Partitioning of individual flexible polymers into a nanoscopic protein pore

Abstract

Polymer dynamics are of fundamental importance in materials science, biotechnology, and medicine. However, very little is known about the kinetics of partitioning of flexible polymer molecules into pores of nanometer dimensions. We employed electrical recording to probe the partitioning of single poly(ethylene glycol) (PEG) molecules, at concentrations near the dilute regime, into the transmembrane beta-barrel of individual protein pores formed from staphylococcal alpha-hemolysin (alphaHL). The interactions of the alpha-hemolysin pore with the PEGs (M(w) 940-6000 Da) fell into two classes: short-duration events (tau approximately 20 micro s), approximately 85% of the total, and long-duration events (tau approximately 100 micro s), approximately 15% of the total. The association rate constants (k(on)) for both classes of events were strongly dependent on polymer mass, and values of k(on) ranged over two orders of magnitude. By contrast, the dissociation rate constants (k(off)) exhibited a weak dependence on mass, suggesting that the polymer chains are largely compacted before they enter the pore, and do not decompact to a significant extent before they exit. The values of k(on) and k(off) were used to determine partition coefficients (Pi) for the PEGs between the bulk aqueous phase and the pore lumen. The low values of Pi are in keeping with a negligible interaction between the PEG chains and the interior surface of the pore, which is independent of ionic strength. For the long events, values of Pi decrease exponentially with polymer mass, according to the scaling law of Daoud and de Gennes. For PEG molecules larger than approximately 5 kDa, Pi reached a limiting value suggesting that these PEG chains cannot fit entirely into the beta-barrel.

FIGURE 1

Model of the αHL pore and relative sizes of the PEG polymers. The section through the αHL pore shows a PEG molecule of 2.0 kDa inside the transmembrane β-barrel. The sites where replacements with cysteine were made are shown (Thr-117 and Leu-135). The Flory radii of four of the PEG molecules used here are shown.

FIGURE 2

Single-channel recordings of the αHL pore in the absence and presence of PEG-0.94 k applied to the trans side of the bilayer. (A) no PEG; (B) 1 mM PEG-0.94 k; (C) 5 mM PEG-0.94 k; (D) 9 mM PEG-0.94 k; and (E) semilogarithmic dwell-time histogram for PEG occupancy events. The PEG-0.94 k concentration was 5 mM and the recording period was 10 s. The bin size is 5 μs. A double-exponential fit was made by the Marquardt-LSQ procedure. The time constants derived from this experiment, uncorrected for missed events, are 19 and 59 μs. For the traces in A–D, the signal, which was obtained at a transmembrane potential of +100 mV, was low-pass filtered at 10 kHz. The other conditions are in Materials and Methods. The histogram in E is based on a signal filtered at 40 kHz.

FIGURE 3

Single-channel recordings of the αHL pore in the absence and presence of PEG-6.0 k applied to the trans side of the bilayer: (A) no PEG; (B) 1 mM PEG-6.0 k; (C) 5 mM PEG-6.0 k; (D) expanded trace of boxed area in B; (E) semilogarithmic dwell-time histogram for PEG occupancy events. The PEG-6.0 k concentration was 5 mM and the recording period was 200 s. The bin size is 5 μs. A double exponential fit was made by the Marquardt-LSQ procedure. The derived time constants, uncorrected for missed events, are 29 and 120 μs. For the traces in A–D, the signal, which was obtained at a holding potential of +100 mV, was filtered at 10 kHz. The histogram in E is based on a signal filtered at 40 kHz.

FIGURE 4

Single-channel recording with the homoheptameric cysteine mutant T117C₇. (A) MePEG-OPSS-0.85 k (1 mM) added to the trans chamber. The current levels are interpreted as follows: 0, fully open channel; 1, one PEG attached; 2, two PEGs attached. (B) Application of 10 mM DTT resulted in the cleavage of both PEG chains from the protein surface. The solution in the chambers contained 1 M KCl, 10 mM Tris·HCl, and 100 μM EDTA, pH 8.5. The signal, which was obtained at a holding potential of +100 mV, was low-pass filtered at 10 kHz.

FIGURE 5

Semilogarithmic plots of the frequency of occurrence of PEG occupancy events versus PEG concentration. The values were corrected for missed events. The fits shown represent linear relationships between frequency of occurrence and PEG concentration. (A) Frequency of occurrence of the short occupancy events for five of the PEGs; (B) frequency of occurrence of the long spike events for five of the PEGs. ▪, PEG-0.94 k; •, PEG-2.0 k; ▴, PEG-3.1 k; ▾, PEG-4.2 k; ♦, PEG-6.0 k. Because τ_on−1 = τ_T/f₁, τ_on−2 = τ_T/f₂, and f₁ + f₂ = 1, the plots in A and B are related; e.g., τ_on−2 = τ_on−1(1/f₁–1).

FIGURE 6

Plots of 1/τ versus PEG concentration. (A) Plot of 1/τ_on versus concentration for PEG-0.94 k: ▪, short occupancy events; •, long occupancy events. A representative experiment is shown. Rate constants, k_on = 1/(τ_on × [PEG]), were derived from the slopes of linear fits to such plots. (B) Plots of 1/τ_off for the long events versus PEG-0.94 k (▪) and PEG-6.0 k (♦) concentration. Representative experiments are shown. The dissociation rate constants, k_off = 1/τ_off, are independent of PEG concentration. A similar result was found for the short events. The kinetics of PEG binding to the αHL protein pore were examined at a holding potential of +100 mV, under conditions similar to those in Figs. 2 and 3. The values of τ were adjusted to account for missed events.

FIGURE 7

Semilogarithmic plot of the formation constant (K_f) for the αHL·PEG complex versus PEG molecular mass. ▴, mean K_f values (± SD, n = 4) for the short occupancy states derived from single-channel experiments to determine the kinetics of free PEG binding. ▾, mean K_f values (± SD, n = 4) for the long occupancy states. Values of K_f were also determined from the rates of chemical modification of L135C₇ with MePEG-OPSS reagents by using the scaling approach (Movileanu et al., 2001). Four experiments were performed for each molecular mass reagent: 0.85 kDa, 1.7 kDa, 2.5 kDa, and 5.0 kDa. ▪, reaction carried out in 300 mM KCl (± SD, n = 4) (Movileanu and Bayley, 2001); •, reaction carried out in 1000 mM KCl (± SD, n = 4). The line is a linear fit to the data from the chemical modification experiments carried out at 1000 mM KCl.