Diffusion-controlled reaction rate to an active site

Traytak, Sergey D.

doi:10.1016/0301-0104(94)00353-c

Cited by 33 publications

(44 citation statements)

References 17 publications

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“…Mathematically, such reactions are described by mixed-boundary value problems, that can be solved only in some specific cases. Traytak considered the case of a diffusion-controlled reaction between a chemically isotropic sphere and a chemically anisotropic one, carrying an axially symmetric circular absorbing patch [14]. He was able to obtain an exact solution of this model by using the formalism of dual series relations (DSR).…”

Section: Appendix Diffusion-controlled Reaction Between Anisotropic mentioning

confidence: 99%

“…In diffusion-driven reactions between two spherical species, one chemically isotropic and the other characterized by a localized reactive site, the steric factor f does not depend on the radius of the target isotropic particle and is well approximated by the square root of the active surface fraction on the anisotropic sphere [14,15] (see also the appendix). According to this simplified description, the steric factor should be f = √ 2σ (R 1 /R e ), where R 1 is the radius of the Fab sphere.…”

Section: Antibodies Looking For Small Antigens: Binding the First Fabmentioning

confidence: 99%

“…Hence, considering the contribution of the two Fabs to the encounter rate to be additive, i.e. assuming for simplicity that the two active tips move in an uncorrelated fashion while exploring the epitope sphere, for small encounter cones one can write [14,15] …”

Section: Antibodies Looking For Small Antigens: Binding the First Fabmentioning

confidence: 99%

“…From our simulations we find that f ∝ r for small antigen radii. Since, for increasingly small values of σ , f vanishes as √ σ for arbitrary values of r [14,15], we assume ρ = αr √ σ , where α is a constant factor. Hence, considering the contribution of the two Fabs to the encounter rate to be additive, i.e.…”

Section: Antibodies Looking For Small Antigens: Binding the First Fabmentioning

confidence: 99%

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A dynamical study of antibody–antigen encounter reactions

et al. 2007

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The effects of internal dynamics in diffusion-driven encounters between macro-molecules represent a problem of broad relevance in molecular biology. In this view, we investigate a typical antigen-antibody reaction chain, based on a coarse-grained mechanical model parameterized directly upon results from single-molecule experiments. We demonstrate that the internal dynamics is a crucial factor in the encounter process. To describe our numerical results, we formulate a simple, intuitive theoretical framework, and we develop it analytically. This enables us to show that the inner dynamics of antibody molecules results in a cooperative behavior of their individual sub-units. Along the same lines, we also investigate the case of double binding to multi-valent antigens. Our results quantify the enhancement of avidity afforded by the double binding in excellent agreement with the available experimental data.

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Section: Appendix Diffusion-controlled Reaction Between Anisotropic mentioning

confidence: 99%

Section: Antibodies Looking For Small Antigens: Binding the First Fabmentioning

confidence: 99%

Section: Antibodies Looking For Small Antigens: Binding the First Fabmentioning

confidence: 99%

Section: Antibodies Looking For Small Antigens: Binding the First Fabmentioning

confidence: 99%

See 2 more Smart Citations

A dynamical study of antibody–antigen encounter reactions

et al. 2007

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“…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].…”

mentioning

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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Coarse-Grained Brownian Dynamics Simulation of Rule-Based Models

Klann

Paulevé

Petrov

et al. 2013

Computational Methods in Systems Biology

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Studying spatial effects in signal transduction, such as colocalization along scaffold molecules, comes at a cost of complexity. In this paper, we propose a coarse-grained, particle-based spatial simulator, suited for large signal transduction models. Our approach is to combine the particle-based reaction and diffusion method, and (non-spatial) rulebased modeling: the location of each molecular complex is abstracted by a spheric particle, while its internal structure in terms of a site-graph is maintained explicit; The particles diffuse inside the cellular compartment and the colliding complexes stochastically interact according to a rulebased scheme. Since rules operate over molecular motifs (instead of full complexes), the rule set compactly describes a combinatorial or even infinite number of reactions. The method is tested on a model of Mitogen Activated Protein Kinase (MAPK) cascade of yeast pheromone response signaling. Results demonstrate that the molecules of the MAPK cascade co-localize along scaffold molecules, while the scaffold binds to a plasma membrane bound upstream component, localizing the whole signaling complex to the plasma membrane. Especially we show, how rings stabilize the resulting molecular complexes and derive the effective dissociation rate constant for it.

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Diffusion-controlled reaction rate to an active site

Cited by 33 publications

References 17 publications

A dynamical study of antibody–antigen encounter reactions

A dynamical study of antibody–antigen encounter reactions

Theory of diffusion-influenced reactions in complex geometries

Coarse-Grained Brownian Dynamics Simulation of Rule-Based Models

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