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The fundamental understanding of loop formation of long polymer chains insolution has been an important thread of research for several theoretical andexperimental studies. Loop formations are important phenomenological parametersin many important biological processes. Here we give a general method forfinding an exact analytical solution for the occurrence of looping of a longpolymer chains in solution modeled by using a Smoluchowski-like equation with adelocalized sink. The average rate constant for the delocalized sink isexplicitly expressed in terms of the corresponding rate constants for localizedsinks with different initial conditions. Simple analytical expressions areprovided for average rate constant.

Understanding looping kinetics of a long polymer molecule in solution. Exact solution for delocalized sink model