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In this paper, the looping kinetics of a long polymer chain in solution hasbeen investigated by using two state model, where one state represents openchain polymer molecule and the other represents closed chain polymer molecule.The dynamics of end-to end distance of both open chain and closed chain polymeris represented by a Smoluchowski-like equation for a single particle under twodifferent harmonic potentials. The coupling between these two potentials areassumed to be a Dirac Delta function in our model. We evaluate two rateconstants, the long term and the average rate constant. We have alsoincorporated the effect of all other chemical reactions involving at least oneend of the open chain polymer molecule - on rate of end-to-end loop formation.The closed chain polymer molecule can be converted to a open chain molecule bybreaking of any bond - the effect of this reaction on the rate of end-to-endloop formation is also considered in our model.

Understanding reversible looping kinetics of a long polymer molecule in solution. Exact solution for two state model with delta function coupling