An easy method for deriving steady-state rate equations.
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ABSTRACT:
SUBMITTER: Waley SG
PROVIDER: S-EPMC1132905 | biostudies-other | 1992 Sep
REPOSITORIES: biostudies-other
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Project description:A method is described for systematically deriving steady-state rate equations. It is based on the schematic method of King & Altman [J. Phys. Chem. (1956) 60, 1375-1378], but is expressed in purely algebraic terms. It is suitable for implementation as a computer program, and a program has been written in FORTRAN IV and deposited as Supplementary Publication SUP 50078 (12 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 indicated in Biochem. J. (1977) 161, 1-2.
| S-EPMC1164868 | biostudies-other
Project description:A schematic method for the derivation of steady-state enzyme rate equations by using the Wang algebra is described. The method is simple, easy to learn and offers a substantial decrease in analytical effort over previously published algorithms. Being essentially an algebraic procedure the method can be readily computerized. Computer programs in BASIC and ALGOL languages have been deposited as Supplementary Publication SUP 50065 (19 pages) at the British Library (Lending Division), Boston Spa, Wetherby, W. Yorkshire LS23 7BQ, U.K., from whom copies can be obtained on the terms indicated in Biochem. J. (1976). 153, 5.
| S-EPMC1172878 | biostudies-other
Project description:Methods of deriving rate equations that rely on repetition of terms for identification of redundant or invalid terms give incorrect results if used with mechanisms in which some rate constants appear more than once.
| S-EPMC1164051 | biostudies-other
Project description:True steady states are a rare occurrence in living organisms, yet their knowledge is essential for quasi-steady-state approximations, multistability analysis, and other important tools in the investigation of chemical reaction networks (CRN) used to describe molecular processes on the cellular level. Here, we present an approach that can provide closed form steady-state solutions to complex systems, resulting from CRN with binary reactions and mass-action rate laws. We map the nonlinear algebraic problem of finding steady states onto a linear problem in a higher-dimensional space. We show that the linearized version of the steady-state equations obeys the linear conservation laws of the original CRN. We identify two classes of problems for which complete, minimally parameterized solutions may be obtained using only the machinery of linear systems and a judicious choice of the variables used as free parameters. We exemplify our method, providing explicit formulae, on CRN describing signal initiation of two important types of RTK receptor-ligand systems, VEGF and EGF-ErbB1.
| S-EPMC4090023 | biostudies-literature
Project description:A FORTRAN 77 program is described for the derivation of steady-state rate equations for enzyme kinetics. Input is very simple and consists of the two enzyme forms and the two rate constants for each step in the mechanism. The program may be run interactively or off-line. The results are produced after collecting together the algebraic coefficients of like concentration terms, taking account of sign. A fully interactive BASIC version running on a BBC Microcomputer is also available. Details of the programs have been deposited as Supplementary Publication SUP 50126 (45 pages) with the British Library Lending Division, Boston Spa, Wetherby, West Yorkshire LS23 7BQ, U.K., from whom copies may be obtained as indicated in Biochem. J. (1984) 217, 5.
| S-EPMC1144331 | biostudies-other
Project description:1. Two methods are described for deriving the steady-state velocity of an enzyme reaction from a consideration of fluxes between enzyme intermediates. The equivalent-reaction technique, in which enzyme intermediates are systematically eliminated and replaced by equivalent reactions, appears the most generally useful. The methods are applicable to all enzyme mechanisms, including three-substrate and random Bi Bi Ping Pong mechanisms. Solutions are obtained in algebraic form and these are presented for the common random Bi Bi mechanisms. The steady-state quantities of the enzyme intermediates may also be calculated. Additional steps may be introduced into enzyme mechanisms for which the steady-state velocity equation is already known. 2. The calculation of fluxes between substrates and products in three-substrate and random Bi Bi Ping Pong mechanisms is described. 3. It is concluded that the new methods may offer advantages in ease of calculation and in the analysis of the effects of individual steps on the overall reaction. The methods are used to show that an ordered addition of two substrates to an enzyme which is activated by another ligand will not necessarily give hyperbolic steady-state-velocity kinetics or the flux ratios characteristic of an ordered addition, if the dissociation of the ligand from the enzyme is random.
| S-EPMC1164536 | biostudies-other
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.
| S-EPMC8718081 | biostudies-literature
Project description:Methods are given whereby the steady-state kinetic characteristics of multienzyme reactions consisting of individual single-enzyme reactions linked by freely diffusible intermediates can be determined quantitatively from the experimentally determined complete algebraic rate equations for the individual reactions. The approach is based on the fact that a valid steady-state rate equation for such a multienzyme reaction, in terms of the rate equations for the individual reactions, can be obtained simply from knowledge of the relative rates of the individual reactions when the multienzyme reaction is in the steady state. A number of model multienzyme reactions, which differ as to structural arrangement of the individual reactions, are examined by this approach. Simple mathematical methods which are applicable to most of these models are given for direct calculation of dependent variables. It is either pointed out or demonstrated with Mathematica that the rate equations for all of these models can be handled very easily with the aid of a personal computer equipped with appropriate equation-solving software. Since the approach permits evaluation of all dependent variables for any specific combination of values for the kinetic parameters and independent variables, numerical values for the flux control coefficients of the individual enzymes can be obtained by direct calculation for a wide variety of conditions and can be compared with those obtained according to the methods of Metabolic Control Analysis. Several such comparisons have been made and in all cases identical results were obtained. The intuitive notion that the individual enzymes of a multienzyme reaction would be equally rate limiting if the total amount of enzyme were being used with maximum efficiency is tested and shown to be incorrect. In the course of this test the flux control coefficient for the individual enzymes were found to be appropriate indicators of relative rate limitation or control by the enzymes and to account properly for differences in specific activity among the enzymes.
| S-EPMC1132564 | biostudies-other
Project description:PurposeSignal-to-noise ratio (SNR) is crucial for high-resolution fMRI; however, current methods for SNR improvement are limited. A new approach, called oscillating steady-state imaging (OSSI), produces a signal that is large and T2∗ -weighted, and is demonstrated to produce improved SNR compared to gradient echo (GRE) imaging with matched effective TE and spatial-temporal acquisition characteristics for high-resolution fMRI.MethodsQuadratic phase sequences were combined with balanced gradients to produce a large, oscillating steady-state signal. The quadratic phase progression was periodic over short intervals such as 10 TRs, inducing a frequency-dependent phase dispersal. Images over one period were combined to produce a single image with effectively T2∗ -weighting. The OSSI parameters were explored through simulation and phantom data, and 2D and 3D human fMRI data were collected using OSSI and GRE imaging.ResultsPhantom and human OSSI data showed highly reproducible signal oscillations with greater signal strength than GRE. Compared to single slice GRE with matched effective TE and spatial-temporal resolution, OSSI yielded more activation in the visual cortex by a factor of 1.84 and an improvement in temporal SNR by a factor of 1.83. Voxelwise percentage change comparisons between OSSI and GRE demonstrate a similar T2∗ -weighted contrast mechanism with additional T2' -weighting of about 15 ms immediately after the RF pulse.ConclusionsOSSI is a new acquisition method that exploits a large, oscillating signal that is T2∗ -weighted and suitable for fMRI. The steady-state signal from balanced gradients creates higher signal strength than single slice GRE at varying TEs, enabling greater volumes of functional activity and higher SNR for high-resolution fMRI.
| S-EPMC7180136 | biostudies-literature
Project description:PurposeOscillating steady-state imaging (OSSI) is an SNR-efficient steady-state sequence with T2∗ sensitivity suitable for FMRI. Due to the frequency sensitivity of the signal, respiration- and drift-induced field changes can create unwanted signal fluctuations. This study aims to address this issue by developing retrospective signal correction methods that utilize OSSI signal properties to denoise task-based OSSI FMRI experiments.MethodsA retrospective denoising approach was developed that leverages the unique signal properties of OSSI to perform denoising without a manually specified noise region of interest and works with both voxel timecourses (oscillating steady-state correction [OSSCOR]) or FID timecourses (F-OSSCOR). Simulations were performed to estimate the number of principal components optimal for denoising. In vivo experiments at 3 T field strength were conducted to compare the performance of proposed methods against a standard principal component analysis-based method, measured using mean t score within an region of interest, number of activations, and mean temporal SNR.ResultsCorrection using OSSCOR was significantly better than the standard method in all metrics. Correction using F-OSSCOR was not significantly different from the standard method using an equal number of principal components. Increasing the number of OSSCOR principal components decreased activation strength and increased the number of suspected false positives. However, increasing the number of principal components in F-OSSCOR increased activation strength with little to no increase in false activation.ConclusionBoth OSSCOR and F-OSSCOR substantially reduce physiological noise components and increase temporal SNR, improving the functional results of task-based OSSI functional experiments. F-OSSCOR demonstrates a proof of concept utilization of coil-localized FID signal information for physiological noise correction.
| S-EPMC7722173 | biostudies-literature