Diffusion and reaction for a spherical source and sink

We study models of two sequential enzyme-catalyzed reactions as a basic functional building block for coupled biochemical networks. We investigate the influence of enzyme distributions and long-range molecular interactions on reaction kinetics, which have been exploited in biological systems to maximize metabolic efficiency and signaling effects. Specifically, we examine how the maximal rate of product generation in a series of sequential reactions is dependent on the enzyme distribution and the electrostatic composition of its participant enzymes and substrates. We find that close proximity between enzymes does not guarantee optimal reaction rates, as the benefit of decreasing enzyme separation is countered by the volume excluded by adjacent enzymes. We further quantify the extent to which the electrostatic potential increases the efficiency of transferring substrate between enzymes, which supports the existence of electrostatic channeling in nature. Here, a major finding is that the role of attractive electrostatic interactions in confining intermediate substrates in the vicinity of the enzymes can contribute more to net reactive throughput than the directional properties of the electrostatic fields. These findings shed light on the interplay of long-range interactions and enzyme distributions in coupled enzyme-catalyzed reactions, and their influence on signaling in biological systems.

Section: A Sequential Enzyme Reaction In Non-electrostatic Casessupporting

confidence: 68%

A model study of sequential enzyme reactions and electrostatic channeling

Eun¹,

Kekenes‐Huskey²,

Metzger³

et al. 2014

“…For the two sites of equal radii an exact solution has been obtained by Samson and Deutsch 10 and McDonald and Strieder, 11 spot interference effects have also been considered theoretically by Traytak et al 12,13 and Uhm et al 14 Theoretical results are also known for small active sites randomly 15 and regularly 16 distributed on the infinite plane. This was first discovered by Pritchin and Salikhov 9 for two reactive spots located at the opposite poles of the spherical molecule.…”

Section: Introductionmentioning

confidence: 95%

Diffusion-influenced reactions of particles with several active sites

Ivanov

Lukzen

2008

The main concern of the present work is consideration of sterically specific liquid-phase reactions in the case where one of the reactants has several active sites. In kinematic approximation we derived compact formulas for partial rate constants of individual active sites. Reaction rates are expressed via the kinetic rate constants and convolutions of the free Green functions over reaction zones. These results are valid for arbitrary geometry of reactants and active sites. Effects of mutual influence of the active sites were studied, their simple estimate was proposed.

“…When the concentration is subjected to the partially reflecting boundary condition on the sink surface ͑7͒ the use of bispherical coordinates leads to recursive equations with respect to unknown coefficients which are not convenient for calculation. [5][6][7][8][9][10] The use of the finite difference Green's function method 18 eliminates this problem. However, the simplest way to derive the flux in this case is by separation of variables in the corresponding local spherical coordinates ͑r i , i , i ͒ with the help of the general translation addition theorem for irregular solid harmonics, 17 1…”

Section: A Neutral Reactantsmentioning

confidence: 99%

Competition effects in diffusion-controlled bulk reactions between ions

Traytak¹,

Barzykin²,

Tachiya³

2007

A numerical solution for competitive diffusion into two static charged sinks is presented and compared against an approximate analytical solution. It is shown that for an attractive Coulomb potential the correction to the total diffusive flux of ionic reactants due to diffusion interaction between sinks may be ignored for large enough values of the Onsager length and thus the reaction rate can be described by the classical Debye formula. On the other hand, for repulsive potentials the competition becomes more profound than in the case of uncharged sinks. However, this effect is of little interest because of a small value of the diffusive flux on the reaction surface.