Exploring transmembrane transport through -hemolysin with grid-steered moleculardynamicsDavid B. Wells, Volha Abramkina, and Aleksei Aksimentiev

Citation: The Journal of Chemical Physics 127, 125101 (2007); doi: 10.1063/1.2770738 View online: http://dx.doi.org/10.1063/1.2770738 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/127/12?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Voltage-controlled insertion of single -hemolysin and Mycobacterium smegmatis nanopores into lipid bilayermembranes Appl. Phys. Lett. 98, 083701 (2011); 10.1063/1.3558902 Folding simulations of gramicidin A into the -helix conformations: Simulated annealing molecular dynamics study J. Chem. Phys. 131, 165103 (2009); 10.1063/1.3247578 Study on the stability of the Quadruplex DNA Structure formed by the human telomeric repeat sequence d [ AG 3( TTAGGG ) 3 ] AIP Conf. Proc. 1071, 62 (2008); 10.1063/1.3033361 Effect of p H on the structure of lipoplexes J. Appl. Phys. 104, 014701 (2008); 10.1063/1.2949705 DNA translocation through -hemolysin nanopores with potential application to macromolecular data storage J. Appl. Phys. 97, 104317 (2005); 10.1063/1.1905791

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Exploring transmembrane transport through �-hemolysin with grid-steeredmolecular dynamics

David B. Wells,a� Volha Abramkina,b� and Aleksei Aksimentievc�

Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA andBeckman Institute for Advanced Science and Technology, University of Illinois at Urbana-Champaign,Urbana, Illinois 61801, USA

�Received 22 May 2007; accepted 19 July 2007; published online 25 September 2007�

The transport of biomolecules across cell boundaries is central to cellular function. While structuresof many membrane channels are known, the permeation mechanism is known only for a select few.Molecular dynamics �MD� is a computational method that can provide an accurate description ofpermeation events at the atomic level, which is required for understanding the transport mechanism.However, due to the relatively short time scales accessible to this method, it is of limited utility.Here, we present a method for all-atom simulation of electric field-driven transport of large solutesthrough membrane channels, which in tens of nanoseconds can provide a realistic account of apermeation event that would require a millisecond simulation using conventional MD. In thismethod, the average distribution of the electrostatic potential in a membrane channel under atransmembrane bias of interest is determined first from an all-atom MD simulation. Thiselectrostatic potential, defined on a grid, is subsequently applied to a charged solute to steer itspermeation through the membrane channel. We apply this method to investigate permeation of DNAstrands, DNA hairpins, and �-helical peptides through �-hemolysin. To test the accuracy of themethod, we computed the relative permeation rates of DNA strands having different sequences andglobal orientations. The results of the G-SMD simulations were found to be in good agreement inexperiment. © 2007 American Institute of Physics. �DOI: 10.1063/1.2770738�

I. INTRODUCTION

�-hemolysin is a bacterial toxin that self-assembles in alipid membrane to form a water-filled transmembrane pore.1

Applying a transmembrane electric potential, solutes of vari-ous molecular weights can be admitted into the channel, in-cluding rather long �up to 1300 nucleotides� single DNA andRNA strands.2,3 The presence of a solute in the channel re-duces the transmembrane ionic current below the open porelevel, which can be used to identify the solute’s type andconcentration.4 Such ionic current blockades in �-hemolysinhave been used to detect small organic analytes,5 metal ions,6

drugs,7 peptides,8 DNA hairpins,9 modified DNA strands,10

proteins,11,12 and to detect rupture events in nanopore forcespectroscopy experiments.13,14 In the case of DNA and RNAstrands, the level of the ionic current blockades depends onthe sequence of the nucleotide fragment confined in the poreconstriction,2,15–17 which in principle can be used to create adevice for high-throughput DNA sequencing.18,19

Although �-hemolysin has been successfully employedas a stochastic sensor in a number of studies, the ionic cur-rent recordings have limited utility, as the level of the ioniccurrent blockade is determined not only by the atomic-detailstructure of the solute, but also by the solute’s microscopicconformation. Hence, to unambiguously interpret the ionic

current recordings, the microscopic conformation of the sol-ute in �-hemolysin has to be determined to atomic resolu-tion. Direct experimental visualization of solute conforma-tion in �-hemolysin is not currently possible.

Molecular dynamics �MD� is a computational methodthat can provide a realistic account of a transmembrane per-meation event.20–30 In this method, a biomolecular system isrepresented by an ensemble of particles that move and inter-act according to the laws of classical mechanics.31 Recently,this method was employed to relate the microscopic confor-mations of DNA in �-hemolysin to the measured ionic cur-rent blockades, revealing that DNA’s global orientation is asignificant factor determining the current blockade.32 Due tothe recent dramatic advances in computational technology,33

the ionic conductance of �-hemolysin can now be accuratelycomputed from all-atom MD simulations.34 Nevertheless, itis still not feasible to simulate using the “brute-force” ap-proach to the permeation of larger solutes, such as DNA andproteins, since typical permeation times of such solutes rangefrom tens of microseconds to milliseconds. In this article, wepresent a computational method that, in tens of nanoseconds,can provide a realistic account of a permeation event thatwould require a millisecond simulation using conventionalMD.

One of the methods developed to overcome the timescale limitation of MD is steered molecular dynamics�SMD�.35,36 In this method, an external force is applied to asolute to facilitate the crossing of free-energy barriers in thechannel, thus reducing the permeation time scale. The ap-

a�Electronic mail: dbwells2@uiuc.edub�Electronic mail: abramkina@gmail.comc�Author to whom correspondence should be addressed. Present address:

Department of Physics, University of Illinois, 1110 W. Green St., Urbana,IL 61801; Tel.: �217� 333-6495; Electronic mail: aksiment@uiuc.edu

THE JOURNAL OF CHEMICAL PHYSICS 127, 125101 �2007�

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plied force is usually implemented by attaching a movingharmonic �spring-like� restraint to one or more atoms in thesystem.35–37 The outcome of many repetitive SMD simula-tions can be related to the profile of the potential of meanforce in the channel through Jarzinsky’s identity.38,39

Coarser-scale simulations of membrane transport, althoughable to describe the general features of the permeationprocess,40–44 by their very design cannot reveal a permeationmechanism that is sensitive to atomic-scale details.

Although SMD is a popular method to investigate per-meation of small solutes through membrane channels,30,45,46

the application of conventional SMD is troublesome in thecase of long linear biopolymers, such as proteins, nucleicacids, or any other biomolecules that are or may transientlybecome structurally disordered during the permeation pro-cess. If a steering force is applied to a terminal of such asolute, this force is likely to distort the solute’s conformation,e.g., overstretch DNA or unfold a protein. An example ofsuch an SMD simulation is shown in Figs. 1�a�–1�d�. Be-cause the time scale of the SMD simulation is too short forrelaxation forces to act in response to the strain produced bythe steering force, the solute enters the channel in a distorted,physiologically unfeasible conformation. Applying the SMDforce to the center of mass of the solute produces similardistortions, as shown in Figs. 1�e�–1�h�.

An alternative method for accelerating the permeationprocesses is to scale up the transmembrane potential thatdrives the solutes across the cell membrane. This methodwas recently employed to simulate the permeation of ionsand DNA through biological and artificial membranes.32,34,47

However, the maximum transmembrane bias that can be ap-plied in such simulations is limited by the stability of themembrane, as a lipid bilayer in an MD simulation is prone tobreaking when the transmembrane bias exceeds �2 V. Thisleads to ion leakage, which subsequently distorts the drivingpotential and thereby results in a simulation of an unrealisticpermeation event. Applying a uniform external electrostaticfield only to the solute’s atoms fails to produce a successfultranslocation, as illustrated in Figs. 1�i�–1�l�.

Here we present a generalization of the SMD methodol-ogy tailored to simulations of membrane potential-driventransport of large solutes. In order to simulate a permeationevent, we amplify the three-dimensional �3D� electrostaticpotential derived from an all-atom MD simulation34 and ap-ply it to the permeating solute only. By doing so we facilitatefaster translocation of solutes without straining the structureof the channel or the membrane. Moreover, as the shape ofthe potential applied to the solutes in our method exactlymatches the transmembrane potential driving the solutes inexperiment, the field of forces is very realistic, and becausethe forces are distributed over the entire solute, the strainintroduced into the solute’s conformation is much smallerthan that introduced by conventional SMD. An example ofsuch a simulation is shown in Figs. 1�m�–1�p�.

In this study, we apply the Grid-SMD �G-SMD� methodto simulate the translocation of DNA through �-hemolysin.First, we investigate how the translocation rate of a DNAstrand depends on the magnitude of the applied potential andexamine the strain introduced into the DNA conformation.Next, we compare the results of G-SMD simulations to ex-periment by measuring the translocation velocity of DNAstrands of different sequences and global orientations. Fi-nally, we apply our method to simulate the permeation of aDNA hairpin and of an �-helical peptide through�-hemolysin, and discuss the limitations and possible arti-facts of the G-SMD method.

II. METHODS

A. Microscopic model of �-hemolysin

An all-atom model of the �-hemolysin channel as-sembled with a lipid bilayer was constructed, simulated, andtested extensively as described in Ref. 34. Atomic coordi-nates of �-hemolysin were taken from the Protein Data Bank�entry 7AHL�. Coordinates of the atoms missing from thecrystallographic structure were reconstructed using the psf-gen structure building module of NAMD.33 All histidine resi-dues were assigned the HSE protonation state �pH 8.0conditions�.34 Water molecules were placed in the internalcavities of the protein using the Dowser program.48 Follow-ing that, a 3 Å layer of water was created around the entireprotein using the Solvate program,36 which also populatedthe transmembrane pore and the seven side channels withwater. The resulting structure was oriented in space to align

FIG. 1. �Color� SMD simulations of DNA translocation through�-hemolysin. �a�–�d� SMD force applied to the phosphorous atom of thefirst nucleotide of the DNA strand. The DNA stretches as it traversesthrough the pore constriction. This 3 ns simulation was done using an SMDpulling velocity of 43 Å/ns and a spring constant of 500 kcal/mol·Å2.�e�–�h� SMD force applied to the center of mass of the DNA strand. �i�–�l�DNA permeation driven by a uniform electric field. This simulation wasperformed by applying constant forces to individual DNA atoms. The mag-nitude of each force was computed as a product of the atomic charge and theelectric field equivalent to a 12 V transmembrane bias. The total simulationtime is 4 ns. �m�–�p� G-SMD simulation of DNA translocation. The trans-membrane bias was set to 1.2 V with the scaling factor of N=10 �seeMethods�. The total simulation time is 5 ns. Animations of these trajectoriesare available in the supplementary information �Ref. 58�.

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the symmetry axis of the transmembrane pore with the z axis.Next, the protein was embedded in a patch of a pre-equilibrated and solvated DPPC lipid bilayer. All lipid mol-ecules that overlapped with the protein stem were removed,along with all water molecules around the stem of the proteinthat overlapped with the lipid bilayer. The protein-lipid com-plex was solvated in a rectangular volume of pre-equilibratedTIP3P �Ref. 49� water molecules. Corresponding to a solu-tion concentration of 1 M, K+, and Cl− ions were added atrandom positions located at least 4 Å away from the protein,DNA and membrane, and 3 Å away from each other. Theresulting system measured 135�137�148 Å3 and included288 678 atoms. Following 2000 steps of minimization withall protein atoms fixed, the system was equilibrated in theNpT ensemble for 1.3 ns with the backbone of the proteinrestrained, and for another 3.0 ns without any restraints.34

B. Microscopic models of single-strandedDNA/�-hemolysin

Single strands of DNA were threaded through the�-hemolysin pore using the phantom pore procedures de-scribed in detail in Refs. 32 and 50. A 58-base pair double-stranded DNA helix was built from individual base pairs inthe geometry suggested by Quanta.51 Single-stranded DNAwas obtained from that structure by removing one of thestrands. The remaining strand was then solvated in a pre-equilibrated volume of TIP3P water molecules; K+ and Cl−

ions were added, corresponding to a 1 M concentration. Theresulting system was equilibrated for 12 ns. The poly�dA�58,poly�dC�58, and poly�dAdC�29 strands were constructed fromthe equilibrated DNA strand by replacing DNA bases withadenine or cytosine.

In order to thread a DNA strand through the�-hemolysin pore, KCl electrolyte was built around a DNAstrand, conforming to the shape of the �-hemolysin pore.32

The shape of the �-hemolysin pore was represented by amathematical surface, which we refer to as a phantom pore.Initially, the phantom pore was made 2 nm wider in diameterthan the pore of �-hemolysin, so that the entire 58-nucleotidestrand could fit into it. The pore was then gradually shrunk ina 2 ns simulation to the shape of the �-hemolysin pore. Atthe same time, 10 pN forces pushed all atoms laying outsideof the shrinking surface toward the center of the pore. At theend of the simulation, the DNA strand adopted a straightconformation that conformed to the shape of the�-hemolysin pore. We carried out two such simulations �inthe NpT ensemble� corresponding to the two global orienta-tions of the DNA strand inside the pore. Each DNA strand, aswell as the ions found in the stem region of the phantompore, were merged with the all-atom model of the�-hemolysin channel. In the resulting structure, water andions covered the DNA strand completely; one such system isshown in Fig. 2�a�. The final systems measured 135�137�183 Å3 and included 356 065 atoms in the case ofpoly�dA�58, 355 952 atoms in the case of poly�dC�58, and356 005 atoms in the case of poly�dAdC�29. Following 2000steps of minimization with all DNA atoms fixed, each systemwas equilibrated for 2 ns in the NpT ensemble.

C. Microscopic model of Z-DNA hairpin/�-hemolysin

The atomic coordinates of a5�-d�CGCGCGTTTTCGCGCG�-3� Z-DNA hairpin weretaken from the Protein Data Bank �code 1D16�. Two CGbase pairs were added at the end of the double-stranded por-tion of the hairpin. The resulting structure was placed in a0.13 M aqueous solution of KCl, and, after a short minimi-zation, was equilibrated for 5 ns at 295 K in the NpT en-semble. During the equilibration, the root mean square de-viation of the DNA structure from the x-ray model fluctuatedwithin 1.75 Å. The equilibrated model of the hairpin wasmerged with �-hemolysin, placing the hairpin into the open-ing of the channel that connects the vestibule with the ciscompartment �see Fig. 2�a� for the cis/trans conventionused�. The termini of the hairpin were located at the level ofthe Asp4 ring of the channel, whereas the loop of the hairpinprotruded outside of the vestibule. The number of ions in thesystem was adjusted to ensure the system’s overall neutrality.The final system �288 618 atoms� was minimized keepingcoordinates of all DNA atoms fixed, and equilibrated for 0.7ns at 295 K. For the first 50 000 steps �50 ps� of the equili-bration, harmonic restraints were applied to the protein,DNA and the lipid bilayer.

D. Microscopic model of �-helicalpeptide/�-hemolysin

A microscopic model of an �-helical peptide was con-structed by mutating the sequence of a template �-helix �Pro-tein Data Bank code 1HTM� into the desired sequence: ML-SRQQSQRQSRQQSQRQSRYLL. The resulting structurewas equilibrated at 310 K in 1 M KCl solution for 8 ns in theNpT ensemble. During the equilibration the peptide pre-served its �-helical structure �95% of the total structure�. Theequilibrated peptide was aligned with the symmetry axis of�-hemolysin. The N-terminal of the peptide was placed at

FIG. 2. �Color� The setup of G-SMD simulations. �a� Microscopic model ofthe �-hemolysin/DNA system suspended in a lipid bilayer membrane. TheDNA atoms are drawn as orange spheres. The channel is drawn as a mo-lecular surface �violet� separating the protein from the membrane and water.This surface is cut by a plane perpendicular to the lipid bilayer, passingthrough the geometrical center of the protein. The DPPC lipid bilayer isshown in green, water and ions are not shown. The stem and vestibulesections of the protein are indicated; the constriction, the narrowest part ofthe channel, lies between them. The model comprises of 356 065 atoms. �b�The electrostatic potential map of �-hemolysin. The figure shows a cutthrough the averaged �over a 5.3 ns MD simulation and the sevenfold sym-metry of �-hemolysin� electrostatic potential along the z axis. A 1.2 V trans-membrane bias was applied in this simulation. This 3D potential is used inour G-SMD simulations to drive translocation of DNA through�-hemolysin.

125101-3 Exploring transmembrane transport J. Chem. Phys. 127, 125101 �2007�

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the level of the Lys131 ring, which is located near the transside entrance into the channel. All water molecules within1.5 Å of the peptide were removed. The resulting systemwas neutral and comprised 288 743 atoms. The system un-derwent 2000 steps of minimization, followed by gradualheating from 0 to 298 K in 10 ps, and subsequent 80 psequilibration. For the first 50 ps of the equilibration coordi-nates of the peptide were restrained by harmonic constraints.

III. MD METHODS

All our MD simulations were performed using the pro-gram NAMD,33 periodic boundary conditions and particlemesh ewald �PME� full electrostatics52 with a dielectric con-stant �=1. PME was computed using a grid spacing of�1.1 Å per grid point in each dimension. Systems com-prised entirely of water, ions and nucleic acids were simu-lated using the AMBER95 �Ref. 53� force field; theCHARMM27 �Ref. 54� force field was employed for allother systems. The temperature was kept at 295 K by apply-ing Langevin forces55 to all heavy atoms; the Langevindamping constant was set to 1 ps−1. The integration timestepchosen was 1 fs. The equilibration in the NpT ensemble wasperformed using the Nosé-Hoover Langevin piston pressurecontrol56 at 1 bar. Van der Waals energies were calculatedusing a smooth �10−12 Å� cutoff. Restraints were imposedby harmonic forces; the force constants were set to1 kcal/mol·Å2. All simulations in an external electric fieldwere carried out in the NVT ensemble.

A. Electrostatic potential

The procedures for determining the average distributionof an electrostatic potential from MD trajectories were de-scribed in detail elsewhere.34 A 5.3 ns simulation of the�-hemolysin system containing no DNA was carried outwhile applying a uniform external electric field equivalent toa 1.2 V bias. The simulation produced 5300 snapshots of thesystem configuration. For every configuration, an instanta-neous distribution of the electrostatic potential was computedusing the PME electrostatics module of NAMD.33 The in-stantaneous potentials were averaged over the entire MD tra-jectory and over the sevenfold symmetry of �-hemolysin. Aslice through such a potential along the xz plane is shown inFig. 2�b�. The electrostatic potential used in our G-SMDsimulation was computed over a 96�96�96 grid usingGaussians of width �=0.395 Å−1.

B. Grid-SMD simulations

To carry out G-SMD simulations, the systems weresimulated in the NVT ensemble, applying an external electricfield equivalent to a 1.2 V bias. Steering forces derived fromthe 3D distribution of the electrostatic potential were appliedto all atoms of DNA using either a tclforces script or a cus-tom version of NAMD. These forces were computed fromthe finite differences of the potential and were scaled withthe charge of the DNA atoms and with the scaling factor N.Only the z components of the forces were applied. In ourG-SMD simulations, we varied the scaling factor N from 0 to10, thereby changing the effective bias from 1.2 to 13.2 V in

the z direction �effective bias is �N+1��1.2 V�. No steeringforce was applied in the xy plane. To keep the potentialaligned with the protein, the latter was restrained throughharmonic forces applied to the �-carbon atoms. Future ver-sions of NAMD will incorporate G-SMD capabilities.

C. Rate of DNA transport

To quantitatively characterize translocation of DNAthrough �-hemolysin, we adapted the method used for com-puting ionic currents.34,47,57 An instantaneous current ofDNA nucleotides was computed as

IDNA�t� =1

�tLMDNA�

i

mi�zi�t + �t� − zi�t�� , �1�

where zi and mi are the z coordinate and the mass of atom i,respectively, L is the extension of the system along the di-rection of the current, and MDNA is the mass of one nucle-otide. The sum in Eq. �1� runs over all DNA atoms in thevolume of interest, which in our case was either the entirechannel or the channel’s constriction. To compute the aver-age translocation velocity at a given bias, instantaneous cur-rents of DNA nucleotides IDNA�t� were first integrated withrespect to time to produce a cumulative current curve; apply-ing a linear regression fit to the cumulative current curveyielded the average translocation velocity.

IV. RESULTS

After the systems comprising DNA, �-hemolysin, lipidbilayer membrane, water and ions were assembled andequilibrated �see Methods�, external fields of different mag-nitudes were applied to the DNA, and the resulting displace-ments of the DNA in the channel were recorded. All simula-tions were carried out applying an electric field equivalent toa 1.2 V transmembrane bias to all atoms in the system.34,47,57

In addition, the z component of the forces derived from theaverage distribution of the electrostatic potential were multi-plied by the scaling factor N and applied to DNA atoms only.The steering forces were not applied in the x and y direc-tions. A table summarizing the results of all MD simulationsperformed is provided in the supplementary information.58

First, we investigate how the introduction of a steeringpotential influences the velocity of DNA translocation. InFig. 3 we plot the cumulative number of permeated nucle-otides against the simulation time for four G-SMD runs inwhich the steering field was applied with the scaling factor Nof 1, 3, 7, and 10. In the same plot we display the results ofa simulation without a steering field, i.e., N=0 �a 1.2 V trans-membrane bias was applied in all simulations�. The DNAwas observed to permeate the channel faster at larger steer-ing fields. In the inset to Fig. 3 we plot the average DNAtranslocation velocity against the effective bias applied, i.e.,�N+1��1.2 V. The DNA translocation velocity was ob-served to scale superlinearly with the effective bias until N=3. Note that at N=3, the translocation velocity is about 1nucleotide per nanosecond, approximately 1000 times fasterthan in experiment.

In order to assess the conformational strain introducedby our method, we analyzed the number of nucleotides in the

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vestibule, constriction and stem �see Fig. 2�a�� as a functionof time. The results of this analysis are shown in Fig. 4. Wefound that for N=1 or 3, the number of nucleotides in thestem remained nearly constant, indicating that virtually noconformational strain was introduced �the rising number ofnucleotides in the vestibule results from DNA relaxation;compare the N=0 case�. The strain remained modest forhigher values of N. We thus conclude that N=3, i.e., an ef-fective bias of 4.8 V, is optimal for G-SMD simulations, as itdoes not distort the conformation of the DNA in �-hemolysinwhile still substantially accelerating its movement. In allsimulations, the hydrophobic stacking of the DNA bases isbroken in the constriction, as it is too narrow for the DNAstrand to fit in the base-stacked conformation. In the stemand in the vestibule the DNA strand is split into groups of

2–4 nucleotides that preserve the base-stacking pattern. Thestructure of the lipid bilayer and of the protein is unaffectedby the steering potential, as it is applied to atoms of DNAonly.

We next investigate whether G-SMD can provide quan-titative insights into the mechanics of DNA translocation,despite the dramatic reduction of the translocation time scale.It has been experimentally shown that the global orientationof a DNA strand in the �-hemolysin channel has a determin-istic effect on the velocity of DNA translocation: when asingle DNA strand of adenine nucleotides �poly�dA� strand�is driven by a transmembrane bias,32 the translocation veloc-ity of the DNA strand in the direction of its 3�-end is about16% higher than that in the direction of its 5�-end. To testwhether G-SMD can capture this rather subtle difference ofthe translocation velocities, we set up two systems in whicha poly�dA�58 strand was threaded through �-hemolysin intwo global orientations, �cis� 3�−dA58−5� �trans� �referredto as A5�� and �cis� 5�-dA58-3� �trans� �A3��. Refer to Fig. 2for the cis/trans convention used in this article. For eachorientation of the poly�dA�58 strand, we carried out fourG-SMD simulations applying an effective bias equivalent to9.6 V, and four simulations at 13.2 V. In Fig. 5, we plot thecumulative number of translocated nucleotides for thepoly�dA�58 systems at a 13.2 V effective bias, indicating bythe color of the lines the orientation of the DNA strand in thepore. In the same figure, we plot a linear regression fit to thecumulative current curves averaged over the four simulations�symbols�. The slope of the fit yields the average transloca-tion velocity 11.2±0.4 nucleotides/ns for A3� and 8.8±0.4nucleotides/ns for A5�; the error is the 90% confidence in-terval estimated from the standard deviation of the currenttraces of the four runs taken together. The same systems at a9.6 V effective bias produced translocation velocities of7.4±0.2 nucleotides/ns for A3� and 6.4±0.2 nucleotides/nsfor A5�, or a ratio of 1.16±0.05, in excellent agreement withthe experimental ratio of 1.16±0.05.32 Hence, we concludethat although the absolute values of the translocation veloci-

FIG. 3. �Color online� Dependence of DNA translocation velocity on steer-ing potential. The total number of nucleotides translocated is plotted againstthe simulation time. Black triangles, white triangles, diamonds, and squaresindicate simulations carried out at a 1.2 V electrostatic field magnified 11, 8,4, and 2 times, respectively; the circles correspond to the simulation carriedout at a 1.2 V bias �no steering force applied�. �Inset� Translocation velocityversus the effective bias. These simulations were carried out using apoly�dA�58 strand in the A5� orientation �5� end of DNA on the trans side;see Fig. 2�a��.

FIG. 4. �Color online� Influence of the driving potential on the conformationof DNA in �-hemolysin. The number of nucleotides in the vestibule �a� andin the stem �b� of the channel are shown as functions of the simulation time.The symbols indicate the scaling of the driving potential: N=0 �circles�,N=1 �squares�, N=3 �diamonds�, N=7 �white triangles�, and N=10 �blacktriangles�. Each trace for N=7 or 10 is an average over four trajectories.These simulations correspond to DNA in the A5� orientation �5� end ofDNA on the trans side; see Fig. 2�a��.

FIG. 5. �Color� Effect of global orientation on DNA translocation velocity.The total number of nucleotides translocated is plotted against the simula-tion time. The chart plots the results of eight simulations, four for each ofthe two global orientations of a poly�dA�58 strand. Red and blue lines cor-respond to A3� �3� end of DNA on the trans side; see Fig. 2�a�� and A5�orientations of the strand; squares and circles indicate a linear regression fitto the above sets of four trajectories. The insets illustrate the conformationsof a poly�dA�58 strand in the �-hemolysin pore.

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ties are much higher than the experimental ones, their ratio isin agreement with experiment.32

It was suggested in Ref. 32 that tilting of the DNA basestoward the 5�-end of the strand in the constriction of�-hemolysin is the molecular origin of the observed direc-tionality of the DNA translocation. However, the conven-tional MD simulation employed in that study could sampleonly a rather small part of the translocation trajectory, inwhich the displacement of DNA originated mostly from therelaxation of the DNA conformation in response to the ap-plied electric field. Using G-SMD we could, for the firsttime, not only simulate the entire translocation of a DNAstrand through �-hemolysin but also carry out our simula-tions multiple times. Visual analysis of the MD trajectoriesconfirmed the original suggestion of Mathé et al.32 that re-orientation of the DNA bases in the constriction of�-hemolysin is responsible for the observed directionality. Inthe insets to Fig. 5 we display conformations of two DNAstrands identical in sequence but different in their global ori-entations. When a DNA strand enters the pore with its 5�-endfirst, the base stacking is more likely to be disrupted due tothe preferential tilt of the DNA bases toward the 5�-end inthe constriction. Animations illustrating translocation ofDNA through �-hemolysin in both orientations are availablein the supplementary information.58

Another factor that can affect the velocity of DNA trans-location is the sequence of the DNA strand. The most prob-able translocation rates of poly�dA�100, poly�dAdC�50 andpoly�dC�100 single-stranded DNA at 25 °C were measured at1.92, 1.36, and 0.76 �s/base, respectively, at a 120 mVdriving bias.15 The global orientation of the strands was notresolved in those experiments. To investigate whetherG-SMD could capture the effect of the DNA sequence on thetranslocation velocity, we carried out twelve additional simu-lations on the system that included a poly�dC�58 strandthreaded through �-hemolysin in two global orientations,�cis� 3�-dC58-5� �trans� �C5�� and �cis� 5�-dC58-3� �trans��C3��, as well as a system of poly�dAdC�29 in one orienta-tion, �cis� 5�-�dAdC�29-3� �trans� �AC3��. These simulationswere carried out using a steering potential of intermediatestrength �N=7� corresponding to a 9.6 V effective bias. Foursimulations at N=3 were also conducted. In Fig. 6 we plotthe cumulative currents for each of the three sequences in thesame global orientation. We found that the poly�dC�58 strandpermeates the pore faster than the poly�dAdC�29 strand,which in turn permeates the pore faster than poly�dA�58,which is in qualitative agreement with experiment.15 As theglobal orientation of poly�dC� strands was not resolved inexperiment, direct quantitative comparison between simula-tion and experiment is not possible. Nevertheless, we notethat the ratios of the translocation velocities obtained withG-SMD are systematically smaller than the ratios of the mostprobable translocation times observed in experiment. For ex-ample, in our simulations we observed poly�dC�58 to moveabout 1.65 times faster than poly�dA�58 in the direction of the3�-end of the strand, whereas the ratio of the most probabletranslocation times is about 2.5 in experiment.15 At this timewe do not know the exact reason for this quantitative dis-crepancy. We note, however, that our G-SMD simulations

were designed to minimize the interactions between DNAand the cap of �-hemolysin, which can arrest the transloca-tion process �see supplementary information.58� Also, we ob-served no anomalously long translocation events forpoly�dA� that, in experiment, result in a very broad distribu-tion of the poly�dA� translocation times.

The ratio of the translocation velocities at differentstrengths of the steering potential is shown in Fig. 7. As inthe case of poly�dA�58, for poly�dC�58 we observed fastertranslocation in the direction of the 3� end of the strand atboth N=3 and N=7. The ratio of the 3�- to 5�-first translo-cation velocities for poly�dA�58 is in the 1.1–1.2 range forN=3, 7, and 10. Overall, the ratio of the translocation veloci-ties was not observed to change dramatically with the scalingof the steering potential for the scaling factors considered.We note, however, that for very large steering potentials, thehydrodynamic drag force on DNA should become compa-rable to the friction forces between the stem of �-hemolysinand DNA, which obviously will reduce the influence of thesequence on the translocation velocity.

FIG. 6. �Color� Effect of sequence on DNA translocation velocity. The totalnumber of nucleotides translocated is plotted against the simulation time.The chart plots the results of 12 simulations, 4 for each of poly�dC�58,poly�dAdC�29 and poly�dA�58, all in the �cis� 5�-3� �trans� orientation �seeFig. 2�a��. Traces of the four trajectories are shown for each sequence,represented by thin lines, as well as linear regression fits indicated by blackdiamonds, red squares and blue circles, corresponding to poly�dC�58,poly�dAdC�29, and poly�dA�58, respectively.

FIG. 7. �Color online� DNA current ratios. Selected DNA current ratios areshown comparing orientation or sequence at different effective biases, e.g.,IC3� / IC5� is the ratio of the nucleotide current of the �cis� 5�-dC58-3� �trans�system to that of the �cis� 3�-dC58-5� �trans� system. Error bars indicate 90%confidence interval estimated from the standard deviations of the currenttraces.

125101-6 Wells, Abramkina, and Aksimentiev J. Chem. Phys. 127, 125101 �2007�

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Some of the permeation traces noticeably deviate from astraight line; an exemplary trajectory is presented in Fig. 8.In some parts of the trajectory, the velocity of DNA translo-cation changes abruptly. Such “steps” in the DNA transloca-tion, however, do not correspond to the translocation of in-dividual nucleotides, as there are fewer steps in thetranslocation traces than nucleotides translocated through thepore. To verify that our procedure for computing DNA cur-rents, which involves integration over the entire volume of�-hemolysin, did not conceal some events that could be as-sociated with the translocation of individual nucleotides, wecomputed the DNA current through the constriction of�-hemolysin only. One such trace in shown Fig. 8 as adashed line. The steps in the resulting traces are sharper, butthe number of steps remains the same. Visual inspection ofthe translocation trajectories with VMD �Ref. 59� revealedthat the steps are associated with broken base stacking of theDNA strand entering the constriction, indicated by the ar-rows in Fig. 8. Two example base conformations are shown

as insets. Thus, our G-SMD simulations suggest that perme-ation of DNA through the constriction of �-hemolysin takesplace in pulses of 2–4 nucleotides that preserve the basestacking pattern of an unconfined strand.

To further explore the capabilities of the G-SMDmethod, we attempted to simulate permeation of a DNA hair-pin and of an �-helical peptide through �-hemolysin. Figures9 and 10, as well as the animations available in the supple-mentary information,58 illustrate the resulting MD trajecto-ries.

It has been suggested that the loop of the hairpin is toobig to fit through the opening in the �-hemolysin cap,9 andthat, in order to permeate through the pore, the hairpin has tounzip. To test whether our G-SMD method can capture thesekey features of the permeation kinetics, we placed a DNAhairpin half-way through the entrance to �-hemolysin’s ves-tibule from the cis side, such that the hairpin loop protrudedoutside of the pore, as shown in Fig. 9�a�. Using the standardprotocol of the G-SMD method, we applied an external po-tential to steer permeation of the hairpin, using a rather largescaling factor of N=15 �the translocation times of DNA hair-pins in experiment are in the millisecond range�. Within thefirst nanosecond of the simulation, the hairpin was observedto slide into the cap’s mouth; the terminal base pair of thehairpin frayed within the first 0.4 ns of the simulation. Thetranslocation halted, however, when the loop reached thelevel of Lys8 residues of �-hemolysin. After about 1.2 ns,one end of the DNA was captured by the constriction of thechannel. The electrostatic force exerted on the capturednucleotides pulled down the rest of the strand, as shown inFig. 9�b�. At this time, half of the hairpin loop slid down intothe vestibule and stem as the hairpin unzipped. The unzippedhairpin moved quickly through the constriction in noticeablesteps. At one point more than one DNA strand was observedto pass through the constriction of �-hemolysin, which couldbe an artifact of using a steering potential that is too high.Future simulations will reveal if such events can indeed takeplace. After about 2.0 ns, all DNA left the vestibule of thepore, shown in Fig. 9�c�. Within the next nanosecond, thehairpin slid down the �-hemolysin stem and adhered to thering of charged residues near the exit from the stem on thetrans side, shown in Fig. 9�d�. Although a more careful simu-lation using a smaller scaling factor needs to be performedbefore any definitive conclusion about the kinetics of hairpintranslocation can be drawn, this preliminary simulation dem-

FIG. 8. �Color online� Steps in DNA current traces. Exemplary traces ofDNA current are shown, both through the entire channel �solid line� as wellas through the constriction only �dashed line�. Rather than a smooth lineartrace, simulations of this system displayed a pronounced steplike current.Inspection with the program VMD �Ref. 59� revealed the steps to be asso-ciated with breaks in the base stacking structure of the DNA entering theprotein constriction, causing temporary halts in the translocation followedby surges of DNA current. Times at which the base stacking was broken inthe constriction are marked by the arrows. The insets show the conforma-tions of the nucleotides in the constriction �Thr145 to Val149� for the struc-ture breaks at 0 ns �left� and 1.9 ns �right�. This simulation corresponds toDNA in the A5� orientation �5� end of DNA on the trans side; see Fig. 2�a��at a 9.6 V effective bias.

FIG. 9. �Color� G-SMD simulation of DNA hairpin translocation through �-hemolysin. This simulation was performed using the scaling factor N=15. TheDNA hairpin is shown in yellow. The snapshots illustrate the conformation of the hairpin at the beginning of the simulation �a�, and after 1.4 �b�, 2.0 �c�, and4.2 ns �d�.

125101-7 Exploring transmembrane transport J. Chem. Phys. 127, 125101 �2007�

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onstrates the wealth of information that can be obtained withG-SMD.

The last system that we used to explore the capabilitiesof G-SMD included a 23-residue �-helix that was initiallyplaced near the entrance to the �-hemolysin stem from thetrans side, as shown in Fig. 10�a�. As the total charge of thepeptide is +4e, we used the same potential as that used toinduce DNA translocation from the cis side. Under a steeringfield with N=10, the peptide was observed to move veryquickly into the pore, until its N-terminus reached the pore’sconstriction, as shown in Fig. 10�b�. The helix maintained its�-helical structure. For the next 14.7 ns, the peptide movedvery slowly through the constriction region of the pore. Inorder to squeeze through the constriction, a few turns of the�-helix unwound. Although after 17.7 ns more than a half ofthe peptide’s residues passed through the �-hemolysin con-striction �Fig. 10�c��, the translocation appeared to be ar-rested due to the interactions between the charged groups ofthe peptide and the charged groups of �-hemolysin at thebottom of the vestibule. Increasing the strength of the steer-ing field by a factor of two �N=20� did not appear to dra-matically accelerate the translocation. The artifacts of such astrong steering potential are evident in Fig. 10�d�: thecharged residues of the peptide aligned along the field linesof the applied potential. Although in this simulation we werenot able to observe a complete permeation event, the simu-lation revealed the transformation of the secondary structureof the peptide in the stem and the constriction regions of�-hemolysin. A longer simulation with a smaller steeringfield is required to reveal how the peptide leaves the porethrough the vestibule of �-hemolysin.

In both simulations, one common artifact of the G-SMDsimulations became apparent: under some conditions, thetranslocation can get arrested in one of the local minima ofthe steering potential. Adding a stochastic component to thedriving potential should enable escape from such localminima, which is the subject of ongoing research.

V. DISCUSSION AND CONCLUSIONS

We have developed and tested the extension of theSteered Molecular Dynamics method to simulations of elec-tric field-driven permeation of large solutes through mem-brane channels. In tens of nanoseconds this method can pro-vide a realistic account of permeation events that wouldrequire millisecond simulations with standard MD. The de-

coupling of the electric field driving the solutes through thechannel from the electric field acting on the rest of the sys-tem allows us to apply high effective biases without affectingthe system’s integrity, greatly reducing the permeation timescale. As the SMD forces in our method act on the entiresolute via a smooth 3D potential, the strain introduced intothe solute’s conformation is small, comparable to the strainobserved during a standard MD simulation.

Using the G-SMD method we investigated the mechan-ics of DNA permeation through �-hemolysin. Our simula-tions revealed that the base-stacking of nucleotides in singleDNA strands has a significant effect on the DNA transloca-tion velocity in �-hemolysin. Our G-SMD results support themolecular mechanism proposed in Ref. 32 to explain thedependence of the DNA translocation velocity on the globalorientation of the DNA strands in the channel, i.e., the pref-erential tilt of the DNA bases toward the 5�-end of the strandnear the channel’s constriction. Due to the dramatic reduc-tion of the translocation time scale and small distortions thatG-SMD introduces into the solute’s conformation, we couldcarry out multiple simulations of the same permeation pro-cess and characterize the outcome in statistical terms. Theoutcome of such simulations can provide the sequence-specific information required for a realistic coarser-scale de-scription of the translocation process.40–44,60–63

Our initial motivation for developing the G-SMDmethod was to enable characterization of the conformationsof large solutes during their transport through �-hemolysin.The results of our simulations demonstrate that the G-SMDmethod can adequately describe permeation not only of lin-ear DNA strands but also of DNA hairpins and small pep-tides. The ensemble of conformations resulting from aG-SMD run can be related to the measured ionic currentblockages using standard MD �Ref. 34� or othermethods.64,65 Next, we investigated if, in addition to screen-ing possible conformations of the solute in the pore, theG-SMD method can adequately describe permeation kineticsand relative translocation velocities. For this purpose we car-ried out G-SMD simulations on DNA strands of differentsequences and global orientations. The obtained ratios of thesimulated translocation velocities of DNA strands in differ-ent global orientations were in excellent quantitative agree-ment with experiment. The ratio of the translocation veloci-ties of DNA homopolymers of different sequence were foundin semiquantitative agreement with experiment. Such good

FIG. 10. �Color� G-SMD simulation of peptide translocation through �-hemolysin. For the first 17.7 ns of this simulation the scaling factor N was set to 10.The scaling factor was increased to 20 for the last 3.8 ns. The peptide atoms are shown as van der Waals spheres colored according to the residue type:positively charged �blue�, uncharged polar �green�, and nonpolar �white�. The snapshots show the conformation of the peptide at the beginning of thesimulation �a�, and after 3 �b�, 17.7 �c�, and 21.5 ns �d�.

125101-8 Wells, Abramkina, and Aksimentiev J. Chem. Phys. 127, 125101 �2007�

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agreement with experiment is encouraging given that ourmethod reduces the permeation time 1000-fold.

G-SMD has proven to be an effective technique forprobing certain processes that cannot be accurately describedusing SMD. As with SMD, however, the magnitude of thesteering forces must be carefully chosen to ensure that thesimulated trajectories correspond to experiment. Ideally, themagnitude of the applied forces and the time scale of thesimulation should allow relaxation forces to dissipate thestrain introduced by the G-SMD protocol.

The G-SMD method extends the applicability of atomic-scale simulations to processes that were previously off-limits. Among the topics to be addressed in the future aremechanisms of protein translocation through membranechannels, selectivity of ion channels and transporters, simu-lations of nanopore devices for high-throughput sequencingof DNA and proteins, and, eventually, the transport of bio-molecules in nanofluidic systems. In addition to studies ofmembrane transport, the G-SMD method is expected to findapplication in multiscale modeling, cryoelectron microscopydata fitting, in developing implicit models of biomaterials,and for simulations of nanoscale hydrodynamics. TheG-SMD method will be further developed to enhance ran-dom forces producing stochastic motion of the solutes in thechannel, to employ a self-consistent electrostatic potential�i.e., one calculated during the G-SMD simulation� to steerpermeation of solutes, and to provide methods for extractingthe potential of mean force from G-SMD trajectories.

ACKNOWLEDGMENTS

This work was supported by the grants from the NationalInstitutes of Health �PHS 5 P41 RR05969 and R01-HG003713�, and the Department of Physics at the Universityof Illinois. The authors gratefully acknowledge supercom-puter time at the Pittsburgh Supercomputer Center and theNational Center for Supercomputing Applications providedvia the Large Resources Allocation Committee Grant No.MCA05S028, as well as time on the Turing cluster at theUniversity of Illinois.

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