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Kinetic Master Equation Modeling of an Artificial Protein Pump Yu Zhang,†,‡ Cheng-Tsung Lai,†,‡ Bruce J. Hinds,§ and George C. Schatz*,†,‡ †

Department of Chemistry, Northwestern University, Evanston, Illinios 60208, United States Center for Bioinspired Energy Science, Northwestern University, Chicago, Illinois 60611, United States § Department of Materials Science and Engineering, University of Washington, Seattle, Washington 98105, United States ‡

S Supporting Information *

ABSTRACT: Biological ion channels and pumps have inspired many efforts to generate artificial counterparts due to their fundamental importance and practical applications. Recent work by Hinds et al. (Adv. Funct. Mater. 2014, 24, 4317−4323) demonstrated a selective protein pump based on an artificial nanopore in which the pump cycles are based on selective binding and release of His-tagged GFP protein ions to a NTA−Ni2+ transition metal complex. In this work, a kinetic master equation method is presented to model this pump and to establish the origin of the variation of selectivity with concentration of imidazole that is involved in the release mechanism. A two-site model with multiple species of proteins is used to mimic the pump mechanism under nonequilibrium conditions. Numerical simulation qualitatively reproduces the experimental selectivity, and uncovers essential ingredients of the pump mechanism. In addition, the binding mechanism between His-tags and NTA−Ni2+ is investigated using molecular dynamics simulations.

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NTA−Ni2+ complex then is used to bind the proteins that have His-tags. In the field of His-tag technology, typical tags consist of five to six consecutive histidine (His) residues, and it has been suggested that 5 His- or 6 His-tags guarantee high selectivity. After binding between His-tags and NTA−Ni2+, imidazole is usually used to release the bound His-tags. It was shown that the dissociation constant of imidazole is just low enough to displace bound tags, but it is not high enough to kick the Ni2+ off the NTA,31 which is optimal for releasing bound tags. Based on the IMAC technique, a selective protein pump was recently designed by employing a delicate binding/ pumping cycle.35 Selective pumping can be achieved by tuning the concentration of imidazole which releases His-tagged green fluorescent protein from NTA-bound states. In this work, a kinetic master equation is employed for the study of this NTA-based protein pump under nonequilibrium conditions. The binding between His-tags and NTA−Ni2+ is also briefly investigated by molecular dynamics simulation. The NTA-based pump, which was involved in protein separation experiments in the Hinds group,35 is based on a structure that is illustrated in Figure 1. Nα,Nα-Bis(carboxymethyl)-L-lysine (NTA) is covalently grafted onto the gold surface. Selective transport between His-tagged green fluorescence protein (HisGFP) and bovine serum albumin protein (BSA) has been demonstrated. BSA was used to mimic a complex protein

INTRODUCTION Control of ion flow is of great importance for biological processes. Ion pumps and ion channels are examples of transporters that create and control the distribution of each species of ions or molecules in all biological systems.1−4 Biological processes have provided rich examples of pumps, such as the proton pump in cytochrome c oxidase,5,6 the sodium−potassium exchange pump,7,8 and Ca2+ pumps.9,10 The remarkable structures of biological ion channels and pumps have been a source of inspiration in the development of their artificial counterparts11−16 due to their fundamental importance and practical applications. Potential applications include sensing, energy harvesting/conversion, water purification, and so on. During the past decades, there is growing research interest in the synthesis, modification, characterization, and modeling of nano channels and pumps.14−27 For instance, a light-driven Ca2+ pump based on a bilayer membrane17 and a light-driven sodium pump27 have been demonstrated. The effects of external ac fields on pumping have also been investigated both experimentally and theoretically.28−30 In addition to ion channels and pumps, researchers are also developing mesoscopic channels and pores to control the flow of large biological molecules, such as proteins. Among many emerging techniques, affinity tags have been widely used for the purification of recombinant proteins as they generally yield highly enriched proteins from a crude cell.31−34 Immobilized metal ion affinity chromatography (IMAC) employs transition metal ions (such as Ni2+) which are immobilized by surfacebound chelators, such as nitrilotriacetic acid (NTA) . The © 2016 American Chemical Society

Received: March 24, 2016 Revised: June 11, 2016 Published: June 14, 2016 14495

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NTA−Ni2+ and then removed the restraint to see whether this NTA−Ni2+/residue pair still maintains a bound state. MD simulations show that residue pair 2−3 bound to NTA−Ni2+ is the most stable pair as shown by Table 1. For the residue 2−3 pair bound to NTA−Ni2+ structures, secondary structural analysis demonstrates that the (His)6 has high propensity for random coil structures, except that residue 3 has a bent conformation as shown by Figure 2. Figure 1. Illustration of system under study. NTA−Ni2+ is grafted onto the gold surface at the entrance of the nanopore. During the binding cycle, the His-GFP is bound to NTA−Ni2+, which causes blockage to BSA. In the pumping cycle, imidazole is driven to the binding site to release the bound GFP and the released GFP is pumped to the right bath driven by the external field.

mixture, as it has same polarity as His-GFP, which can be a challenge in electrophoretic-based protein separations. The protein pump system involves a two-cycle process, with a binding cycle followed by a pumping cycle. During the first binding cycle, a small positive bias is applied to the NTA−Ni2+/ gold surface. This attracts anionic His-GFP and BSA proteins to the binding surface. At the same time, the positive potential repels imidazole from the binding surface such that it remains in the right side compartment. Binding of His-GFP results in accumulation of His-GFP onto the binding surface, and since the His-GFP diameter is only a factor of 3 smaller than the pore diameter, this blocks the nanopore. The transport of BSA (comparable in size to His-GFP) is also blocked even though BSA is not immobilized by the binding surface. In the subsequent pumping cycle, the positive potential on the gold surface is removed and a bias voltage is applied to the electrode pair outside of the membrane. This external field drives cationic imidazole from the permeate side to the binding sites to release bound His-GFP, and the field also pumps the released anionic His-GFP across the membrane to the permeate side. By tuning the amount of imidazole, the fraction of released His-GFP can be controlled. As long as His-GFP is not totally released, transport of BSA is still suppressed while His-GFP can be pumped through the channel. Thus, selective pumping of HisGFP can be achieved by delicate control of the binding/ pumping cycles and imidazole concentration.

Figure 2. Structure of 2−3 pair. (A) DSSP analysis and (B) representative bound structure of NTA−Ni2+ with 2−3 residue pair.

The MD simulations indicate that the binding between Histags and NTA−Ni2+ is not very strong. Since it is the imidazole rings of the His-tags that are responsible for the binding process, these His-tags can be released when excess imidazole is provided. This binding/release equilibrium is ideal for protein separation, as the binding of the His-tagged protein to NTA− Ni2+ blocks the nano pore, preventing the other proteins from transporting through the pore. However, knowing the detailed binding process is not enough for modeling the protein pump kinetics. Due to the large time scale of protein transport through the pore, atomistic simulations of the protein pump are not feasible. Instead a kinetic model that enables the systematic study of protein transport through the pore under external stimulus is a necessary simplification. Such a model will simplify the complicated binding process of His-tags to NTA−Ni2+ while still incorporating the released His-tagged protein from the Ni2+ by imidazole. The transport of other proteins through the pore is limited by the concentration of the His-tagged protein on the binding sites, while the amount of released Histagged protein that can be pumped through the pore is controlled by the concentration of imidazole. Thus, the Histagged protein can be collected on one site to mimic the binding to NTA−Ni2+ in kinetic theory, and then the imidazole release corresponds to transport to the other site. In the next section, the operation of the protein pump under nonequilibrium conditions is modeled by a kinetic master equation method.36−40

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MOLECULAR DYNAMICS SIMULATION In order to get a better understanding of the detailed interaction between NTA−Ni2+ and the (His)6 peptide, we performed all atom molecular dynamics (MD) simulations (see Supporting Information for details of the MD simulations) . As the NTA−Ni2+ has two free coordination sites, there are 15 different residue pairs from the (His)6 that can bind to NTA− Ni2+. Due to steric hindrance, we hypothesized that only a few pairs can form a stable structure with the NTA−Ni2+. We simulated the 15 possible combinations to see which residue pair has a higher preference in binding to NTA−Ni2+. We initially put a distance restraint between the residue pair and

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KINETIC MASTER EQUATION The two-site model that we will use to model the protein pump is a specific application of a more general theory that assumes that there are many physical sites and many species of particles.

Table 1. Stability of Histidine Residue Pair Binding to NTA−Ni2+ residue pair stable rate (%) residue pair stable rate (%)

1−2 15 2−6 10

1−3 10 3−4 10

1−4 10 3−5 5 14496

1−5 10 3−6 0

1−6 5 4−5 30

2−3 50 4−6 25

2−4 20 5−6 10

2−5 5

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the external force vanishes ( f ij = 0) and energy of the state is time-independent, the system relaxes to an equilibrium state α −βEi with a Boltzmann probability distribution, i.e., Pi ∝ ni,μ e . Consequently, there is no net flux between two arbitrary states. In contrast, the net flux when not at equilibrium can be controlled by tuning the barrier, energy, and driving force. The energy of each state can be evaluated from the energy of each species of particle at each site, i.e., Ei = ∑μ μ(ni, μ). The interaction between particles is not explicitly considered in this model, but particle blocking effects will be incorporated into the transition rate expressions. Then, the total energy at site μ of a given state is simply given by the summation of singleparticle energy at the site, μ(ni , μ) = ∑α Eμ0, αniα, μ. In principle, the energy of each state is also affected by the external field. The external field drives the system out of equilibrium (i.e., Boltzmann distribution is broken) and provides a driving force for particle transport. In this work, the effect of the external field is included in the driving force, as discussed later. The barrier Bij is the instantaneous energy of the system when a particle from site ν moves through the single-particle barrier Bαμν on its way to site μ with other particles remaining in their sites,39,40

We assume that the system has M sites and N species. The state 1 of the system is given by i = {ni,1, ..., ni,M}, where ni,μ = (ni,μ , ..., N ni,μ) denotes the occupation of each species of particle on site μ of state i. At the ensemble level, the system is described by the instantaneous probability distribution {Pi(t)} which evolves according to the master equation37−40 d Pi(t ) = dt

∑ R ijPj(t ) (1)

j

where Rij is the transition rate from state j to i and Rii = −∑j≠iRji. The corresponding probability current from state j to i is then given by Jij (t ) = R ijPj(t ) − R jiPi(t )

(2)

The first and second terms on the right-hand side (RHS) of the above equation denote the probability flux flowing from state j to i and i to j, respectively. The difference between the former and latter gives the net probability flux flowing from j to i. Once the probability distribution is known, the average density of particles on each site can be readily calculated through ⟨nαμ⟩ = α ∑iPini,μ . The sites of the system are typically chosen to be local energy minima associated with particles undergoing transport. In this work, it is assumed that only one particle may make a transition at any instant. Under this condition, the transition rate Rij is nonzero only when states i and j differ by the placement of a single particle. The placement of a single particle can be either particle transfer from site μ to site ν (j + eαμ − eαν → i) or particle exchange with bath (j ± eαμ → i), where +eαμ (−eαμ) denotes the injection (extraction) of a particle into (from) site μ. Hence, the particle currents, Jμν(t) from site ν to site μ, Jrμμ(t) from site μ to reservoir rμ and Jμrμ(t) from reservoir rμ to site μ, are given by α (t ) Jμν

=

∑ Jij (t ),

j+

e αμ

−

e αν

α Bij = Bμν +

σ≠ν

Bαμν

where is the barrier of moving α species of particle from site ν to μ. Since the energy of the initial state is Ej = ∑σ σ (nj, σ ), the energy difference along the transition is given by α Bij − Ej = Bμν + ν(nj , ν − e αν ) − ν(nj , ν)

μ

∑ Jij (t ),

α

→i

R ij = R 0njα, ν e j − e αμ → i

=

∑ Jij (t ),

j+

e αμ

R ij = R 0 e (3)

The key ingredient of the master equation approach is the transition rate between two states. Here we use the Arrhenius expression41 to represent the transition rate from j to i in terms of an energy barrier and driving force, R ij =

R 0njα, ν

e

(4)

njα, ν niα, μ

−β[Brαμμ − Eμ0, α − f rα μ /2]

,

μ

−β[Bμαrμ − μrα − f μαr /2] μ

μ

f μαr = (xrμ − xμ)qαEext +  αμrμ

,

j − e αμ → i j + e αμ → i

(6)

(7)

α

where xμ and q are the coordinates of the μth site and the charge of α particle, respectively. Eext is the strength of the external field.  αμν ( αμrμ ) in eq 7 accounts for other source of driving forces, such as binding and inner electrostatic interaction. As shown above, the transition rate, Rij, is dependent on a set α ,  αμν}. When the system is driven of parameters, {Eμ0, α , Eext , Bμν by a field that varies periodically in time (with periodicity τ), the barriers will also be periodic, and the system can relax to a periodic steady state. Once the system relaxes to a unique periodic steady state, Pi(t + τ) = Pi(t) is satisfied. The total number of transported particles over a time period τ is given by the integral,

where Bij is the barrier for the transition and Ej is the (free) energy of the state before the transition. The factor nαj,ν indicates the number of particles contributing to the currents. f ij = −f ji denotes external driving force due to coupling with some external agent, such as an external field. The load distribution factor 0 ≤ θij ≤ 1 describes how these forces affect the two transition rates. By definition, θij + θji = 1. In this work, θij = 1/2 is used. It is obvious to verify that the transition rates satisfy local detailed balance,42 R ij/R ji =

j + e αμ − e αν → i

,

α f μν = (xν − xμ)qαEext +  αμν

μ

−β[Bij − Ej − fij θij]

α − f μν /2]

Here μαrμ is the chemical potential of the bath rμ and fαμν accounts for the driving force for particle transport. Considering the influence of external field, the driving force can be written as

→i

i

0, α

R ij = R 0njα, ν e−β[Bμν − Eν

i

Jμαr (t ) μ

(5)

Consequently, the transition rate can be rewritten as

i

Jrαμ (t ) =

∑ σ (nj ,σ) + ν(nj ,ν − eαν )

e−β(Ei − Ej − fij ). Hence, the

kinetic master equation satisfies microscopic reversibility, as is essential for consistency with more fundamental molecular models (for instance molecular dynamics simulations). When 14497

DOI: 10.1021/acs.jpcc.6b03076 J. Phys. Chem. C 2016, 120, 14495−14501

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The Journal of Physical Chemistry C Φαμν =

∫t′

t ′+ τ

α Jμν (t ) d t

the binding site by the external field. Hence, a barrier for IDZ transport is introduced to mimic the effect of the external field on the dynamic transport of IDZ. Moreover, an additional parameter is introduced in this barrier that determines the effect of changing the concentration of IDZ. In short, the barriers of the three particles are assumed to be

(8)

Dynamic variation of barriers and driving force will typically generate nonzero integrated currents, and it is these currents that we will examine to determine pump efficiency and ion selectivity. In the next section, a two-site version of the kinetic master equation method is employed to study the protein pump driven by an external field. To adapt this model to the protein pump experiment,35 we consider three major species of particles: Histagged green fluorescence protein (GFP), bovine serum albumin protein (BSA), and imidazole (IDZ), with BSA and GFP negatively charged and IDZ positively charged. The external field is directed to the left bath in the release (pumping) cycle. In the two-site model the binding site in Figure 1 is taken to be site 1 and the permeate site is site 2. In the binding cycle, the positive bias applied to the gold surface attracts GFP and BSA to the binding site, and GFP is bound to NTA−Ni2+ on the inner surface of the pore. Binding of GFP blocks the pore and suppresses the transport of BSA. At the same time, positively charged IDZ is repelled from the binding surface by the positive bias voltage and pumped back to the permeate site. In the release/pumping cycle, the positive potential on the metal surface is removed and a large voltage is applied to the electrode pair outside of the membrane. Driven by the large external field, IDZ is able to transport from the permeate site to the binding site where GFP is released due to the stronger binding affinity between IDZ and NTA−Ni2+. Afterward, the released GFP is pumped to the permeate site driven by the external field. Considering two sites and three species of particles in the open systems and that each site can be either occupied or unoccupied by each species of particle, there are totally 23×2 = 64 states. The chemical potentials of BSA and GFP in each bath are assumed to be the same (μαrμ = 0). The intrinsic energy of each species of particle on the different sites is also considered to be zero, i.e., E0,α μ = 0. In addition, the intrinsic transition rate between sites R0 for the three species of particles are also assumed to be the same and is set as R0 = 1 for simplicity. All of the quantities are in units of KBT. For GFP, there is an additional attractive energy that accounts for the binding phenomena. The free energy change of the binding/dissociation reaction [C] (A + B ⇌ C) is ΔG = ln[KD] + ln [A][B] , where KD is the

GFP GFP B12 = B21 = −0.5 ln[δ + n1IDZ] + 1 BSA BSA B12 = B21 = −0.5 ln[δ + n1IDZ] − 0.5 ln[δ + 1 − n1GFP] IDZ B12 = a − E(t )

(9)

−3

δ = 10 is introduced to avoid divergence since the occupation number can only be 0 or 1. The factor a is taken as a parameter to control the density of IDZ. The external field is allowed to oscillate as a function of time using E(t) = 5 sin2(πt/τ), where the factor of 5 reflects the coupling (or strength) of the electric field to the charges on each species. Uptake of GFP/BSA from the left bath is also dependent on the concentration of IDZ on the binding site. At low IDZ density, GFP is more attracted by the NTA−Ni2+. Moreover, the presence of a positive potential in the binding cycle promotes the uptake of GFP/BSA. To mimic this attraction in the binding cycle, a driving force is applied to the uptake of GFP/BSA, which is modeled as GFP IDZ 1GFP + δ] r1 = −  r11 = − ln[n1 BSA GFP 1BSA + δ] + 4 r1 = − r11 = ln[1 − n1

(10)

The first line of eq 10 indicates that the attraction of GFP is enhanced at lower IDZ density. The second line of eq 10 demonstrates the blockage of BSA in the presence of GFP. It should be noted that, except for the barriers and driving forces defined in eqs 9 and 10, the other barriers and forces are set to zero. The coordinates of the baths and two sites in eq 7 (used in determining field strengths) are set as 1 1 1 1 [xr1 , x1 , x 2 , xr2] = ⎡⎣ − 2 , − 6 , 6 , 2 ⎤⎦.

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RESULTS AND DISCUSSION The evolution of the particle concentrations with different IDZ density is shown in Figure 3, where the periodicity of the external field is taken to be τ = 50. The corresponding fluxes

dissociation constant. For the case of binding GFP/IDZ to NTA−Ni2+, increasing the concentration of IDZ promotes the IDZ−Ni2+ binding and reduces the concentration of Ni2+. The change in concentration of Ni2+ is proportional to the density of IDZ. Consequently, the free energy change (ΔG) of GFP− Ni2+ binding is proportional to ln [⟨nIDZ 1 ⟩]. Since binding of GFP suppresses the mobility of GFP within the pore, the free energy change in binding reaction can be employed in determining the barrier for GFP transport. Therefore, this barrier is modeled as depending on the concentration of IDZ. In addition, binding of GFP to Ni2+ increases the concentration of GFP at the binding site, and as a result, transport of BSA is blocked due to the steric effect. Hence, the barrier for BSA transport is also modeled as a function of the GFP’s concentration. In the binding cycle, IDZ is repelled from the binding site when the positive potential is applied to the gold surface, while in the release/pumping cycle, IDZ is driven to

Figure 3. Evolution of concentrations under periodic external field. (a) Top left: a = 5. (b) Top right: a = 8. (c) Bottom left: a = 10. (d) Bottom right: a = 11.7. 14498

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Figure 5, respectively. This shows approximately exponential decay of selectivity with respect to density of IDZ. The

through the nanopore are plotted in Figure 4. From the upper left panel to the right bottom panel, the concentration of IDZ is

Figure 4. Particle flux through the nanopore under external field. (a) Top left: a = 5; ⟨nIDZ 1 ⟩ = 0.59; the selectivity S (defined as ΦGFP/ΦBSA) is 1.08. (b) Top right: a = 8; ⟨nIDZ 1 ⟩ = 0.20; S = 1.25. (c) Bottom left: a IDZ = 10; ⟨nIDZ 1 ⟩ = 0.036; S = 2.35. (d) Bottom right: a = 11.7, ⟨n1 ⟩ = 0.069; S = 7.87.

gradually reduced. In the upper left panel: the concentration of IDZ is higher than in the rest of the panels. Due to the high IDZ concentration, IDZ is more likely bound to NTA−Ni2+. Consequently, a large amount of GFP is released by IDZ. As shown in the figure, the concentration of GFP in the binding site drops significantly from 1 to 0.70 with increasing IDZ’s concentration from 0 to 1. Consequently, the nanopore is less crowded and the barrier for BSA transport is reduced. In this regime, the maximum BSA current can be as large as that of GFP as shown by the upper left panel of Figure 4. Hence, the calculated selectivity (defined as S = ΦGFP/ΦBSA) is 1.08, which means that the nanopore has no selectivity in pumping proteins in this regime. In order to pump GFP selectively, the transport of BSA should be suppressed. Thus, the concentration of GFP in the binding site should be neither too large nor too small. If the concentration is too large, it is easy to imagine that the transport of GFP is also totally blocked. On the other hand, if the GFP concentration in the binding site is too small, there is no blockage to BSA. The optimal condition is that the nanopore is partially blocked, in which case the transport of BSA is suppressed while GFP can go through the pore after release results from a limited amount of IDZ. Hence, the IDZ concentration should be carefully tuned to balance the GFP transport and protein selectivity. As shown in Figure 3, reducing the IDZ concentration leads to decrease of the released GFP and stronger blockage of BSA. Even though the flux of GFP is also reduced as result of binding to NTA−Ni2+ (as shown in Figure 4), this flux drops more slowly than for BSA since the balance between the binding and release enables the transport of GFP, while BSA is repelled from the binding site by GFP due to the steric effect. Accordingly, the selectivity is increased at the cost of reducing GFP flux. As shown in the right bottom panel of Figure 3, the selectivity can be quite high when the IDZ density is low enough. The selectivity between the two proteins and GFP flux are plotted against IDZ density in the top and bottom panels of

Figure 5. Selectivity between the GFP and BSA (top panel) and GFP flux (bottom panel) versus IDZ density (in blue), which shows qualitative agreement with experimental results (in red). Experimental data is taken from ref 21.

simulations of selectivity and GFP flux are qualitatively consistent with experimental measurements that are also plotted. The plots in Figure 5 indicates that low IDZ density promotes protein separation. But when the IDZ density is reduced, the flux of GFP is also significantly reduced even though selectivity is high. Since the external field is kept unchanged, decreasing the GFP flux corresponds to a drop in the pumping efficiency. Therefore, the concentration of IDZ should be tuned to balance the selectivity and pumping efficiency in practical applications.

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SUMMARY In summary, the kinetic master equation approach is a powerful tool to study transport in molecular machines, including machines that operate far from equilibrium. In this work, a simple two-site model is employed to study a recently developed field-driven protein pump that uses binding of His-tagged proteins in an artificial nanopore to achieve selectivity. In addition, MD simulations are employed to study the detailed binding mechanism, revealing the stable His/ NTA−Ni2+ binding configurations. The binding/pumping cycle in this artificial protein pump is modeled as depending on the barrier for particles to transition between sites on either end of the pore. The resulting model qualitatively describes the experimental measurements, especially the effect of imidazole on the selectivity for transport of the His-tagged protein 14499

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compared to another protein that is not tagged. The kinetic model demonstrated that the interactions between different species of particles play a crucial role on the selective transport of proteins. The model also shows that proper tuning of the binding/release cycle is critical to achieving high selectivity. Even though the barriers do not affect the equilibrium or steady-state distributions, they play crucial roles in determining the nonequilibrium flux. Even though the low IDZ concentration improves the pumping selectivity, this high selectivity is achieved at the cost of reducing pumping efficiency. In practical applications, balance between selectivity and pumping efficiency will be important. The qualitative agreement between the model and experimental observations suggests that the predictive power of the kinetic master model is good. In the current work, the barrier is assumed using empirical parameters. However, the barrier can be in principle be calculated from the potential of mean force (PMF) via molecular dynamics simulation. However, the PMF calculation is nontrivial due to the large length scale and time scale. A coarse-grained model may be an alternative way to obtain the PMF.43 The combination of coarse-grained model and kinetic master equation would provide a powerful method for modeling of molecular transport through nanopores for arbitrary time scale.

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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/acs.jpcc.6b03076. Details of molecular dynamics simulations (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +1 847-491-5657. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported as part of the Center for Bio-Inspired Energy Science, an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Basic Energy Sciences, under Award #DE-SC0000989-002. MD calculations were supported by NSF Grant CHE-1465045. Experimental data were supported by NSF CBET-1460922 and NIH NIDA R01DA018822.

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REFERENCES

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