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

## TL;DR

This paper presents an exact analytical solution for the looping kinetics of long polymer chains in solution, modeled by a Smoluchowski-like equation with a delocalized sink, providing explicit expressions for rate constants.

## Contribution

It introduces a general method to analytically solve polymer looping kinetics with a delocalized sink, extending previous localized sink models.

## Key findings

- Explicit average rate constant expressions derived
- Method applicable to various initial conditions
- Enhances understanding of polymer loop formation dynamics

## Abstract

The fundamental understanding of loop formation of long polymer chains in solution has been an important thread of research for several theoretical and experimental studies. Loop formations are important phenomenological parameters in many important biological processes. Here we give a general method for finding an exact analytical solution for the occurrence of looping of a long polymer chains in solution modeled by using a Smoluchowski-like equation with a delocalized sink. The average rate constant for the delocalized sink is explicitly expressed in terms of the corresponding rate constants for localized sinks with different initial conditions. Simple analytical expressions are provided for average rate constant.