Phylogeny of the SNARE vesicle fusion machinery yields insights into the conservation of the secretory pathway in fungi

<p>Abstract</p> <p>Background</p> <p>In eukaryotic cells, directional transport between different compartments of the endomembrane system is mediated by vesicles that bud from a donor organelle and then fuse with an acceptor organelle. A family of integral membrane proteins, termed soluble N-ethylmaleimide-sensitive factor attachment receptor (SNARE) proteins, constitute the key machineries of these different membrane fusion events. Over the past 30 years, the yeast <it>Saccharomyces cerevisiae </it>has served as a powerful model organism for studying the organization of the secretory and endocytic pathways, and a few years ago, its entire set of SNAREs was compiled.</p> <p>Results</p> <p>Here, we make use of the increasing amount of genomic data to investigate the history of the SNARE family during fungi evolution. Moreover, since different SNARE family members are thought to demarcate different organelles and vesicles, this approach allowed us to compare the organization of the endomembrane systems of yeast and animal cells. Our data corroborate the notion that fungi generally encompass a relatively simple set of SNARE proteins, mostly comprising the SNAREs of the proto-eukaryotic cell. However, all fungi contain a novel soluble SNARE protein, Vam7, which carries an N-terminal PX-domain that acts as a phosphoinositide binding module. In addition, the points in fungal evolution, at which lineage-specific duplications and diversifications occurred, could be determined. For instance, the endosomal syntaxins Pep12 and Vam3 arose from a gene duplication that occurred within the Saccharomycotina clade.</p> <p>Conclusion</p> <p>Although the SNARE repertoire of baker's yeast is highly conserved, our analysis reveals that it is more deviated than the ones of basal fungi. This highlights that the trafficking pathways of baker's yeast are not only different to those in animal cells but also are somewhat different to those of many other fungi.</p

Untangling the evolution of Rab G proteins: implications of a comprehensive genomic analysis.

RIGHTS : This article is licensed under the BioMed Central licence at http://www.biomedcentral.com/about/license which is similar to the 'Creative Commons Attribution Licence'. In brief you may : copy, distribute, and display the work; make derivative works; or make commercial use of the work - under the following conditions: the original author must be given credit; for any reuse or distribution, it must be made clear to others what the license terms of this work are.BACKGROUND: Membrane-bound organelles are a defining feature of eukaryotic cells, and play a central role in most of their fundamental processes. The Rab G proteins are the single largest family of proteins that participate in the traffic between organelles, with 66 Rabs encoded in the human genome. Rabs direct the organelle-specific recruitment of vesicle tethering factors, motor proteins, and regulators of membrane traffic. Each organelle or vesicle class is typically associated with one or more Rab, with the Rabs present in a particular cell reflecting that cell's complement of organelles and trafficking routes. RESULTS: Through iterative use of hidden Markov models and tree building, we classified Rabs across the eukaryotic kingdom to provide the most comprehensive view of Rab evolution obtained to date. A strikingly large repertoire of at least 20 Rabs appears to have been present in the last eukaryotic common ancestor (LECA), consistent with the 'complexity early' view of eukaryotic evolution. We were able to place these Rabs into six supergroups, giving a deep view into eukaryotic prehistory. CONCLUSIONS: Tracing the fate of the LECA Rabs revealed extensive losses with many extant eukaryotes having fewer Rabs, and none having the full complement. We found that other Rabs have expanded and diversified, including a large expansion at the dawn of metazoans, which could be followed to provide an account of the evolutionary history of all human Rabs. Some Rab changes could be correlated with differences in cellular organization, and the relative lack of variation in other families of membrane-traffic proteins suggests that it is the changes in Rabs that primarily underlies the variation in organelles between species and cell types

Reproducing Kernels of Generalized Sobolev Spaces via a Green Function Approach with Distributional Operators

In this paper we introduce a generalized Sobolev space by defining a semi-inner product formulated in terms of a vector distributional operator $\mathbf{P}$ consisting of finitely or countably many distributional operators $P_n$, which are defined on the dual space of the Schwartz space. The types of operators we consider include not only differential operators, but also more general distributional operators such as pseudo-differential operators. We deduce that a certain appropriate full-space Green function $G$ with respect to $L:=\mathbf{P}^{\ast T}\mathbf{P}$ now becomes a conditionally positive definite function. In order to support this claim we ensure that the distributional adjoint operator $\mathbf{P}^{\ast}$ of $\mathbf{P}$ is well-defined in the distributional sense. Under sufficient conditions, the native space (reproducing-kernel Hilbert space) associated with the Green function $G$ can be isometrically embedded into or even be isometrically equivalent to a generalized Sobolev space. As an application, we take linear combinations of translates of the Green function with possibly added polynomial terms and construct a multivariate minimum-norm interpolant $s_{f,X}$ to data values sampled from an unknown generalized Sobolev function $f$ at data sites located in some set $X \subset \mathbb{R}^d$. We provide several examples, such as Mat\'ern kernels or Gaussian kernels, that illustrate how many reproducing-kernel Hilbert spaces of well-known reproducing kernels are isometrically equivalent to a generalized Sobolev space. These examples further illustrate how we can rescale the Sobolev spaces by the vector distributional operator $\mathbf{P}$. Introducing the notion of scale as part of the definition of a generalized Sobolev space may help us to choose the "best" kernel function for kernel-based approximation methods.Comment: Update version of the publish at Num. Math. closed to Qi Ye's Ph.D. thesis (\url{http://mypages.iit.edu/~qye3/PhdThesis-2012-AMS-QiYe-IIT.pdf}

Approximation of Stochastic Partial Differential Equations by a Kernel-based Collocation Method

In this paper we present the theoretical framework needed to justify the use of a kernel-based collocation method (meshfree approximation method) to estimate the solution of high-dimensional stochastic partial differential equations (SPDEs). Using an implicit time stepping scheme, we transform stochastic parabolic equations into stochastic elliptic equations. Our main attention is concentrated on the numerical solution of the elliptic equations at each time step. The estimator of the solution of the elliptic equations is given as a linear combination of reproducing kernels derived from the differential and boundary operators of the SPDE centered at collocation points to be chosen by the user. The random expansion coefficients are computed by solving a random system of linear equations. Numerical experiments demonstrate the feasibility of the method.Comment: Updated Version in International Journal of Computer Mathematics, Closed to Ye's Doctoral Thesi

Computing Topology Preservation of RBF Transformations for Landmark-Based Image Registration

In image registration, a proper transformation should be topology preserving. Especially for landmark-based image registration, if the displacement of one landmark is larger enough than those of neighbourhood landmarks, topology violation will be occurred. This paper aim to analyse the topology preservation of some Radial Basis Functions (RBFs) which are used to model deformations in image registration. Mat\'{e}rn functions are quite common in the statistic literature (see, e.g. \cite{Matern86,Stein99}). In this paper, we use them to solve the landmark-based image registration problem. We present the topology preservation properties of RBFs in one landmark and four landmarks model respectively. Numerical results of three kinds of Mat\'{e}rn transformations are compared with results of Gaussian, Wendland's, and Wu's functions

On spherical averages of radial basis functions

A radial basis function (RBF) has the general form $$s(x)=\sum_{k=1}^{n}a_{k}\phi(x-b_{k}),\quad x\in\mathbb{R}^{d},$$ where the coefficients a 1,…,a n are real numbers, the points, or centres, b 1,…,b n lie in ℝ d , and φ:ℝ d →ℝ is a radially symmetric function. Such approximants are highly useful and enjoy rich theoretical properties; see, for instance (Buhmann, Radial Basis Functions: Theory and Implementations, [2003]; Fasshauer, Meshfree Approximation Methods with Matlab, [2007]; Light and Cheney, A Course in Approximation Theory, [2000]; or Wendland, Scattered Data Approximation, [2004]). The important special case of polyharmonic splines results when φ is the fundamental solution of the iterated Laplacian operator, and this class includes the Euclidean norm φ(x)=‖x‖ when d is an odd positive integer, the thin plate spline φ(x)=‖x‖2log  ‖x‖ when d is an even positive integer, and univariate splines. Now B-splines generate a compactly supported basis for univariate spline spaces, but an analyticity argument implies that a nontrivial polyharmonic spline generated by (1.1) cannot be compactly supported when d>1. However, a pioneering paper of Jackson (Constr. Approx. 4:243–264, [1988]) established that the spherical average of a radial basis function generated by the Euclidean norm can be compactly supported when the centres and coefficients satisfy certain moment conditions; Jackson then used this compactly supported spherical average to construct approximate identities, with which he was then able to derive some of the earliest uniform convergence results for a class of radial basis functions. Our work extends this earlier analysis, but our technique is entirely novel, and applies to all polyharmonic splines. Furthermore, we observe that the technique provides yet another way to generate compactly supported, radially symmetric, positive definite functions. Specifically, we find that the spherical averaging operator commutes with the Fourier transform operator, and we are then able to identify Fourier transforms of compactly supported functions using the Paley–Wiener theorem. Furthermore, the use of Haar measure on compact Lie groups would not have occurred without frequent exposure to Iserles’s study of geometric integration

Genome Wide Meta-analysis Highlights the Role of Genetic Variation in RARRES2 in the Regulation of Circulating Serum Chemerin.

Chemerin is an adipokine proposed to link obesity and chronic inflammation of adipose tissue. Genetic factors determining chemerin release from adipose tissue are yet unknown. We conducted a meta-analysis of genome-wide association studies (GWAS) for serum chemerin in three independent cohorts from Europe: Sorbs and KORA from Germany and PPP-Botnia from Finland (total N = 2,791). In addition, we measured mRNA expression of genes within the associated loci in peripheral mononuclear cells by micro-arrays, and within adipose tissue by quantitative RT-PCR and performed mRNA expression quantitative trait and expression-chemerin association studies to functionally substantiate our loci. Heritability estimate of circulating chemerin levels was 16.2% in the Sorbs cohort. Thirty single nucleotide polymorphisms (SNPs) at chromosome 7 within the retinoic acid receptor responder 2 (RARRES2)/Leucine Rich Repeat Containing (LRRC61) locus reached genome-wide significance (p<5.0×10?8) in the meta-analysis (the strongest evidence for association at rs7806429 with p = 7.8×10?14, beta = ?0.067, explained variance 2.0%). All other SNPs within the cluster were in linkage disequilibrium with rs7806429 (minimum r2 = 0.43 in the Sorbs cohort). The results of the subgroup analyses of males and females were consistent with the results found in the total cohort. No significant SNP-sex interaction was observed. rs7806429 was associated with mRNA expression of RARRES2 in visceral adipose tissue in women (p<0.05 after adjusting for age and body mass index). In conclusion, the present meta-GWAS combined with mRNA expression studies highlights the role of genetic variation in the RARRES2 locus in the regulation of circulating chemerin concentrations

Bayesian Probabilistic Numerical Methods in Time-Dependent State Estimation for Industrial Hydrocyclone Equipment

The use of high-power industrial equipment, such as large-scale mixing equipment or a hydrocyclone for separation of particles in liquid suspension, demands careful monitoring to ensure correct operation. The fundamental task of state-estimation for the liquid suspension can be posed as a time-evolving inverse problem and solved with Bayesian statistical methods. In this article, we extend Bayesian methods to incorporate statistical models for the error that is incurred in the numerical solution of the physical governing equations. This enables full uncertainty quantification within a principled computation-precision trade-off, in contrast to the over-confident inferences that are obtained when all sources of numerical error are ignored. The method is cast within a sequential Monte Carlo framework and an optimized implementation is provided in Python

Sequential Analysis of Trans-SNARE Formation in Intracellular Membrane Fusion

SM proteins stabilize cis-SNARE complexes leading to a specific preferred topology for trans-SNARE formation