Identification of transmembrane domains that regulate spatial arrangements and activity of prokineticin receptor 2 dimers

The chemokine prokineticin 2 (PK2) activates its cognate G protein-coupled receptor (GPCR) PKR2 to elicit various downstream signaling pathways involved in diverse biological processes. Many GPCRs undergo dimerization that can modulate a number of functions including membrane delivery and signal transduction. The aim of this study was to elucidate the interface of PKR2 protomers within dimers by analyzing the ability of PKR2 transmembrane (TM) deletion mutants to associate with wild type (WT) PKR2 in yeast using co-immunoprecipitation and mammalian cells using bioluminescence resonance energy transfer. Deletion of TMs 5-7 resulted in a lack of detectable association with WT PKR2, but could associate with a truncated mutant lacking TMs 6-7 (TM1-5). Interestingly, TM1-5 modulated the distance, or organization, between protomers and positively regulated Gαs signaling and surface expression of WT PKR2. We propose that PKR2 protomers form type II dimers involving TMs 4 and 5, with a role for TM5 in modulation of PKR2 function

Fractional Diffusion and Medium Heterogeneity: The Case of the Continuos Time Random Walk

In this contribution we show that fractional diffusion emerges from a simple Markovian Gaussian random walk when the medium displays a power-law heterogeneity. Within the framework of the continuous time random walk, the heterogeneity of the medium is represented by the selection, at any jump, of a different time-scale for an exponential survival probability. The resulting process is a non-Markovian non-Gaussian random walk. In particular, for a power-law distribution of the time-scales, the resulting random walk corresponds to a time-fractional diffusion process. We relates the power-law of the medium heterogeneity to the fractional order of the diffusion. This relation provides an interpretation and an estimation of the fractional order of derivation in terms of environment heterogeneity. The results are supported by simulations

Exact first-passage time distributions for three random diffusivity models

We study the extremal properties of a stochastic process $x_t$ defined by a Langevin equation $\dot{x}= \sqrt{2D_o V (B_t )} \xi_t$, where $\xi$ is a Gaussian white noise with zero mean, $D_0$ is a constant scale factor, and $V (B_t)$ is a stochastic "diffusivity" (noise strength), which itself is a functional of independent Brownian motion $B_t$. We derive exact, compact expressions in one and three dimensions for the probability density functions (PDFs) of the first passage time (FPT) $t$ from a fixed location $x_0$ to the origin for three different realisations of the stochastic diffusivity: a cut-off case $V (B_t) = \Theta(B_t)$ (Model I), where $\Theta(z)$ is the Heaviside theta function; a Geometric Brownian Motion $V (B_t) = exp(B_t)$ (Model II); and a case with $V (B_t) = B_t^2$ (Model III). We realise that, rather surprisingly, the FPT PDF has exactly the L\'evy-Smirnov form (specific for standard Brownian motion) for Model II, which concurrently exhibits a strongly anomalous diffusion. For Models I and III either the left or right tails (or both) have a different functional dependence on time as compared to the L\'evy-Smirnov density. In all cases, the PDFs are broad such that already the first moment does not exist. Similar results are obtained in three dimensions for the FPT PDF to an absorbing spherical target

Langevin equation in complex media and anomalous diffusion

The problem of biological motion is a very intriguing and topical issue. Many efforts are being focused on the development of novel modelling approaches for the description of anomalous diffusion in biological systems, such as the very complex and heterogeneous cell environment. Nevertheless, many questions are still open, such as the joint manifestation of statistical features in agreement with different models that can also be somewhat alternative to each other, e.g. continuous time random walk and fractional Brownian motion. To overcome these limitations, we propose a stochastic diffusion model with additive noise and linear friction force (linear Langevin equation), thus involving the explicit modelling of velocity dynamics. The complexity of the medium is parametrized via a population of intensity parameters (relaxation time and diffusivity of velocity), thus introducing an additional randomness, in addition to white noise, in the particle’s dynamics. We prove that, for proper distributions of these parameters, we can get both Gaussian anomalous diffusion, fractional diffusion and its generalizations.V.S. acknowledges BCAM Internship Program, Bilbao, for the financial support to her internship research period during which she developed her master’s thesis research useful for her master’s degree in Physics at University of Bologna. S.V. acknowledges the University of Bologna for the financial support through the ‘Marco Polo Programme’ for her PhD research period abroad spent at BCAM, Bilbao, useful for her PhD degree in Physics at University of Bologna. P.P. acknowledges financial support from Bizkaia Talent and European Commission through COFUND scheme, 2015 Financial Aid Program for Researchers, project number AYD–000–252 hosted at BCAM, Bilbao

Exact distributions of the maximum and range of random diffusivity processes

We study the extremal properties of a stochastic process $x_t$ defined by the Langevin equation ${\dot {x}}_{t}=\sqrt{2{D}_{t}}\enspace {\xi }_{t}$, in which $\xi_t$ is a Gaussian white noise with zero mean and $D_t$ is a stochastic 'diffusivity', defined as a functional of independent Brownian motion $B_t$. We focus on three choices for the random diffusivity $D_t$: cut-off Brownian motion, $D_t \sim \Theta(B_t)$, where $\Theta(x)$ is the Heaviside step function; geometric Brownian motion, $D_t \sim  exp(−B_t)$; and a superdiffusive process based on squared Brownian motion, ${D}_{t}\sim {B}_{t}^{2}$. For these cases we derive exact expressions for the probability density functions of the maximal positive displacement and of the range of the process $x_t$ on the time interval $t \in (0, T)$. We discuss the asymptotic behaviours of the associated probability density functions, compare these against the behaviour of the corresponding properties of standard Brownian motion with constant diffusivity ($D_t = D_0$) and also analyse the typical behaviour of the probability density functions which is observed for a majority of realisations of the stochastic diffusivity process

Centre-of-mass like superposition of Ornstein-Uhlenbeck processes: A pathway to non-autonomous stochastic differential equations and to fractional diffusion

We consider an ensemble of Ornstein–Uhlenbeck processes featuring a population of relaxation times and a population of noise amplitudes that characterize the heterogeneity of the ensemble. We show that the centre-of-mass like variable corresponding to this ensemble is statistically equivalent to a process driven by a non-autonomous stochastic differential equation with time-dependent drift and a white noise. In particular, the time scaling and the density function of such variable are driven by the population of timescales and of noise amplitudes, respectively. Moreover, we show that this variable is equivalent in distribution to a randomly-scaled Gaussian process, i.e., a process built by the product of a Gaussian process times a non-negative independent random variable. This last result establishes a connection with the so-called generalized grey Brownian motion and suggests application to model fractional anomalous diffusion in biological systems.”Marco Polo Programme” (University of Bologna

Genetically encoded intrabody sensors report the interaction and trafficking of β-arrestin 1 upon activation of G protein-coupled receptors

Agonist stimulation of G protein-coupled receptors (GPCRs) typically leads to phosphorylation of GPCRs and binding to multifunctional proteins called β-arrestins (βarrs). The GPCR-βarr interaction critically contributes to GPCR desensitization, endocytosis, and downstream signaling, and GPCR-βarr complex formation can be used as a generic readout of GPCR and βarr activation. Although several methods are currently available to monitor GPCR-βarr interactions, additional sensors to visualize them may expand the toolbox and complement existing methods. We have previously described antibody fragments (FABs) that recognize activated βarr1 upon its interaction with the vasopressin V2 receptor C-terminal phosphopeptide (V2Rpp). Here, we demonstrate that these FABs efficiently report the formation of a GPCR-βarr1 complex for a broad set of chimeric GPCRs harboring the V2R C terminus. We adapted these FABs to an intrabody format by converting them to single-chain variable fragments (ScFvs) and used them to monitor the localization and trafficking of βarr1 in live cells. We observed that upon agonist simulation of cells expressing chimeric GPCRs, these intrabodies first translocate to the cell surface, followed by trafficking into intracellular vesicles. The translocation pattern of intrabodies mirrored that of βarr1, and the intrabodies co-localized with βarr1 at the cell surface and in intracellular vesicles. Interestingly, we discovered that intrabody sensors can also report βarr1 recruitment and trafficking for several unmodified GPCRs. Our characterization of intrabody sensors for βarr1 recruitment and trafficking expands currently available approaches to visualize GPCR-βarr1 binding, which may help decipher additional aspects of GPCR signaling and regulation

Selective endocytosis of Ca(2+)-permeable AMPARs by the Alzheimer's disease risk factor CALM bidirectionally controls synaptic plasticity

AMPA-type glutamate receptors (AMPARs) mediate fast excitatory neurotransmission, and the plastic modulation of their surface levels determines synaptic strength. AMPARs of different subunit compositions fulfill distinct roles in synaptic long-term potentiation (LTP) and depression (LTD) to enable learning. Largely unknown endocytic mechanisms mediate the subunit-selective regulation of the surface levels of GluA1-homomeric Ca(2+)-permeable (CP) versus heteromeric Ca(2+)-impermeable (CI) AMPARs. Here, we report that the Alzheimer's disease risk factor CALM controls the surface levels of CP-AMPARs and thereby reciprocally regulates LTP and LTD in vivo to modulate learning. We show that CALM selectively facilitates the endocytosis of ubiquitinated CP-AMPARs via a mechanism that depends on ubiquitin recognition by its ANTH domain but is independent of clathrin. Our data identify CALM and related ANTH domain-containing proteins as the core endocytic machinery that determines the surface levels of CP-AMPARs to bidirectionally control synaptic plasticity and modulate learning in the mammalian brain

First passage and first hitting times of Lévy flights and Lévy walks

Abstract For both Lévy flight and Lévy walk search processes we analyse the full distribution of first-passage and first-hitting (or first-arrival) times. These are, respectively, the times when the particle moves across a point at some given distance from its initial position for the first time, or when it lands at a given point for the first time. For Lévy motions with their propensity for long relocation events and thus the possibility to jump across a given point in space without actually hitting it (‘leapovers’), these two definitions lead to significantly different results. We study the first-passage and first-hitting time distributions as functions of the Lévy stable index, highlighting the different behaviour for the cases when the first absolute moment of the jump length distribution is finite or infinite. In particular we examine the limits of short and long times. Our results will find their application in the mathematical modelling of random search processes as well as computer algorithms