is allosterically regulated by a number of interacting partners. UHRF1 has previously been reported to regulate DNMT1 in multiple ways, including control of substrate specificity and the proper genome targeting. In this review, we discuss the recent advances in our understanding of the regulation of DNMT1 enzymatic activity by UHRF1 and highlight a number of unresolved questions. DNA methylation is one of the best-characterized epigenetic changes that have a critical role in numerous biological processes including gene expression, genomic imprinting, X chromosome inactivation and genome stability ,2,3. In Methylation on CpG sites in promoters generally leads to gene repression by either inhibiting transcription factor binding or recruiting the repressive complex to the promoter region . TherefoMounting evidence has demonstrated that DNMT1 alone is not sufficient to maintain the global DNA methylation throughout cell division. Indeed, structural and biochemical analyses have suggested that DNMT1 is a self-inhibited enzyme, as DNMT1 N-terminal regulatory domains including replication foci targeting sequence (RFTS) domain and CXXC domain show autoinhibitory effect on DNMT1 enzymatic activity. Therefore, additional protein factors are required to release DNMT1 from its self-inhibited state. UHRF1 has emerged in recent studies to be one of such regulators ,16,17. IDNMT1 is a multi-modular protein consisting of a DMAP1-binding domain, RFTS domain, a CXXC domain, two BAH domains and a C-terminal catalytic domain A. NumeroEarlier studies have revealed that RFTS domain regulates DNMT1 enzymatic activity through an auto-inhibitory mechanism, as explained by structural analysis showing that RFTS domain occupies DNMT1 catalytic pocket and prevents substrate DNA binding  23,26].,26.23,26UHRF1 is a multifunctional epigenetic regulator that bridges DNA methylation with multiple histone post-translational modifications such as histone methylation, ubiquitination and acetylation. A number of studies have demonstrated that UHRF1 interacts directly with DNMT1 and is essential in DNA methylation maintenance B. The UHUHRF1 is proposed to adopt a closed autoinhibited conformation due to extensive inter-domain interactions within the protein ,49,50. GMoreover, UHRF1 UBL domain has just been reported to allosterically regulate UHRF1 E3 ligase activity towards histone H3 ,56. UHRFNishiyama et al. first demonstrated that UHRF1 can ubiquitinate histone H3 on K23, and ubiquitinated H3 is subsequently recognized by DNMT1 . The proConsidering that UHRF1 N-terminal UBL domain structurally resembles ubiquitin, Li et al. went on to test if the UBL domain of UHRF1 could interact with DNMT1 RFTS domain . Indeed,UHRF1 UBL has also been revealed to interact with the ubiquitin conjugating E2 enzyme UbcH5a to stabilize the active E2/UHRF1/ubiquitin complex and direct mono-ubiquitination towards histone H3 ,56, whicMounting evidence suggests that crosstalk between DNA methylation and histone modifications occurs to maintain DNA methylation patterns during replication. Previous reports have indicated that binding of UHRF1 to H3K9me2/3 is indispensable for DNMT1 association with chromatin. Disruption of the interaction between UHRF1 and H3K9me2/3 or H3R2 leads to loss of DNMT1 chromatin localization and global hypomethylation ,41,59. IHistone H3 N-terminal residues such as K14, K18 and K23 can be acetylated or ubiquitinated, acetylation of these residues would preclude ubiquitination on the same sites. Previous studies have shown that HDAC1/2 associate with nascent chromatin during replication , DNMT1 aBased on the current knowledge, we propose a simplified working model for the DNMT1/UHRF1 complex in maintenance DNA methylation : (i) TheThe past several years have witnessed tremendous advances in our understanding of the regulatory mechanisms involved in maintenance DNA methylation. However, many questions remain to be addressed due to the complex interaction network of DNMT1, UHRF1 and other partner factors. UHRF1-dependent histone H3 ubiquitination is critical for maintenance DNA methylation, but it seems that ubiquitinated histone H3 exists transiently during replication, and USP7 has been suggested to be a histone H3 deubiquitinase . It was Recent evidence indicates that DNMT1 RFTS domain is a versatile protein interaction module. It has been demonstrated that DNMT1 RFTS domain interacts with the SRA domain and the interaction could stimulate DNMT1 enzymatic activity ,35,69,71Lastly, Karg et al. have recently reported PAF15 is a major substrate for mono-ubiquitination by UHRF1 . Dynamic


The structure of human MICAL3 provides information about its mechanism. MICAL is an oxidoreductase that participates in cytoskeleton reorganization via actin disassembly in the presence of NADPH. Although three MICALs  have been identified in mammals, only the structure of mouse MICAL1 has been reported. Here, the first crystal structure of human MICAL3, which contains the flavin-containing monooxygenase (FMO) and calponin-homology (CH) domains, is reported. MICAL3 has an FAD/NADP-binding Rossmann-fold domain for monooxygenase activity like MICAL1. The FMO and CH domains of both MICAL3 and MICAL1 are highly similar in structure, but superimposition of the two structures shows a different relative position of the CH domain in the asymmetric unit. Based on kinetic analyses, the catalytic efficiency of MICAL3 dramatically increased on adding F-actin only when the CH domain was available. However, this did not occur when two residues, Glu213 and Arg530, were mutated in the FMO and CH domains, respectively. Overall, MICAL3 is structurally highly similar to MICAL1, which suggests that they may adopt the same catalytic mechanism, but the difference in the relative position of the CH domain produces a difference in F-actin substrate specificity. Truncated forms of MICAL1 comprising the FMO and CH domains  and the FMO domain  were amplified from human MICAL1 cDNA purchased from the Korean Human Gene Bank. The oligonucleotide primers used for amplification can be found in Supplementary Table S1. After PCR amplification, hMICAL3FMOCH was cloned into the pET-28b plasmid (Novagen) using the restriction enzymes BamHI and XhoI. Other MICAL forms were digested with the same enzymes and inserted into the pET-28a vector. E213G and R530G substitutions were introduced into hMICAL3FMOCH in pET-28b by site-directed mutagenesis . The cells were grown at 37°C to an optical density at 600 nm (OD600) of approximately 0.6 in LB medium and were induced at 18°C with 0.5 mM isopropyl β-d-1-thiogalactopyranoside (IPTG). After 18 h, the cells were harvested by centrifugation at 2300g for 1 h and stored at −20°C.The DNA regions encoding the FMO and CH domains of MICAL3  equilibrated with binding buffer  and eluted with elution buffer . The purified MICAL proteins (except for hMICAL3FMOCH) were concentrated using Amicon ultracentrifugal filters  and stored at −80°C. For the subsequent crystallization experiments, hMICAL3FMOCH was concentrated and further purified by gel-filtration chromatography on a Superdex S200 column  using elution buffer consisting of 50 mM Tris pH 8.5, 100 mM NaCl, 1 mM 1,4-dithiothreitol, 1% glycerol. The predicted molecular weight of hMICAL3FMOCH is ∼79.4 kDa. The monomeric form identified in some fractions during gel-filtration chromatography was collected, concentrated to 25 mg ml−1 using Amicon ultracentrifugal filters and stored at −80°C.For each MICAL form, the harvested cells were lysed by sonication in a buffer consisting of 50 m2.3.M Bicine–NaOH pH 9.0, 10%(v/v) (±)-2-methyl-2,4-pentanediol (MPD) (Hampton Research). For crystal optimization, we employed the hanging-drop vapor-diffusion method in a 24-well VDX plate (Hampton Research). Crystals were optimized by growth in 0.1 M Bicine–NaOH pH 9.2, 7%(v/v) MPD for one day. For cryoprotection, crystals were transferred into a reservoir solution containing 20%(v/v) glycerol before flash-cooling in liquid nitrogen.Crystals were grown by sitting-drop vapor-diffusion screening at 293 K using the MCSG-1, MCSG-2, MCSG-3 and MCSG-4 screening kits (Anatrace) on an Intelli-Plate 96 (Hampton Research), in which 0.5 µl human MICAL3 solution was mixed with an equal volume of screening solution. The initial crystallization condition was 0.1 2.4.SCALEPACK and DENZO from the HKL-2000 program package  as the initial models. Molecular replacement was performed with Phenix, model building was performed with Coot and final refinement was conducted with REFMAC5 in the CCP4 suite  were immediately applied onto a carbon-coated grid which had previously been glow-discharged  for 3 min in air. The grids were negatively stained using 1% uranyl acetate. The prepared grids were examined on a Tecnai 10 transmission electron microscope  equipped with a lanthanum hexaboride (LaB6) cathode operating at 100 kV (the instrumentation used at Kangwon Center for Systems Imaging). Images were collected using a US1000 CCD camera  at a magnification of 0.32 nm per pixel  and incubated for 1 h on ice. Following ultracentrifugation at 100 000g for 1 h at 4°C, the supernatant that contained G-actin was separated carefully. 10× polymerization buffer  was then added to the supernatant and incubated at 25°C for 1 h with shaking. After polymerization, the F-actin was diluted to 8 µM with F-buffer (a mixture of G-buffer and polymerization buffer in a 9:1 ratio) and stored on ice until necessary. NADPH was dissolved in 20 mM Tris–HCl to make a 10 mM stock that was serially diluted as needed. NADPH and MICAL proteins were prepared at ten times the final concentration and 10 µl of each was added to 80 µl F-buffer (without F-actin) or F-actin. For the NADPH standard, the binding buffer for MICAL purification was added instead of the MICAL protein. All experiments were performed in triplicate, and the reaction was recorded every 10 s for 15 min. Kinetic parameters were calculated by fitting a nonlinear regression to the Michaelis–Menten equation using GraphPad Prism 5.NADPH consumption was monitored in 96-well microplates at a wavelength of 340 nm using a SpectraMax i3 spectrophotometer (Molecular Devices). All reactions were executed in an F-buffer-based assay mixture. The F-actin was prepared according to the supplier’s instructions. 1 mg of actin from rabbit skeletal muscle (Cytoskeleton Inc.) was reconstituted in 100 µl distilled water. It was diluted to 50 µ3.3.1.hMICAL3) in actin sulfoxidation, recombinant hMICAL3 containing the FMO and CH domains (hMICAL3FMOCH) was expressed and purified for crystallization. The structure of hMICAL3FMOCH was determined at 1.9 Å resolution. hMICAL3 contains multiple domains: FMO, CH, Lin11, Isl-1, Mec-3 (LIM) and C-terminal coiled-coil domains. In particular, the FMO and CH domains of MICAL3 are homologous to the FMO and CH domains of MICAL1 and MICAL2 [Fig. 1a)] and are known to play a role in methionine sulfoxidation and actin binding, respectively  for its catalytic activity  and 1c)]. The crystallographic Rwork and Rfree factors are 20.4% and 22.4%, respectively, and the Ramachandran favored region score is ∼98.1% . The hMICAL3FMOCH structure shows that the CH domain interacts with the FMO domain, as is the case in mouse MICAL1 ].The CH domain of 3.3.et al., 2006hMICAL1FMO, hMICAL1FMOCH, hMICAL3FMO and hMICAL3FMOCH). It is known that MICAL has NADPH oxidase activity that underlies F-actin disassembly simultaneously with the oxidation of NADPH  and 3b)]. When F-actin was not added, the kcat/Km value for hMICAL3FMO (∼2.4794 s−1 M−1) was similar to that for hMICAL3FMOCH (∼2.0776 s−1 M−1). However, the kcat/Km value for hMICAL3FMOCH (∼30.9857 s−1 M−1) increased dramatically on adding F-actin, while the kcat/Km value for hMICAL3FMO (∼2.8793 s−1 M−1) changed little even after adding F-actin  compared with hMICAL1FMOCH (∼6 times). Consequently, these results reveal that the CH domain of hMICAL3 participates in increasing the F-actin substrate specificity, leading to enhanced catalytic efficiency. Moreover, it appears that the CH domain of hMICAL3 might make a more efficient interaction with the FMO domain for F-actin substrate specificity relative to the CH domain of hMICAL1. We chose two residues, Glu213 in the FMO domain and Arg530 in the CH domain, which were predicted to be key residues associated with the interaction between the FMO and CH domains and mutated them to examine the effect of disrupting the FMO–CH interaction on the catalytic efficiency . Notably, the kinetic parameters of hMICAL3FMOCHΔ213,530, including the initial velocity and catalytic efficiency, are more similar to those of hMICAL3FMO than hMICAL3FMOCH . It was reported that the CH domain of mMICAL1 was located at position B ]. There is an invisible region (residues 495–517) between the C-terminus of the FMO domain and the N-terminus of the CH domain in the hMICAL3FMOCH structure, with a distance of ∼25.3 Å. Essentially, the calculated distances between the FMO and CH domains are ∼25.3 Å for position A, ∼48.8 Å for position B and 68.9 Å for position C. Therefore, considering the distance of the invisible region, the CH domain of hMICAL3 fits position A. Furthermore, we performed electron microscopy followed by single-particle analysis to identify the relative position of the CH domain in hMICAL3 ] and the fitting of the crystal structure of MICAL3 to the 3D volume of negatively stained MICAL3 molecules supports the idea that the CH domain is located at position A [c.f. the 3D reconstruction in Fig. 6b) and the models in Fig. 5a)]. We then built an initial model of the MICAL3FMOCH–F-actin interaction [Fig. 6c)] using position A; the active site seems to be close to the D-loop where the target methionine residues are found.The sequence similarity between the FMO domains of L3 Fig. 6. The vis4.et al., 2013et al., 2019mMICAL1FMOCH and hMICAL3FMOCH are structurally highly similar and share the same catalytic function of depolymerizing F-actin via oxidation of the two conserved methionine residues  in mMICAL1. Therefore, this could suggest that different binding conformations are adopted by the FMO and CH domains in hMICAL3 and mMICAL1. Although hMICAL3 and mMICAL1 have highly conserved FMO and CH domains  in ns Fig. 3, there aL1 Fig. 7. The seqes Fig. 7. Therefoet al., 2011hMICAL1 and hMICAL3 reveal that when F-actin is present as a substrate, MICALFMOCH shows a much higher catalytic efficiency than MICALFMO. In the case of MICALFMO, there was no significant change in the activity depending on the presence of F-actin as a substrate. These kinetic data demonstrate that the FMO domain has catalytic activity but that the CH domain must be present for substrate specificity. Moreover, it was shown that the activity of MICALFMO is slightly higher than that of MICALFMOCH without F-actin. These two results suggest that the FMO domain performs the catalytic function regardless of the CH domain but that the CH domain is essential for the F-actin substrate specificity of MICALs. In addition, type 2 CH domains do not possess the ability to bind directly to F-actin, as described previously (Vanoni et al., 2013et al., 2011The FMO domain that exhibits monooxygenase activity is localized at the N-terminus of MICAL and is highly conserved among species. The CH domain that is usually found in actin-binding proteins is adjacent to the FMO domain and is also highly conserved. CH domains are classified into three types: types 1, 2 and 3. Whereas type 3 CH domains are mainly found in regulatory proteins associated with muscle contraction and signaling proteins, type 1 and 2 CH domains are usually found in cytoskeletal proteins (Zhou FMOCH protein by replacing Glu213 and Arg530, two residues that are important for maintaining the interaction between the FMO and CH domains. Upon mutation, the catalytic efficiency is reduced to levels consistent with hMICALFMO. Thus, these findings consistently support the idea that interaction between the FMO and CH domains increases the F-actin substrate specificity and the subsequent catalytic efficiency. Finally, although MICAL has catalytic activity for methionine oxidation, only actin is currently known to be its substrate. The mechanism of sulfoxidation remains disputed and is considered to be owing to direct oxidation by the transfer of a single oxygen molecule or via an indirect oxidation by the production of reactive oxygen species such as hydrogen peroxide. However, it was found that consumption of NADPH without F-actin substrate produced hydrogen peroxide in MICAL1 and MICAL3, but this was not proportional to the activity level of F-actin disassembly (Wu et al., 2018We also examined the change in catalytic efficiency upon mutating the MICAL3human MICAL3, 6iciPDB reference: 10.1107/S2052252519015409/lz5030sup1.pdfSupplementary table and figures. DOI: