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The state space of a polymer molecule is analysed. We show how the size ofthe state space can be reduced on the basis of symmetry. In the reduced statespace, the probability of a new state (termed below as class) is equal to thenumber of old states represented by the new state multiplied by the probabilityof each old state. As an application, the electrophoretic motion of themolecule in gel is considered. We discuss the influence of the gel medium andof external field on the molecule states, with absorbing states of hookedmolecules playing a major role. We show that in the case of strong fields boththe velocity and the diffusion coefficient decrease with field. Finally, weevaluate the time of relaxation to and from the absorbing states. This is donewith a continuous version of the exact enumeration method for weightednetworks.

A circular polymer chain in a gel - the reduction of the state space