>

Other Definitions of Information Do Not Apply to Molecular Machines

The formulation for R accounts for a single molecular machine either gaining or losing information as it cycles through its operations [Schneider, 1991]. A similar formula, $I = \sum_{i=1}^{\Omega} P_{i, after} log_{2} (P_{i, after} / P_{i, before})$[Hobson, 1971,Schneider & Stormo, 1989] gives the maximum information an observer could gain by observing a system. I is always zero or positive [Hobson, 1971]. If we were to start a molecular machine in some state A, and we later observe it in another state B ( $P_{i, A} \neq P_{i, B}$, for some i) then I_AB > 0. If the machine returns to A, then I_BA > 0, so I_AB + I_BA > 0, meaning that the observer learned the details of how the machine performed this cycle. But the machine itself is in the same state as it began, so it cannot have gained any information, just as a computer memory does not gain any information if we fill it with data and then remove the data again. Thus only a path independent function of state, such as R, is appropriate to use for the information a single molecular machine gains during its operation. External observers and the measurements they may make are not relevant to the problem.