The diffusive interaction in diffusion-limited reactions: the time-dependent case

Traytak, Sergey D.

doi:10.1016/0301-0104(94)00397-s

Cited by 23 publications

(26 citation statements)

References 15 publications

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“…In addition, it might be forced to find its target within a specific confining geometry, which in principle can be modeled through a collection of reflecting boundaries. Such settings define a genuinely many-body problem, as the overall flux of ligands is shaped by the mutual screening among all the different reactive boundaries (the reactive environment), known as diffusive interaction [39][40][41]. In the following we show how this kind of problems can be formulated and solved in a rather general form.…”

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confidence: 99%

Theory of diffusion-influenced reactions in complex geometries

Galanti

Fanelli

Traytak

et al. 2016

Phys. Chem. Chem. Phys.

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Chemical reactions involving diffusion of reactants and subsequent chemical fixation steps are generally termed "diffusion-influenced" (DI). Virtually all biochemical processes in living media can be counted among them, together with those occurring in an ever-growing number of emerging nano-technologies. The role of the environment's geometry (obstacles, compartmentalization) and distributed reactivity (competitive reactants, traps) is key in modulating the rate constants of DI reactions, and is therefore a prime design parameter. Yet, it is a formidable challenge to build a comprehensive theory able to describe the environment's "reactive geometry". Here we show that such a theory can be built by unfolding this many-body problem through addition theorems for special functions. Our method is powerful and general and allows one to study a given DI reaction occurring in arbitrary "reactive landscapes", made of multiple spherical boundaries of given size and reactivity. Importantly, ready-to-use analytical formulas can be derived easily in most cases. Diffusion-influenced reactions (DIR) are ubiquitous in many contexts in physics, chemistry and biology [1,2] and keep on sparking intense theoretical and computational activity in many fields [3][4][5][6][7][8][9][10][11]. Modern examples of emerging nanotechnologies that rely on controlled alterations of diffusion and reaction pathways in DIRs include different sorts of chemical and biochemical catalysis involving complex nano-reactors [12,13], nanopore-based sequencing engines [14] and morphology control and surface functionalization of inorganic-based delivery vehicles for controlled intracellular drug release [15,16].However, while the mathematical foundations for the description of such problems have been laid nearly a century ago [17], many present-day problems of the utmost importance at both the fundamental and applied level are still challenging. Notably, arduous difficulties arise in the quantification of the important role played by the environment's geometry (obstacles, compartmentalization) [18] and distributed reactivity (patterns of competitive reaction targets or traps) in coupling transport and reaction pathways in many natural and artificial (bio)chemical reactions [1,19,20].A formidable challenge in modeling environmentrelated effects on chemical reactions is represented by the intrinsic many-body nature of the problem. This is brought about essentially by two basic features, common to virtually all realistic situations, namely (i) finite density of reactants and other inert species (in biology also referred to as macromolecular crowding [21,22]) and (ii) confining geometry of natural or artificial reaction domains in 3D space. In general, the presence of multiple reactive and non-reactive particles/boundaries cannot be neglected in the study of (bio)chemical reactions occurring in real milieux, where the geometrical compactness of the environment may have profound effects, such as first-passage times that are non-trivially influenced by the starti...

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confidence: 99%

Theory of diffusion-influenced reactions in complex geometries

Galanti

Fanelli

Traytak

et al. 2016

Phys. Chem. Chem. Phys.

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“…II A by fitting κ(t) with (6) on each particle. Indeed, it can be shown that the functional form (6) holds also in the case of multiple sinks [11,12].…”

Section: Configurations With Multiple Absorbersmentioning

confidence: 99%

Point-particle method to compute diffusion-limited cellular uptake

et al. 2018

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We present an efficient point-particle approach to simulate reaction-diffusion processes of spherical absorbing particles in the diffusion-limited regime, as simple models of cellular uptake. The exact solution for a single absorber is used to calibrate the method, linking the numerical parameters to the physical particle radius and uptake rate. We study configurations of multiple absorbers of increasing complexity to examine the performance of the method, by comparing our simulations with available exact analytical or numerical results. We demonstrate the potentiality of the method in resolving the complex diffusive interactions, here quantified by the Sherwood number, measuring the uptake rate in terms of that of isolated absorbers. We implement the method in a pseudospectral solver that can be generalized to include fluid motion and fluid-particle interactions. As a test case of the presence of a flow, we consider the uptake rate by a particle in a linear shear flow. Overall, our method represents a powerful and flexible computational tool that can be employed to investigate many complex situations in biology, chemistry and related sciences.

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“…This feature of the method is especially important for problems of diffusive interactions of spherical sinks (e.g. [1,2,20,21]) and electrostatic interactions of spherical conductors (e.g. [5,22]), where such integrals are the primary quantities of interest.…”

Section: Introductionmentioning

confidence: 99%

“…Additionally, the present approach allows one to derive a large-time asymptotic series for the solution and to obtain a closed-form steady-state solution as its limiting value at infinite time. Asymptotic expressions for surface integrals of the boundary fluxes can then be used in problems of diffusive interactions of spherical sinks to estimate important effective parameters [2]. Since most of the available commercial software packages use a time-stepping procedure for transient problems, an accurate large-time computation of the solution and surface integrals of its gradient would require a significant computational effort using these methods.…”

Section: Introductionmentioning

confidence: 99%

“…Thus, the solutions derived here are important in several applications governed by one of these differential equations, such as heat conduction in porous materials, diffusive interactions of spherical sinks (e.g. [1,2]), interactions of spherical particles in potential flow (e.g. [3]), and electrostatic interactions of spherical conductors [4,5].…”

Section: Introductionmentioning

confidence: 99%

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