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Distribution of cross-linked states. (A) Illustration of how the 20 distinct labeled states can be assigned to one of the four cross-linked states: 0 dimers per ring (green), 1 dimer per ring (blue), 2 dimers per ring (red), and 3 dimers per ring (purple). These weights are collected in the matrix 
. (B) The matrix product 
yields four equations, 
where m is an integer between 0 and 3 that corresponds to the size of the population of heptameric rings with m dimers.
