Translocation of non-interacting heteropolymer protein chains in terms of single helical propensity and size

In this work we present an analytical framework to calculate the average translocation time τ required for an ideal proteinogenic polypeptide chain to cross over a small pore on a membrane. Translocation is considered to proceed as a chain of non-interacting amino acid residues of sequence {X_j} diffuses through the pore against an energy barrier Δℱ, set by chain entropy and unfolding-folding energetics. We analyze the effect of sequence heterogeneity on the dynamics of translocation by means of helical propensity of amino acid residues. In our calculations we use sequences of fifteen well-known proteins that are translocated which span two orders of magnitude in size according to the number of residues N. Results show non-symmetric free energy barriers as a consequence of sequence heterogeneity, such asymmetry in energy may be useful in differentiated directions of translocation. For the fifteen polypeptide chains considered we found conditions when sequence heterogeneity has not a significant effect on the time scale of translocation leading to a scaling law τ ∝ N^ν, where ν ∼ 1.6 is an exponent that holds for most ground state energies. We also identify conditions when sequence heterogeneity has a great impact on the time scale of translocation, in consequence, no more scaling laws for τ there exist.