An exact model calculation of the diffusion controlled intramolecular rate constant

Abstract

An exact calculation of the diffusion controlled first-order intramolecular rate constant k1 is given for the harmonic spring model and for any type of reaction sink in the frame work of the Wilemski–Fixman theory. For a one parameter spherically symmetric sink the resulting exact expansion for k−11 in terms of the sink parameter γ, k−11 = (√π/2Λγ)+(ln2−1)/Λ+0.5(√πγ/Λ)+⋅⋅⋅, gives the same γ→0 behavior of other known asymptotic calculations obtained for simpler diffusion controlled reaction theories. Also, the mean first passage time for end-to-end contact may be evaluated and results coincident to the third term in the expansion with the exact result given by the first passage time approach theory. These results support the vicinity of the Wilemski–Fixman closure approximation.

Kinetics of diffusion-limited catalytically activated reactions: An extension of the Wilemski–Fixman approach

“…A detailed discussion of this approximation can be found in Refs. [19,37,38]. Applying it to our case of the catalytically-activated diffusion-limited trapping reactions, we have:…”

“…[ 19,37,38]. Applying it to our case of the catalytically-activated diffusion-limited trapping reactions, we have:…”

“…, m(x) being defined in equation (38). Note that the correlations that are neglected in the Wilemski-Fixman approximation cannot be estimated precisely, so that it is difficult to find how they affect the different terms included into the reaction constant.…”

Confinement and viscoelastic effects on chain closure dynamics

“…The WF formalism has also been used to calculate the mean closure times for unconfined polymers with bending stiffness 13 and with long-range excluded volume interactions, 17 , and is generally felt to provide a sensible approach to the study of cyclization dynamics. 6,7,21 However, its utility in analyzing actual data may depend on how closely experimental conditions ensure that the closure reaction is diffusion limited. Experiments performed on synthetic DNA and RNA, for instance, often rely on fluorescence quenching to measure reaction times, and in that case the kinetics of electron transfer, which introduce other timescales into the problem, may need to be accounted for.…”

“…3 The importance of the cyclization reaction is, of course, not confined to biopolymers alone, but extends to other polymeric systems as well, including many with industrial and commercial applications. 4 Over the last several years, a great deal of theoretical research has therefore been devoted to the development of models of the dynamics of chain cyclization, [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] with a special emphasis on understanding how the mean reaction time varies with chain properties, particularly the molecular weight. Because of the intrinsic many-body character of the cyclization reaction in polymers (which in any realistic description requires a treatment of all the monomers in the chain, including their mutual excluded volume and hydrodynamic interactions), calculations of reaction times and similar quantities are generally non-trivial, and require numerous approximations.…”