Accuracy of analytical-numerical solutions of the Michaelis-Menten equation

González-Parra, Gilberto; Acedo, L.; Arenas, Abraham J.

doi:10.1590/s1807-03022011000200011

Cited by 9 publications

(6 citation statements)

References 23 publications

(19 reference statements)

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“…As aforementioned, this is valid even at single molecule level. , Since the formulation of the problem, a century and more ago, only a handful of solutions have been given, which are valid in limited ranges of the sets of variables that describe the system. ,− Analytical studies based on perturbative schemes and/or suitable series have also been carried out. ,− …”

Section: Methodsmentioning

confidence: 99%

Complex Media and Enzymatic Kinetics

et al. 2016

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Enzymatic reactions in complex environments often take place with concentrations of enzyme comparable to that of substrate molecules. Two such cases occur when an enzyme is used to detect low concentrations of substrate/analyte or inside a living cell. Such concentrations do not agree with standard in vitro conditions, aimed at satisfying one of the founding hypotheses of the Michaelis-Menten reaction scheme, MM. It would be desirable to generalize the classical approach and show its applicability to complex systems. A permeable micrometrically structured hydrogel matrix was fabricated by protein cross-linking. Glucose oxidase enzyme (GOx) was embedded in the matrix and used as a prototypical system. The concentration of H2O2 was monitored in time and fitted by an accurate solution of the enzymatic kinetic scheme, which is expressed in terms of simple functions. The approach can also find applications in digital microfluidics and in systems biology where the kinetics response in the linear regimes often employed must be replaced.

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Section: Methodsmentioning

confidence: 99%

Complex Media and Enzymatic Kinetics

et al. 2016

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“…Therefore, the computation time of the whole process depends on many variables such as, the spectra, time step (for DTM and the finite difference scheme) and number of realizations. However, it has been mentioned in other works that the DT M is faster than the multistage Adomian method, but the Runke-Kutta methods require less computation time in comparison with DTM and multistage Adomian [12].…”

Section: Numerical Resultsmentioning

confidence: 96%

“…In addition, randomness is introduced in the diffusion P DE which models several physical processes and to the best of our knowledge this whole process has not be done before. The differential transformation method has been applied in several works and recently has been extended successfully to random differential equations [12], [13]. The randomness is incorporated since inaccuracies in the physical measurements can affect several inputs of the diffusion P DE such as diffusion coefficient, source term, boundary and initial conditions, and can thus introduce some degree of uncertainty.…”

Section: Introductionmentioning

confidence: 99%

Analytical-Numerical Solution of a Parabolic Diffusion Equation Under Uncertainty Conditions Using DTM with Monte Carlo Simulations

Parra¹,

Arenas²,

Cogollo

2015

ing.cienc.

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A numerical method to solve a general random linear parabolic equation where the diffusion coefficient, source term, boundary and initial conditions include uncertainty, is developed. Diffusion equations arise in many fields of science and engineering, and, in many cases, there are uncertainties due to data that cannot be known, or due to errors in measurements and intrinsic variability. In order to model these uncertainties the corresponding parameters, diffusion coefficient, source term, boundary and initial conditions, are assumed to be random variables with certain probability distributions functions. The proposed method includes finite difference schemes on the space variable and the differential transformation method for the time. In addition, the Monte Carlo method is used to deal with the random variables. The accuracy of the hybrid method is investigated numerically using the closed form solution of the deterministic associated ResumenUn método numérico para resolver una ecuación parabólica general aleatoria lineal donde el coeficiente de difusión, el término fuente, las condiciones de contorno e iniciales incluyen la incertidumbre, se ha desarrollado. Ecuaciones de difusión surgen en muchos campos de la ciencia y la ingeniería, y en muchos casos, existen la incertidumbres debido a los datos que no se pueden saber, o debido a errores en las mediciones y la variabilidad intrín-seca. Para modelar estas incertidumbres los parámetros correspondientes, coeficiente de difusión, término fuente, condiciones de contorno e iniciales, se suponen que son variables aleatorias con determinadas distribuciones de probabilidad. Basándose en los resultados numéricos, se obtienen los intervalos de confianza y valores medios esperados para la solución. Además, se obtienen con las soluciones numéricas-analíticas del método híbrido propuesto.Palabras clave: modelos lineales de difusión aleatorios; condiciones de incertidumbre; Esquemas de diferencias finitas; método de transformación diferencial; solución analítica-numérica

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“…The values of w and u 0 are fixed by Equations ( 11) and (25), respectively. Remember that u 2 = u 3 = 0 in this case, and the rest of the coefficients are obtained by the recurrence relation in Equation (23). The result is a precessing elliptic orbit with an advance of the perihelion per revolution given by:…”

Section: Simulation Results and Applicationsmentioning

confidence: 99%

“…These techniques are in the spirit of traditional analysis of linear differential equations, and they provide solutions in closed analytical form with a series of coefficients that can be obtained by recurrence. For example, by using the modal transseries method, we solved the SIRmodel of epidemiology [21,22], the Michaelis-Menten equation for enzyme kinetics [23], the Lorenz system in the laminar regime [24], and Einstein's field equations for planar gravitational waves [4].…”

Section: Introductionmentioning

confidence: 99%

Exact Solution for Relativistic Trajectories Using Modal Transseries

2020

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In this article, we design a novel method for finding the exact solution of the geodesic equation in Schwarzschild spacetime, which represents the trajectories of the particles. This is a fundamental problem in astrophysics and astrodynamics if we want to incorporate relativistic effects in high precision calculations. Here, we show that exact analytical expressions can be given, in terms of modal transseries for the spiral orbits as they approach the limit cycles given by the two circular orbits that appear for each angular momentum value. The solution is expressed in terms of transseries generated by transmonomials of the form e−nθ, n=1, 2, …, where θ is the angle measured in the orbital plane. Examples are presented that verify the effect of the solutions.

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Accuracy of analytical-numerical solutions of the Michaelis-Menten equation

Cited by 9 publications

References 23 publications

Complex Media and Enzymatic Kinetics

Complex Media and Enzymatic Kinetics

Analytical-Numerical Solution of a Parabolic Diffusion Equation Under Uncertainty Conditions Using DTM with Monte Carlo Simulations

Exact Solution for Relativistic Trajectories Using Modal Transseries

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