Article pubs.acs.org/JACS
Design of Multifunctional Nanogate in Response to Multiple External Stimuli Using Amphiphilic Diblock Copolymer Kai Huang Department of Biomedical Engineering, Northwestern University, Evanston, Illinois 60208, United States
Igal Szleifer* Department of Biomedical Engineering and Department of Chemistry and Chemistry of Life Processes Institute, Northwestern University, Evanston, Illinois 60208, United States S Supporting Information *
ABSTRACT: Nature uses the interplay between hydrophobic and electrostatic interactions of disordered proteins to orchestrate complicated molecular gates such as the nuclear pore complex to control the transport of biological masses. Inspired by nature, we here theoretically show that welldefined gate shape, sensitive response to pH and salt concentration, and selectivity in cargo transport can be simultaneously achieved by grafting amphiphilic diblock copolymers made of sequence-controlled hydrophobic and ionizable monomers on the inner surface of solid-state nanopore. As a result, multiple functions such as ionic gating and molecular filtering can be implemented into one single copolymer nanogate. The gate structure and thermodynamics is a result of the self-assembly of the sequence-designed copolymer in the confined geometry that minimizes the free energy of the system. Our theory further predicts a phase transition and discontinuous charge regulation of the confined copolymer that allows logical gating in biosensors and nanofluidic devices. As an example of application, a nanolocker with the potential of molecular pumping has also been designed with the cooperation of two amphiphilic copolymer gates. Our results highlight the importance of polymer sequence in nanogating, and these insights can be used to guide the rational design of polymer-coated smart nanopores.
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INTRODUCTION Life processes happen in cellular compartments connected by gates or channels at nanoscale that have evolved to smartly select their passengers. While these biological gates and channels await full decipher of their mechanisms, artificial nanopores and nanochannels have been made to serve as gates and channels in new devices such as biosensors1−7 and nanofluidics.8−12 Designing bioinspired men-made gates for nanopores and nanochannels has attracted great research interests in the past decade to approach intelligent control of molecular and ionic transport.13−16 Gating in response to temperature,17−19 light,20−24 and pH25−30 are often realized with surface-grafted polymer materials31 whose aggregation and extension depends on their protonation status and intermolecular interactions that are tunable by those ambient stimuli. For example, an artificial ion pump can be built by functionalizing the two ends of a nanochannel with pHresponsive polyelectrolytes that can alternatively open or close.32 While a diversity of stimuli-responsive properties spans in different synthetic systems, most of the polymers employed in © 2017 American Chemical Society
nanopores and nanochannels are limited to homosequences, and form nanogates with simple structures governed by entropy. Since advanced functions often demand delicate structures, being able to build highly structured polymer nanogates is desired to reach the full potential of smart nanopores/channels. Back to the example of the ion pump, a less disheveled polymer gate would save space for the further miniaturization of the artificial pump. Nevertheless, engineering nontrivial nanostructures can be prohibitively difficult as everything is required to be at the right place at nanoscale, not to mention in a confined geometry like a pore or a channel. One strategy to overcome this challenge is to let the polymers self-assemble into functional structures like those intrinsically disordered proteins do in the nuclear pore complex (NPC).33−36 Despite the controversy on the transport mechanism in the NPC,37−41 the sequences of the intrinsically disordered proteins or nucleoporins (Nups) have been decoded and are found to be clearly heterogeneous. There is no doubt Received: February 28, 2017 Published: April 19, 2017 6422
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where nθl (r′,α,r) is the number of type l monomers that the polymer tethered at r′ has in the volume element between r and r+dr when it is in conformation α. σ is the polymer grafting density. The third term in eq 1 represents the electrostatic energy, which is associated with ρQ(r), the average charge density at r, given by the following:
that the function of the NPC arises from the intricate combination of these heterogeneous Nups. Going from proteins to polymers, we have even more choices of functional motifs that can respond to a wide spectrum of external stimuli. Therefore, besides the gate architecture optimization, sequenced-controlled polymers42−46 with a collection of distinct motifs would also allow the integration of multiple stimuli-responses13,15,47−50 and functions into one single nanogate, which could further minimize and intellectualize the nanodevice. On the basis of the knowledge from man-made polymer nanopores and inspired by the NPC, we in this work explored the possibility of self-assembling specifically designed diblock copolymer sequences into multifunctional structure in the confined geometry of nanopores/channels. We used a molecular theory (see methods section and the Supporting Information, SI, for more details) that has been proven successful in characterizing the behavior of end-tethered polymer in nanopores/channels51−55 and in other geometries.56−59 We started with a relatively simple design of polymer sequence that divides the chain into two blocks: one polyelectrolyte block grafted to the wall and one hydrophobic block toward the center of the pore. The molecular theory predicted that such a diblock copolymer coating of the nanopore enables a highly structured gate that not only regulates the mobile charges inside the pore in a pH-responsive way but also emulates the molecular filtering function of the NPC. We studied the phase behavior of the confined diblock copolymer and found a sharp transition between a wallcondensed phase and a center-condensed phase across a transition pH or salt concentration. To further illustrate the potential of the diblock copolymer gate, we combined two cooperative gates with distinct pH-responses to build a sufficiently small nanolocker as an examplary multigate nanodevices. The insights from this work could be useful in guiding the rational design of smart bioinspired nanopores/ channels. On the other hand, what we have learned from the smart nanogate here architected with heterogeneous copolymers could help the understanding of the more complicated NPC.
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⟨ρQ (r)⟩ =
∑ ρi (r)qi + ⟨nb(r)⟩fb (r)qb + ρQ,particle (r) i
(3)
where i runs over all charged mobile species, f b(r) is the fraction of the ionizable monomers that are charged at r and ρQ,particle(r) is the number density of charges that the model particle carries at r. The fourth term in eq 1 represents the mixing entropy between the charged and uncharged states of the polyelectrolyte. The last term is the attractive interaction between the particle and the polymer. The free energy is minimized with constraints that impose the incompressibility and the electroneutrality of the system. To allow for an efficient investigation of the system, we take advantage of the symmetry of the nanopore and assume that the system possesses azimuthal symmetry, that is, we allow only for inhomogeneities in the axial and radial directions. In other words, the free energy is minimized for a 2D system. We use the rotational isometric state model (RIS)60 to generate a representative set of 106 end-tethered polymer conformations. Due to the hydrophobic interaction, the polymers only explore a highly limited fraction of the conformation space. We therefore implement a biased sampling technique to enhance the sampling efficiency. More details of the theoretical framework, the free energy minimization, the consideration of symmetry, discretization process and sampling technique can be found in the SI.
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RESULTS Polymer Sequence Design and Gate Architecture. There is a huge space of polymer sequences we can use to coat nanopores. After many tests, we limited ourselves to the following design, which will be demonstrated to be a simple but promising step beyond the homopolymer. We employ diblock copolymers to coat a thin nanopore as shown in Figure 1A. We grafted a weak polyelectrolyte block of polymer to the inner surface of the nanopore, which block itself is a copolymer of alternating ionizable and nonionizable monomers as shown in
THEORETICAL METHODS
To model the nanopore/channel grafted with copolymers, we use a molecular theory that explicitly accounts for the size, shape, conformation and charge distribution of all molecular species in the system. We minimize the free energy of the system which is written in general terms as follows: mix F = − TS + EvdW + Eelectro + Facid − base + Ecargo
(1)
On the right-hand side of eq 1, the first term −TS is the entropy contribution to the free energy, including the translational entropies of solvent molecules, cations, anions, protons and hydroxyl ions, and the conformational entropy of the polymer. More specifically, the conformational entropy is written as ∑α P(α) lnP(α), where P(α) is the probability of a polymer being in conformation α. The second term EvdW considers an effective attractive energy of a Lennard−Jones form, between the number densities of polymer at different positions. The number density of monomer type l is constructed based on the conformational probability: ⟨nl(r)⟩ = σ
∫ dr′ ∑ P(r′, α)nlθ(r′, α , r) α
Figure 1. (A) Schematic representation of the nanopore. Left: topview. Right: sideview. The two blocks of the diblock copolymer are colored in red (polyelectrolyte) and green (hydrophobic), respectively. (B) The sequences of the diblock copolymers with the grafting ends on the left and the free ends on the right. Acidic ionizable monomers are shown in red, basic ionizable in blue, and hydrophobic nonionizable in green. Left: diblock copolymer sequence with acidic monomers. Right: diblock copolymer sequence with basic monomers.
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Figure 2. Wall phase and the center phase of the tethered diblock copolymer at low and high pHs. (A,B) Schematic representation of the polymergrafted nanopores in the two states (as a simple proof of concept we only show one layer of polymer here but keep in mind there are multiple layers in our simulation). (C,D) Sideview of the local volume fraction of the diblock copolymer in the two states. (E,F) Sideview of the local salt concentration in the two states. (G,H) Sideview of the charge regulation factor (the ratio between the local ionization probability and expectation from the bulk dilute solution) in the two states.
between the blocks is expected to scale with the size of the nanopore. For a nanopore of 24 nm in diameter (D) and 8 nm in width (L), we use a 40-monomer-long weak polyelectrolyte block and a 30-monomer-long hydrophobic block. There are 4 grafting heights (see Figure 1A) on the inner surface of the nanopore, with a spacing of 2 nm in-between. Ten copies of diblock copolymers are grafted at each height, rendering a coverage density about 0.13 polymers per squared nanometer. While the 4 grafting heights along the z axis are considered in a discrete way, we assume an azimuthal symmetry and homogeneous polymer distribution rotationally around z axis. The monomer diameter and bond length are both 0.5 nm. The ionizable monomers can be either acidic or basic, with opposite pH responses. Comprehending the gating behavior with one kind of ionization will make the understanding of the other one straightforward. Thus, we will focus on polymer with acidic monomers when we study the properties of a single gate. Molecular theory depicts the gate structures of the amphiphilic diblock copolymer at low and high pHs. The pKa of the acidic monomers is set to be 5. As shown in Figure 2A (schematically) and Figure 2C (molecular theory), at pH = 3, a pH lower than the pKa of the acidic monomer, the polyelectrolyte block is mostly uncharged and contracted,
Figure 1B. The surface of the nanopore is considered to be hydrophilic, devoid of strong interactions with the polymers. The ionizable monomers are hydrophilic when charged at certain pHs, but can turn hydrophobic when they are neutral. The nonionizable monomers are always neutral and hydrophobic. We use the nonionizable monomers to separate the ionizable ones so that if the latter get charged the overall electrostatic repulsion would not be too strong. With the countervailing attractive and repulsive interactions, this weak polyelectrolyte block of copolymer can stretch and contract according to the pH of the environment. Succeeding this weak polyelectrolyte block is a hydrophobic block, which is made of purely nonionizable hydrophobic monomers. Thus, the free end of the diblock copolymer is sticky and tends to aggregate at any pH. In a confined geometry of dimension comparable to the molecular size of the grafted polymer, the exact chainlength of the copolymer and the ratio between its two blocks are also crucial to the performance of the nanopore. If the ratio between the weak polyelectrolyte block and the hydrophobic block is too low, then the copolymer will not have enough sensitivity to external-stimuli. If the ratio is too high, then the copolymer will not have enough hydrophobic driving force to self-assemble when the ionizable monomers get charged. Like the overall length of the copolymer, the appropriate ratio 6424
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of pH as shown in Figure 3. Given enough time for the system to relax, a sharp transition (see Figure 3A) can happen between
leading to a collapse of the whole diblock copolymer (including the hydrophobic block) to the wall. Going to pH = 7, well above the pKa of the acidic monomer, the polyelectrolyte block get charged and stretched while the hydrophobic block aggregates at the center of the pore. As a result, the copolymer adapts a gate structure shown in Figure 2B (schematically) and Figure 2D (molecular theory). The morphology of such a center-phase of the diblock copolymer is in stark contrast with the one of the charged homopolymer (see the SI) that is more dilute and generally homogeneously distributed inside and outside the pore. The confined spatial distribution of the amphiphilic diblock copolymer allows a gating that is localized inside the nanopore, which would facilitate the miniaturization of nanofluidic devices integrated with multiple nanogates. Since fluid transport through thin pores is faster than through long channels, the smart gating in thin nanopores demonstrated here is also beneficial for the efficiency of nanofluidic devices.12 One important and widely studied application of nanopores is ionic gating,61−66 which means that the conductivity of the nanopore is tunable. The conductivity is largely determined by the concentration of mobile charge carriers or salts inside the nanopore. It is known that a nanopore grafted with homopolyelectrolyte can boost the conductivity when the polymers are charged, as mobile counterions enrich in the pore. The ionic gating function is reserved with the new design of the nanogate using amphiphilic diblock copolymer, as implied by the pH-dependent salt distributions shown in Figure 2E,F. In the wall phase at low pH (Figure 2E), the aggregated polymer near the wall excludes ions from that region, and a decrease of the conductivity comparing to that of a system without polymer-coating is expected. When charged (Figure 2F), the polyelectrolyte block of the diblock copolymer attracts counterions and therefore a rise of the conductivity is expected. It is worth noting that inside the nanopore, the net charge of polymers is not necessarily identical to what is expected from free dilute solution, as the acid−base equilibrium can shift in order to reduce the electrostatic repulsion and to favor the hydrophobic interaction. Such a charge regulation effect, indicated by the ratio between the local ionization probability (if a monomer is present) and the expectation from the bulk dilute solution, is demonstrated in Figure 2G,H. For the wall phase at low pH (Figure 2G), the probability of monomers being uncharged near the wall are almost doubled compared to that expected from free solution. The driving force of the charge regulation is a gain of enthalpy that overcompensates the cost of the chemical equilibrium shift, when the aggregated acidic monomers stay uncharged and interact hydrophobically. An even stronger charge regulation is found in the center phase of the diblock copolymer gate at high pH, in the center region of the nanopore where water is depleted due to the aggregation of hydrophobic polymer (Figure 2H). The morphologydependent charge regulation in the nanopore reflects the strong coupling between all the chemical and physical interactions in the confined system. The molecular organization of the confined polymer is therefore a result of the balance of all these different forces that minimizes the total free energy of the system. Morphology Transition and Charge Regulation. Having shown the behavior of the amphiphilic diblock copolymer at low and high pHs, we now turn to answer the question of when and how the transition happens between the wall phase and center phase. Molecular theory predicts a coexistence of the two phases of the system in a wide window
Figure 3. (A) Polymer volume fraction in the two phases at the transition pH. Upper: topview (schematic representation based on the predictions from molecular theory). Lower: sideview (predictions from molecular theory). (B) Free energy difference (ΔF = Fcenter − Fwall) between the center phase (C) and the wall phase (W). The pKa of the acidic monomers is 5 and the observed transition pH is 5.12. The gray domain marks the approximate pH window where the two phases coexist. (C) Ionization fractions (averaged over all the acidic monomers) in the two phases. Filled symbols for the stable phases and empty for the metastable phases. Blue symbols for the wall phase and red for the center phase. The gray domain marks the approximate pH window where the two phases coexist.
the two phases at a transition pH where the free energies of the two phases even. In other words, the diblock copolymer does not continuously protrude toward the center to close the gate, but rather abruptly extend itself to adapt a center phase at the transition pH. There is a free energy barrier expected between the two phases and the diblock copolymer nanogate could stay in a metastable state for a time scale that depends on the height of the energy barrier. For neutral homopolymer brushes grafted on flat surfaces, such a free energy barrier has been recently demonstrated by Gleria et al. using a molecular theory combined with the improved string method.67 In this present study, we test the stabilities of the two phases at varying pHs and are able to estimate the boundaries of pH window for the coexistence as shown in Figure 3B. The dashed curve in Figure 3B shows the free energy difference between the two phases ΔF = Fcenter − Fwall. Within the coexistence window below the transition pH, the wall phase is stable and the center phase metastable, and vice versa above the transition pH. Interest6425
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wall phase. On the other hand, a high salt concentration can efficiently screen the repulsion between the charged polymer monomers. Therefore, unless highly charged at high pH, the polyelectrolyte block of the copolymer is less stretchable as the conformational entropy is against the extension. As a result, in a salty solution the wall phase is more energetically favorable than the center phase at intermediate pH. Between the two extremes of the salt concentrations, a minimum of the transition pH is predicted as the polyelectrolyte block can easily stretch without paying large energetic penalty. Figure 4 demonstrates that at low salt concentration, the state of the nanogate is sensitive to both the pH and the salt concentration. Thanks to this sensitivity, the nanogate is multistimuli responsive and can be controlled by both the pH and the salt concentration of the outer solution. Selective Transport of Cargoes through the Gate. In addition to the ionic gating, the copolymer nanogate in its center phase can also serve as a molecular filter that selectively passes the cargoes. To test the filtering performance of the nanogate, we calculated the potential of mean force (PMF) for a variety of different nanoparticles. We limit the PMF calculation to large cargo size since small cargoes, insensitive to its surface properties, can diffuse easily through the peripheral region of the nanopore where the polymer density is low. We therefore use a particle diameter of 6 nm and assign them with different charges and hydrophobicities. While a neutral hydrophilic particle interacts with the polymer nanogate only sterically, a charged hydrophobic particle also interacts with the gate electrostatically and hydrophobically. In our test, there are six combinations of charge and hydrophobicity of the nanoparticles, namely, neutral hydrophilic (Hphi), neutral hydrophobic (Hpho), positively charged hydrophilic (Hphi+), positively charged hydrophobic (Hpho+), negatively charged hydrophilic (Hphi−) and negatively charged hydrophobic (Hpho−). The charge amplitude of the charged particles is kept at 50e. The hydrophobicity scale in terms of the particle− polymer attraction strength is a constant among all the particles which leads to a reasonable contact minimum (a few kT) between the Hpho particle and the hydrophobic core of the copolymer gate when they get in touch. Figure 5C shows the PMFs of these six typical cargoes through the nanopore along the central axis at pH = 7. The free energy is set to zero for a reference system, where the test particle is in the bulk solution (far from the pore). As the core of the nanogate is hydrophobic and the periphery is negatively charged, the Hphi− particle is most repelled, both by the electrostatic repulsion and by the enthalpy cost of breaking the hydrophobic interactions between the polymers. A huge free energy barrier around 175kT ensures a blockage of the Hphi− particle through the nanopore. This barrier drops to around 150kT for the Hphi and Hpho− particles, and around 100 kT for the Hpho and Hphi+ particles. By further combining hydrophobic interaction and electrostatic attraction, that is in the case of the Hpho+ particle, a much lower free energy barrier (around 40 kT) can be achieved. Such a barrier is sandwiched by two energy wells that correspond to the state of the Hpho+ particle partially fusing with the nanogate but without penetrating it. When fully penetrated, the hydrophobic part of the amphiphilic diblock copolymer forms a ring around the particle and the contact details depend on the nature of particle. For instances, as demonstrated in Figure 5A,B, the Hpho+ particle has a much larger contact area with the nanogate than the Hphi− particle does.
ingly, the center-phase is predicted to be metastable in a wider range of pH than the wall-phase is. According to previous study of tethered neutral homopolymers in nanopore, the relative stability of the polymer phases further depends on the interaction strength and range of interpolymer interactions.68 The wide pH window of coexistent polymer phases reached here is a result of (1) the interplay between hydrophobic attraction and electrostatic repulsion of the confined polymers, and (2) the specific copolymer sequence designed for the nanoconfinement. With the pH-sensitive coexistence of polymer morphologies, the nanogate is expected to display hysteresis under cycled pH change. The two polymer phases undergo different charge regulations at various pHs. Figure 3C compares the total polymer charges of the two phases, but keep in mind that these charges are very differently specially distributed owing to the distinct polymer morphologies. Associated with the abrupt morphology transition, there is a discontinuity in the total polymer charge of the system across the transition pH. Jumping from the wall phase to the center phase, the diblock copolymer not only extends its polyelectrolyte block to a larger space but also escalates its ionization rate stiffly. The synergy of these two effects is expected to boost the conductivity of the nanopore in a discontinuous way. This discontinuous charge regulation is especially intriguing as it opens opportunities for highly sensitive biosensors and logical ionic gating in nanofluidic devices.69 We have repeated the free energy calculations for the two phases at varying salt concentrations in the bulk solution. Figure 4 shows the phase diagram of the copolymer nanogate
Figure 4. Phase diagram of the diblock copolymer gate at various pHs and salt concentrations. Circles: center phase. Squares: wall phase. Triangles: transition points. The metastable states are not included here.
regarding to pH and salt concentrations. Interestingly, the transition pH is not only sensitive to the bulk salt concentration but also displays a nonmonotonic trend. Namely, the transition happens at pH much higher than the pKa of the acidic monomer when the bulk salt concentration is very low. The transition pH then decreases when salt concentration goes up. A minimum of the transition pH is reached around the physiological salt concentration. Beyond that point, the transition pH rises as the solution get saltier. The key to understanding such nontrivial behavior of the nanogate is, again, the subtle balance between the different chemical and physical interactions in the system. At low salt concentration, the electrostatic repulsion between charged polymer monomers could be so strong that the system would shift the acid−base equilibrium to retain a low ionization fraction that favors the 6426
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nanopore is reminiscent of the double-well potential model used by Tu et al.70 to explain the transport of large cargo through the NPC. However, the free energy landscape in our system is much stiffer than that expected in the NPC, indicating that the hydrophilic spacers in the latter serve to flatten the free energy landscape to allow faster traffic. Molecular Locker Built with Two Nanogates. So far we have focused on the behavior and function of single diblock copolymer nanogate. To prove the potential of the integration of multiple nanogates, we here, as an example, demonstrate how a molecular locker can be constructed by grafting a nanochannel with two polymer gates. Consider a vertical nanochannel amounted with two gates, one upper and one lower. For the locking purpose, cooperation of the two gates is needed to realize three states of the channel: upper gate open/ lower gate closed, upper gate closed/lower gate open, and both gates closed. To be alternately open or closed at one systematical pH, the two gates must have different responses to the pH. In the case of the amphiphilic diblock copolymer, we use acidic monomers with a pKa of 6 in the polyelectrolyte block of upper gate and basic monomers with a pKa of 8 in the polyelectrolyte block of the lower gate. The centers of the two gates are separated with a distance of the pore diameter that is 24 nm. We inspected the behavior of the double-gate nanochannel with molecular theory. The polymer spatial distribution and electrostatic potential inside the nanopore at different pHs are shown in Figure 6. At pH = 5 (Figure 6A), a pH lower than the pKa of both the acidic and basic monomers, the upper acidic gate collapses to the wall whereas the lower basic one adapts a center phase. A macromolecule or nanoparticle, assumed to be hydrophilic so that it cannot diffuse through the hydrophobic polymer, can enter the nanochannel from the upper reservoir through the acidic gate, but will be blocked out from the lower one by the basic gate. If one increases the pH to 7 (Figure 6C), higher than the pKa of the acidic monomers but still lower than the pKa of the basic ones, then both gates will be in their center phases and the cargo inside the nanochannel will be therefore trapped. Finally, if the pH further rises to 9 (Figure 6E), higher than the pKa of both gates, then the upper gate will stay in its center phase while the lower one collapses to wall, opening the pathway for the trapped cargo to be released into the lower reservoir. Such a pH-responsive nanolocker could be further developed into a nanopump if external work can be done during the above steps. For example, electrostatic potential can be applied to the inner surface of the nanopore to attract charged cargoes to the chamber from a low concentration reservoir before the locking, and then expel the locked cargoes to a high concentration reservoir when the path back is blocked. It merits a note that the density distribution of the weak polyelectrolyte block in the center phase in Figure 6A,E is slightly more bloated than that in Figure 6C, due to the higher ionization rate (almost saturated) of the former. Without the hydrophobic spacers in the weak polyelectrolyte block, the center phase will not be as stable at saturated ionization. Nevertheless, the smart diblock nanogate can remain viable in the absence of the spacers as long as the ionization rate is not too high. The advantage of the diblock copolymer gate architecture is that it allows a well-bounded nanochamber (Figure 6C) to be formed between the well-shaped nanogates. With the homopolymer gate structure (see SI), one can imagine that it is not possible to minimize the length of the chamber to the
Figure 5. Polymer volume fraction profile around a negatively charged hydrophilic particle (A) and a positively charged hydrophobic particle (B). (C) PMFs of the transport of various particles at pH = 7: neutral hydrophilic (Hphi), neutral hydrophobic (Hpho), positively charged hydrophilic (Hphi+), positively charged hydrophobic (Hpho+), negatively charged hydrophilic (Hphi−), and negatively charged hydrophobic (Hpho−). Inset: the height of the free energy barrier and the depth of the free energy well as a function of pH for the Hpho+ particle.
The results clearly show the coupling between the free energy landscape of the cargo transport and the cargo-induced reconstruction of the nanogate, and therefore suggests distinct transport dynamics for different cargoes. The cargo-sensitive transport allows the nanogate to filter the cargoes according to their charge and hydrophobicity. In this example, hydrophobic cargoes with positive charge are selected to pass the nanogate with least resistance. It is straightforward to expect a different cargo selectivity by flipping or neutralizing the charge of the polymer nanogate. Furthermore, as the gate is pH-responsive, one can easily tune the free energy landscape of the transport of the cargo by pH control. As shown in the inset of Figure 5C, the height of the barrier and depth of the well both decrease with a decreasing pH that brings the nanogate close to the transition to the wall phase. This trend can be understood as the center phase of the nanogate becomes less stable toward the transition point and succumb more easily to the passage of the cargo. Once the transition happens, the polymers collapse to the wall and the gate opens to let the cargoes pass freely though the nanopore. The sequence of the diblock copolymer in our artificial nanopore resembles that of the long disordered FGnucleoporins (Nup100, Nup116) of the NPC, in a coarsegrained way. The general pattern of these sequences is that, most charged groups are distributed near the tethering end of the chain and most hydrophobic groups reside near the free end. The fact that our diblock copolymer in its center phase can mimic the cargo selectivity of the NPC suggests that the long Nups of the NPC could adapt a similar morphology to form a plug in the center of the pore. The double-well free energy landscape experienced by the Hpho+ particle in our artificial 6427
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diblock copolymer is designed to have a polyelectrolyte block near the wall and a hydrophobic block toward the center. Upon polymer ionization, such a design aligns the swelling part of the polymer with the bulky periphery of the pore that is far from the pore-axis and the aggregating part of the polymer with the more confined center of the pore. The neutral spacers between the charged groups in the polyelectrolyte block buffer the electrostatic repulsion to stabilize this center phase. When the polyelectrolyte block gets uncharged and becomes hydrophobic, the whole diblock copolymer collapses onto the wall. The nanogate can change its morphology from the extended center phase to the collapsed wall phase abruptly, accompanied by a remarkable discontinuous charge regulation. Such a sharp transition, reflecting the spontaneous global reconfiguration of hydrophobic interaction, electrostatic interaction, and acid− base equilibrium, can be triggered by either the pH or the salt concentration of the solution. Our theory also predicted a wide window of pH for the two phases to coexist with one of them being metastable, which means there will be a free energy barrier between the two phases for the transition to overcome. We have proven that ionic gating and molecular filtering can be integrated into one singe nanogate, which could find wide applications in biosensing, molecular filtering, and nanofluidics. For an example of application, we have demonstrated a nanolocker that allows molecular trapping and can be further developed into a nanopump. The end-tethered diblock copolymers investigated here resemble the long FG-Nups in the NPC in an abstract way. Knowing the sequence-structure−function relation of these polymers under confinement is valuable in understanding the NPC structure and its transport mechanism which still remains elusive despite extensive studies.53,71−82 The fact that relatively simple design of the polymer sequence work very well for nanogating implies that assembling charged hydrophilic and neutral hydrophobic motifs into separate blocks could serve as a general principle for building smart hairy nanopores, which might has been exploited by nature in the case of NPC. There are other important features in the NPC that we do not mimic in our artificial nanopore. For example, there are hydrophilic spacers separating the hydrophobic FG motifs that are expected to critically affect the interprotein associations. Comparison between our previous study of a full NPC where no center plug is found53 and the center phase we obtained in this artificial nanopore highlights the importance of spacers on tuning the stability of any possible self-assembled structure in the center of pore. On the other hand, while the long Nups are reported to play a primary role in the nuclear pore transport, the NPCs are found not able to function fully without the aids from the short Nups. The behavior of the short Nups together with the effect of spacers will be covered in our future studies that aim to provide more intuitive understanding of the NPC. Functionalization of nanopores with sequence-controlled polymers42−46 is a rich field of many promising applications, but could be limited by the lack of design principles against the vast polymer sequence space. We have shown that molecular theory is a powerful tool to guide the desired rational design, as it considers the molecular details of polymer conformational entropy, the local charge regulation, and gives access to the thermodynamic properties and phase diagram of the system. Its relatively high efficiency allows systematic study of the effect of polymer sequence on the properties of the nanopores. With thorough theoretical knowledge and advanced polymerization techniques, eventually it will become possible to program the
Figure 6. Polymer volume fraction and electrostatic potential (only half of the pore is shown) of the double-gate nanochannel at different pHs. (A,B) pH = 5, (C,D) pH = 7, and (E,F) pH = 9. The pKa of the acidic monomers in the upper gate is 6 and the pKa of the basic monomers in the lower gate is 8.
extent that is comparable to the diameter of the pore. The miniaturization of the nanochamber between the double diblock copolymer gates demonstrated here is essential to future techniques of single macromolecular trapping or pumping based on nanochannels. Lastly, we shall point out that the double-gate nanochannel can also serve as an ion pump. As shown in Figure 6B,D,F, selfbuilt electrostatic potential in the gating area can alternatively gate the ionic conductivity. By combining pH control and external electric field, ionic pumping can be achieved in a similar way to the molecular pumping. Such an ion pump based on nanochannel but with a micrometer scale length and homopolymer double gates has been already realized experimentally by Zhang et al.32 The insights from these theoretical findings can be used to design new generation of nanopumps with all its dimensions in nanoscale.
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CONCLUSIONS In summary, we demonstrated through a molecular theory that multifunctional nanogate with multistimuli responses can be built by the self-assembly of end-grafted diblock copolymers with specific sequence confined in nanopores/channels. The 6428
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functions of nanopores with sequenced-designed polymers. We believe the field of nanogating with sequenced-polymer-coating is rich in possibilities and only limited by our imaginations.
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ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/jacs.7b02057. Formulation of the theory, minimization of the free energy, symmetry considerations, discretization and numerical solution, biased sampling, and hompolymer gate (PDF)
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AUTHOR INFORMATION
Corresponding Author
*
[email protected] ORCID
Kai Huang: 0000-0001-8400-9341 Igal Szleifer: 0000-0002-8708-0335 Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS The authors acknowledge financial support from the National Science Foundation Grant CBET-1403058. The authors thank Dr. Rikkert Nap and Dr. Mario Tagliazucchi for assistance and technical supports, and Dr. Estefania Gonzalez Solveyra for discussion of the manuscript.
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