Hot Spots for Agonists, Antagonists in Family A members
This study, published about four months ago, worths being highlighted.
Chemogenomic Analysis of G-Protein Coupled Receptors and Their Ligands Deciphers Locks and Keys Governing Diverse Aspects of Signalling
J.D. Wichard, A. ter Laak, G. Krause, N. Heinrich, R. Kühne, G. Kleinau.
PLosOne 6(2): e16811.
Briefly, they have gathered 100 Family A. GPCRs with known ligands and G-protein association from IUPHAR database. In total of 1664 receptor-ligand pairs including 767 full agonists, 184 partial agonists and 713 antagonists were considered. They have then looked into statistical interdependence between two variables: chemical properties of ligands and amino acid residues in the GPCRs
By an information-based approach, they have demonstrated that the extracellular domains are likely involved in either antagonistic or agonistic effects, whereas ECL2 and TM2/3 are more likely involved in agonistic action, and targeting at the top of TM5/6 may favour antagonistic action. The residues likely participate in the actions were shown with Ballesteros-Weinstein numbering scheme in rhodopsin crystal structure (Figure 3, colour-coded as in Figure 2, in their paper). Also presented was the frequency of chemical properties for antagonists and agonists for those GPCRs in their Figure 4.
In their analysis, G-protein preferences encoded in protein sequences were looked into, and the results were mapped onto Rhodopsin figure (Figure 6, colour-coded as in Figure 5). They have correlated G-protein coupling preferences extensively with the upper region of the TM domains, enabling to relate ligand binding to the effector activation.
Technical points: The mutual dependency of random variables were quantified as mutual information in estimating theoretical entropy (see the original publication for equations, the approximation method for systematic errors, and the significance test in Gaussian distribution).
Their result of multiple sequence alignment through a profile HMM as in HMMER is available to download at Dr. R. Kühne’s webpage in Leibniz-Institut für Molekulare Pharmakologie.
30 June 2011
27 June 2011
Antagonist Binding to H1 Histamine Receptor
The newly obtained crystal structure of H1 histamine receptor (H1R) by Shimamura et al. reveals the doxepin-binding cavity. Doxepin is a tricyclic antidepressant, widely prescribed before the popularisation of SSRI.
Enjoy the views below.
PDB file: 3RZE
Structure of the human histamine H1 receptor in complex with doxepin.
Nature 2011 Jun 22. doi: 10.1038/nature 10236.
Shimamura T, Shiroishi M, Weyand S, Tsujimoto H, Winter G, Katritch V, Abagyan R, Cherezov V, Liu W, Han GW, Kobayashi T, Stevens RC, Iwata S.
Molecule: a chimeric human H1R with lysozyme
Lengths: 452 amino acids
Method: X-ray diffraction, 3.10 angstrom resolution
Ligand: Doxepin on PubChem
The over all view from the extracellular space. The colour code: rainbow gradient from dark blue (TM1) to red (helix 8); ligand (doxepin) in white, and phosphate ion in orange with oxygens in red.
Close-up views….
Viewed from TM2 and TM3 sides. The residues numbered with Ballesteros & Weinberg scheme applicable for Family A GPCRs.
Viewed from TM3 side, slightly tilted to see the cavity from the extracellular side.
See how Lys 5.39 and Tyr 6.55 interacting to close the cavity as if to capture the bound-antagonist momentarily in the antagonist-stabilised form. Tyr 3.33 and Trp 4.56 also joins the hydrophobic gatherings.
The newly obtained crystal structure of H1 histamine receptor (H1R) by Shimamura et al. reveals the doxepin-binding cavity. Doxepin is a tricyclic antidepressant, widely prescribed before the popularisation of SSRI.
Enjoy the views below.
PDB file: 3RZE
Structure of the human histamine H1 receptor in complex with doxepin.
Nature 2011 Jun 22. doi: 10.1038/nature 10236.
Shimamura T, Shiroishi M, Weyand S, Tsujimoto H, Winter G, Katritch V, Abagyan R, Cherezov V, Liu W, Han GW, Kobayashi T, Stevens RC, Iwata S.
Molecule: a chimeric human H1R with lysozyme
Lengths: 452 amino acids
Method: X-ray diffraction, 3.10 angstrom resolution
Ligand: Doxepin on PubChem
The over all view from the extracellular space. The colour code: rainbow gradient from dark blue (TM1) to red (helix 8); ligand (doxepin) in white, and phosphate ion in orange with oxygens in red.Close-up views….
Viewed from TM2 and TM3 sides. The residues numbered with Ballesteros & Weinberg scheme applicable for Family A GPCRs.
Viewed from TM3 side, slightly tilted to see the cavity from the extracellular side.See how Lys 5.39 and Tyr 6.55 interacting to close the cavity as if to capture the bound-antagonist momentarily in the antagonist-stabilised form. Tyr 3.33 and Trp 4.56 also joins the hydrophobic gatherings.
24 June 2011
About Girdin
Here is a few things about Girdin.
Girdin (Girders of actin filament) is also known as:
Akt phosphorylation enhancer (APE),
Coiled-coil domain-containing protein 88A,
G alpha-interacting vesicle-associated protein (GIV),
Hook-related protein 1 (HkPP1).
Girdin is a large protein (1871 amino acid lengths) which forms homodimer, whereby it potentially engages in multiple interactions. It is expressed broadly (Enomoto et al. 2005). It has a guanine nucleotide exchange factor (GEF) motif that associate preferentially with Gαi (Garcia-Marcos, Ghosh, & Farquhar 2009).
Girdin interacts with:
Akt1 (a.k.a. protein kinase B) to enhance its kinase action. Girdin itself does not have a kinase activity.
Cytoskeletal proteins: microtubules, actin.
Disrupted in schizophrenia 1 (DISC1) which is involved in proliferation of neural progenitor cells during brain development and in adult neurogenesis in dentate gyrus.
Dynamin, a GTPase.
Gαi/0; the amino acid residues (178 - 270) of Gαi3 favour Girdin associating with Gαi3 over Gα0 (Garcia-Marcos, Ghosh & Farquhar 2010).
GPCRs: lysophosphatidic acid receptor (LPAR), formylmethionylleucylphenylalanine receptor (fMLPR).
Phosphatidylinositol 4-phosphate (PI4P), also weakly with phosphatidylinositol 3-phosphate (PI3P).
Receptor Tyrosine Kinases: EGFR, IGFR1, VEGFR.
Garcia-Marcos et al. has presented a working model of protein interaction map around Girdin and Gαi (2011. Figure 7. p.682).
Notable activities:
It can be activated by phosphorylation by epidermal growth factor (EGF) through the action of phosphoinositide 3-kinase (PI3K) or by Akt.
It promotes cell migration through interactions with Akt and actin (Enomoto et al. 2005; Garcia-Marcos, Ghosh & Farquhar 2010). Girdin-Gαi3 was shown to induce migration in mammalian cell by enhancing Akt and remodelling the actin cytoskeleton (Ghosh et al. 2008).
In a combined effort, activator of G-protein signalling 3 (AGS3), Gαi3, and Girdin regulates autophagy through PI3K and Akt (Garcia-Marcos et al. 2011).
With its versatile binding property, Girdin homodimers could act as adaptors joining two separate functional proteins; this indicates its possible regulatory roles in cellular processes initiated by GPCRs, of Gαi-coupled in particular. For instance, by forming a multimer including dynamin, Girdin might initiate the internalisation of receptors by directly interacting receptors at the same time, or by interacting with Gαi present nearby the Gαi-coupled receptors. Clarifying how Girdin could regulate functions of Gαi-coupled receptors would reveal another mechanism of cellular regulation of the receptor pharmacology in detail, as well as providing another component for the intracellular signalling network involving GPCRs.
References
Enomoto A et al. 2005. Akt/PKB regulates actin organization and cell motility via Girdin/APE. Dev Cell. 9: 389-402.
Garcia-Marcos M, Ghosh P, & Farquhar MG. 2009. GIV is a nonreceptor GEF for Gαi with a unique motif that regulates Akt signaling. PNAS 106: 3178–3183.
Garcia-Marcos M et al. 2010. A Structural Determinant That Renders Gαi Sensitive to
Activation by GIV/Girdin Is Required to Promote Cell Migration. J Bio Chem. 285: 12765–12777.
Garcia-Marcos M et al. 2011. A GDI (AGS3) and a GEF (GIV) regulate autophagy by balancing G protein activity and growth factor signals. MBoC. 22: 673-686.
Ghosh P et al. 2008. Activation of Gαi3 triggers cell migration via regulation of GIV. J. Cell Biol. 182: 381–393.
Here is a few things about Girdin.
Girdin (Girders of actin filament) is also known as:
Akt phosphorylation enhancer (APE),
Coiled-coil domain-containing protein 88A,
G alpha-interacting vesicle-associated protein (GIV),
Hook-related protein 1 (HkPP1).
Girdin is a large protein (1871 amino acid lengths) which forms homodimer, whereby it potentially engages in multiple interactions. It is expressed broadly (Enomoto et al. 2005). It has a guanine nucleotide exchange factor (GEF) motif that associate preferentially with Gαi (Garcia-Marcos, Ghosh, & Farquhar 2009).
Girdin interacts with:
Akt1 (a.k.a. protein kinase B) to enhance its kinase action. Girdin itself does not have a kinase activity.
Cytoskeletal proteins: microtubules, actin.
Disrupted in schizophrenia 1 (DISC1) which is involved in proliferation of neural progenitor cells during brain development and in adult neurogenesis in dentate gyrus.
Dynamin, a GTPase.
Gαi/0; the amino acid residues (178 - 270) of Gαi3 favour Girdin associating with Gαi3 over Gα0 (Garcia-Marcos, Ghosh & Farquhar 2010).
GPCRs: lysophosphatidic acid receptor (LPAR), formylmethionylleucylphenylalanine receptor (fMLPR).
Phosphatidylinositol 4-phosphate (PI4P), also weakly with phosphatidylinositol 3-phosphate (PI3P).
Receptor Tyrosine Kinases: EGFR, IGFR1, VEGFR.
Garcia-Marcos et al. has presented a working model of protein interaction map around Girdin and Gαi (2011. Figure 7. p.682).
Notable activities:
It can be activated by phosphorylation by epidermal growth factor (EGF) through the action of phosphoinositide 3-kinase (PI3K) or by Akt.
It promotes cell migration through interactions with Akt and actin (Enomoto et al. 2005; Garcia-Marcos, Ghosh & Farquhar 2010). Girdin-Gαi3 was shown to induce migration in mammalian cell by enhancing Akt and remodelling the actin cytoskeleton (Ghosh et al. 2008).
In a combined effort, activator of G-protein signalling 3 (AGS3), Gαi3, and Girdin regulates autophagy through PI3K and Akt (Garcia-Marcos et al. 2011).
With its versatile binding property, Girdin homodimers could act as adaptors joining two separate functional proteins; this indicates its possible regulatory roles in cellular processes initiated by GPCRs, of Gαi-coupled in particular. For instance, by forming a multimer including dynamin, Girdin might initiate the internalisation of receptors by directly interacting receptors at the same time, or by interacting with Gαi present nearby the Gαi-coupled receptors. Clarifying how Girdin could regulate functions of Gαi-coupled receptors would reveal another mechanism of cellular regulation of the receptor pharmacology in detail, as well as providing another component for the intracellular signalling network involving GPCRs.
References
Enomoto A et al. 2005. Akt/PKB regulates actin organization and cell motility via Girdin/APE. Dev Cell. 9: 389-402.
Garcia-Marcos M, Ghosh P, & Farquhar MG. 2009. GIV is a nonreceptor GEF for Gαi with a unique motif that regulates Akt signaling. PNAS 106: 3178–3183.
Garcia-Marcos M et al. 2010. A Structural Determinant That Renders Gαi Sensitive to
Activation by GIV/Girdin Is Required to Promote Cell Migration. J Bio Chem. 285: 12765–12777.
Garcia-Marcos M et al. 2011. A GDI (AGS3) and a GEF (GIV) regulate autophagy by balancing G protein activity and growth factor signals. MBoC. 22: 673-686.
Ghosh P et al. 2008. Activation of Gαi3 triggers cell migration via regulation of GIV. J. Cell Biol. 182: 381–393.
21 June 2011
A New Class of Regulatory Motifs for Gi-subunit
Through bioinformatics and structural analysis, the authors of this paper have identified an evolutionary conserved motifs in calcium binding proteins, Nucleobindin-1 and -2.
G protein binding sites on Calnuc (nucleobindin 1) and NUCB2 (nucleobindin 2) define a new class of Gαi-regulatory motifs.
M Garcia-Marcos, PS Kietrsunthorn, H Wang, P Ghosh & MG Farquhar. 2011. JBC in press
Department of Cellular and Molecular Medicine, George Palade Laboratories of Cellular and Molecular Medicine, University of California, San Diego, USA.
The calcium binding proteins are:
Nucleobindin-1 (aka CALNUC) is a major calcium binding protein of the Golgi, involved in calcium homeostasis.
Nucleobindin-2 (gene name: NUCB2) is a calcium binding protein, possibly involved in calcium homeostasis; it has a broader, cellular distribution than the above.
The two are reported to shares 62% sequence identity.
The conserved motif identified has a similarity to GEF sequence of Girdin (aka GIV) , a multifunctional protein that has been reported to interact with Gαi/0/s but not with Gαq/11/12/13 (Le-Niculescu et al. 2005).
The motif was shown to be evolutionally conserved in those proteins, from invertebrates to humans.
Both Nucleobindin-1 and -2 were demonstrated to bind preferentially to Gαi3 at its inactive state.
They have also shown that Gαi3 binding likely occurs when the Nucleobindin-1 or -2 are in calcium-unbound state.
Ref.
Le-Niculescu H et al. 2005. Identification and Characterization of GIV, a Novel Gαi/s-interacting Protein Found on COPI, Endoplasmic Reticulum-Golgi Transport VesiclesJ Biol Chem 280: 22012-22020
Through bioinformatics and structural analysis, the authors of this paper have identified an evolutionary conserved motifs in calcium binding proteins, Nucleobindin-1 and -2.
G protein binding sites on Calnuc (nucleobindin 1) and NUCB2 (nucleobindin 2) define a new class of Gαi-regulatory motifs.
M Garcia-Marcos, PS Kietrsunthorn, H Wang, P Ghosh & MG Farquhar. 2011. JBC in press
Department of Cellular and Molecular Medicine, George Palade Laboratories of Cellular and Molecular Medicine, University of California, San Diego, USA.
The calcium binding proteins are:
Nucleobindin-1 (aka CALNUC) is a major calcium binding protein of the Golgi, involved in calcium homeostasis.
Nucleobindin-2 (gene name: NUCB2) is a calcium binding protein, possibly involved in calcium homeostasis; it has a broader, cellular distribution than the above.
The two are reported to shares 62% sequence identity.
The conserved motif identified has a similarity to GEF sequence of Girdin (aka GIV) , a multifunctional protein that has been reported to interact with Gαi/0/s but not with Gαq/11/12/13 (Le-Niculescu et al. 2005).
The motif was shown to be evolutionally conserved in those proteins, from invertebrates to humans.
Both Nucleobindin-1 and -2 were demonstrated to bind preferentially to Gαi3 at its inactive state.
They have also shown that Gαi3 binding likely occurs when the Nucleobindin-1 or -2 are in calcium-unbound state.
Ref.
Le-Niculescu H et al. 2005. Identification and Characterization of GIV, a Novel Gαi/s-interacting Protein Found on COPI, Endoplasmic Reticulum-Golgi Transport VesiclesJ Biol Chem 280: 22012-22020
20 June 2011
A Bioluminescent Detection of Calcium-Induced Protein Translocation
An experimental technique for detecting protein translocation to the plasma membrane has been developed by the authors of the publication below:
Translocation of signalling proteins to the plasma membrane revealed by a new bioluminescent procedure.
C Giorgi, A Romagnoli, C Agnoletto, L Bergamelli, G Sorrentino, M Brini, T Pozzan, J Meldolesi, P Pinton, & R Rizzuto. 2011. BMC Cell Biology. 12:27.
Department of Experimental and Diagnostic Medicine, Section of General Pathology, Interdisciplinary Center for the Study of Inflammation (ICSI) and LTTA center, University of Ferrara, Italy. Aequotech s.r.l., Ferrara, Italy. Vita-Salute San Raffaele Scientific Institute and IIT Network, Milan, Italy. Dept. Biochemistry and Dept. Experimental Veterinary Sciences, University of Padua, Italy. Dept. Biomedical Sciences, University of Padua, and CNR Institute of Neuroscience, Padua Unit, Italy. Venetian Institute of Molecular Medicine, Padua, Italy.
They have developed this method making a use of calcium-sensitive photoprotein, aequorin from jellyfish (aequorea victoria).
Aequorin:
- Bioluminescent protein with an emission peak at 470 nm (blue);
- About 200 amino acids in length;
- A calcium sensor with a property of a logarithmic correlation between [calcium] and light emission; the strength of the light emission upon calcium binding is said to be proportional to ≈ the 3rd power of the calcium concentration (Pinton et al. 2007).
Not only the reported advantages of this method over those previously utilised for a similar purpose (e.g. GFP probes, β-galactosidase complementation, or more traditional immunocytochemistry followed by analysing sub-cellular fractions), the established property of bioluminescence by aequorin on calcium binding as above, means that the light signal could be numerically evaluated to estimate [calcium] at which the subject molecule is recruited to the plasma membrane upon receptor activation as well as the time it takes.
With no doubt such detailed information would provide useful parameters in relevant model simulations.
Please find about the method in detail in their original publication.
Reference
Pinton P, Rimessi A, Romagnoli A, Prandini A, Rizzuto R. 2007. Biosensors for the detection of calcium and pH. Methods Cell Biol. 80: 297-325.
An experimental technique for detecting protein translocation to the plasma membrane has been developed by the authors of the publication below:
Translocation of signalling proteins to the plasma membrane revealed by a new bioluminescent procedure.
C Giorgi, A Romagnoli, C Agnoletto, L Bergamelli, G Sorrentino, M Brini, T Pozzan, J Meldolesi, P Pinton, & R Rizzuto. 2011. BMC Cell Biology. 12:27.
Department of Experimental and Diagnostic Medicine, Section of General Pathology, Interdisciplinary Center for the Study of Inflammation (ICSI) and LTTA center, University of Ferrara, Italy. Aequotech s.r.l., Ferrara, Italy. Vita-Salute San Raffaele Scientific Institute and IIT Network, Milan, Italy. Dept. Biochemistry and Dept. Experimental Veterinary Sciences, University of Padua, Italy. Dept. Biomedical Sciences, University of Padua, and CNR Institute of Neuroscience, Padua Unit, Italy. Venetian Institute of Molecular Medicine, Padua, Italy.
They have developed this method making a use of calcium-sensitive photoprotein, aequorin from jellyfish (aequorea victoria).
Aequorin:
- Bioluminescent protein with an emission peak at 470 nm (blue);
- About 200 amino acids in length;
- A calcium sensor with a property of a logarithmic correlation between [calcium] and light emission; the strength of the light emission upon calcium binding is said to be proportional to ≈ the 3rd power of the calcium concentration (Pinton et al. 2007).
Not only the reported advantages of this method over those previously utilised for a similar purpose (e.g. GFP probes, β-galactosidase complementation, or more traditional immunocytochemistry followed by analysing sub-cellular fractions), the established property of bioluminescence by aequorin on calcium binding as above, means that the light signal could be numerically evaluated to estimate [calcium] at which the subject molecule is recruited to the plasma membrane upon receptor activation as well as the time it takes.
With no doubt such detailed information would provide useful parameters in relevant model simulations.
Please find about the method in detail in their original publication.
Reference
Pinton P, Rimessi A, Romagnoli A, Prandini A, Rizzuto R. 2007. Biosensors for the detection of calcium and pH. Methods Cell Biol. 80: 297-325.
18 June 2011
Rhodopsin Inactivation Mechanism II
Kinetics of Rhodopsin Deactivation and Its Role in Regulating Recovery and Reproducibility of Rod Photoresponse
G Caruso, P Bisegna, L Lenoci, D Andreucci, VV Gurevich, HE Hamm, E DiBenedetto. 2010. PLoS Comput Biol 6(12): e1001031.
Construction Technologies Institute, National Research Council, Rome, Italy, Department of Civil Engineering, University of Rome Tor Vergata, Rome, Italy, Department of Pharmacology, Vanderbilt University Medical Center, Tennessee, USA, Department of Mathematical Methods and Models, University of Rome La Sapienza, Rome, Italy, Department of Mathematics, Vanderbilt University, Tennessee, USA.
Aims of the study:
In photo-transduction, a single photon response (SPR) via rhodopsin occurs typically with a low variability, regardless of the dynamic nature of the receptor activation. The kinetics of rhodopsin inactivation was investigated to find what contribute to the variability most.
A query:
What does lead to the known variability: a random number of turnoff steps, sojourn period between steps, or both?
Model method:
Continuous Time Markov Chain (CTMC) of receptor actions, interfaced with a spatio-temporal model of photo-transduction.
Results:
The randomness of the period at which receptor stays in each phosphorylation state contribute to coefficient of variation (CV: standard deviation/mean). The randomness of the number of receptor turnoff steps has a negligible effect.
Their conclusion:
A randomness of sojourn time in number of phosphorylation steps for receptor shutoff is responsible for variability of the photo-transduction. The diffusion of the second messengers acts as a variability suppressor. The geometry of the rod outer segment might also contribute.
Model
The model was aimed to assess the effect of parameters on rhodopsin deactivation reaction.
Key components of the model in a sequence of Bernoulli trials:
The phosphorylation status of rhodopsin at active state (R*), acquiring i − 1 phosphate;
The rate of GRK phosphorylation (λi);
The rate of phosphorylation quenching by arrestin (μi);
The G-protein activation by R* (νi);
The sojourn time for R* phosphorylated (si), of mean (τi).
The WT responses alone were not sufficient to identify the parameters, and so they sought them along with other experimental observations in mutant mice (Hanson et al. 2006; 2007; Raman et al. 2005; Vishnivetskiy et al. 2007).
With the parameters identified, the R* deactivation cascade was translated by CTMC into the probabilities Pi(t) for receptor to be in the i-th state at time t. The output measured for activated effector (E*) was used as input in the spatio-temporal model (Andreucci et al. 2003; Bisegna et al. 2008; Caruso et al. 2005; 2006), which describes the dynamic behaviours of cGMP and calcium ions in the cytoplasm and the generation of current jtot(t) which flows through the cell membrane as a function of time t.
The variability of the effector E*:
E*(t) --- n. of E* at time t;
E*int (t) = ∫ E*(s)ds --- activity of E* up to time t;
E*area = ∫ E* (t)dt --- activity of E* over the whole lifetime;
E*(t*peak) --- Peak value of E*(t)
The natural variable functionals of the current:
I(t) = 1− (jtot(t) / jdark) --- current suppression at time t;
Iint (t) = ∫ I(s)ds --- charge suppression up to time t;
Iarea = ∫ I(t)dt --- chage suppression over the time course;
I (tpeak) --- peak value of I(t).
See their original paper for the figures of CV (linked above).
The CTMC model enables independent assessment of the effects by the random components on the variability. The effect such as the randomness of sojourn period can be isolated from the randomness due to variable numbers of receptor shutoff steps, as follows.
Three sets of simulations performed:
A. In the first case, the number of steps to R* shutoff was fixed to integer closest to mean N. A random sojourn time was applied to R*: si was generated according to their exponential distribution with τi, which is the inverse of (λi + μi);
B. In the second, the si of R* at their τi was fixed, and the R* was left to shutoff in k random steps. The value of k was generated by a series of Bernoulli trails wherein the probability of phosphorylation is λi / (λi + μi) and the probability of arrestin binding is μi / (λi+ μi);
C. Third case left both si and k remain being at random.
After about 5000 simulations up to 3 s, mean, SD and CV are computed for effector and the normalised current suppression (described in the original document).
Findings:
The CV for B was negligible, but it was produced by A similarly as in C; hence it is the randomness in the sojourn time that contribute to CV of E*. Their simulation showed a similar pattern for variability of the current. The single-photon response generated by unphosphorylated R* were highly reproducible within about 10 s. The average number of steps for receptor shutoff was estimated to be 4 steps.
Estimations:
k
The estimation of k was made based on the experiments by Wilden (1995): G-proteins, PDE and cGMP were mixed in a pool with a sufficient quantity of rhodopsin Ri, which can have up to 6 phosphate groups; Ri was activated by a flash of light to isomerise, and the rate of cGMP depletion was recorded. Form Wilden’s data they assumed the catalytic activity of R* as:
νi = vRGe^(−kv(i−1)) i = 1,…,n. ^ : to the power of ()
where νi = vRG indicates R* in initial unphosphorylated state.
Further derived was an equation based on experimental observations:
1 = [cGMP]’7/[cGMP]’1 ≈ (khydv7ϕ7[cGMP])/(khydv1ϕ1[cGMP]) = 10ν7/νRG
where ϕ denotes number of receptor isomerisation and [cGMP]i indicates [cGMP] at i-th phosphorylation state of R* and [cGMP]’ at a saturating light levels. At the limiting rates, [cGMP]i are almost the same for all i due to hydrolysation by [E*]sat. The rate of depletion [cGMP]’1 applied for an experiment with rhodopsin R1 (no phosphate) with activity ν1~νRG, and ϕ1 can be obtained from an experiment with rhodopsin R7 (6 phosphates) and ν7, provided that the ϕ7 is 10-fold larger than ϕ1. Then, 10 = e^(kv6), kv was approximated to be ≈ 0.38 thereby. ^ : to the power of
Arresitin binding rate and its affinity for R
They took the binding as if an irreversible act for deactivating R*, and counted only the high enough affinities which make the R*-Arr half-life significantly greater than the time-course of the single-photon response. Arrestin-binding was reported to be equivalently low for unphosphorylated and mono-phosphorylated R*, and three phosphate groups are required for a full association to occur (Vishnivetskiy et al. 2007); based on the data obtained by Vishnivetskiy et al., they have set the sequence for arresting binding rate accordingly to the phosphorylation level as
μ1 = μ2 = μ3 = 0, μi = μ0, i = 4,…,n.
where μ0 is the arrestin binding rate at maximum affinity after sufficient phosphorylation; n in the model gives arresting binding that terminates transducin (Gt) activation.
NB: i − 1 number of phosphates attached to R* at each step.
References
Andreucci D et al. 2003. Mathematical model of the spatio-temporal dynamics of second messengers in visual transduction. Biophys J 85: 1358–1376.
Bisegna P et al. 2008. Diffusion of the second messengers in the cytoplasm acts as a variability suppressor of the single photon response in vertebrate phototransduction. Biophys J 94: 3363–3383.
Caruso G et al. 2005. Mathematical and computational modeling of spatio-temporal signaling in rod phototransduction. IEE Proc Syst Biol 152: 119–137.
Caruso G et al. 2006. Modeling the role of incisures in vertebrate phototransduction. Biophys J 91: 1192–1212.
Hanson SM et al. 2006. Visual arrestin binding to microtubules involves a distinct conformational change. J Biol Chem 281: 9765–9772.
Hanson SM et al. 2007. Each rhodopsin molecule binds its own arrestin. Proc Natl Acad Sci USA 104: 3125–3128.
Raman D et al. 2005. Threshold mechanism of arrestin activation: two rhodopsin-attached phosphates are necessary and sufficient for high-affinity arrestin binding. In: Association for Research in Vision and Ophthalmology Annual Meeting; 1-4 May 2005; Fort Lauderdale, Florida, USA.
Vishnivetskiy SA et al. 2007. Regulation of arrestin binding by rhodopsin phosphorylation level. J Biol Chem 282: 32075–32083.
Wilden U. 1995. Duration and amplitude of the light-induced cGMP hydrolysis in vertebrate photoreceptors are regulated by multiple phosphorylation of rhodopsin and by arrestin binding. Biochemistry 34: 1446–1454.
Kinetics of Rhodopsin Deactivation and Its Role in Regulating Recovery and Reproducibility of Rod Photoresponse
G Caruso, P Bisegna, L Lenoci, D Andreucci, VV Gurevich, HE Hamm, E DiBenedetto. 2010. PLoS Comput Biol 6(12): e1001031.
Construction Technologies Institute, National Research Council, Rome, Italy, Department of Civil Engineering, University of Rome Tor Vergata, Rome, Italy, Department of Pharmacology, Vanderbilt University Medical Center, Tennessee, USA, Department of Mathematical Methods and Models, University of Rome La Sapienza, Rome, Italy, Department of Mathematics, Vanderbilt University, Tennessee, USA.
Aims of the study:
In photo-transduction, a single photon response (SPR) via rhodopsin occurs typically with a low variability, regardless of the dynamic nature of the receptor activation. The kinetics of rhodopsin inactivation was investigated to find what contribute to the variability most.
A query:
What does lead to the known variability: a random number of turnoff steps, sojourn period between steps, or both?
Model method:
Continuous Time Markov Chain (CTMC) of receptor actions, interfaced with a spatio-temporal model of photo-transduction.
Results:
The randomness of the period at which receptor stays in each phosphorylation state contribute to coefficient of variation (CV: standard deviation/mean). The randomness of the number of receptor turnoff steps has a negligible effect.
Their conclusion:
A randomness of sojourn time in number of phosphorylation steps for receptor shutoff is responsible for variability of the photo-transduction. The diffusion of the second messengers acts as a variability suppressor. The geometry of the rod outer segment might also contribute.
Model
The model was aimed to assess the effect of parameters on rhodopsin deactivation reaction.
Key components of the model in a sequence of Bernoulli trials:
The phosphorylation status of rhodopsin at active state (R*), acquiring i − 1 phosphate;
The rate of GRK phosphorylation (λi);
The rate of phosphorylation quenching by arrestin (μi);
The G-protein activation by R* (νi);
The sojourn time for R* phosphorylated (si), of mean (τi).
The WT responses alone were not sufficient to identify the parameters, and so they sought them along with other experimental observations in mutant mice (Hanson et al. 2006; 2007; Raman et al. 2005; Vishnivetskiy et al. 2007).
With the parameters identified, the R* deactivation cascade was translated by CTMC into the probabilities Pi(t) for receptor to be in the i-th state at time t. The output measured for activated effector (E*) was used as input in the spatio-temporal model (Andreucci et al. 2003; Bisegna et al. 2008; Caruso et al. 2005; 2006), which describes the dynamic behaviours of cGMP and calcium ions in the cytoplasm and the generation of current jtot(t) which flows through the cell membrane as a function of time t.
The variability of the effector E*:
E*(t) --- n. of E* at time t;
E*int (t) = ∫ E*(s)ds --- activity of E* up to time t;
E*area = ∫ E* (t)dt --- activity of E* over the whole lifetime;
E*(t*peak) --- Peak value of E*(t)
The natural variable functionals of the current:
I(t) = 1− (jtot(t) / jdark) --- current suppression at time t;
Iint (t) = ∫ I(s)ds --- charge suppression up to time t;
Iarea = ∫ I(t)dt --- chage suppression over the time course;
I (tpeak) --- peak value of I(t).
See their original paper for the figures of CV (linked above).
The CTMC model enables independent assessment of the effects by the random components on the variability. The effect such as the randomness of sojourn period can be isolated from the randomness due to variable numbers of receptor shutoff steps, as follows.
Three sets of simulations performed:
A. In the first case, the number of steps to R* shutoff was fixed to integer closest to mean N. A random sojourn time was applied to R*: si was generated according to their exponential distribution with τi, which is the inverse of (λi + μi);
B. In the second, the si of R* at their τi was fixed, and the R* was left to shutoff in k random steps. The value of k was generated by a series of Bernoulli trails wherein the probability of phosphorylation is λi / (λi + μi) and the probability of arrestin binding is μi / (λi+ μi);
C. Third case left both si and k remain being at random.
After about 5000 simulations up to 3 s, mean, SD and CV are computed for effector and the normalised current suppression (described in the original document).
Findings:
The CV for B was negligible, but it was produced by A similarly as in C; hence it is the randomness in the sojourn time that contribute to CV of E*. Their simulation showed a similar pattern for variability of the current. The single-photon response generated by unphosphorylated R* were highly reproducible within about 10 s. The average number of steps for receptor shutoff was estimated to be 4 steps.
Estimations:
k
The estimation of k was made based on the experiments by Wilden (1995): G-proteins, PDE and cGMP were mixed in a pool with a sufficient quantity of rhodopsin Ri, which can have up to 6 phosphate groups; Ri was activated by a flash of light to isomerise, and the rate of cGMP depletion was recorded. Form Wilden’s data they assumed the catalytic activity of R* as:
νi = vRGe^(−kv(i−1)) i = 1,…,n. ^ : to the power of ()
where νi = vRG indicates R* in initial unphosphorylated state.
Further derived was an equation based on experimental observations:
1 = [cGMP]’7/[cGMP]’1 ≈ (khydv7ϕ7[cGMP])/(khydv1ϕ1[cGMP]) = 10ν7/νRG
where ϕ denotes number of receptor isomerisation and [cGMP]i indicates [cGMP] at i-th phosphorylation state of R* and [cGMP]’ at a saturating light levels. At the limiting rates, [cGMP]i are almost the same for all i due to hydrolysation by [E*]sat. The rate of depletion [cGMP]’1 applied for an experiment with rhodopsin R1 (no phosphate) with activity ν1~νRG, and ϕ1 can be obtained from an experiment with rhodopsin R7 (6 phosphates) and ν7, provided that the ϕ7 is 10-fold larger than ϕ1. Then, 10 = e^(kv6), kv was approximated to be ≈ 0.38 thereby. ^ : to the power of
Arresitin binding rate and its affinity for R
They took the binding as if an irreversible act for deactivating R*, and counted only the high enough affinities which make the R*-Arr half-life significantly greater than the time-course of the single-photon response. Arrestin-binding was reported to be equivalently low for unphosphorylated and mono-phosphorylated R*, and three phosphate groups are required for a full association to occur (Vishnivetskiy et al. 2007); based on the data obtained by Vishnivetskiy et al., they have set the sequence for arresting binding rate accordingly to the phosphorylation level as
μ1 = μ2 = μ3 = 0, μi = μ0, i = 4,…,n.
where μ0 is the arrestin binding rate at maximum affinity after sufficient phosphorylation; n in the model gives arresting binding that terminates transducin (Gt) activation.
NB: i − 1 number of phosphates attached to R* at each step.
References
Andreucci D et al. 2003. Mathematical model of the spatio-temporal dynamics of second messengers in visual transduction. Biophys J 85: 1358–1376.
Bisegna P et al. 2008. Diffusion of the second messengers in the cytoplasm acts as a variability suppressor of the single photon response in vertebrate phototransduction. Biophys J 94: 3363–3383.
Caruso G et al. 2005. Mathematical and computational modeling of spatio-temporal signaling in rod phototransduction. IEE Proc Syst Biol 152: 119–137.
Caruso G et al. 2006. Modeling the role of incisures in vertebrate phototransduction. Biophys J 91: 1192–1212.
Hanson SM et al. 2006. Visual arrestin binding to microtubules involves a distinct conformational change. J Biol Chem 281: 9765–9772.
Hanson SM et al. 2007. Each rhodopsin molecule binds its own arrestin. Proc Natl Acad Sci USA 104: 3125–3128.
Raman D et al. 2005. Threshold mechanism of arrestin activation: two rhodopsin-attached phosphates are necessary and sufficient for high-affinity arrestin binding. In: Association for Research in Vision and Ophthalmology Annual Meeting; 1-4 May 2005; Fort Lauderdale, Florida, USA.
Vishnivetskiy SA et al. 2007. Regulation of arrestin binding by rhodopsin phosphorylation level. J Biol Chem 282: 32075–32083.
Wilden U. 1995. Duration and amplitude of the light-induced cGMP hydrolysis in vertebrate photoreceptors are regulated by multiple phosphorylation of rhodopsin and by arrestin binding. Biochemistry 34: 1446–1454.
17 June 2011
Models for Arrestin-1 and GRK1 Competition in Rhodopsin Inactivation
Arrestin Competition Influences the Kinetics and Variability of the Single-Photon Responses of Mammalian Rod Photoreceptors
T Doan, AW Azevedo, JB Hurley, and F Rieke. 2009. J Neurosci. 29(38):11867–11879.
Departments of Physiology and Biophysics and Biochemistry, and Howard Hughes Medical Institute, University of Washington, Seattle, Washington.
Background:
Rhodopsin absorbs a photon to activate G-protein transducin (Gt), that in turn closes cGMP-gated channels, thereby initiating an amplified electrical signal in rod photoreceptors. The signal generation is regulated at the level of rhodopsin by GPCR kinase 1 (GRK1) and arrestin-1. GRK1 bind to rhodopsin and phosphorylate at the C-terminal region; subsequent arrestin-1 binding to rhodopsin inactivates it. GRK1 and arrestin-1 share a portion of binding sites partially overlapping. Arrestin-1 binding affinity varies depending on phosphorylation status of the receptor.
Hypothesis:
Competition between arrestin-1 and GRK1 modulates rhodopsin activation by regulating GRK1 binding to rhodopsin.
Measured:
How alterations in the concentration of GRK1 and arrestin-1 affect the kinetics and variability of the single-photon responses of a rod.
Biological experiments:
They have recorded rod response by electrophysiology, and then isolated responses of each photon absorbed. In doing so, they have employed wild-type and mutant mice, the latter were homozygotes or heterozygotes knockout of arrestin-1 and/or GRK1. The expression of GRK1, arrestin-1, β-tublin, PDEs, RGSs were quantified.
Mathematical models:
Markov model for rhodopsin phosphorylation
Suppose the duration of rhodopsin phosphorylation depends on the competition of GRK1 and arrestin-1, and the time required for phosphorylation, a single phosphorylation step leading to rhodopsin inactivation can be treated as a Markov chain. The event was assumed to occur recurrently as dissociated GRK1 restarts the sequence presented in the figure below.

The first reaction (1) slows receptor inactivation, reactions (1-3) are repeated until sufficient number of phosphate groups are attached, and the receptor is inactive at 4.
Two determinants concerned in the events were:
How long rhodopsin binds to arrestin-1;
The time required for GRK1 binding relative to time spent for phosphorylation.
As the determinants are affected by four rate constants (α, β, γ, δ) as in the figure above, the model included differential equations to compute:
the ratio of β/α to find rate constants for arrestin-1association/dissociation; and
the ratio of γ/δ to find rate constants for GRK1 binding and phosphorylation catalysis.
The model assumed that β scaled linearly with the arrestin-1 concentration, and γ scaled linearly with the GRK1 concentration.
Four active receptor states were considered:
1. Arrestin-bound (R*Arr),
2. Unbound active (R*),
3. GRK1-bound (R*GRK),
4. Phosphorylated (R*Pn).
The mean phosphorylation time (between R* and R*Pn) was computed by iterating the probability of each state at time t with an updating transition matrix M containing relevant transition rates for given rate constants.
The model did not include:
Gt which also competes with arrestin-1 and GRK1 for rhodopsin binding. However, the effect of Gt was considered in the other model.
Stochastic transduction cascade model
The motivation of the model was to find how the time-dependent variance of the photon response depends on the relative inactivation rates of rhodopsin and Gt.
The model assumed that:
rhodopsin inactivates through a series of phosphorylations events by GRK1;
a rate constant of GRK1 binding (γ) is eight times larger than that of phosphorylation catalysis (δ) accordingly to the experimental results of this study;
each phosphorylation cycle controlled an equal fraction of the total rhodopsin activity, for multiple phosphorylation cycles contribute in inactivating the receptor (each phosphorylation step consistently contributed to receptor inactivation, so that the rate constant is decreased linearly with the number of phosphate group attached); and
the increased affinity of arrestin-1 by phosphorylation favour competing GRK1 for rhodopsin association.
The time course of a photon-activated rhodopsin was converted to a current change via either a linear or nonlinear approximation to the transduction cascade.
In the linear, the approximation was made with a Fourier transform by the formula including: the temporal frequency in radians per second (ω), dark [cGMP] (GD), the rate constant for PDE activity (ϕ), the rate constant for removal of calcium ions by cation exchange channels (θ), the dark PDE activity (PD). The inverse of ϕ gives a measure of average Gt activity. GD was determined from observed dark current (ID) as ID = kGD^3 where k = .0026 pA/μM^3.
In the non-linear, the response passed through a compressive linearity, to derive the current. A compression, which reduced sensitivity of observed current to variations in rhodopsin activity, could be caused by local saturation of the transduction cascade.
The relevant formulae are given in the method section of the original paper.
The model parameters were restricted by the essential properties of the observed single-photon responses, which are the low variability of rhodopsin, the late time-to-peak position and the symmetricity of the time-dependent variance.
Two of their models satisfied the above constrains:
1) In this model, each phosphorylation site contributed equally to rhodopsin inactivation.
On average, 5.6 phosphorylation cycles were completed before inactivation by arrestin. No compression was applied for this model.
2) Rhodopsin was inactivated through maximum of 4 phosphorylation cycles, with average value of 3.7 until arrestin binds. Compression was required to minimise response variability to meet experimental levels observed (saturation in the transduction cascade was needed to explain the low response variability). This model is a simplified versio of model introduced by Bisegna et al (2008).
The two models shared a common ground: rhodopsin inactivates more slowly than Gt.
Conclusions:
Competition between arrestin-1 and GRK1 modulates single-photon receptor kinetics.
The kinetic model (as in the diagram above) predicted that reducing [arrestin-1] 10-fold from physiological level would increase the period rhodopsin is available for GRK1 from ≈15 to ≈60%.
Competition between arrestin-1 and GRK1 reduces variability in rhodopsin inactivation. Decreasing [arrestin-1] and/or [GRK1] increased single-photon response variability.
The receptor active for a relatively long duration. The light-activated PDE action decreased when the arrestin-1 concentration was decreased. The changes in the kinetics with altered [arrestin-1] and/or [GRK1] relates with changes in GRK1 binding rates predicted by the model. They have demonstrated that the time-dependent variance of the single-photon responses can be explained by a long rhodopsin lifetime.
References
Doan T et al. 2009. Arrestin Competition Influences the Kinetics and Variability of the Single-Photon Responses of Mammalian Rod Photoreceptors. J Neurosci. 29(38):11867–11879.
Bisegna P et al. 2008. Diffusion of the second messengers in the cyto- plasm acts as a variability suppressor of the single photon response in vertebrate phototransduction. Biophys J. 94:3363–3383.
Arrestin Competition Influences the Kinetics and Variability of the Single-Photon Responses of Mammalian Rod Photoreceptors
T Doan, AW Azevedo, JB Hurley, and F Rieke. 2009. J Neurosci. 29(38):11867–11879.
Departments of Physiology and Biophysics and Biochemistry, and Howard Hughes Medical Institute, University of Washington, Seattle, Washington.
Background:
Rhodopsin absorbs a photon to activate G-protein transducin (Gt), that in turn closes cGMP-gated channels, thereby initiating an amplified electrical signal in rod photoreceptors. The signal generation is regulated at the level of rhodopsin by GPCR kinase 1 (GRK1) and arrestin-1. GRK1 bind to rhodopsin and phosphorylate at the C-terminal region; subsequent arrestin-1 binding to rhodopsin inactivates it. GRK1 and arrestin-1 share a portion of binding sites partially overlapping. Arrestin-1 binding affinity varies depending on phosphorylation status of the receptor.
Hypothesis:
Competition between arrestin-1 and GRK1 modulates rhodopsin activation by regulating GRK1 binding to rhodopsin.
Measured:
How alterations in the concentration of GRK1 and arrestin-1 affect the kinetics and variability of the single-photon responses of a rod.
Biological experiments:
They have recorded rod response by electrophysiology, and then isolated responses of each photon absorbed. In doing so, they have employed wild-type and mutant mice, the latter were homozygotes or heterozygotes knockout of arrestin-1 and/or GRK1. The expression of GRK1, arrestin-1, β-tublin, PDEs, RGSs were quantified.
Mathematical models:
Markov model for rhodopsin phosphorylation
Suppose the duration of rhodopsin phosphorylation depends on the competition of GRK1 and arrestin-1, and the time required for phosphorylation, a single phosphorylation step leading to rhodopsin inactivation can be treated as a Markov chain. The event was assumed to occur recurrently as dissociated GRK1 restarts the sequence presented in the figure below.
The first reaction (1) slows receptor inactivation, reactions (1-3) are repeated until sufficient number of phosphate groups are attached, and the receptor is inactive at 4.
Two determinants concerned in the events were:
How long rhodopsin binds to arrestin-1;
The time required for GRK1 binding relative to time spent for phosphorylation.
As the determinants are affected by four rate constants (α, β, γ, δ) as in the figure above, the model included differential equations to compute:
the ratio of β/α to find rate constants for arrestin-1association/dissociation; and
the ratio of γ/δ to find rate constants for GRK1 binding and phosphorylation catalysis.
The model assumed that β scaled linearly with the arrestin-1 concentration, and γ scaled linearly with the GRK1 concentration.
Four active receptor states were considered:
1. Arrestin-bound (R*Arr),
2. Unbound active (R*),
3. GRK1-bound (R*GRK),
4. Phosphorylated (R*Pn).
The mean phosphorylation time (between R* and R*Pn) was computed by iterating the probability of each state at time t with an updating transition matrix M containing relevant transition rates for given rate constants.
The model did not include:
Gt which also competes with arrestin-1 and GRK1 for rhodopsin binding. However, the effect of Gt was considered in the other model.
Stochastic transduction cascade model
The motivation of the model was to find how the time-dependent variance of the photon response depends on the relative inactivation rates of rhodopsin and Gt.
The model assumed that:
rhodopsin inactivates through a series of phosphorylations events by GRK1;
a rate constant of GRK1 binding (γ) is eight times larger than that of phosphorylation catalysis (δ) accordingly to the experimental results of this study;
each phosphorylation cycle controlled an equal fraction of the total rhodopsin activity, for multiple phosphorylation cycles contribute in inactivating the receptor (each phosphorylation step consistently contributed to receptor inactivation, so that the rate constant is decreased linearly with the number of phosphate group attached); and
the increased affinity of arrestin-1 by phosphorylation favour competing GRK1 for rhodopsin association.
The time course of a photon-activated rhodopsin was converted to a current change via either a linear or nonlinear approximation to the transduction cascade.
In the linear, the approximation was made with a Fourier transform by the formula including: the temporal frequency in radians per second (ω), dark [cGMP] (GD), the rate constant for PDE activity (ϕ), the rate constant for removal of calcium ions by cation exchange channels (θ), the dark PDE activity (PD). The inverse of ϕ gives a measure of average Gt activity. GD was determined from observed dark current (ID) as ID = kGD^3 where k = .0026 pA/μM^3.
In the non-linear, the response passed through a compressive linearity, to derive the current. A compression, which reduced sensitivity of observed current to variations in rhodopsin activity, could be caused by local saturation of the transduction cascade.
The relevant formulae are given in the method section of the original paper.
The model parameters were restricted by the essential properties of the observed single-photon responses, which are the low variability of rhodopsin, the late time-to-peak position and the symmetricity of the time-dependent variance.
Two of their models satisfied the above constrains:
1) In this model, each phosphorylation site contributed equally to rhodopsin inactivation.
On average, 5.6 phosphorylation cycles were completed before inactivation by arrestin. No compression was applied for this model.
2) Rhodopsin was inactivated through maximum of 4 phosphorylation cycles, with average value of 3.7 until arrestin binds. Compression was required to minimise response variability to meet experimental levels observed (saturation in the transduction cascade was needed to explain the low response variability). This model is a simplified versio of model introduced by Bisegna et al (2008).
The two models shared a common ground: rhodopsin inactivates more slowly than Gt.
Conclusions:
Competition between arrestin-1 and GRK1 modulates single-photon receptor kinetics.
The kinetic model (as in the diagram above) predicted that reducing [arrestin-1] 10-fold from physiological level would increase the period rhodopsin is available for GRK1 from ≈15 to ≈60%.
Competition between arrestin-1 and GRK1 reduces variability in rhodopsin inactivation. Decreasing [arrestin-1] and/or [GRK1] increased single-photon response variability.
The receptor active for a relatively long duration. The light-activated PDE action decreased when the arrestin-1 concentration was decreased. The changes in the kinetics with altered [arrestin-1] and/or [GRK1] relates with changes in GRK1 binding rates predicted by the model. They have demonstrated that the time-dependent variance of the single-photon responses can be explained by a long rhodopsin lifetime.
References
Doan T et al. 2009. Arrestin Competition Influences the Kinetics and Variability of the Single-Photon Responses of Mammalian Rod Photoreceptors. J Neurosci. 29(38):11867–11879.
Bisegna P et al. 2008. Diffusion of the second messengers in the cyto- plasm acts as a variability suppressor of the single photon response in vertebrate phototransduction. Biophys J. 94:3363–3383.
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