Characterizations of some free random variables by properties of conditional moments of third degree polynomials

We investigate Laha-Lukacs properties of noncommutative random variables (processes). We prove that some families of free Meixner distributions can be characterized by the conditional moments of polynomial functions of degree 3. We also show that this fact has consequences in describing some free Levy processes. The proof relies on a combinatorial identity. At the end of this paper we show that this result can be extended to a q-Gausian variable.Comment: Journal of Theoretical Probability, 201

Complex formation of EphB1/Nck/Caskin1 leads to tyrosine phosphorylation and structural changes of the Caskin1 SH3 domain.

Scaffold proteins have an important role in the regulation of signal propagation. These proteins do not possess any enzymatic activity but can contribute to the formation of multiprotein complexes. Although scaffold proteins are present in all cell types, the nervous system contains them in the largest amount. Caskin proteins are typically present in neuronal cells, particularly, in the synapses. However, the signaling mechanisms by which Caskin proteins are regulated are largely unknown. Here we demonstrate that EphB1 receptor tyrosine kinase can recruit Caskin1 through the adaptor protein Nck. Upon activation of the receptor kinase, the SH2 domain of Nck binds to one of its tyrosine residues, while Nck SH3 domains interact with the proline-rich domain of Caskin1. Complex formation of the receptor, adaptor and scaffold proteins results in the tyrosine phosphorylation of Caskin1 on its SH3 domain. The phosphorylation sites were identified by mass-spectrometry as tyrosines 296 and 336. To reveal the structural consequence of this phosphorylation, CD spectroscopy was performed. This measurement suggests that upon tyrosine phosphorylation the structure of the Caskin1 SH3 domain changes significantly. Taken together, we propose that the scaffold protein Caskin1 can form a complex with the EphB1 tyrosine kinase via the Nck protein as a linker. Complex formation results in tyrosine phosphorylation of the Caskin1 SH3 domain. Although we were not able to identify any physiological partner of the SH3 domain so far, we could demonstrate that phosphorylation on conserved tyrosine residues results in marked changes in the structure of the SH3 domain

Integration of linear and dendritic actin nucleation in Nck-induced actin comets

The Nck adaptor protein recruits cytosolic effectors such as N-WASP that induce localized actin polymerization. Experimental aggregation of Nck SH3 domains at the membrane induces actin comet tails-dynamic, elongated filamentous actin structures similar to those that drive the movement of microbial pathogens such as vaccinia virus. Here we show that experimental manipulation of the balance between unbranched/branched nucleation altered the morphology and dynamics of Nck-induced actin comets. Inhibition of linear, form-in-based nucleation with the small-molecule inhibitor SMIFH2 or overexpression of the formin FH1 domain resulted in formation of predominantly circular-shaped actin structures with low mobility (actin blobs). These results indicate that formin-based linear actin polymerization is critical for the formation and maintenance of Nck-dependent actin comet tails. Consistent with this, aggregation of an exclusively branched nucleation-promoting factor (the VCA domain of N-WASP), with density and turnover similar to those of N-WASP in Nck comets, did not reconstitute dynamic, elongated actin comets. Furthermore, enhancement of branched Arp2/3-mediated nucleation by N-WASP overexpression caused loss of the typical actin comet tail shape induced by Nck aggregation. Thus the ratio of linear to dendritic nucleation activity may serve to distinguish the properties of actin structures induced by various viral and bacterial pathogens.Fil: Surtayeva, Sofya. University of Connecticut School of Medicine; Estados Unidos. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Velle, Katrina B.. University of Connecticut; Estados UnidosFil: Campellone, Kenneth G.. University of Connecticut; Estados UnidosFil: Talman, Arthur. Yale School of Medicine; Estados UnidosFil: Alvarez, Diego Ezequiel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Investigaciones Biotecnológicas. Universidad Nacional de San Martín. Instituto de Investigaciones Biotecnológicas; ArgentinaFil: Agaisse, Hervé. Yale School of Medicine; Estados UnidosFil: Wu, Yi I.. University of Connecticut School of Medicine; Estados UnidosFil: Loew, Leslie M.. University of Connecticut School of Medicine; Estados UnidosFil: Mayer, Bruce J.. University of Connecticut School of Medicine; Estados Unido

Phosphorylation of nephrin induces phase separated domains that move through actomyosin contraction

© The Author(s), 2019. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Kim, S., Kalappurakkal, J. M., Mayor, S., & Rosen, M. K. Phosphorylation of nephrin induces phase separated domains that move through actomyosin contraction. Molecular Biology of the Cell, 30(24), (2019): 2996–3012, doi:10.1091/mbc.E18-12-0823.The plasma membrane of eukaryotic cells is organized into lipid and protein microdomains, whose assembly mechanisms and functions are incompletely understood. We demonstrate that proteins in the nephrin/Nck/N-WASP actin-regulatory pathway cluster into micron-scale domains at the basal plasma membrane upon triggered phosphorylation of transmembrane protein nephrin. The domains are persistent but readily exchange components with their surroundings, and their formation is dependent on the number of Nck SH3 domains, suggesting they are phase separated polymers assembled through multivalent interactions among the three proteins. The domains form independent of the actin cytoskeleton, but acto-myosin contractility induces their rapid lateral movement. Nephrin phosphorylation induces larger clusters at the cell periphery, which are associated with extensive actin assembly and dense filopodia. Our studies illustrate how multivalent interactions between proteins at the plasma membrane can produce micron-scale organization of signaling molecules, and how the resulting clusters can both respond to and control the actin cytoskeleton.We thank Hongtao Yu (University of Texas Southwestern Medical Center [UTSW]) for providing the HeLa cell line used in this work; Dan Billadeau and Timothy Gomez (Mayo Clinic) for providing antibodies; Nico Stuurman (University of California, San Francisco) for assistance with STORM imaging; Kate Luby-Phelps and Abhijit Bugde (UTSW Live Cell Imaging Core Facility) for their assistance in epifluorescence and spinning disk confocal experiments; Sudeep Banjade for advice on designing the S3, S2, S1 constructs; Khuloud Jaqaman (UTSW) for advice on cluster motility analysis; Salman Banani and Jonathan Ditlev (UTSW) for critical reading of the manuscript; and members of the Rosen lab and participants in the MBL/HHMI Summer Institutes for advice and helpful discussions. This work was supported by a Howard Hughes Medical Institute Collaborative Innovation Award; the Welch Foundation (I-1544 to M.K.R.); a J.C. Bose Fellowship from the Department of Science and Technology, government of India (to S.M.); a Margadarshi Fellowship from the Wellcome Trust—Department of Biotechnology, India Alliance (IA/M/15/1/502018 to S.M.). Research in the Rosen lab is supported by the Howard Hughes Medical Institute

Structure of the interleukin-2 tyrosine kinase Src homology 2 domain; comparison between X-ray and NMR-derived structures

The crystal structure of the interleukin-2 tyrosine kinase Src homology domain (Itk SH2) is described and it is found that unlike in studies of this domain using NMR spectroscopy, cis-trans-prolyl isomerization is not readily detected in the crystal structure. Based on similarities between the Itk SH2 crystal form and the cis form of the Itk SH2 NMR structure, it is concluded that it is likely that the prolyl imide bond at least in part adopts the cis conformation in the crystal form. However, the lack of high-resolution data and the dynamic nature of the proline-containing loop mean that the precise imide-bond conformation cannot be determined and prolyl cis-trans isomerization in the crystal cannot be ruled out. Given the preponderance of structures that have been solved by X-ray crystallography in the Protein Data Bank, this result supports the notion that prolyl isomerization in folded proteins has been underestimated among known structures. Interestingly, while the precise status of the proline residue is ambiguous, Itk SH2 crystallizes as a domain-swapped dimer. The domain-swapped structure of Itk SH2 is similar to the domain-swapped SH2 domains of Grb2 and Nck, with domain swapping occurring at the β-meander region of all three SH2 domains. Thus, for Itk SH2 structural analysis by NMR spectroscopy and X-ray crystallography revealed very different structural features: proline isomerization versus domain-swapped dimerization, respectively