On well-posed boundary conditions and energy stable finite volume method for the linear shallow water wave equation

We derive and analyse well-posed boundary conditions for the linear shallow water wave equation. The analysis is based on the energy method and it identifies the number, location and form of the boundary conditions so that the initial boundary value problem is well-posed. A finite volume method is developed based on the summation-by-parts framework with the boundary conditions implemented weakly using penalties. Stability is proven by deriving a discrete energy estimate analogous to the continuous estimate. The continuous and discrete analysis covers all flow regimes. Numerical experiments are presented verifying the analysis.Comment: 23 pages, 4 figure

The use of chemogenetic approaches to study the physiological roles of muscarinic acetylcholine receptors in the central nervous system

Chemical genetic has played an important role in linking specific G protein-coupled receptor (GPCR) signalling to cellular processes involved in central nervous system (CNS) functions. Key to this approach has been the modification of receptor properties such that receptors no longer respond to endogenous ligands but rather can be activated selectively by synthetic ligands. Such modified receptors have been called Receptors Activated Solely by Synthetic Ligands (RASSLs) or Designer Receptors Exclusively Activated by Designer Drugs (DREADDs). Unlike knock-out animal models which allow detection of phenotypic changes caused by loss of receptor functions, RASSL and DREADD receptors offer the possibility of rescuing "knock-out" phenotypic deficits by administration of the synthetic ligands. Here we describe the use of these modified receptors in defining the physiological role of GPCRs and validation of receptors as drug targets

Targeted elimination of G proteins and arrestins defines their specific contributions to both intensity and duration of G protein-coupled receptor signalling

G protein-coupled receptors (GPCRs) can initiate intracellular signalling cascades by coupling to an array of heterotrimeric G proteins and arrestin adaptor proteins. Understanding the contribution of each of these coupling options to GPCR signalling has been hampered by a paucity of tools to selectively perturb receptor function. Here we employ CRISPR/Cas9 genome editing to eliminate selected G proteins (Gαq and Gα11) or arrestin2 and arrestin3 from HEK293 cells, together with the elimination of receptor phosphorylation sites, to define the relative contribution of G proteins, arrestins and receptor phosphorylation to the signalling outcomes of the free fatty acid receptor 4 (FFA4). A lack of FFA4-mediated elevation of intracellular [Ca2+] in Gαq/Gα11-null cells and agonist-mediated receptor internalization in arrestin2/3-null cells confirmed previously reported canonical signalling features of this receptor, thereby validating the genome-edited HEK293 cells. FFA4-mediated ERK1/2 activation was totally dependent on Gq/11 but intriguingly was substantially enhanced for FFA4 receptors lacking sites of regulated phosphorylation. This was not due to a simple lack of desensitization of Gq/11 signalling because the Gq/11-dependent calcium response was desensitized by both receptor phosphorylation and arrestin-dependent mechanisms whilst a substantially enhanced ERK1/2-response was only observed for receptors lacking phosphorylation sites and not in arrestin2/3-null cells. In conclusion, we validate CRISPR/Cas9 engineered HEK293 cells lacking Gq/11 or arrestin2/3 as systems for GPCR signalling research and employ these cells to reveal a previously unappreciated interplay of signalling pathways where receptor phosphorylation can impact on ERK1/2 signalling through a mechanism that is likely independent of arrestins

Distinct phosphorylation clusters determines the signalling outcome of the free fatty acid receptor FFA4/GPR120

It is established that long-chain free fatty acids including ω-3 fatty acids mediate an array of biological responses through members of the free fatty acid receptor family, which includes FFA4. However, the signalling mechanisms and modes of regulation of this receptor class remain unclear. Here we employ mass spectrometry to determine that phosphorylation of mouse (m)FFAR4 occurs at five serine and threonine residues clustered in two separable regions of the C terminal tail, designated cluster 1 (Thr347, Thr349 and Ser350) and cluster 2 (Ser357 and Ser361). Mutation of these phospho-acceptor sites to alanine completely prevented phosphorylation of mFFA4 but did not limit receptor coupling to ERK1/2 activation. Rather an inhibitor of Gq/11 proteins completely prevented receptor signalling to ERK1/2. In contrast, the recruitment of arrestin 3, receptor internalization and activation of Akt were regulated by mFFA4 phosphorylation. The analysis of mFFA4 phosphorylation-dependent signalling was extended further by selective mutations of the phospho-acceptor sites. Mutations within cluster 2 did not affect agonist activation of Akt but instead significantly compromised receptor internalization and arrestin 3 recruitment. Distinctly, mutation of the phospho-acceptor sites within cluster 1 had no effect on receptor internalization and a less extensive effect on arrestin 3 recruitment, but significantly uncoupled the receptor from Akt activation. These unique observations define differential effects on signalling mediated by phosphorylation at distinct locations. This hallmark feature supports the possibility that the signalling outcome of mFFA4 activation can be determined by the pattern of phosphorylation (phosphorylation barcode) at the C-terminus of the receptor

Differential G-protein-coupled receptor phosphorylation provides evidence for a signaling bar code.

G-protein-coupled receptors are hyper-phosphorylated in a process that controls receptor coupling to downstream signaling pathways. The pattern of receptor phosphorylation has been proposed to generate a "bar code" that can be varied in a tissue-specific manner to direct physiologically relevant receptor signaling. If such a mechanism existed, receptors would be expected to be phosphorylated in a cell/tissue-specific manner. Using tryptic phosphopeptide maps, mass spectrometry, and phospho-specific antibodies, it was determined here that the prototypical G(q/11)-coupled M(3)-muscarinic receptor was indeed differentially phosphorylated in various cell and tissue types supporting a role for differential receptor phosphorylation in directing tissue-specific signaling. Furthermore, the phosphorylation profile of the M(3)-muscarinic receptor was also dependent on the stimulus. Full and partial agonists to the M(3)-muscarinic receptor were observed to direct phosphorylation preferentially to specific sites. This hitherto unappreciated property of ligands raises the possibility that one mechanism underlying ligand bias/functional selectivity, a process where ligands direct receptors to preferred signaling pathways, may be centered on the capacity of ligands to promote receptor phosphorylation at specific sites

Concomitant action of structural elements and receptor phosphorylation determines arrestin-3 interaction with the free fatty acid receptor FFA4.

In addition to being nutrients, free fatty acids act as signaling molecules by activating a family of G protein-coupled receptors. Among these is FFA4, previously called GPR120, which responds to medium and long chain fatty acids, including health-promoting ω-3 fatty acids, which have been implicated in the regulation of metabolic and inflammatory responses. Here we show, using mass spectrometry, mutagenesis, and phosphospecific antibodies, that agonist-regulated phosphorylation of the human FFA4 receptor occurred primarily at five residues (Thr(347), Thr(349), Ser(350), Ser(357), and Ser(360)) in the C-terminal tail. Mutation of these residues reduced both the efficacy and potency of ligand-mediated arrestin-3 recruitment as well as affecting recruitment kinetics. Combined mutagenesis of all five of these residues was insufficient to fully abrogate interaction with arrestin-3, but further mutagenesis of negatively charged residues revealed additional structural components for the interaction with arrestin-3 within the C-terminal tail of the receptor. These elements consist of the acidic residues Glu(341), Asp(348), and Asp(355) located close to the phosphorylation sites. Receptor phosphorylation thus operates in concert with structural elements within the C-terminal tail of FFA4 to allow for the recruitment of arrestin-3. Importantly, these mechanisms of arrestin-3 recruitment operate independently from Gq/11 coupling, thereby offering the possibility that ligands showing stimulus bias could be developed that exploit these differential coupling mechanisms. Furthermore, this provides a strategy for the design of biased receptors to probe physiologically relevant signaling

An investigation into the pharmacology and regulation of the M1, M3 and M4 muscarinic acetylcholine receptors

Functional selectivity, which highlights the ability of ligands to differentially activate the signalling pathways linked to G protein-couple receptors (GPCRs) has provided an avenue for developing ligands with greater safety profiles. Pilocarpine (Pilo), a non-selective muscarinic acetylcholine receptor (mAChR) agonist has been shown to differentially activate G protein subtypes linked to the M3 mAChR. In this study the pharmacology of Pilo was further investigated using a number of readouts. When compared to methacholine (MCh), a reference agonist, Pilo appeared to preferentially stimulate inositol phosphates production than global receptor phosphorylation. The ligand also appeared to preferentially promote phosphorylation of Ser412 at the third intracellular loop of the receptor than Ser577 at the C-terminal tail. This differential phosphorylation may be linked to the fact that these residues are phosphorylated by distinct protein kinases. However, such preferential phosphorylation was not evident at the mutant M3 RASSL receptor that was engineered to respond to Clozapine-N-oxide (CNO). This mutant receptor was phosphorylated in response to CNO stimulation in a similar manner as the wild-type M3 mAChR responding to ACh. Allosteric modulation has been considered an attractive approach to selectively target GPCR subtypes for multiple disease indications. BQCA and LY2033298 have been shown to act allosterically at the M1 and M4 mAChR, respectively. In this study, we provided evidence that BQCA is probe dependent and the compound is more potent as an affinity modulator of ACh than Pilo. However BQCA did not significantly potentiate the phosphorylation state of the M1 mAChR following stimulation with a sub-maximal concentration of ACh. Similar results were obtained for LY2033298 at the M4 mAChR which suggest that allosteric modulators do not promote a receptor conformation that increases the accessibility of phosphorylation sites to protein kinases

Reply to "Letter to the editor: 'Systems biology versus reductionism in cell physiology'"

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Challenges of assigning protein kinases to in vivo phosphorylation events. Focus on "Use of LC-MS/MS and Bayes' theorem to identify protein kinases that phosphorylate aquaporin-2 at Ser256"

reversible phosphorylation plays an important role in regulating the functions of many cellular proteins. This posttranslational modification acts as a molecular switch to turn proteins on and off in an acute and transient manner (4). Although there have been major advances in recent years in mass spectrometry-based proteomics to evaluate and quantify phosphoproteins in complex samples (3), this area presents significant challenges. It is in this context that Bradford et al. (2) report in this issue of American Journal of Physiology-Cell Physiology their work describing the protein kinases that potentially phosphorylate a key residue (Ser256) in aquaporin-2, a protein expressed in renal inner medullary collecting duct (IMCD) cells, which regulate water transport and renal water excretion. Although Ser256 is among four COOH-terminal sites that are phosphorylated in aquaporin-2 in response to the action of vasopressin on renal collecting duct cells, this phosphorylation event is thought to be key in controlling the trafficking of aquaporin-2 to the apical membrane of those cells and in regulating other phosphorylation events in the COOH-terminal tail. Bradford et al. employed bioinformatics, together with protein kinase inhibitors and mass spectrometry-based phosphoproteomics, to determine the potential protein kinases that phosphorylate aquaporin-2 on Ser256