Ratcheting in post-translational protein translocation: a mathematical model.

We have developed a non-steady-state mathematical model describing post-translational protein translocation across the endoplasmic reticulum membrane. Movement of the polypeptide chain through the channel in the endoplasmic reticulum membrane is considered to be a stochastic process which is biased at the lumenal side of the channel by the binding of BiP (Kar2p), a member of the Hsp70 family of ATPases (ratcheting model). Assuming that movement of the chain through the channel is caused by passive diffusion (Brownian ratchet), the model describes all available experimental data. The optimum set of model parameters indicates that the ratcheting mechanism functions at near-maximum rate, being relatively insensitive to variations of the association or dissociation rate constants of BiP or its concentration. The estimated rate constant for diffusion of a polypeptide inside the channel indicates that the chain makes contact with the walls of the channel. Since fitting of the model to the data required that the backward rate constant be larger than the forward constant during early diffusion steps, translocation must occur against a force. The latter may arise, for example, from the unfolding of the polypeptide chain in the cytosol. Our results indicate that the ratchet can transport polypeptides against a free energy of about 25 kJ/mol without significant retardation of translocation. The modeling also suggests that the BiP ratchet is optimized, allowing fast translocation to be coupled with minimum consumption of ATP and rapid dissociation of BiP in the lumen of the ER. Finally, we have estimated the maximum hydrophobicity of a polypeptide segment up to which lateral partitioning from the channel into the lipid phase does not result in significant retardation of translocation.