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Simplifications of the derivations and forms of steady-state equations for non-equilibrium random substrate-modifier and allosteric enzyme mechanisms.

ABSTRACT: The steady-state equations for "random" enzymic mechanisms (ones with alternative routes for substrate and enzyme to form enzyme-substrate complexes) are non-Michaelian and very complicated when a quasi-equilibrium approximation cannot be used. General methods for simplifying their forms and derivations are given and applied to several single-substrate mechanisms of general or topical interest. The special simplifications resulting from partial ordering of reaction mechanism, from gross inequalities of rate constants, and from special relationships between catalytic and dissociation rate constants, are considered with reference to allosteric mechanisms. Some equations mentioned, but not given here, and more detailed working out of some of those given, have been deposited as Supplementary Publication SUP 50069 (18 pages) at the British Library Lending Division, Boston Spa, Wetherby, West Yorkshire LS23 7BQ, U.K., from whom copies can be obtained on the terms given in Biochem. J. (1976) 153, 5.

SUBMITTER: Whitehead EP

PROVIDER: S-EPMC1164140 | biostudies-other | 1976 Dec

REPOSITORIES: biostudies-other

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Project description:We used a simple experimental approach to clarify some contradictory predictions of the collision coupling and equilibrium models (e.g. ternary complex, two-state ternary complex or quinternary complex), which describe G-protein-mediated beta-adrenergic receptor signalling in essentially different manners. Analysis of the steady-state coupling of beta-adrenoceptors to adenylate cyclase in turkey erythrocyte membranes showed that: (1) in the absence of an agonist, Gpp(NH)p (a hydrolysis-resistant analogue of GTP) can activate adenylate cyclase very slowly; (2) this activity reaches a steady state in approx. 5 h, the extent of activity depending on the concentration of the nucleotide; (3) isoprenaline-activated steady-state adenylate cyclase can be inactivated by propranolol (a competitive antagonist that relaxes the receptor activation), in the presence of Gpp(NH)p (which provides a virtual absence of GTPase) and millimolar concentrations of Mg2+ (the rate of this inactivation is relatively fast); (4) increasing the concentration of Gpp(NH)p can saturate the steady-state activity of adenylate cyclase. The saturated enzyme activity was lower than that induced by isoprenaline under the same conditions. This additional agonist-induced activation was reversible. In the light of these results, we conclude that agonist can also activate the guanine nucleotide-saturated system in the absence of GTPase by a mechanism other than guanine nucleotide exchange. We explain these phenomena in the framework of a quinternary complex model as an agonist-induced and receptor-mediated dissociation of guanine nucleotide-saturated residual heterotrimer, the equilibrium concentration of which is not necessarily zero. These results, which suggest a continuous interaction between receptor and G-protein, can hardly be accommodated by the collision coupling model that was originally suggested for the present experimental system and then applied to many other G-protein systems. Therefore we attempt to unify the equilibrium and collision coupling approaches to provide a consistent theoretical basis for the G-protein-mediated beta-adrenergic receptor signalling in turkey erythrocyte membranes.

Project description:BackgroundAgeing and cachexia cause a loss of muscle mass over time, indicating that protein breakdown exceeds protein synthesis. Deuterium oxide (D2 O) is used for studies of protein turnover because of the advantages of long-term labelling, but these methods introduce considerations that have been largely overlooked when studying conditions of protein gain or loss. The purpose of this study was to demonstrate the importance of accounting for a change in protein mass, a non-steady state, during D2 O labelling studies while also exploring the contribution of protein synthesis and breakdown to denervation-induced muscle atrophy.MethodsAdult (6 months) male C57BL/6 mice (n = 14) were labelled with D2 O for a total of 7 days following unilateral sciatic nerve transection to induce denervation of hindlimb muscles. The contralateral sham limb and nonsurgical mice (n = 5) were used as two different controls to account for potential crossover effects of denervation. We calculated gastrocnemius myofibrillar and collagen protein synthesis and breakdown assuming steady-state or using non-steady-state modelling. We measured RNA synthesis rates to further understand ribosomal turnover during atrophy.ResultsGastrocnemius mass was less in denervated muscle (137 ± 9 mg) compared with sham (174 ± 15 mg; P < 0.0001) or nonsurgical control (162 ± 5 mg; P < 0.0001). With steady-state calculations, fractional synthesis and breakdown rates (FSR and FBR) were lower in the denervated muscle (1.49 ± 0.06%/day) compared with sham (1.81 ± 0.09%/day; P < 0.0001) or nonsurgical control (2.27 ± 0.04%/day; P < 0.0001). When adjusting for change in protein mass, FSR was 4.21 ± 0.19%/day in denervated limb, whereas FBR was 4.09 ± 0.22%/day. When considering change in protein mass (ksyn ), myofibrillar synthesis was lower in denervated limb (2.44 ± 0.14 mg/day) compared with sham (3.43 ± 0.22 mg/day; P < 0.0001) and non-surgical control (3.74 ± 0.12 mg/day; P < 0.0001), whereas rate of protein breakdown (kdeg, 1/t) was greater in denervated limb (0.050 ± 0.003) compared with sham (0.019 ± 0.001; P < 0.0001) and nonsurgical control (0.023 ± 0.000; P < 0.0001). Muscle collagen breakdown was completely inhibited during denervation. There was a strong correlation (r = 0.83, P < 0.001) between RNA and myofibrillar protein synthesis in sham but not denervated muscle.ConclusionsWe show conflicting results between steady- and non-steady-state calculations on myofibrillar protein synthesis and breakdown during periods of muscle loss. We also found that collagen accumulation was largely from a decrease in collagen breakdown. Comparison between sham and non-surgical control demonstrated a crossover effect of denervation on myofibrillar protein synthesis and ribosomal biogenesis, which impacts study design for unilateral atrophy studies. These considerations are important because not accounting for them can mislead therapeutic attempts to maintain muscle mass.

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Simplifications of the derivations and forms of steady-state equations for non-equilibrium random substrate-modifier and allosteric enzyme mechanisms.

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