Chaperone-assisted translocation of a polymer through a nanopore

Using Langevin dynamics simulations, we investigate the dynamics of chaperone-assisted translocation of a flexible polymer through a nanopore. We find that increasing the binding energy $\epsilon$ between the chaperone and the chain and the chaperone concentration $N_c$ can greatly improve the translocation probability. Particularly, with increasing the chaperone concentration a maximum translocation probability is observed for weak binding. For a fixed chaperone concentration, the histogram of translocation time $\tau$ has a transition from long-tailed distribution to Gaussian distribution with increasing $\epsilon$. $\tau$ rapidly decreases and then almost saturates with increasing binding energy for short chain, however, it has a minimum for longer chains at lower chaperone concentration. We also show that $\tau$ has a minimum as a function of the chaperone concentration. For different $\epsilon$, a nonuniversal dependence of $\tau$ on the chain length $N$ is also observed. These results can be interpreted by characteristic entropic effects for flexible polymers induced by either crowding effect from high chaperone concentration or the intersegmental binding for the high binding energy.

💡 Research Summary

In this work the authors employ Langevin dynamics simulations to investigate how binding proteins (chaperones) assist the translocation of a flexible polymer through a nanoscale pore. The polymer is modeled as a two‑dimensional bead‑spring chain with finitely extensible nonlinear elastic (FENE) bonds, while chaperones are represented by mobile Lennard‑Jones (LJ) particles of the same size as the monomers. Attractive LJ interactions between a chaperone and a monomer are characterized by a binding energy ε, and the chaperone concentration is quantified by the number of chaperones N_c placed in a fixed simulation box (64 × 64 σ²). The system is thermostatted via the Langevin equation with parameters chosen to correspond to realistic physical scales (σ≈1.5 nm, bead mass ≈936 amu, k_B T≈1.2 ε₀).

The study focuses on three central questions: (i) how ε and N_c affect the probability of successful translocation (P_trans), (ii) how they influence the mean translocation time τ, and (iii) whether optimal values of ε or N_c exist that minimize τ. By running at least 1 000 successful events for each parameter set, the authors obtain statistically robust results.

Key findings on translocation probability: P_trans rises sharply with increasing ε for any fixed N_c, eventually saturating at high ε. This reflects the classic “Brownian ratchet” picture—strong binding prevents backward diffusion of the polymer. When ε is small (weak binding), P_trans initially increases with N_c but then displays a pronounced maximum before declining at higher concentrations. The decline is attributed to crowding on the trans side: many bound chaperones raise the entropic barrier, increase the frequency of unbinding events, and thus reduce the net forward bias. Consequently, the interplay between the binding‑generated pulling force (F_bind) and the entropic resistance from the trans side (F_trans,e) determines the observed non‑monotonic behavior.

The distribution of translocation times also depends on ε. For weak binding (ε≈1.3) the histogram is long‑tailed, indicative of a stochastic first‑passage process dominated by rare binding events. At strong binding (ε≈5.0) the histogram becomes Gaussian, showing that the pulling force dominates and the dynamics become more deterministic.

Regarding τ, several regimes emerge. For short polymers (N ≤ 64) τ decreases rapidly with ε and then plateaus; the reduction is explained by the increase of F_bind and the ratchet effect that suppresses backward motion. However, for longer chains (N ≥ 128) and low chaperone concentrations (N_c≈30), τ exhibits a minimum at an intermediate ε. The authors rationalize this by noting that at very high ε the chaperones quickly saturate the leading segment of the chain, leaving no free chaperones for later segments; the translocation then proceeds by diffusion, which is slower. Conversely, at too low ε the binding frequency is insufficient to generate a strong forward bias. Thus an optimal ε balances rapid binding with enough free chaperones to assist the whole chain.

The dependence of τ on chaperone concentration is similarly non‑monotonic. At low N_c the scarcity of chaperones limits the pulling force, leading to long τ. As N_c increases, τ drops because more binding events occur. Beyond a certain concentration, however, τ rises again because the entropic penalty from crowding on the trans side outweighs the benefit of additional binding. This yields a clear minimum of τ versus N_c for each ε.

The authors also analyze the waiting‑time distribution, i.e., the interval between successive monomers exiting the pore. For moderate ε (≈2.5) the waiting time quickly reaches a steady value, indicating fast binding/unbinding cycles. For strong ε (≈7.5) the waiting time grows dramatically after about half the chain has passed, confirming that the front‑loaded chaperones block further binding and the process becomes diffusion‑limited.

Overall, the paper demonstrates that chaperone‑assisted polymer translocation cannot be described solely by a simple ratchet mechanism. Instead, the dynamics result from a competition between a binding‑generated pulling force and entropic forces arising from crowding and inter‑segmental binding, both of which depend sensitively on ε, N_c, and polymer length N. These insights have direct relevance for biological processes such as protein import into organelles, viral DNA injection, and for technological applications like nanopore sequencing and targeted drug delivery, where tuning chaperone concentration and binding affinity could optimize transport efficiency.