Complex ligand-protein systems: a globally convergent iterative method for the n × m case

Pradines, Joël; Hasty, Jeff; Pakdaman, Khashayar

doi:10.1007/s002850100086

Cited by 8 publications

(7 citation statements)

References 21 publications

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“…This entails solving the following nonlinear system of equations that yield the concentration of free species for a binding reaction consisting of one receptor ( R ), one Nb ( N ) and n ligands ( L i ) at equilibrium:

where subscripts f and t indicate respectively free and total concentrations and the equilibrium binding constants of ligands ( K ) and nanobody ( M ) are defined as in supplemental (analysis of binding cooperativity). Exact numerical solutions were obtained using a globally convergent iterative algorithm 33 , which was coded as add-in function for MS-Excel 34 . The built-in optimizer “Solver” was used to minimize the sum of squares difference between predicted and experimental data (choosing the Newton search option and setting convergence threshold at 10 −12 ).…”

Section: Methodsmentioning

confidence: 99%

Allosteric nanobodies reveal the dynamic range and diverse mechanisms of G-protein-coupled receptor activation

Staus

Strachan

Manglik

et al. 2016

Nature

310

270

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G-protein coupled receptors (GPCRs) modulate many physiological processes by transducing a variety of extracellular cues into intracellular responses. Ligand binding to an extracellular orthosteric pocket propagates conformational change to the receptor cytosolic region to promote binding and activation of downstream signaling effectors such as G proteins and β-arrestins. It is widely appreciated that different agonists can share the same binding pocket but evoke unique receptor conformations leading to a wide range of downstream responses (i.e., ‘efficacy’)1. Furthermore, mounting biophysical evidence, primarily using the β-adrenergic receptor (β2AR) as a model system, supports the existence of multiple active and inactive conformational states2–5. However, how agonists with varying efficacy modulate these receptor states to initiate cellular responses is not well understood. Here we report stabilization of two distinct β2AR conformations using single domain camelid antibodies (nanobodies): a previously described positive allosteric nanobody (Nb80) and a newly identified negative allosteric nanobody (Nb60)6,7. We show that Nb60 stabilizes a previously unappreciated low affinity receptor state which corresponds to one of two inactive receptor conformations as delineated by X-ray crystallography and NMR spectroscopy. We find that the agonist isoproterenol has a 15,000-fold higher affinity for the β2AR in the presence of Nb80 compared to Nb60, highlighting the full allosteric range of a GPCR. Assessing the binding of 17 ligands of varying efficacy to the β2AR in the absence and presence of Nb60 or Nb80 reveals large ligand-specific effects that can only be explained using an allosteric model which assumes equilibrium amongst at least three receptor states. Agonists generally exert efficacy by stabilizing the active Nb80-stabilized receptor state (R80). In contrast, for a number of partial agonists, both stabilization of R80 and destabilization of the inactive, Nb60-bound state (R60) contribute to their ability to modulate receptor activation. These data demonstrate that ligands can initiate a wide range of cellular responses by differentially stabilizing multiple receptor states.

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Section: Methodsmentioning

confidence: 99%

Allosteric nanobodies reveal the dynamic range and diverse mechanisms of G-protein-coupled receptor activation

Staus

Strachan

Manglik

et al. 2016

Nature

310

270

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“…1 to 3 numerically using an algorithm that has been described previously (Costa et al, 1992;Onaran et al, 1993). This algorithm has been proved to converge to a unique solution vector for the free species (Pradines et al, 2001). Once the concentrations of the free species are thus obtained, the concentrations of all the other species can be readily calculated by using the definitions of the reaction constants given above.…”

Section: Methodsmentioning

confidence: 99%

Coupling of β2-Adrenoceptors to XLα_s and Gα_s: A New Insight into Ligand-Induced G Protein Activation

Kaya

Uğur²,

Öner³

et al. 2009

J Pharmacol Exp Ther

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G␣ s and extra-large G␣ s (XL␣ s ) can both transduce receptor activation into intracellular cAMP generation. It is unknown, however, whether these two GNAS-locus products display distinct properties with respect to receptor coupling. Here, we show that XL␣ s couples to the ␤2-adrenoceptor more efficiently than G␣ s . In transfected human embryonic kidney 293 cells and mouse embryonic fibroblasts null for both G␣ s and XL␣ s (2B2 cells), basal cAMP accumulation mediated by XL␣ s was higher than that mediated by G␣ s . Inverse agonist treatment reduced G␣ s -mediated basal activity, whereas its effect was markedly blunted on XL␣ s -mediated basal activity. Rank order of ligand efficacies regarding cAMP accumulation was the same when the receptor was coupled to XL␣ s or G␣ s . However, ligandinduced and XL␣ s -mediated cAMP generation was higher than that mediated by G␣ s . The relatively high efficiency of XL␣ smediated cAMP generation was conditional, disappearing with increased level of receptor expression or increased efficacy of ligand. Full-agonist responses in XL␣ s -and G␣ s -expressing cells were comparable even at low receptor levels, whereas partial agonist responses became comparable only when the receptor expression was increased (Ͼ3 pmol/mg). Radioligand binding studies showed that the high-affinity component in agonist binding to ␤2-adrenoceptor was more pronounced in cells expressing XL␣ s than those expressing G␣ s . We discuss these findings in the framework of current receptor-G protein activation models and offer an extended ternary complex model that can fully explain our observations. Heterotrimeric G proteins, consisting of ␣, ␤, and ␥ subunits, constitute a large family of signaling proteins that transmit receptor signals to intracellular effectors. Upon interaction with an active receptor, G proteins undergo a conformational change that results in guanine-nucleotide exchange on the ␣ subunit and dissociation of ␣ and ␤␥ subunits. Dissociated subunits interact with intracellular effectors to modulate their activity. Among others, G s protein has specifically evolved to transmit receptor signals to the stimulation of adenylyl cyclase that leads to intracellular generation of the second messenger cAMP (for reviews, see Gilman, 1987;Hamm, 1998).The ␣ subunits of G s are encoded by the complex GNAS locus on the chromosome 20q13 (Kozasa et al., 1988). This locus generates multiple products through the splicing of different alternative first exons onto a common downstream exon (exon 2). In addition, alternative splicing of exon 3 of G␣ s gene results in long and short forms of G␣ s protein (Bray et al., 1986). A recently identified product of the GNAS locus is the extra-large ␣ s (XL␣ s ) protein, in which the first exon of G␣ s is replaced by the XL-exon that encodes, in rat, 347 instead of 47 amino acids in the amino terminus of G␣ s (Kehlenbach et al., 1994). In contrast to G␣ s , which is expressed ubiquitously, XL␣ s is expressed particularly in neuroendocrine tissues and derived f...

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“…However, such parametric solutions can be obtained for particular N ≤ 3. For larger N , numerical techniques have been developed to obtain numerical solutions given given specified values of [ P ] total , K D( i ) and [ M i ] total for each i [28, 29]. Thus, if K D( i ) are known from independent single-metal fluorescence quenching experiments, then Eq.…”

Section: Methodsmentioning

confidence: 99%

“…S1.2): where corresponds to the fluorescence signal if site j is fully saturated and corresponds to the fluorescence signal if both site 1 and site 2 are fully saturated. Like in the single-site model, parametric solutions can only be obtained for N < 3, but the numerical solution algorithm in [29] may be used to obtain numerical solutions for specified values of [ P ] total , K D( i ) and [ M i ] total for each i . Since this equation depends on an additional parameter related to the formation of the second-order complexes M i M j P for i ≠ j , predictions based on parameters inferred from single-metal experiments alone are not permissible.…”

Section: Methodsmentioning

confidence: 99%

“…S1.2): where corresponds to the fluorescence signal if site j is fully saturated and corresponds to the fluorescence signal if both site 1 and site 2 are both fully saturated. Like in the single-site model, parametric solutions can only be obtained for N ≤ 3, but the numerical solution algorithm in [29] may be used to obtain numerical solutions for specified values of [ P ] total , K D( i ) and [ M i ] total for each i for multi-site systems. Since Eq.…”

Section: Methodsmentioning

confidence: 99%

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Quantifying metal ion specificity of the nickel-binding proteinCcNikZ-II fromClostridium carboxidivoransin the presence of competing metal ions

Diep

Kell

Yakunin

et al. 2022

Preprint

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Many proteins bind transition metal ions as cofactors to carry out their biological functions. Despite wild-type binding affinities for transition metal ions being predominantly dictated by the Irving- Williams series, in vivo metal ion binding specificity is ensured by intracellular mechanisms that regulate free metal ion concentrations. However, a growing area of biotechnology research considers the use of metal-binding proteins in vitro to purify specific metal ions from wastewater, where specificity is dictated by the protein's metal binding affinities. A goal of metalloprotein engineering is to modulate these affinities to improve a protein's specificity towards a particular metal; however, the quantitative relationship between the affinities and the equilibrium metal-bound protein fractions depends on the underlying binding kinetics. Here we demonstrate a high-throughput intrinsic tryptophan fluorescence quenching method to validate kinetic models in multi-metal solutions for CcNikZ-II, a metal-binding protein from Clostridium carboxidivorans. Using our validated models, we quantify the relationship between binding affinity and specificity in different classes of metal- binding models for CcNikZ-II. We further demonstrate that principles for improving specificity through changes in binding specificity are qualitatively different depending on the competing metals, highlighting the power of mechanistic models to guide metalloprotein engineering targets.

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Complex ligand-protein systems: a globally convergent iterative method for the n × m case

Cited by 8 publications

References 21 publications

Allosteric nanobodies reveal the dynamic range and diverse mechanisms of G-protein-coupled receptor activation

Allosteric nanobodies reveal the dynamic range and diverse mechanisms of G-protein-coupled receptor activation

Coupling of β2-Adrenoceptors to XLα_s and Gα_s: A New Insight into Ligand-Induced G Protein Activation

Quantifying metal ion specificity of the nickel-binding proteinCcNikZ-II fromClostridium carboxidivoransin the presence of competing metal ions

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Complex ligand-protein systems: a globally convergent iterative method for the n × m case

Cited by 8 publications

References 21 publications

Allosteric nanobodies reveal the dynamic range and diverse mechanisms of G-protein-coupled receptor activation

Allosteric nanobodies reveal the dynamic range and diverse mechanisms of G-protein-coupled receptor activation

Coupling of β2-Adrenoceptors to XLαs and Gαs: A New Insight into Ligand-Induced G Protein Activation

Quantifying metal ion specificity of the nickel-binding proteinCcNikZ-II fromClostridium carboxidivoransin the presence of competing metal ions

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Product

Resources

About

Coupling of β2-Adrenoceptors to XLα_s and Gα_s: A New Insight into Ligand-Induced G Protein Activation