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1 and follow the evolution of the length of the detached part of the filament, which is still assumed to be of uniform length over the timescale of observation. The results, shown in Fig.?2a, suggest that the detached length grows diffusively in time. This behavior can be explained by a simple scaling argument that balances the viscous dissipation rate P�� ? ��(l/t)2l, where l is the length of the detached filament with the elastic power that drives unbinding Pe ? (B��2 �C Sr2c)l/t?= B(��2 �C(��c)2)l/t, and yields l ? (B(��2 �C(��c)2)t/��)1/2. The slowing-down of unbinding with time arises because the ever-lengthening unbound part takes a longer and longer time to move through the viscous environment; eventually once the unbound part has formed a circular ring, this diffusive behavior will likely be replaced by linear Stokesian [http://www.selleckchem.com/products/MDV3100.html Enzalutamide] dynamics, although we do not reach this limit in our simulations. In contrast, if the subunits break off as soon as they?unbind from the substrate, viscous dissipation is localized to a region near the dynamic detachment zone, and the?viscous?dissipation rate P�� ? ��(l/t)2a, so that now l???B(��2 �C(��c)2)t/a��. To verify this relation, we use numerical simulations where we remove the subunit when it detaches from the substrate; the results shown in Fig.?2b confirm that we indeed capture this Stokesian limit as well. When we introduce quenched disorder into the structural parameter ��c ? via the dependence of the substrate [http://www.selleck.cn/products/PLX-4032.html Vemurafenib] stiffness S ? through its coefficient of variation Cv ?, unbinding occurs stochastically. [http://www.selleckchem.com/products/abt-199.html see more] In Fig.?3a ?, we show the results of simulations for the steady-state value of the average local bending angle j����j/N��j��j/N as a function of the intrinsic bond angle ? ??= ���� ?, for different values of the coefficient of variation Cv ?, keeping the average stiffness constant (in this example ��=0.05��=0.05). Because every calculation starts with a particular realization of the quenched disorder, our results are shown as averages over different realizations of the disorder. We note that disorder causes the unbinding of the filament to occur for values of ? ? that are larger than when disorder is absent (Cv ??= 0). The seemingly counterintuitive result that disorder makes the system stronger is immediately rationalized once we realize that this is only true because unbinding is always ruled by the strongest region, unlike material fracture or failure that is controlled by the weakest bond ( 20). For N ? independent random variables Si ?, distributed according to Eq. 5, the probability that the maximum is