Ligand diffusion and receptor mediated internalization: Michaelis–Menten kinetics

Maalmi, Mostafa; Strieder, William; Varma, Arvind

doi:10.1016/s0009-2509(01)00167-1

Cited by 10 publications

(7 citation statements)

References 14 publications

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“…Indeed, for the signaling reaction, the receptor binding at the cellular sink is always first order, 6,25 while substrate uptake may be first order as well. 15,26 It has been shown that volumetric reaction within the spherical sink can be accurately represented by an effective surface reaction rate model. 13 There are two different approaches for solving twosphere problems, bispherical coordinates 12 and twin spherical expansions, 27 and in each approach an infinite series is generated whose coefficients must be determined from a corresponding infinite set of linear equations arising from the boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

Diffusion and reaction for a spherical source and sink

McDonald¹,

Strieder²

2003

The Journal of Chemical Physics

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Enhancement of the recollision rate in diffusion-influenced reactions in an inhomogeneous mediumTwo chemically active spheres in an infinite medium, one a zeroth-order reactant source and the other a first-order sink, are considered for various sphere size ratios, center-to-center distances, and sink strengths from chemical to diffusion controlled conditions. This source-sink model simulates some aspects of biological mutualism interactions between different cells. Infinite series expansions in a single index n are obtained for the sink reaction rate and reactant concentration profiles using the bispherical expansion. Each of the coefficients, generated exactly by a matrix elimination method, is expressed in terms of nested, continued fractions easily evaluated for the given n. At intermediate and larger sink-source separation distances the sink reaction rate decays harmonically. For smaller sink-source separations with a highly reactive small sink, a local maximum in the sink reaction rate is found.

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Section: Introductionmentioning

confidence: 99%

Diffusion and reaction for a spherical source and sink

McDonald¹,

Strieder²

2003

The Journal of Chemical Physics

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“…5 the same time, there are models discussed with respect to modelling of the molecular feedback control in ligand-receptor regulation and in ligand transport regulation [8,23,24]. In our study Michaels-Menten control has been chosen, as a first-stage of the allosteric control extension of our cellular model [25].…”

Section: Accepted M Manuscriptmentioning

confidence: 99%

Allosteric control model of bone remodelling containing periodical modes

Moroz¹,

Wimpenny²

2007

Biophysical Chemistry

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To help to understand the modelling process that occurs when a scaffold is implanted it is vital to understand the rather complex bone remodelling process prevalent in native bone.We have formulated a mathematical model that predicts osteoactivity both in scaffolds, as well as in bone in vivo and could set a basis for the more detailed allosteric models. The model is extended towards a bio-cybernetic vision of basic multicellular unit (BMU) action, when some of the regulation loops have been modified to reflect the allosteric control mechanisms, developed by Michaels-Menten, Hill, Koshland-Nemethy-Filmer, Monod-Wyman-Changeux.By implementation of this approach a four-dimensional system was obtained that shows steady cyclic behaviour using a wide range of constants with clear biological meaning. We have observed that a local steady-state appears as a limiting cycle in multidimensional phase space and this is discussed in this paper. Physiological interpretation of this limiting four-dimension cycle possibly related to a conservative-like value has been proposed. Analysis and simulation of the model has shown an analogy between this conservative value, as a kind of substrateenergy regenerative potential of the bone remodelling system with a molecular nature, and to the classical physical value -energy. This dynamic recovery potential is directed against both mechanical and biomechanical damage to the bone. Furthermore, the current model has credibility when compared to the normal bone remodelling process. In the framework of widely recognised Hill mechanisms of allosteric regulation the cyclic attractor, described formerly for a pure cellular model, prevails for different forms of feedback control. This result indicates the viability of the proposed existence of a conservative value (analogous to energy) that characterises the recovery potential of the bone remodelling cycle. Linear stability analysis has been performed in order to determine the robustness of the basic state, however, additional work is required to study a wider range of constants.

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“…For example, Tosaka and Miyake [8] analyzed a mathematical model for oxygen diffusion in a spherical cell using an integral equation method. Maalmi et al [9] presented the mathematical expressions for the steady-state reaction rate and the associated reactant concentration profiles using semianalytical and numerical methods. Indira and Rajendran studied a mathematical model based on polyphenol oxidase catechol as a prototype enzymatic electro system [10].…”

Section: Introductionmentioning

confidence: 99%

Approximations for the Concentration and Effectiveness Factor in Porous Catalysts of Arbitrary Shape: Taylor Series and Akbari-Ganji’s Methods

UshaRani¹,

Rajendran²,

Abukhaled³

2021

MMEP

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A mathematical model of reaction-diffusion problem with Michaelis-Menten kinetics in catalyst particles of arbitrary shape is investigated. Analytical expressions of the concentration of substrates are derived as functions of the Thiele modulus, the modified Sherwood number, and the Michaelis constant. A Taylor series approach and the Akbari-Ganji's method are utilized to determine the substrate concentration and the effectiveness factor. The effects of the shape factor on the concentration profiles and the effectiveness factor are discussed. In addition to their simple implementations, the proposed analytical approaches are reliable and highly accurate, as it will be shown when compared with numerical simulations.

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Ligand diffusion and receptor mediated internalization: Michaelis–Menten kinetics

Cited by 10 publications

References 14 publications

Diffusion and reaction for a spherical source and sink

Diffusion and reaction for a spherical source and sink

Allosteric control model of bone remodelling containing periodical modes

Approximations for the Concentration and Effectiveness Factor in Porous Catalysts of Arbitrary Shape: Taylor Series and Akbari-Ganji’s Methods

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