Reversible phosphorylation of proteins is a post-translational modification that regulates all aspect of life through the antagonistic action of kinases and phosphatases. Protein kinases are well characterized, but protein phosphatases have been relatively neglected. Protein phosphatase 1 (PP1) catalyzes the dephosphorylation of a major fraction of phospho-serines and phospho-threonines in cells and thereby controls a broad range of cellular processes. In this review, I will discuss how phosphatases were discovered, how the view that they were unselective emerged and how recent findings have revealed their exquisite selectivity. Unlike kinases, PP1 phosphatases are obligatory heteromers composed of a catalytic subunit bound to one (or two) non-catalytic subunit(s). Based on an in-depth study of two holophosphatases, I propose the following: selective dephosphorylation depends on the assembly of two components, the catalytic subunit and the non-catalytic subunit, which serves as a high-affinity substrate receptor. Because functional complementation of the two modules is required to produce a selective holophosphatase, one can consider that they are split enzymes. The non-catalytic subunit was often referred to as a regulatory subunit, but it is, in fact, an essential component of the holoenzyme. In this model, a phosphatase and its array of mostly orphan substrate receptors constitute the split protein phosphatase system. The set of potentially generalizable principles outlined in this review may facilitate the study of these poorly understood enzymes and the identification of their physiological substrates. Life depends on the controlled regulation of the activity of thousands of proteins. Protein phosphorylation is a post-translational modification that controls the fate, location and activity of the majority of cellular proteins. Protein phosphorylation occurs predominantly on serines and threonines, with kinases catalyzing the addition of a phosphate group and phosphatases reversing this. One can think of protein phosphorylation as a switch to turn signaling on or off through the antagonistic action of kinases and phosphatases. However, the reality may be more nuanced. It is likely that protein phosphorylation provides a versatile way to control protein function and fate through the constant antagonistic actions of kinases and phosphatases, both being most probably highly regulated. In that sense, the state of a given protein would oscillate between a phosphorylated and a non-phosphorylated state to adjust cellular functions to various signals resulting from changes in conditions.There are ∼500 kinases in humans  and ∼189in vitro situation, it is believed that there is no free PP1 in cells, which is instead associated with one or two among an array of diverse non-catalytic subunits [Protein phosphatase 1 (PP1) is an abundant protein that catalyzes most serine–threonine dephosphorylation in cells. Historically, PP1 has been purified following a procedure that dissociated it from its interactors . The ressubunits . These cI will begin this review with a historical overview of the discovery of protein phosphatases and integrate historical findings with recent observations.a and an inactive form, phosphorylase b. Phosphorylase b becomes active upon the addition of AMP, whereas a is active without it. Remarkably, Cori and Green figured out that a contains a non-protein prosthetic group, which they reported correctly was covalently attached, because it could not be dissociated easily. Its removal needed an enzyme, contained in muscles and other tissues, which they named PR: the prosthetic group-removing enzyme [a is still widely used as a model substrate to study protein phosphatases. Yet, as we know, protein phosphorylation reversibly regulates most cellular proteins and there are thousands of phosphorylated sites [Gerty Cori and Arda Green, working on glycogen phosphorylase, an enzyme that catalyzes the rate-limiting step of glycogenolysis, discovered protein phosphorylation by discovering the first phosphatase activity . Phosphog enzyme . The prog enzyme . Now, 75a active in Cori and Green's preparation? Therein lies a frequent pattern underlying important scientific discoveries: Krebs and Fischer did not give up in the face of failure, they worked to understand what causes their problem.The discovery of the first protein kinase followed, as often in science, a rather tortuous path. Ed Krebs trained as a post-doc with Cori and Green, but he struggled to produce active phosphorylase in his own laboratory. He was not the only one to fail replicating the results of Cori and Green (see references within ). Ed Krea form of phosphorylase appeared following filtration through filter paper. If this step was omitted, phosphorylase b was recovered. The effect of filtration was accounted for by the presence of metals in the paper: washing the paper abolished the effects, while adding paper ashes recapitulated the effect, indicating that the factor, required to activate phosphorylase, was inorganic. This led Krebs and Fischer to discover that they could convert their phosphorylase b into a upon incubation in a cell-free extract in the presence of a divalent metal ion and ATP [Scrutinizing the differences between procedures, with rigor and diligence, Krebs and Fischer realized that the  and ATP . Krebs aThe discovery of the phosphorylation of phosphorylase, which was the opposite reaction to the dephosphorylation reaction discovered by Cory and Green was, as we now know, the first illustration of a general principle that controls all aspects of life: the reversible phosphorylation of proteins.It is important to emphasize that seminal discoveries in the phosphatase field were made before DNA cloning became available. For many years, laboratories were measuring activities of different preparations, rendering direct comparisons difficult. The literature from this period is somewhat cryptic and confusing, but two excellent review articles summarize the paths that led to the discovery of serine/threonine phosphatases ,10.a phosphatase upon combined precipitation with ammonium sulfate and ethanol [Another breakthrough in the path of the PP1 phosphatase discovery came, as often in science, serendipitously. In 1974, Howard Brandt, Derck Killilea and Ernest Lee noted a marked up to 43 fold) activation of the phosphorylase  fold acta was inhibited by the phosphorylation of a potent and heat-stable inhibitor [a phosphatase inhibitors, Inhibitor-1 and -2, which were heat-stable and trypsin-sensitive, was reported [2+ inhibited glycogen synthase phosphatase activity, it was proposed that these inhibitors could confer substrate specificity [The finding that partially purified phosphorylase phosphatase is inactivated by protein kinase A (PKA) (then known as ‘cyclic AMP-dependent protein kinase’) paved the way for the discovery of PP1 inhibitors . Inactivnhibitor . The folreported . Becausecificity .In 1977, Philip Cohen and coworkers identified three phosphatases of different apparent molecular mass and substrate specificities that they named phosphatase 1, 2 and 3 . They alThese findings shaped the future of phosphatase research by introducing the notion that phosphatases have broad substrate selectivity. Consolidating this idea, Thomas Ingebritsen and Cohen tested the selectivity of the four known serine/threonine phosphatases on many more substrates and concluded that ‘protein phosphatase-1 (PP1) and protein phosphatase 2A have very broad substrate specificities’ . The difa by PP1 [DARPP-32 is a phospho-protein, originally purified from rat brain with biochemical properties similar to inhibitor-1 . Like ina by PP1 .M, because it was purified from muscle) subunit [a, glycogen synthase b1 and b2, phosphorylase kinase α and β subunits) are controlled by reversible phosphorylation, the following notion emerged: the glycogen-binding subunit targets PP1c to glycogen to increase the concentration of these otherwise nonselective enzymes near the phospho-protein substrates, which are the enzymes regulating glycogen metabolism [Before it was realized that protein phosphorylation controls every aspect of life, the studies of phosphatases originated from work on glycogen metabolism. In contrast with PP2A and PP2C, which can be readily extracted, nearly all active PP1 in muscle is bound to particles of glycogen, myofibrils and the sarcoplasmic reticulum . The gly subunit . Knowingtabolism . This cotabolism . In thisThe concept of targeting subunits was extended with the purification of the smooth muscle myosin-bound phosphatase which contains two subunits in addition to PP1c . Over th2+ and Fe2+, located at the base of a shallow cleft that can accommodate phospho-serine and phospho-threonine [The three-dimensional structure of PP1c was solved in 1995, revealing a new fold and the catalytic mechanism ,27. PP1chreonine ,27. The hreonine , throughhreonine . The binIn contrast with the tyrosine phosphatases, as well as acid and alkaline phosphatases, PP1c dephosphorylation is catalyzed in a single step by a metal-activated water molecule. Metal ions stabilize negative charges and render the phosphate ester more susceptible to nucleophilic attack. It was noted that the surface of PP1c does not have a peptide-binding cleft, unlike serine/threonine kinases which possess a pronounced peptide-binding cleft important for substrate selectivity . Thus, wVarious functions of regulatory subunits have been proposed, as reviewed below.a [In vitro, they exhibit the same function as Inhibitor-1: they bind PP1c and inhibit the dephosphorylation of phosphorylase a by PP1. More recently, over 45 different proteins have been reported to bind to PP1c and to inhibit dephosphorylation of phosphorylase a [a in vitro  subunit  lead to a, glycogen synthase b1 and b2, phosphorylase kinase α and β subunits) are regulated by PP1. Glycogen is a polymer of glucose and glycogen synthesis is tightly regulated to maintain glucose homeostasis. Thus, alterations of glycogen metabolism can have detrimental consequences on glucose metabolism, for instance diabetes. Therefore, one must wonder if targeting PP1c to glycogen is sufficient for the tight and highly regulated control of the dephosphorylation of the diverse enzymes in glycogen metabolism  . PP2A, lPPPs arose from a common ancestor  and sharhttps://www.genenames.org/cgi-bin/genefamilies/set/693). These paralogs arose recently [Yeast has one PP1c, Glc7, mammals have three. They are referred to as PP1 α, β and γ isoforms but should, in fact, be called paralogs as they are encoded by three different genes localized on chromosome 11, 2 and 12, respectively (recently . PP2A haPhosphorylation of the α subunit of eukaryotic translation initiation factor 2 (eIF2α) is a vital first line of defense against many stresses. In mammals, four different eIF2α kinases sense various stresses and respond by phosphorylating eIF2α to reduce protein synthesis . GCN2, t134.5 gene of herpes simplex virus: mutants lacking a functional γ134.5 gene failed to escape the shutdown of protein synthesis that followed viral infection [134.5 is homologous to the carboxy-terminal domain of the product of the growth arrest and DNA damage gene Gadd34 (now PPP1R15A) [134.5 [134.5 interacted with PP1c [134.5 protein, had higher eIF2α phosphatase activity. This activity was sensitive to Inhibitor-2 [134.5-containing lysates had a lower phosphatase activity towards phosphorylase a [134.5 has the attributes of a PP1 regulatory subunit [Knowledge of the function of the mammalian eIF2α phosphatases stems from their homology to a viral protein. In 1994, Joany Chou and Bernard Roizman discovered the function of the γnfection . They noPP1R15A)  and inde) [134.5 . Chou an) [134.5 . The Roiith PP1c . The funibitor-2 . Conversrylase a . In subs subunit .134.5 following viral infection [Shirish Shenolikar and colleagues later recapitulated key findings from the Roizman laboratory and showed that PPP1R15A formed a complex with PP1c . David Rnfection . The disnfection . Unlike nfection . Cells lnfection  or PPP1Rnfection  have inc134.5, enhance dephosphorylation of eIF2α. However, how these proteins achieve their function was unknown until recently.As described above, there is abundant evidence that in cells, the non-catalytic subunits of PP1c, PPP1R15A and PPP1R15B, similar to γFollowing seminal work from David Barford's laboratory, who solved the structure of a fragment of the G-regulatory subunit bound to PP1c and thereby discovered the RVXF conserved in many regulatory subunits , structuThe structure of Inhibitor-2 bound to PP1c explains its function: Inhibitor-2 binding occluded the active site of PP1c, thereby revealing how it inhibited PP1c: substrates cannot reach the active site when Inhibitor-2 was bound to PP1c . ImportaKeeping in mind the variety of functions attributed to regulatory subunits , how regulatory PPP1R15A and PPP1R15B could affect eIF2α phosphorylation in cells was unclear until recently.a by PP1c [134.5, who also showed that γ134.5 enhanced dephosphorylation of eIF2α [in vitro: PPP1R15A had no effect on eIF2α dephosphorylation when added to PP1c. At this point, only one function of PPP1R15A, its inhibitory activity, was replicated in vitro [Shenolikar and colleagues demonstrated that recombinant PPP1R15A inhibited dephosphorylation of phosphorylase  by PP1c . A similof eIF2α . Howeverin vitro .a by PP1c [a. We then aimed to develop an assay that revealed the function of these regulatory subunits towards eIF2α. We found that, when using sub-stoichiometric concentration of PP1c, the dephosphorylation of eIF2α depends on the addition of PPP1R15A or PPP1R15B  bound to PP1c was unable to dephosphorylate eIF2α [With a large body of cellular data from various laboratories indicating that PPP1R15A and PPP1R15B enhance eIF2α dephosphorylation, it became important to reconstitute this function with recombinant proteins. We first replicated the findings of Shenolikar, finding that recombinant PPP1R15A inhibited dephosphorylation of phosphorylase  by PP1c . We alsoPPP1R15B . Ron andomplexes . Therefote eIF2α . The rec513–636 and PPP1R15B636–698) were not functional because they did not allow PP1c to dephosphorylate eIF2α [After having reconstituted the function and selectivity of eIF2α holophosphatases, we were in a position to decode the function of the non-catalytic subunits. In agreement with what had been seen before, we found that the carboxy-terminal region of PPP1R15s, which contains a canonical RVxF motif, binds to PP1c with high affinity . Howeverte eIF2α . This deWe found that an essential function encoded by the amino-terminal region of PPP1R15s is to provide a high-affinity binding site for its substrate . A studyWe found that while PP1c has only a low affinity for eIF2α, that of the PPP1R15–PP1c was much higher. Importantly, when PP1c was bound to an irrelevant non-catalytic subunit, such as PPP1R3A, it did not bind to eIF2α  Figure . This pra, phosphorylase kinase and glycogen synthase), thereby inhibiting their dephosphorylation.The molecular basis for the selectivity of PPP1R15–PP1c holoenzymes may also apply to other holoenzymes. In light of the findings obtained while studying the eIF2α phosphatases, I can propose the following interpretation of an earlier study on the myosin phosphatase  Figure . RegulatPP1c is the catalytic subunit of hundreds of holophosphatase complexes. As a result, catalytic inhibitors of PP1c cannot be selective. Therefore, phosphatases have been traditionally overlooked by drug discovery programs, while kinases are among the top targets in pharmaceutical industry . BecauseI work on protein quality control systems, which are the major cellular defense mechanisms against misfolded proteins . AccumulGuanabenz, an α2-adrenergic agonist, was used to treat hypertension . In a meThis showed that selective inhibition of a phosphatase can be achieved by targeting its non-catalytic subunit. We next thought that the same paradigm could be used to inhibit other phosphatases. However, as there were no methods available to enable the identification of selective inhibitors of non-catalytic subunits, there was no obvious path towards generalizing this concept.This represented both a challenge and an opportunity. Realizing that we knew little about the function of PPP1R15s, we reasoned that if we wanted to develop assays to identify selective phosphatase inhibitors by targeting non-catalytic subunits, we needed to understand their function. This led us to reconstitute eIF2α holophosphatases with recombinant proteins and to elucidate their function. As discussed above, we found that PPP1R15 provided the substrate receptor function to the holoenzyme . With knHaving been able to reconstitute selective and functional holoenzymes, we then developed an assay for target-based discovery of inhibitors of non-catalytic phosphatase subunits. We used surface plasmon resonance (SPR) to screen for selective serine/threonine phosphatase inhibitors. Different holoenzymes could be reconstituted on an SPR CHIP and used to screen for selective binders. The latter could then be tested in cell-based assays to measure target (accumulation of phospho-substrate) and pathway  engagement. The same experiments could be conducted with knockout cells to filters off-target molecules. The mechanisms of action of the inhibitors could then be validated in biochemical assays. This outlines a drug discovery platform for selective phosphatase inhibitors .Figure Our previous work highlighted the benefit of PPP1R15A inhibition. However, because PPPR15A expression is inducible, PPP1R15A inhibition is restricted to diseases where it is expressed. Therefore, we became interested in targeting constitutively expressed PPP1R15B, because we suspected that selective inhibition of PPP1R15B would circumvent the limitations associated with PPP1R15A inhibition, while conferring a proteostatic benefit. This idea was supported by earlier findings showing that knockdown of PPP1R15B protected cells against diverse stresses . AlthougThis work establishes the power and benefit of inhibiting PPP1R15s. PPP1R15A inhibitors may be useful in diseases where it is expressed, such as those involving ER stress, while PPP1R15B inhibitors may be useful for disorders where the abnormally folded proteins accumulate outside the ER . The assThere does not exist a category of science to which one can give the name applied science. There is science and the applications of science, bound together as the fruit of the tree which has borne it.).Reflecting on the path that led to the discovery of PPP1R15 inhibitors, it all started serendipitously. We did not set out to discover how to inhibit phosphatases. It is the discovery of PPP1R15A inhibitors that perked my interest in this class of enzymes. With the discovery of inhibitors, we gained tools to explore the biology. This led us to develop assays and a drug discovery platform. The druggability of these enzymes reinforces the need to characterize these enzymes, and their substrates and knowledge in this area will, in turn, open new avenues in cell biology as well as in drug discovery. I believe that we should not consider basic research as separate to drug discovery. As Louis Pasteur said « Il n'y a pas d'un côté la recherche fondamentale et de l'autre la recherche appliquée. Il y a la recherche et les applications de celle-ci, unies l'une à l'autre comme le fruit de l'arbre est uni à la branche qui l'a porté » . This model implies that PP1 phosphatases are split enzymes with both subunits being essential . Why dida.As discussed above, regulatory subunits were initially defined as inhibitors. This came about because PP1c was extensively purified, dissociated from the other components of physiological and selective holophosphatase complexes, and dephosphorylation reactions were performed on phosphorylase a. However, it is unlikely that hundreds of proteins have evolved to inhibit the dephosphorylation of phosphorylase. The split phosphatase model explains the dual functions of non-catalytic subunits of PP1: providing high-affinity for the cognate substrate and, consequently, inhibiting the low activity of the catalytic subunit on non-cognate substrate (As many studies have shown, many proteins containing a binding site for PP1c inhibit PP1c from dephosphorylating phosphorylase ubstrate . It is abona fide inhibitors of PP1c among the hundreds of non-catalytic subunits, which, like Inhibitor-2, may occlude the catalytic site. However, the vast majority of non-catalytic subunits are probably not inhibitors but orphan substrate receptors. This idea provides a simple framework for uncovering the functions of holophosphatases. The assays we have developed to elucidate the function and substrate selectivity of PPP1R15 are applicable to all phosphatases and should enable that rapid progress is this understudied area of biology.There may well be a few


Cellular functions of arrestins are determined in part by the pattern of phosphorylation on the G protein-coupled receptors (GPCRs) to which arrestins bind. Despite high-resolution structural data of arrestins bound to phosphorylated receptor C-termini, the functional role of each phosphorylation site remains obscure. Here, we employ a library of synthetic phosphopeptide analogues of the GPCR rhodopsin C-terminus and determine the ability of these peptides to bind and activate arrestins using a variety of biochemical and biophysical methods. We further characterize how these peptides modulate the conformation of arrestin-1 by nuclear magnetic resonance (NMR). Our results indicate different functional classes of phosphorylation sites: ‘key sites’ required for arrestin binding and activation, an ‘inhibitory site’ that abrogates arrestin binding, and ‘modulator sites’ that influence the global conformation of arrestin. These functional motifs allow a better understanding of how different GPCR phosphorylation patterns might control how arrestin functions in the cell. The cellular functions of arrestins are determined in part by the pattern of phosphorylation on the G protein-coupled receptors (GPCRs) to which arrestins bind. Here, authors use a library of synthetic phosphopeptide analogues of the GPCR rhodopsin C-terminus and determine the ability of these peptides to bind and activate arrestins using a variety of biochemical and biophysical methods. To control this signaling process, cells have developed a regulated system of GPCR desensitization beginning with their phosphorylation through specialized GPCR kinases (GRKs), which results in the subsequent recruitment and binding of arrestins3. Arrestins inhibit G-protein activation, mediate GPCR internalization, and possibly stimulate G-protein-independent signaling9. Phosphorylation of multiple sites within the C-terminus and/or intracellular loops of GPCRs is essential for the recruitment of arrestins10. The binding of arrestin-1 to rhodopsin has been reported to be controlled simply by the number of phosphorylated sites12. Other studies have suggested that different phosphorylation patterns on the intracellular C-terminal tail (the “phosphorylation barcode”) of GPCRs can induce conformationally distinct active states of arrestins that result in a variety of cellular outcomes24. Recently, a common phosphorylation motif required for arrestin recruitment was proposed by Zhou et al. based on the crystal structure of a rhodopsin-arrestin-1 complex25. However, the proposed code is based on limited structural data  and it does not account for the significant mass of published data indicating the functional importance of the other phosphorylation sites within the rhodopsin C-terminus30. The lack of consensus in the literature regarding the relative importance of the seven potential phosphorylation sites and the pattern of phosphorylation for the recruitment and activation of arrestin-1 motivated the current study.G-protein-coupled receptors (GPCRs) detect and translate extracellular events such as changes in hormone or neurotransmitter concentration into intracellular responses by activating signaling effector proteins such as G proteins25.Here, we systematically evaluate how the pattern of phosphorylation in the GPCR rhodopsin modulates affinity for arrestin, arrestin activation, and influences the global conformation of arrestin. Our approach was based on a library of synthetic phosphopeptides mimicking different phosphorylation states of the C-terminus of rhodopsin, and we measure arrestin affinity, activation and conformational modulation using a variety of biochemical and biophysical methods. Based on this analysis, we assign distinct functional roles to the individual phosphorylation sites, within a wider motif than described by Zhou et al.31, and (2) Why do arrestin-2 and arrestin-3 have different preferences for these two receptor classes? The functional motifs we define here provide a molecular-level description of how GPCR phosphorylation patterns potentially control the cellular functions of arrestins17 as well as a framework for interpreting the role of specific phosphorylation events in signaling outcomes.Our results help explain two outstanding questions in the field: (1) Why do some GPCRs interact transiently with arrestins while others form stable long-lived complexes, the so-called class “A” and class “B” receptors10. Therefore, we first probed a peptide microarray of the rhodopsin C-terminus containing all possible combinatorial phosphorylation patterns from mono- to tri-phosphorylated peptides with a purified mCherry-arrestin-1 fusion protein , namely peptides 7P, 6P, 4P, 3Pa, 3Pb, 3Pc, and 3Pd, contained pT340 and pS343  and 3Pf (containing inhibitory site pT342)  compared to 5P (lacking pS343), and abrogated binding when inhibitory site pT342 was present  Fig. , Table 2ent Fig. , Table 2ent Fig. , a “clas35. The digestion of arrestin-1 in the presence of nonphosphorylated peptide resulted in three major bands, whereas in the presence of the fully phosphorylated peptide 7P two major bands were observed  for the phosphorylated C-terminus of rhodopsin39. Note that digestion of arrestin-2 was accelerated in the presence of 7P, 6P, and 4P peptides, but not in the presence of the other binding peptides, including 5P . We therefore employed site-specific fluorescently labeled mutants of arrestin-1 to evaluate the potential of the different phosphopeptides to induce arrestin activation and receptor binding. Specifically, we quantified ternary complexes of fluorescently labeled arrestin-1 mutants, nonphosphorylated rhodopsin in native rod outer segment (ROS) membranes, and differently phosphorylated peptides   Figs. . The 5P 7) Figs. . Surpris7) Figs. . This ab42 and has been observed in the crystal structure of arrestin-2 bound to a vasopressin V2 receptor-derived phosphopeptide37. These changes may also reflect the dynamic sampling of different conformational states which is consistent with the differential line broadening (as reflected by the reduction of the peak intensity) observed for sites distal to the peptide binding site during titration of strong binders , the beta sandwich of the C-domain (L240 & E262), and the long inter-domain loop between β-strands 17 and 18 I312). The chemical shift changes observed at sites far away from the putative phosphopeptide binding site might be due to inter-domain twisting that affects solvent accessibility or changes in H-bond length at the β-strand interfaces  we designate “modulator sites”  in the rod cells. Notably, rhodopsin containing only threonines was not effectively phosphorylated , and its deactivation in the rod cell was apparently independent of GRK1 and arrestin-1 29. These results suggest that other, arrestin-1-independent mechanisms might exist in the rod cell to deactivate this mutant rhodopsin.Two previous in situ studies have suggested that phosphorylated threonines may be more important for arrestin recruitment to rhodopsin than phosphorylated serines37, the key phosphorylation sites pT360 and pS363  interact with multiple “phosphosensors” near the polar core and three-element interaction on arrestin-2, while the inhibitory site pS362  is more solvent exposed . How might phosphorylation between the two key sites be either inhibitory or neutral, depending on the overall phosphorylation level? In the crystal structure of arrestin-2 bound to V2Rppsed Fig. . The phoIn the case of arrestin-2 no similar inhibitory effect of site pT342 was observed. The increased propensity of C-tail displacement in this arrestin isoform might allow the active conformation to be stabilized by a few specific interactions with phosphate groups on the peptide. Alternatively, R7 in arrestin-2 could stabilize pT342 (see above) and thereby negate its inhibitory effect. Notably, the inhibitor site is present in the C-termini of many GPCRs Fig. , which r52. However, our data suggest that the relative contributions of these two receptor components to activation are different for arrestin-2 and arrestin-3. For arrestin-2, the C-tail tends to be spontaneously displaced more frequently in the basal state  and mouse  sequence differ only at site 335 . We found that the modulatory site T335 is not critical for arrestin affinity and activation, and it is likely redundant to S334 and T336. The analysis by Zhou et al. was limited to pT336, pS338 and E341, which were resolved on the C-terminus of the receptor interacting with positively charged pockets on arrestin-1. Despite the insight the structural context affords for this one example of a phosphorylation motif, only a systematic analysis of the effects of different phosphorylation patterns can reveal the regulatory effects of each site on arrestin function. Among the phosphopeptides we analyzed, all but two of the nonbinders (3Pf and 3Ph) contained the barcode motif Zhou et al. proposed on the basis of their structure to be necessary for binding, whereas three of the binders  did not. The wider phosphorylation motifs we describe here expand not only the size of the coding region but go further in assigning distinct functions to the different regions within the receptor C-terminus. That being said, the current study was  limited to rhodopsin-derived peptides, and future experiments using peptides derived from other GPCRs will be required to validate the universality of the proposed motifs and to reveal other receptor-specific arrestin binding determinants. For example, in the crystal structure of the rhodopsin-arrestin-1 complex25, E341, which is positioned between the two key sites, is observed to interact with functionally important charged residues, namely the phosphosensor K15 48. This interaction could contribute to the specificity of rhodopsin for arrestin-1 binding33.The phosphorylation motif we propose here expands upon that which was recently proposed by Zhou et al. based on the crystal structure of the rhodopsin-arrestin-1 complex37, as well as studies showing that arrestin activation and cellular functions are controlled by multiple phosphorylation moieties spread over a large coding region in the GPCR C-terminus50. In summary, the phosphorylation motifs we identify here, which control affinity, activation, inhibition and modulation of global conformation, would support complex regulation mechanisms for the structurally flexible and functionally versatile arrestins.Our proposed phosphorylation motifs are consistent with the multiple and physically extended interactions seen in the crystal structure of arrestin-2 bound to V2Rpp32.Peptides were synthesized using combinatorial Fmoc Solid Phase Synthesis strategy. The coupling methods applied were specific for each amino acid and were determined based on the phosphorylation pattern as described by Samarasimhareddy et al.57. The constructs contained an N-terminal hexa histidine tag linked by a linker that contained a Tobacco Etch Virus cleavage site . PCR was used to introduce the monomerizing arrestin-1 mutations 58. Note that this mutant was employed for fluorescence anisotropy, trypsin digestion, and NMR experiments. Wild-type arrestin-2 and -3 were used for fluorescence anisotropy and trypsin digestion experiments. For the peptide array experiment, an N-terminal mCherry-arrestin-1 fusion construct was cloned that had a six residue linker (GSGGGS) between the two proteins. The arrestin-1 in this construct had the wild-type sequence. Note that this construct differs slightly from that previously published60 and was optimized for purification. We verified the functionality of this fusion construct using the standard centrifugal pull-down assay using phosphorylated rhodopsin in native ROS membranes44.Synthesized cDNAs of bovine arrestin-1, human arrestin-2 and human arrestin-3 were ordered from Genewiz, amplified by PCR and cloned . Pellets were resuspended in 180 ml solubilization buffer  glycerol), frozen and stored at −20 °C.NiCo (DE3) cells (New England Biolabs) were transformed with plasmid containing the arrestin gene and plated on selective medium. A single colony was used to inoculate 500 ml of lysogenic broth medium, and cells were grown at 30 °C/160 rpm overnight. Forty milliliter of starting culture was used to inoculate 500 ml of terrific broth media containing 50 µg/ml carbenicillin in a 2 l baffled flask (12×). The culture was incubated in a shaker at 37 °C/160 rpm for 3–4 h until an OD2H, 15N, 13C-Arrestin-1 the cells were harvested after reaching an OD600 of 2.0 by centrifugation (2000 × g for 20 min). The pellets were resuspended immediately afterwards in 2 l M9 media  containing 50 µg/ml carbenicillin. The solution consisting of cells and M9 media was divided into four 2 l baffled flask. They were cultured in the new media for 1 h at 37 °C before they were cooled down to 20 °C. The induction and harvesting was carried out as described for the expression of unlabeled arrestins.For the expression of For the expression of the mCherry-arrestin-1 fusion, 1000 μM IPTG was added for induction at 37 °C. The cells were harvested after 2 h post induction by centrifugation (3000 × g for 20 min). Pellets were resuspended in 60 ml solubilization buffer frozen and stored at −20 °C.g, 1 h, 4 °C). The supernatant was filtered through 3−4 syringe filters (0.45 μm), and imidazole (30 mM) was added before the lysate was loaded onto a 5 ml Ni-NTA FF crude column . The column was washed with ten column volumes of buffer A  glycerol, 8 mM 2‑mercaptoethanol). A step elution with IMAC B buffer (same as A but with 500 mM imidazole) was performed. The eluted-fractions were pooled and dialyzed against SQ120  glycerol and 14.3 mM 2‑mercaptoethanol) overnight in the presence of TEV (10:1 molar ratio of protein to TEV). The dialyzed solution was slowly diluted with SQ0-buffer (0 mM NaCl) to a concentration of 40 mM NaCl. The protein was loaded directly after the dilution onto the SQ column (15 ml resin). The column was washed until the baseline stabilized before switching to the elution buffer (SQ120 containing 120 mM NaCl for arrestin-1 or SQ200 containing 200 mM NaCl for arrestin‑2/‑3). Ten-milliliter fractions were collected and protein-containing fractions were pooled. The NaCl concentration was increased to 300 mM before the protein was concentrated with a Vivaspin concentrator  to approximately 3 mg/ml. The concentrated protein was flash frozen in 200 µl aliquots and stored at −80 °C.Cell pellets from 6 l of culture were thawed and topped up to a total volume of 240 ml with solubilization buffer. Two tablets of EDTA-free protease inhibitor (Complete-Roche), a small spatula of DNAse (Sigma) and 8 mM 2‑mercaptoethanol were freshly added before the cells were lysed by sonication . Ultracentrifugation was performed to remove the insoluble fraction  present in ROS was achieved by adding ATP and MgCl2 and illuminating the ROS with light as described previously43. Nonphosphorylated ROS membranes were treated identically except that no ATP was added. After illumination 50 mM hydroxylamine was added to the bleached ROS membranes to yield retinal-free opsin. Rhodopsin was regenerated by adding a threefold molar excess of 11-cis-retinal, which was prepared from commercially available all-trans-retinal and purified by HPLC62. Regeneration was terminated by the addition of 20 mM o-tert-butyl-hydroxylamine63. Rhodopsin concentration was determined by absorbance difference spectrum  after bleaching the rhodopsin in the presence of hydroxylamine.ROS membranes were prepared from frozen bovine retina obtained from W.L. Lawson Company (USA) or from bovine eyes obtained from a slaughterhouse near Berlin. The American bovine tissue was obtained from animals slaughtered under guidelines set forth by the Humane Slaughter Act (US Public Law 85–765), and all retinal tissue regardless of origin was approved for laboratory use by the State Office for Health and Social Affairs (LAGeSo Berlin). ROS isolation was carried out as previously describedwww.r-project.org). All peptides were present in duplicate on the array, and two independently synthesized arrays were used; hence, the average signals from four measurements per peptide were used for data analysis. In order to identify the contribution of each phosphorylation site to arrestin-1 binding, two different approaches were used: (1) All peptides were ordered by their fluorescence intensity (binding to arrestin-1) and plotted in a binary heatmap that showed whether a site was phosphorylated or not. (2) A linear regression with an exhaustive, bidirectional, stepwise subset approach  was applied, with the Akaike information criterion to evaluate fits, using the MASS and leaps packages in R. The following fitting function was used, whereby each phosphorylation site was represented by an individual term in the linear regression:The 384-peptide microarray containing all possible combinatorial phosphorylation patterns from mono- to tri-phosphorylated peptides derived from the rhodopsin C-terminus was ordered from Intavis (Germany). The peptide array was rehydrated by dropwise addition of 96% ethanol to the surface, followed by extensive washing of the surface with deionized water. The blocking of the peptide array was performed with 3% (w/v) bovine serum albumin (BSA) in incubation buffer, which consisted of 20 mM Bis-Tris propane pH 7.0, 250 mM NaCl and 10% (v/v) glycerol. The peptide array was washed twice for 5 min after 1 h of blocking. The peptide array was then incubated with the 5–10 μM mCherry-arrestin-1 at RT for 4 h. The peptide array was then rinsed twice with buffer before the bound protein was detected by mCherry fluorescence with automated exposure time setting (Amersham Imager 600). The analysis was performed using the open source software ImageJ and its plugin Protein Array Analyzer, Microsoft Excel and R  for 10 min. The labeled and precipitated peptide was sedimented, and the supernatant was removed. The peptide was resuspended again in ice-cold acetone, stored for 1 h at −20 °C and centrifuged  for 10 min. This procedure was repeated until the supernatant did not contain any color when it was diluted with 50 mM PBS buffer, pH 7.0. The precipitated peptide was dried at RT in the dark. It was dissolved in 50 µl of 20 mM Bis-Tris propane pH 7.0 and 150 mM NaCl and its concentration was determined by absorbance. A molar extinction coefficient of 70,000/M/cm at pH 7.0 was assumed for calculating the concentration of the labeled peptide stock.0.1–0.2 mg of lyophilized peptide was dissolved in 50 µl of 50 mM phosphate-buffered saline (PBS) buffer at pH 7.0, and then two molar equivalents of fluorescein-5-maleimide dye stock dissolved in dimethylsulfoxid was added. The reaction was carried out at RT in the dark. After 1 h the reaction was topped up with 1 ml of ice-cold 100% acetone and stored until the next day at −20 °C. The precipitated peptide was centrifuged  for 2 min and stored at RT for 20 min. The reading was performed by default settings of PHERAstar plate-reader (BMG Labtech) and excitation‑/emission-wavelengths of 485 nm (12 nm bandpass)/520 nm (30 nm bandpass) were used. The analysis was performed using Origin2016  software by fitting the data to a one-to-one binding model:r stands for anisotropy, R0 stands for anisotropy of the ligand,  ΔR stands for anisotropy of the complex minus anisotropy of the ligand, P stands for the concentration of protein, and Kd stands for the dissociation constant of the ligand.An 11-step serial dilution series of arrestin in 20 mM Bis-Tris propane pH 7.0, 150 mM NaCl, 8 mM 2‑mercaptoethanol, 2% (w/w) BSA, 0.02% (v/v) Tween-20 was prepared and transferred to a black high-bottom 384-well plate (Greiner). As control for free peptide, a position with only buffer was included. The peptide was added at a final concentration of 20 nM to each well. The plate was closed by a clear cover and vortexed for 15 s. Afterwards it was centrifuged (800 × Arrestin (60 µg) was mixed at a 1 to 1.2 molar ratio with peptide and preincubated at RT for 5 min before 1 μl of 0.15 mg/ml trypsin stock was added. The enzymatic digestion was carried out at 35 °C . At certain time points , 5 μl aliquots were quenched with heat incubation in the presence of 20 μl SDS loading buffer  and then subjected to SDS PAGE. Bands were visualized with InstantBlue (Expedeon).43. The basic construct was a modified wild-type sequence that contained no native cysteines  nor tryptophans (W194F). Single cysteine residues were introduced by PCR at sites 72 or 197 as previously described43. The I72C mutant was labeled with monobromobimane (Thermo Fisher) and is referred to as I72B. The F197C mutant was labeled with N,N′-Dimethyl-N-(Iodoacetyl)-N′-Ethylenediamine  and is referred to as F197NBD. Labeling was carried out as previously described61. Both labeled mutants were assessed to be functionally similar to wild-type arrestin-1 using the Extra Meta II assay, which determines the ability of arrestin-1 to bind and stabilize the active Meta II form of rhodopsin64.Recombinant bovine arrestin-1 cloned into the pET15b vector was expressed and purified as describedUnder dim-red light, samples were prepared that contained nonphosphorylated rhodopsin (10 µM) in ROS membranes, 1 µM arrestin-1 I72B or F197NBD, ±100 µM peptide in 50 mM HEPES, 130 mM NaCl, pH 7 (150 or 200 µl sample volume). One hundred microliters of the sample was used for fluorescence measurements, and the remainder was used for the centrifugal pull-down assay (50 µl per assay). Steady-state fluorescence measurements were performed using a SPEX Fluorolog (1680) instrument in front-face mode. Bimane fluorescence was recorded using an excitation wavelength of 400 nm and emission 424–600 nm, and NBD fluorescence was recorded using an excitation wavelength of 500 nm and emission 524–660 . Excitation slits were narrowed to 0.1−0.2 nm to minimize light-activation of rhodopsin, and emission slits were set at 4 nm. Pull-down analysis was performed by centrifuging samples at 16,000 × g for 10 min at 20 °C. Selected samples were light activated (>495 nm) for 15 s prior to centrifugation (appr. 60 s delay time). Following centrifugation, the supernatants were removed, and the pellets were solubilized in loading buffer containing 2% SDS and subjected to SDS PAGE. Bands were visualized using Coomassie Brilliant Blue.P ≤ 0.05, **P ≤ 0.01, ***P ≤ 0.001 and ****P ≤ 0.0001 or ‘−’ if no calculation was possible due to no measurable Kd value in case of fluorescence anisotropy phosphopeptide binding assays.The statistical analysis of the affinity measurements, the site-directed fluorescence spectroscopy experiments and pull-down experiments were performed in Prism6 using ANOVA analysis. The significance between two values is given either by “ns” = no statistical significance, *2H,15N,13C-labeled arrestin-1 aliquots were thawed quickly under running water, transferred to 30 kDa-cutoff Vivaspin  centrifugal spin concentrators, and concentrated to approximately 600 μM. The concentrator was immediately transferred into a beaker filled with 400 ml of NMR buffer 1 or 2 (see below) carried by a floatation device. The dialysis was performed at 4 °C overnight. On the next day the concentration was determined by UV absorbance at 280 nm . Lyophilized peptides were dissolved in NMR buffer 2 and dialyzed with a self-made dialyzing device consisting of the top of a 1.5 ml Eppendorf tube and a dialysis membrane . The dialysis was performed at 4 °C overnight, and the peptide concentration was determined by its absorbance at 205 nm . The NMR sample was mixed and 5% D2O was added. Afterwards it was transferred to a 3 mm Shigemi tube using a plastic syringe connected to a piece of Teflon high performance chromatography tubing using a luer lock (Pharmacia) and sealed with a piece of Parafilm M. NMR buffer 1: 25 mM Bis-Tris propane pH 7.0, 150 mM NaCl, 10 mM DTT and 0.02% NaN3; NMR buffer 2: 350 mM MOPS (adjusted with Bis-Tris propane) pH 7.0, 5 mM NaH2PO4, 14.3 mM 2‑mercaptoethanol and 0.02% NaN3. Buffer 2 was necessary for titrations experiments to avoid systematic changes in pH due to addition of phosphopeptides.4 (Bruker) in a 5 mm NMR tube. Pulse lengths were calibrated for 1H manually and for 13C/15N using an in-house automated procedure. pH was monitored using the position of the phosphate signal in NMR buffer 2 as an internal reference and varied by no more than 0.03 pH units during peptide titration experiments. TROSY experiments were recorded with internal ETH pulse sequences, whereas 3D triple resonance TROSY experiments were recorded using the manufacturer’s pulse sequences. Spectra were processed in TopSpin 3.2 (Bruker) and calibrated using external 4,4-dimethyl-4-silapentane-1-sulfonic acid in the NMR buffer. All further data analysis was performed in CARA65 (www.nmr.ch), Excel and Origin.NMR measurements were performed on Bruker Avance III-HD 600 or 900 MHz spectrometer using a CTCI cryo-cooled probehead. At the beginning of all experimental series the temperature was calibrated to 298 K using a sample of 99.8% methanol-d66 were used as basis for the assignments in this work. Minor differences in peak positions were observed due to the use of a different buffer composition, but for most resonances only slight shifts in peak positions were observed. Assignments were confirmed using triple resonance spectra measured with samples with protein concentration of 350–600 μM. The backbone amide resonance assignment had a completeness of approximately 40%.The previously published assignments of arrestin-115N,1H]TROSY experiments, where the sample from the previous step of the titration series was recycled and topped up with a peptide stock (5 mM) as well as arrestin-1 to reach the next aimed stoichiometric ratio at a constant arrestin concentration. As a control, a TROSY spectrum containing arrestin-1 and nonphosphorylated C-terminal peptide (0P) at a 1:10 molar ratio was measured, which showed some minor changes in peak intensity for a small set of signals when compared to the corresponding spectrum obtained with protein alone. These changes in intensity may be caused by weak interactions mediated by four acidic residues (two aspartates and two glutamates) in the peptide sequence. The position of signals was followed from their starting point at 0:1 peptide:arrestin-1 ratio up to the endpoint at 10:1 ratio. TROSYs were measured for 18−48 h each on a 600 MHz spectrometer.The concentration of arrestin-1 was held constant at 100 µM and the peptide was added at stoichiometric arrestin-1:peptide ratios of 1:0 , 1:1, 1:4 and 1:10. Each titration series consisted of four TROSY spectra obtained with a given peptide:protein ratio and the spectrum of the reference protein alone was calculated using the formula:δNprotein is the chemical shift of the amide 15N signal for the protein alone, δHprotein is the corresponding chemical shift for the 1H signal, and the corresponding values for the protein in the presence of peptide are indicated by the same symbols with superscript peptide + protein.The chemical shift perturbation of each The program MODELLER9.14 was used to create a full-length representation of arrestin-1 . A total of 100 models were created and subjected to 300 iterations each. One of the top scoring models using a discrete optimized protein energy potential was selected by eye and equilibrated using the Implicit solvent modeler GBSW with the CHARM-Gui and NAMD2.10.Further information on experimental design is available in the Supplementary InformationPeer Review FileReporting SummarySource Data


Acoustic data from the Canada Basin Acoustic Propagation Experiment are discussed. These recordings were obtained under seasonally varying sea ice to the north of Alaska during a period of 154 days. They contain signals from sources that were deployed at ranges of 17.5, 29.6, and 237.8 km and ambient sounds from marine mammals and ice-related events. After the area was covered with ice, the amplitude of receptions from the most distant source gradually decreased as scattering features on the underside of the ice developed during fracturing, drifting, ridging, and rafting events. Improvements are presented for an Arctic acoustic model that is based on the parabolic equation method, and the approach is applied to a problem in which variable ice thickness acts as a loss mechanism by scattering energy out of the waveguide. Some of the recordings have a harmonic signature that is believed to be associated with the resonances of ice floes rubbing together, but variations in the harmonics over short time scales cannot be explained in terms of the resonances of an isolated floe. This behavior may be related to the coupling of vibrations at contact points that vary during the relative motions of floes. Participants from several institutions carried out the deployment phase of CANAPE during two sea trips to the north of Alaska in 2016. This paper discusses acoustic recordings that were obtained on an array of receivers that was deployed during CANAPE. These data cover a period of 154 days and include signals from sources that were deployed at ranges of 17.5, 29.6, and 237.8 km from the array and ambient sounds from sea mammals and ice-related events. Some of the recordings consist of harmonics that are believed to be associated with the resonances of ice floes3. The pronounced variations of the harmonics cannot be explained in terms of the resonances of an isolated floe; this effect may be related to the coupling of the vibrations of floes at moving contact points. Data from CANAPE are compared with results obtained with the parabolic equation method4, which is useful for solving large-scale wave propagation problems in which there are gradual horizontal variations in the parameters of the medium. An improved approach for handling variations in ice thickness is presented for the Arctic parabolic equation5, which was not available during previous studies in Arctic acoustics13. Applying this model for parameter ranges relevant to CANAPE led to a better understanding of the requirements for obtaining stable solutions.Changing conditions in the Arctic, such as diminishing sea ice14, the results were not tested initially but were later found to be in agreement with a coupled mode solution15. When it was applied to a problem involving refraction of acoustic waves by the zonal winds in the atmosphere of Jupiter16, the results were tested only in a qualitative sense using ray solutions. Accuracy is tested here for problems in Arctic acoustics using a finite-element model for directly solving the elastic wave equation17. It is not practical to run this model at high frequencies, but it is usually sufficient to test the accuracy of a parabolic equation model at low frequencies since (a) continuous horizontal variations in the properties of the medium become more gradual on the scale of a wavelength as frequency increases and (b) horizontal variations associated with a sloping interface do not scale with frequency.The parabolic equation method is based on the assumption that outgoing energy dominates energy that is backscattered toward the source in an environment in which horizontal variations are gradual. Due to an unmatched combination of accuracy and efficiency, this approach is often applied to large-scale wave propagation problems before it becomes practical to fully test the results using other approaches. When it was applied to a mode cut-off problem in which trapped modes in the ocean couple into beams of energy in the sedimentx is the horizontal coordinate and the parameters of the medium are initially assumed to depend only on the depth z. The elastic wave equation may be written in the form5,ux is the horizontal derivative of the horizontal displacement and w is the vertical displacement. The depth operators that appear in L and M are defined by the equations,ω is the angular frequency, λ and are defined by cp and cs are the compressional and shear wave speeds. The compressional and shear attenuations The parabolic equation method is described here for a two-dimensional problem in an elastic medium, where For this non-conventional set of dependent variables, there is no mentclass2pt{minim5 and references therein, solutions based on Eq. , an additional ten elements in the lower horizontal subarray, and a receiver spacing of 0.432 m in both directions. On October 19, the array was deployed in 151.2 m of water at 72.7054°N 158.9691°W, with the upper horizontal subarray 93 m below the surface. Acoustic data were recorded on each receiver at 24 bits and a sampling rate of 12 kHz for 45 minutes every four hours until the batteries ran out after March 22, 2017. The array and its data were recovered on September 3, 2017. This data set represents a broad range of spatial, frequency, and temporal sampling, but the initial study presented here focuses on temporal variations and ambient sounds, for which it is sufficient to consider data from a single receiver.20. For some cases, an approach that was proposed for handling a sloping fluid-solid interface requires the introduction of an artificial intermediate region and relatively fine sampling in the computational grid19. The approach presented here provides comparable accuracy but greater efficiency, which can be a significant advantage at relatively high frequencies.Horizontal variations in the environment may be handled by approximating in terms of a series of regions in which the elastic parameters depend only on depth. In each region, the factorization in Eq.  is exacti and t denote the incident and transmitted quantities and the subscripts A and B denote evaluation on the incident and transmitted sides of the vertical interface. Conserving half of the quantities at a vertical interface may not produce accurate solutions, but it is possible to obtain accurate solutions for many problems involving sloping interfaces between ice and water with the condition,21 for the acoustic case 19.In the exact solution, the horizontal displacement, vertical displacement, normal stress 19. For these problems, a 25 Hz source is located in a water column in which c = 1500 m/s; the parameters of the ice are cp = 3500 m/s, cs = 1750 m/s, 3, cp = 3400 m/s, cs = 1700 m/s, 3r < 3 km, 100 m for r > 7 km, and linearly increasing between these values for 3 km < r < 7 km. For the upslope case, the thickness of the ice is 100 m for r < 3 km, 20 m for r > 7 km, and linearly decreasing between these values for 3 km < r < 7 km. In the comparisons with a finite-element solution17 in Figs 19, which were obtained using an approach that is less efficient.The accuracy of the approximate condition for conserving energy in Eq.  is illusX is defined by Eq.  exists for some ranges of the parameters. The operator square root in Eq.  may be aX = −1, as can be seen from the example in Fig. n = 10 and 4 of an acoustics problem in a 500 m thick homogeneous waveguide, where the sound speed is 1500 m/s and the condition p = 0 applies at the top and bottom boundaries. At 50 Hz, all of the eigenvalues are mapped on or above the real axis, which is required for stability. The eigenvalues are more densely spaced at 250 Hz, and two of them are mapped slightly below the real axis. These eigenvalues are the cause of the stability problem, and they correspond to nearly vertical propagation. Stable solutions may be obtained by introducing attenuation that affects these eigenvalues but does not have a significant affect on eigenvalues that correspond to the propagating modes. For the examples presented here, stable parabolic equation solutions were obtained by allowing the attenuation to artificially increase deep within the sediment.The exact square root function maps Erignathus barbatus) in Audio 25. The area was free of ice until near the end of the second sea trip. An early stage of ice appears in the image in Fig. All of the acoustic recordings discussed here were obtained in 2017 on one of the end receivers of the top row of the array. All of the signal types that were transmitted by the two nearby sources are audible in Audio 3. Only odd harmonics should be excited according to an analysis based on SH waves in plates of ice2, but even and odd harmonics are excited in the recording in Fig. SH modes to acoustic modes in the water should be relatively weak, but the received signal was strong for this event. The variations of the harmonics in Fig. Some sounds that originate in the ice, such as the ones in Audio 30. Evidence of these processes appears in the images in Figs 31, with a mean draft of 3.5 m, rms topographic variation of 1.38 m, characteristic length of 100 m, fractal dimension of 1.5, and normalized skewness of 1.41. The speed of sound in the water column is a linear function of depth, with c = 1430 m/s at z = 0 (the surface of the ice) and c = 1460 m/s at z = 400 m. The parameters of the ice are cp = 3500 m/s, cs = 1750 m/s, 3, cp = 1700 m/s, cs = 800 m/s, 3, z = 175 m. Appearing in Figs Appearing in Fig. mentclasspt{minimaApplications to CANAPE data motivated improvements to the Arctic parabolic equation model that are useful at higher frequencies than had been considered previously. The accuracy of an approximate energy-conservation condition for handling variable ice thickness is comparable to the accuracy of an approach that requires the introduction of an artificial intermediate material and fine sampling in the numerical grid. Some rotated rational approximations of the square root function map a short segment of the real axis below the real axis in the complex plane, and this can cause stability issues when the ocean depth is sufficiently large relative to a wavelength. The Arctic parabolic equation was used to illustrate how scattering from under-ice features acts as a loss mechanism. The received signal from a distant source began to lose intensity well after the area was covered with ice, apparently due to the time it takes for under-ice features to develop during fracturing, drifting, ridging, and rafting processes.32. Due to the weak coupling of sounds from ice-related events into propagating modes33 and attenuation associated with scattering from under-ice features, distant ice-fracturing events  could be detected at a lower rate than would be expected based simply on geometry.The array of receivers recorded for 154 days and captured many sounds from marine mammals and ice-related events. A mechanism was proposed for variations of harmonics that were previously identified with the resonances of ice floes rubbing together. The resonance frequencies of an isolated floe cannot be used to explain this behavior. Since the vibrations of two floes in contact are coupled, the resonance frequencies should vary as the contact points vary during the relative motion of the floes. This study involved data from only one receiver. By processing data from multiple receivers, it should be possible to determine the locations of ice fracturing events, possibly even for cases in which a developing fracture behaves as a moving acoustic sourceAudio S1Audio S2Audio S3Audio S4Audio S5Audio S6Movie S1


Programmed cell death-1 (PD-1) is an inhibitory immune checkpoint receptor that negatively regulates the functioning of T cell. Although the direct targets of PD-1 were not identified, its inhibitory action on the TCR signaling pathway was known much earlier. Recent experiments suggest that the PD-1 inhibits the TCR and CD28 signaling pathways at a very early stage ─ at the level of phosphorylation of the cytoplasmic domain of TCR and CD28 receptors. Here, we develop a mathematical model to investigate the influence of inhibitory effect of PD-1 on the activation of early TCR and CD28 signaling molecules. Proposed model recaptures several quantitative experimental observations of PD-1 mediated inhibition. Model simulations show that PD-1 imposes a net inhibitory effect on the Lck kinase. Further, the inhibitory effect of PD-1 on the activation of TCR signaling molecules such as Zap70 and SLP76 is significantly enhanced by the PD-1 mediated inhibition of Lck. These results suggest a critical role for Lck as a mediator for PD-1 induced inhibition of TCR signaling network. Multi parametric sensitivity analysis explores the effect of parameter uncertainty on model simulations. Activation and subsequent proliferation of T cell are crucial events preceding pathogen clearance. However, proper functioning of the immune system also relies on the ability of T cells to promote self-tolerance. Hence, these processes are tightly controlled at multiple levels by regulatory mechanisms. T cellsThe finding that cancer cells can be recognized and destroyed by the immune system, has established the field of cancer immunology and the interaction between cancer cells and immune system is being studied extensively , 12. CanMathematical models have been an integral part in understanding complex biological phenomena such as apoptosis , cell cyTo better understand the molecular basis of PD-1 induced inactivation of T cell signaling molecules, we constructed a deterministic mathematical model of PD-1 regulatory pathway. The proposed model investigates the role of feedback regulatory mechanisms in inhibition of early TCR signaling by PD-1. The model simulations provides the mechanistic basis of several features of PD-1 mediated inhibition that were observed in the recent experiments done using the reconstitution system by Hui et al .TCR is stimulated by the binding of cognate p-MHC (peptide-major histocompatibility complex) present on the surface of antigen-presenting cells. Stimulation of TCR results in the phosphorylation of cytoplasmic domain of the TCR complex at the ITAMs (Immunoreceptor tyrosine-based activation motifs) by the Src family tyrosine kinase, Lck (Lymphocyte specific protein tyrosine kinase). Phosphorylated CD3 ITAMs recruit Zap70 (Zeta-chain-associated protein of 70 KDa), a Syk family kinase. Studies on ZAP70 phosphorylation have shown that Y315 and Y319 are initially phosphorylated by Lck and this in turn allows the Y493 present in the activation loop of the Zap70 to get phosphorylated. Phosphorylation of Y493 has shown to be crucial for the complete activation of the kinase Zap70 , 48. Actin vitro reconstitution system, the cytosolic domains of receptors and membrane bound proteins were tethered to the surface of LUVs (large unilamellar vesicles) and the cytosolic signaling components were added to the solution. FRET based techniques were used to quantify the phosphorylation state of the receptors involved. These experiments demonstrated that Shp2 recruited by the cytosolic domain of PD-1 receptor can directly dephosphorylate the cytosolic tails of CD3ζ and CD28. The key findings of the experiments are that the CD28 is preferentially dephosphorylated in response to increasing PD-1 concentration whereas the CD3ζ chain and the other components of the TCR signaling tested are less sensitive to the inhibitory effect of PD-1. Further these findings were also confirmed using a cell based experiment employing Jurkat T cells and Raji B cells.PD-1 receptor is stimulated by binding to its ligand, PD-L1 or PD-L2 expressed on the surface of APCs (Antigen Presenting Cells) . StudiesWe have constructed an ordinary differential equation (ODE) based mathematical model for the early signaling events following the TCR, CD28 and PD-1 stimulation. The full network diagram of the model is given in active). Shp2 binds to both the singly and doubly phosphorylated PD-1 to form the complexes referred as CP1 and CP2 respectively. Shp2 bound to the phosphorylated PD-1 (CP2and CP1) distributively self-dephosphorylate the PD-1 to return either CP1 or mono/unphosphorylated PD-1 and thereby releasing Shp2 from the complex. CD28 and CD3ζ receptors are phosphorylated by the active Lck kinase and dephosphorylated by the Shp2 bound to the phosphorylated PD-1 (CP1 and CP2). We must mention here that free Shp2 does not have any catalytic activity. We used Michaelis-Menten kinetics to model these phosphorylation and dephosphorylation reactions.Ligated PD-1 receptor is doubly phosphorylated in distributive manner by the active Lck kinase  is phosphorylated by active Lck at tyrosine Y315 initially to form Zap70a1 and then at tyrosine Y493 to form Zap70a2. Zap70a2 is considered as the active form of Zap70 and it phosphorylates LAT, referred as LATi, to form phosphorylated LAT, referred as LATa. Although LATi is phosphorylated at several sites by active Zap70, the individual phosphorylation events of LAT molecule are not considered separately in the model to reduce the complexity and therefore these phosphorylations are considered as processive in nature. LATa is considered to be the active form of LAT and it binds to the adaptor protein Gads to form the complex Gadsa. Gadsa in turn interacts with free Slp76 to form LATa-Gads-Slp76 complex referred as Slp76i. Slp76 bound to the LATa-Gads complex is phosphorylated by Zap70a2 to form the complex Slp76a.Phosphorylation of CD28 and CD3ζ lead to engagement of free PI3K and free Zap70 to form PI3Ki), b. phosphorylated only at Y394 (Lckya), c. phosphorylated only at Y505 (Lckyi), d.Y394 and Y505 phosphorylated sequentially (Lckyiya) and e. Y505 and Y394 phosphorylated consecutively (Lckpi). Consequently, among all forms of Lck in the model, only Lckya and Lckyiya were considered to be active and are capable of phosphorylating their substrates. All these reactions are modeled using mass action rate law of chemical reactions.Experimental and molecular dynamics studies have shown that phosphorylation of Lck at Y394 has an activating effect and whereas Y505 is inhibitory. FurtherExperimental results by Hui et al on the r1 and CP2 are assumed to have same catalytic activity in dephosphorylation of all of its substrates. For doubly phosphorylated Lck, dephosphorylation of Y394 is faster than that of Y505. Such preferential dephosphorylation of activating tyrosine by SHP-1 has been observed earlierVNA and σ = [L]VNAfaL, where [P], [L], V, NA, f and aL are concentration of protein, concentration of phospholipid, volume, Avogadro’s number, fraction of exposed lipid and the area of each lipid head. For a liposome of diameter 200 nm, ~52.6% of total lipids were found to present on the outer membrane of liposome [et al. [2.Units of concentration and time in the model are nM and seconds, respectively. Hence, initial concentrations of species were provided in nM. In few cases, nM concentrations in the simulation results were converted to molecules/μmmembrane . The surliposome . Thus wi [et al. ), the prWe benchmarked our model by performing several simulations corresponding to the experiments done by Hui et al on the biochemical reconstitution system. It includes the time course of recruitment of Shp2, Zap70 and PI3k to PD-1, CD3ζ and CD28 respectively; comparison of phosphorylation activity of Lck on CD3ζ and CD28; dissociation of Zap70 and PI3k from their corresponding receptors in the absence of Lck activity; the dephosphorylation of TCR signaling molecules and CD28 due to PD-1.1 and CP2 complexes. Results from We investigated the recruitment of Shp2 to the PD-1 receptor upon its phosphorylation by Lck. Upon introduction of Lck at time zero, Shp2 rapidly binds to PD-1 and the extent of binding increases with PD-1 concentration . Here wei and PI3Kb considering that all of the CD28 and CD3ζ are already phosphorylated leading to full engagement of PI3K and Zap70 respectively. The initial concentrations of Lck and PD-1 were also set to zero. Then to determine the dephosphorylation kinetics we used a non-zero concentration of CP2 complex as a proxy for membrane bound Shp2 used in the experimental protocol. In order to be consistent with the experimental protocol we did not allow self-dephosphorylation, dissociation and the degradation of CP2 complex. In experiments Hui et al used full length Shp2 protein and it was directly attached to the membrane of vesicles. As observed in the experiments, simulations results showed that the percentage of free PI3K and Zap70 increases monotonically with time with similar rates.Next we investigated the kinetics of Lck phosphorylation and PD-1 mediated dephosphorylation of receptors in absence of each other. We determined the kinetics of engagement of PI3K and Zap70 to their respective receptors upon Lck mediated phosphorylation of CD28 and CD3ζ in absence of PD-1 . SimilarTill now we showed the kinetics of phosphorylations or dephosphorylations in absence of either PD-1 or Lck. Now we investigated the kinetics when both of them are present essentially simulating the whole network. Simulation results showed that in presence of PD-1 the steady state values of free PI3K and Zap70 are higher than in absence of PD-1 . See Figure C in 50 value of CD28 is smaller in several orders of magnitude than that of CD3ζ highlighting the sensitivity of CD28 towards PD-1  and activation of Slp76 are affected only at very high concentration of PD-1  showed that PD-1 dephosphorylates both the activating (Y394) and inhibitory (Y505) tyrosine amino acid residues of Lck . Althougver time . A two dver time  that abo1 and CP2 (PD-1-Shp2 complexes) do not dephosphorylate Lck but dephosphorylate its usual target CD28 and CD3ζ. In the absence of Lck dephosphorylation by PD-1/Shp2 complexes, the inhibitory effect on Zap70 and Slp76 molecules are shown in These observations raise the question, how significant is the inactivation of Lck in inhibiting the TCR and CD28 early signaling molecules. To explore this, we performed simulations where CP1 and CP2 complexes, decrease their stability and the inactivation of Lck decreases the phosphorylation of PD-1 thus inhibiting the formation of these inhibitory complexes.We have shown that after rapid engagement Shp2 dissociates from the PD-1 at later time . To testPredictions and output of a mathematical model rely largely on parameter values. Hence, it is crucial to test the robustness of the model output to changes in parameters. Parameter sensitivity analysis is a technique extensively used for mathematical models to determine the fluctuations in the model output due to uncertainty in the parameters used. We used global parameter sensitivity analysis where all the chosen parameters are varied simultaneously to explore their collective effect on the dynamics of the system see . Global 1) Shp2 recruitment by PD-1:1 and CP2 complexes and parameters for Lck auto-phosphorylation and dephosphorylation. This module includes 15 parameters  and representative cumulative frequency distributions for most and least sensitive parameters were provided in Figure E in p,pd1 and ka,shp which are the phosphorylation rate constant of PD-1 and association rate constant of Shp2 to phosphorylated PD-1. Their K-S statistic values are approximately 0.13. Shp2 recruitment is relatively robust to changes in the phosphorylation and dephosphorylation rate constants of Lck.Dissimilarity measure, K-S statistic see  was calc2) PI3K recruitment by phosphorylated CD28:a,pi3k, rate constant for association of PI3K to phosphorylated CD28 was the most influential, with a K-S statistic value of ~0.3, in affecting PI3K recruitment. Parameter kd,pi3k, dissociation rate constant of PI3K from CD28, had a K-S statistic value of 0.1. However, the K-S statistic for other parameters were less than 0.05, suggesting that PI3K recruitment is insensitive to a wider range of these parameter values around their optimized values  Slp76 activation:p1,zap, kp2,zap, kp,lat and kp,slp are high , highlighting their relative importance in determining the Slp76 activation  for a heterogeneous population of cells. Therefore in a way our model sets the background for predicting the outcome of the system in presence of population heterogeneity.Our proposed model is deterministic in nature considering all the cells in a population as identical in every aspect. Therefore the physiological basis of dose response curves with varying quantity/dose of signaling molecules such as Lck, PD-1, CD28 and CD3ζ in our model needs to be highlighted. A clonal population of cell exhibits large cell-to-cell variation in cellular content, shape, size and cell cycle phases due to intrinsic and extrinsic source of heterogeneity. The variations in expression of key signaling components, both in upstream and downstream pathways, ultimately lead to heterogeneous response across the population –74. AlthA key feature in PD-1 pathway is the presence of a negative feedback loop involving PD-1 and Shp2 . In thisEarly TCR signaling has numerous potential implications. Recently, a study has shown a direct role of early TCR signaling in the activation of the enzyme pyruvate dehydrogenase kinase 1 (PDHK1). Consequently, mitochondrial import of pyruvate is inhibited and aerobic glycolysis is promoted . Hence, in vivo scenario could be considerably different from the network modeled here. Future improvements in the model could potentially result in a better prediction and reproduction of in vivo scenario. Although the impact of PD-1 on Lck activity was explored here, regulation of Lck activity is very complex due to the action of several other kinases and phosphatases such as Csk and CD45[Experiments done on membrane based reconstitution system are considered physiologically more realistic when compared to traditional solution based experiments for signaling studies. Althoug and CD45. Model s and CD45, 85. MorFinally, the proposed model is based on a set of deterministic dynamical equations. Although our deterministic model recaptures many key experimental observations however being deterministic in nature it is not capable of explaining single cell data which requires stochastic modeling. It is established that in the early T cell receptor activation pathway population heterogeneity of key signaling proteins, such as Lck, Zap70, play a crucial role . HoweverTo implement global sensitivity analysis, we make use of multi parametric sensitivity analysis (MPSA) where multiple parameters are selected together for testing the sensitivity. Each parameter was picked from a uniform distribution with a range ±50% of the optimized parameter value used in the model . We usedS1 File(DOCX)Click here for additional data file.


Portal vein system thrombosis (PVST) is potentially fatal for patients if the diagnosis is not timely or the treatment is not proper. There hasn’t been any available technique to detect clinic risk factors to predict PVST after splenectomy in cirrhotic patients. The aim of this study is to detect the clinic risk factors of PVST for splenectomy and cardia devascularization patients for liver cirrhosis and portal hypertension, and build an efficient predictive model to PVST via the detected risk factors, by introducing the machine learning method. We collected 92 clinic indexes of splenectomy plus cardia devascularization patients for cirrhosis and portal hypertension, and proposed a novel algorithm named as RFA-PVST  to detect clinic risk indexes of PVST, then built a SVM (support vector machine) predictive model via the detected risk factors. The accuracy, sensitivity, specificity, precision, F-measure, FPR , FNR , FDR , AUC (area under ROC curve) and MCC (Matthews correlation coefficient) were adopted to value the predictive power of the detected risk factors. The proposed RFA-PVST algorithm was compared to mRMR, SVM-RFE, Relief, S-weight and LLEScore. The statistic test was done to verify the significance of our RFA-PVST.Anticoagulant therapy and antiplatelet aggregation therapy are the top-2 risk clinic factors to PVST, followed by D-D (D dimer), CHOL (Cholesterol) and Ca . The SVM (support vector machine) model built on the clinic indexes including anticoagulant therapy, antiplatelet aggregation therapy, RBC (Red blood cell), D-D, CHOL, Ca, TT (thrombin time) and Weight factors has got pretty good predictive capability to PVST. It has got the highest PVST predictive accuracy of 0.89, and the best sensitivity, specificity, precision, F-measure, FNR, FPR, FDR and MCC of 1, 0.75, 0.85, 0.92, 0, 0.25, 0.15 and 0.8 respectively, and the comparable good AUC value of 0.84. The statistic test results demonstrate that there is a strong significant difference between our RFA-PVST and the compared algorithms, including mRMR, SVM-RFE, Relief, S-weight and LLEScore, that is to say, the risk indicators detected by our RFA-PVST are statistically significant.The proposed novel RFA-PVST algorithm can detect the clinic risk factors of PVST effectively and easily. Its most contribution is that it can display all the clinic factors in a 2-dimensional space with independence and discernibility as y-axis and x-axis, respectively. Those clinic indexes in top-right corner of the 2-dimensional space are detected automatically as risk indicators. The predictive SVM model is powerful with the detected clinic risk factors of PVST. Our study can help medical doctors to make proper treatments or early diagnoses to PVST patients. This study brings the new idea to the study of clinic treatment for other diseases as well. Portal vein system thrombosis (PVST) refers to the blockage or narrowing of the portal vein, splenic and superior mesenteric veins, or intrahepatic portal vein branches, by a thrombus . It is rWe first propose a novel feature selection algorithm named RFA-PVST  to detect the clinic risk factors of PVST, then we introduce the typical learning machine SVM to build the predictive model to PVST. We collect the clinic data of 92 splenectomy and cardia devascularization patients for cirrhosis and portal hypertension from the highest level hospital in PR China.In our RFA-PVST, we propose the definition of discernibility and independence for each index to imply the capability of it in telling a PVST patient from non-PVST patients, and the differences of an index to other indices, respectively. The detected clinic indexes are with much higher discernibility and independence. The SVM model built on the detected risk factors can effectively tell PVST patients from non-PVST patients, and help medicine doctors to make proper cure decisions or early diagnoses to potential PVST patients. 5-fold cross validation experimental results on the aforementioned 92 clinic patients, and the statistic test between RFA-PVST and available famous feature selection algorithms demonstrate that the clinic risk factors detected by our RFA-PVST are statistically significant on which a very powerful predictive model is built.This section will display the clinic risk factors of PVST detected by our proposed RFA-PVST, and the power of these risk factors in recognizing PVST patients by the performance of the SVM model based on them in terms of its accuracy shorted as Acc in the following of this paper, sensitivity, specificity, precision, F-measure, FPR , FNR , FDR , AUC (area under ROC curve) and MCC (Matthews correlation coefficient). The performance comparison are shown between our RFA-PVST and the available feature selection algorithms including mRMR , SVM-RFEFigure α = 0.05 of our proposed RFA-PVST and mRMR, SVM-RFE, Relief, S-weight and LLEScore are displayed in Table Friedman’s test with The multiple comparison test between each pair of algorithms at the confidence level of 0.95 is displayed in Table This section will discuss all of the experimental results displayed in the section of results.RD is useful in detecting the clinic indexes with higher risk degree. The red circle clinic indexes in Fig. The results in Fig. The results in Table The results in Table The results in Table p < 0.05 holds for all metrics used to do statistic test, including Acc, AUC, Sensitivity, Specificity, and Precision. So we can conclude that the strong significant difference exist between our RFA-PVST and the compared algorithms, including mRMR, SVM-RFE, Relief, S-weight and LLEScore, that is the risk indicators detected by our RFA-PVST are statistically significant.It can be seen from the results in Table The multiple comparison test results in Table A novel algorithm named RFA-PVST is proposed to detect the clinic risk indicators of PVST for splenectomy and cardia devascularization patients for liver cirrhosis and portal hypertension. The discernibility and independence are defined for each clinic index. All of the clinic indexes are scatted in a 2-dimensional space with independence and discernibility as y-axis and x-axis, respectively. Those clinic indexes in top-right corner of the 2-dimensional space are detected automatically as risk indicators. The SVM classifier is built on the detected risk indicators to predict whether the PVST will happen or not on a splenectomy plus cardiac devascularization patient for liver cirrhosis and portal hypertension.5-flod cross validation experiments on the clinic data of 92 patients disclose that antiplatelet aggregation therapy is the riskiest clinic index, followed by anticoagulant therapy. Taking the two therapies may lead to PVST for splenectomy plus cardiac devascularization patients for liver cirrhosis and portal hypertension. CHOL, Ca, and D-D are also important risk factors. Anticoagulant therapy, antiplatelet aggregation therapy, RBC, D-D, CHOL, Ca, TT, and weight comprise the clinic risk indicators to PVST. The predictive model based on these 8 risk indicators is very powerful.Furthermore, the comparison between our proposed RFA-PVST and available typical feature selection algorithms including mRMR, SVM-RFE, Relief, S-weight and LLEScore demonstrate that our RFA-PVST is very powerful to detect the risk clinic indicators to recognize PVST from non-PVST patients. The significant test between the aforementioned algorithms reveal that there is strong significant difference between our RFA-PVST and the famous available feature selection algorithms. In addition, it is fantastic that our study results are coincident with that from references , 37 abouWe can conclude that our study is significant in the field of detecting risk factors causing PVST for splenectomy and cardia devascularization patients for liver cirrhosis and portal hypertension. It can help medical doctors to make proper treatments or early diagnoses to PVST patients. This study also provides a new idea to the clinic treatment of other diseases.This section will first introduce the data used in this paper, then the preprocessing method will be introduced for the data. It should be noted that we are authorized to use the data under the condition of deleting the privacy information of patients. Then the SVM learning machine will be briefly introduced. After that we will introduce the idea of our proposed novel algorithm RFA-PVST in detail, and the methods building a SVM classifier in the clinic risk factors detected by our RFA-PVST. Finally the statistical test method will be introduced to value the significant difference between our RFA-PVST and other classic methods.This subsection will cover the data information and the data preprocessing methods used in this paper.We collected clinic data of 92 patients of splenectomy with cardia devascularization for liver cirrhosis and portal hypertension from one of the first level hospital in PR China. The patients are partitioned into two groups, one is composed of 52 patients with PVST, and the other is of 40 patients without PVST. The PVST group comprises 30 male and 22 female patients, and the ages of these patients are from 20 to 71 with average age and standard deviation of 47 ± 10. The non-PVST group is composed of 22 male and 18 female patients with ages from 27 to 77, and the average age with standard deviation is 47.9 ± 10.8. The descriptions of the data can be found in Table 59 patients from HBV (Hepatitis B virus) cirrhosis, with 64.13% ratio.8 patients of HCV (Hepatitis C Virus) cirrhosis, about 8.70% ratio.7 patients for autoimmune cirrhosis with 7.61% ratio.4 idiopathic cirrhosis patients with the ratio of 4.35%.2 alcohol type cirrhosis patients with 2.17% ratio.2 patients from idiopathic hypersplenism cirrhosis with the ratio of 2.17%.1 splenic infarction cirrhosis patient with the ratio of 1.09%.1 budd-chiari syndrome patient with the ratio of 1.09%.1 gaucher disease patient with the ratio of 1.09%.1 patient for both HBV + HCV with the ratio of 1.09%.1 virus untyped cirrhosis patient with the ratio of 1.09%.1 hypoferric anemia cirrhosis patient with the ratio of 1.09%.1 patients for idiopathic thrombocytopenic purpura, and with 1.09%.1 patient for primary hypersplenism with the ratio of 1.09%.1 patient from portal cavernous transformation with 1.09% ratio.1 patient for liver cirrhosis with 1.09%.The causes of the cirrhosis and portal hypertension and the distributions for these 92 patients are here.The clinic indexes of these 92 patients are listed in Table The age and the bleeding volume indexes use the original record value. Gender, anticoagulant therapy, and antiplatelet aggregation therapy are treated as Boolean variables, where male is 0 and female is 1, and without anticoagulant therapy is expressed as 0 and 1 otherwise, and without antiplatelet aggregation therapy is 0 and 1 otherwise. The median of measurable values is taken as the value for that measurable clinic indexes. If PVST occurred then the label for the patient is 1, which belongs to positive class, otherwise the label is − 1, belonging to negative class.xi, j is the specific value of the jth index for the ith patient, and max(xj), and min (xj) are the maximum and minimum value of the jth index, respectively.μi is the mean value of index j (1 ≤ j ≤ 33), and its standard deviation is σi, then the discretized value for the index is di, j in ..2).1\doSVM is a typical learning machine coined by Vapnik in 1920s . It is bK = x ⋅ x'.linear kernel functions: K = (x ⋅ x '  + 1)d, d is positive integers.polynomial kernel function: K = exp(−‖x − x'‖2/σ2), σ is positive real.radial basis kernel function: The popular used kernel functions are here.Feature selection is to detect several features from original ones to construct the feature subset making a specific criterion optimized . The natWe propose RFA-PVST algorithm to detect clinic risk factors of PVST for splenectomy and cardia devascularization patients for cirrhosis and portal hypertension, so as to build the predictive model for PVST via the detected risk factors. The 92 post-splenectomy and cardia devascularization patients comprise exemplars for liver cirrhosis and portal hypertension, and their clinic indexes as features. The detecting clinic risk indexes is in fact a feature selection procedure.We define the discernibility and independence for each clinic index, and plot the curve of independence with discernibility for all clinic indexes in a 2-dimensional space with discernibility and independence as x-axis and y-axis, respectively. All clinic indexes in top-right corner of the 2-dimensional space comprise risk factors for they are with both comparatively high discernibility and high independence, while the less risk ones lie in bottom-left corner. To quantify how much contributions of a clinic index to telling a PVST patient form non-PVST patients, we define the risk degree for each clinic index as the product of its discernibility and its independence, that is, the area of the rectangle enclosed by coordinate lines and axes in the 2-dimensional space. Consequently the clinic indexes with much higher risk degree than the rest ones are detected out and the SVM classifier is built based on the risk factors to predict whether the splenectomy and cardia devascularization patients for liver cirrhosis and portal hypertension are PVST patients or not.D = {x1, x2, ⋯, xn} ∈ Rm × n, where m is the number of patients and n the number of clinic indexes. We define disj, indj, and RDj to express the discernibility, independence, and risk degree for the clinic index j(1 ≤ j ≤ n), respectively in (Let training dataset ively in –7)..D = {x1,Discernibility: Let N0 and N1 be the number of patients with and without PVST, respectively, and S(j) be the statistics of Wilcoxon signed rank test for clinic index j, xi, j is the value of sample i in its clinic index j, then the discernibility disj of clinic index j is defined in (S(j) is calculated in : The risk degree of clinic index j is defined as the product of its discernibility and independence in ; calculate indj for clinic index j in eq. (5); calculate RDj for clinic index j in equation in (8); END //of FOR Plot all clinic indexes in the 2-dimensional space with discernibility as x-axis and independence as y-axis; Select clinic indexes in top-right corner to comprise set S of risk factors;END5-cross validation experiments are conducted, and SVM learning machines with RBF  kernel functions are adopted. The proposed RFA-PVST is used to detect risk factors of PVST. The SVM classifier is constructed based on the detected risk factors. The performance of this SVM classifier is compared to that based on the indices by available feature selection algorithms to evaluate the power of RFA-PVST in detecting factors to recognize PVST patients.γ for SVM. The grid search technique is to first set the specific range for C and γ, respectively, then test each pair of  on training subset by cross validation experiments to find the best pair of . Finally, the pair  with the highest cross validation accuracy is the best pair parameters to be selected.The kernel function and its parameters are very important for a SVM learning machine . We takeS. Then we construct the new training subset TSnew whose exemplars only embodying risk factors from set S. The best pair of parameters  is found on TSnew. Finally the SVM classifier is built based on the best pair of parameters  and the new training subset TSnew to predict PVST.5-fold cross validation experiments are done on our collected clinic data of splenectomy plus cardia devascularization for liver cirrhosis and portal hypertension. The patients with PVST and without PVST are partitioned into 5 balanced parts respectively, so as to get 5 subsets of exemplars for 5-fold cross validation experiments. The RFA-PVST algorithm is conducted on training subset to get risk factors to construct set The power of our proposed RFA-PVST is evaluated in two aspects. First, it is evaluated by the performance of the SVM classifier built on the selected risk indexes by proposed RFA-PVST. Second, it is evaluated by the significant statistic test between the SVM classifiers built on the risk indexes by RFA-PVST and by other popular feature selection algorithms.The performance of the SVM classifier is tested by exemplars in test subset in terms of predictive accuracy shorted as Acc, sensitivity, specificity, precision, F-measure, FPR , FNR , FDR , AUC(Area under an ROC curve) and MCC(Matthews correlation coefficient). ROC is the acronym of receiver operating characteristic curve, which is a very famous metric to evaluate a model. AUC is the quantity value of ROC , 48. Then0 and  n1 are the number of patients in the test subset with and without PVST respectively, and are referred to as the number of exemplars respectively in positive and negative class, and n = n0 + n1 is the total number of patients in the test subset, and ri is the rank of the ith patient in descending order of its probability to be a PVST patient. The minimum start rank is set to 1.From the above metric definitions, we can see that sensitivity expresses the ratio of detecting PVST patients from the true PVST patients, while specificity indicates the ratio of recognizing non-PVST patients from patients without PVST, and precision implies the ratio of the true PVST patients among the recognized PVST patients by our SVM predictive model. F-measure is the harmonic mean of precision and sensitivity.α = 0.05 of algorithms in terms of Acc, AUC, sensitivity, specificity, and precision of the SVM predictive models of PVST with same number of risk indexes detected by each algorithm, respectively.The statistic test is undertaken between the SVM classifiers built on the risk indexes detected by our RFA-PVST and by the aforementioned very popular feature selection algorithms from –36 to ve