Simplification of reversible Markov chains by removal of states with low equilibrium occupancy

We present a practical method for simplifying Markov chains on a potentially large state space when detailed balance holds. A simple and transparent technique is introduced to remove states with low equilibrium occupancy. The resulting system has fewer parameters. The resulting effective rates between the remaining nodes give dynamics identical to the original system's except on very fast timescales. This procedure amounts to using separation of timescales to neglect small capacitance nodes in a network of resistors and capacitors. We illustrate the technique by simplifying various reaction networks, including transforming an acyclic four-node network to a three-node cyclic network. For a reaction step in which a ligand binds, the law of mass action implies a forward rate proportional to ligand concentration. The effective rates in the simplified network are found to be rational functions of ligand concentration. ► A simple technique for simplifying Markov chains on a large state space. ► The approach is illustrated by several analogies from physics. ► The technique is presented by several examples. ► Our method works for multi-ligand dependent molecules as well. ► Our study should have a broad impact in the field of single-molecule dynamics.