A first-passage approach to the thermal breakage of a discrete one-dimensional chain

Using the first passage method for a Markov process, we theoretically study the fragmentation rate of a discrete one-dimensional chain (Rouse model). The fragmentation occurs due to thermal fluctuations. Assuming equilibrium initial conditions, we obtain an expression for the fragmentation rate of the one-dimensional filament as a function of the number of monomers, the position of the breaking point along the filament, the ratio of the bond energy to the thermal energy, and the Rouse relaxation time. We also obtain the fragmentation rate for a fixed initial configuration of the chain by numerically solving a Volterra equation. Our results reduce to those of previous theoretical studies at the appropriate limits, and spell out the role of the relevant time scales. The prediction of our model for the fragmentation rate of insulin fibrils under optimal growth conditions for the solution appears to be consistent with experimental data from other studies.