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Sensing of protein molecules through nanopores: a molecular dynamics study
This content has been downloaded from IOPscience. Please scroll down to see the full text. 2014 Nanotechnology 25 155502 (http://iopscience.iop.org/0957-4484/25/15/155502) View the table of contents for this issue, or go to the journal homepage for more
Download details: IP Address: 138.100.4.44 This content was downloaded on 05/01/2015 at 14:22
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Nanotechnology Nanotechnology 25 (2014) 155502 (7pp)
doi:10.1088/0957-4484/25/15/155502
Sensing of protein molecules through nanopores: a molecular dynamics study Sridhar Kumar Kannam1 , Sung Cheol Kim1 , Priscilla R Rogers1 , Natalie Gunn1 , John Wagner2 , Stefan Harrer1 and Matthew T Downton2 1
IBM Research Australia, 204 Lygon Street, 3053 Carlton, Victoria, Australia IBM Research Collaboratory for Life Sciences—Melbourne, Victorian Life Sciences Computation Initiative, The University of Melbourne, Victoria, 3010, Australia 2
E-mail: [email protected] Received 1 December 2013, revised 28 January 2014 Accepted for publication 13 February 2014 Published 20 March 2014
Abstract
Solid-state nanopores have been shown to be suitable for single molecule detection. While numerous modeling investigations exist for DNA within nanopores, there are few simulations of protein translocations. In this paper, we use atomistic molecular dynamics to investigate the translocation of proteins through a silicon nitride nanopore. The nanopore dimensions and profile are representative of experimental systems. We are able to calculate the change in blockade current and friction coefficient for different positions of the protein within the pore. The change in ionic current is found to be negligible until the protein is fully within the pore and the current is lowest when the protein is in the pore center. Using a simple theory that gives good quantitative agreement with the simulation results we are able to show that the variation in current with position is a function of the pore shape. In simulations that guide the protein through the nanopore we identify the effect that confinement has on the friction coefficient of the protein. This integrated view of translocation at the nanoscale provides useful insights that can be used to guide the design of future devices. Keywords: nanopores, protein sensing, biomolecular detection, biosensors (Some figures may appear in colour only in the online journal)
1. Introduction
patch-clamp apparatus. Analytes, such as proteins, which are of similar size as the pore can then be placed in the solution and will be detected if they pass through the pore by a transient drop in the measured ionic current. Translocation events are typically characterized by the magnitude of the change in the current and its duration. Specificity for a particular molecule can be conferred by functionalizing the surface of the pore with an appropriate, assay specific coating, though there are alternatives. Niedzwiecki et al used highly specific RNA aptamers that bind to a target protein to detect its presence [1]. The combined aptamer and protein complex is too large to pass through the nanopore in their experiments leading to a change in the rate of translocation events. Silicon nitride (SiN) nanopores are frequently used in biomolecular detection due to their manufacturability and robustness. Han et al demonstrated the detection of BSA proteins [2], while Fologea and coworkers estimated the
Over the past decade, DNA sequencing using nanopore technology has received great interest due to its ability to probe the molecular details of single strands of DNA. Research in this area is still vigorous due to the obvious potential for creating a new generation of sequencing technologies that are rapid, cheap and ubiquitous. However, there is also great scope for generating new biosensors that do not rely on precise control and electronic sensing of molecules, but have much simpler designs based around surface functionalization and the long established technique of resistive pulse sensing. The principle on which these devices work is straightforward. A pore with size in the range 5–50 nm is drilled through a thin membrane and then submerged within an electrolyte. An external voltage applied across the membrane drives an ionic current through the pore that can be detected using a 0957-4484/14/155502+07$33.00
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change in the effective charge of BSA with variation in the pH of the solution [3]. Using the same pore, they also found a larger current drop was associated with the larger fibrinogen molecule. Plesa et al found anomalous translocation rates for small proteins due to their shorter translocation times and lower signal to noise ratio [4]. New designs have been developed which utilize functionalization of the pore or electrostatic trapping [5–8]. Several other studies have been carried out to study protein structure, conformation and folding using nanopores [9–11]. Reviews of sensing proteins and single molecules can be found in [12–17]. Simulation studies of biomolecular translocation through nanopores have focused attention on nucleic acids. Luan et al have investigated the control of single-stranded DNA in solidstate nanopores using electrostatic traps, pore coating and solvent viscosity [18–20]. Using coarse-grained modeling and Langevin dynamics, Kong and Muthukumar studied protein sensing in the α-hemolysin nanopore [21]. They investigated the effect of length and anchoring position of polyethylene glycol which is used to functionalize the pore. Gumbart and Schulten characterized the SecYEβ translocon by translocating alanine and leucine helices using MD simulations, demonstrating the flexibility of SecYEβ as a channel to conduct molecules [22]. Coarse-grained models have also been used to investigate the translocation and diffusion of small proteins in nanopores [23, 24]. The scope and breadth of previous work has to a certain extent been limited by the scale of simulations that can be attempted. In the following work, we use atomistic molecular dynamics simulations to investigate the translocation of a test protein through a solid-state nanopore that has a non-cylindrical profile. We measure the ionic current for several different situations in which one or more proteins are held at static positions within the pore. From this we extract the geometric dependence of the pore conductance on protein position. This is interpreted in terms of a commonly used framework for calculating the pore conductance adapted to a non-cylindrical pore. We then investigate the translocation of proteins through the pore. Since experimental translocation timescales are not currently accessible to atomistic molecular dynamics simulation we use the steered molecular dynamics (SMD) technique to guide proteins through the pore at an accelerated rate. After establishing a range of steering velocities that leave the protein conformationally stable, we examine the position dependent friction coefficient and the reorientation of the protein within the pore. Combining static and dynamic simulation protocols in this way allows us to create a picture of both the response of the pore ionic current to the presence of a protein and the change in the dynamics of the protein during its confinement within the pore.
Figure 1. Schematic representations of the systems studied. (a) The
SiN nanopore (gray) and protein (red, white, blue, green) are depicted in space-filling representations. The pore length is 20 nm, and has the hourglass profile shown with minimum and maximum diameters of 10 and 12.5 nm. The surface of the water box is shown in space-filling representation and potassium and chlorine atoms are shown as yellow and blue spheres (for clarity only 10% of the ions are shown). (b) The secondary and quaternary structure of streptavidin; the four monomers are represented in different colors. (c) Representations of the different systems studied where we have varied the position of the proteins and the number of proteins inside the pore. Only the SiN nanopore and the proteins are shown. (i) open pore, (ii)–(vii) one protein in the system, (ix)–(xi) two proteins inside the pore, and (xii) three proteins inside the pore.
aligned with the z-axis. For a test protein we use streptavidin (pdb access code: 1sws), a 52.8 kDa tetrameric molecule that has a radius of gyration of 2.2 nm. A secondary structure representation of the protein that shows its fold is shown in figure 1(b) with the four monomers given different colors. The pore and protein were solvated in 1 M aqueous potassium chloride solution and a hexagonal prism shaped periodic box was used with fluid reservoirs of 10 nm thickness on either side of the pore. Approximately 4700 atoms of each ion type were added to match the desired electrolyte density and ensure zero net charge for the entire system. Atomistic simulations that considered the interactions between all of the atoms in the simulation were performed using the NAMD molecular dynamics package [25] with the CHARMM force field [26] and the TIP3P water model; VMD was used for visualization and analysis [27]; a cut-off of 1.2 nm was used for non-bonded short-ranged interactions; and simulations were performed at a temperature of 295 K using a Langevin thermostat. In all cases, configurations were
2. Simulation details
The simulated pore consists of a SiN membrane of length 20 nm with the hourglass profile shown in figure 1(a). The pore diameter is 10 nm at its thinnest point and 12.5 nm at the pore entrance and exit. The origin of our coordinate system is placed at the center of the pore and its long axis is 2
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Figure 2. Results from static protein simulations. (a) Typical ionic current traces for open and protein occupied pores at voltage 5 V. The dotted lines represent the average current during the final 0.5 ns of simulation time. (b) Current as a function of voltage for open and protein occupied pores. The conductance of the pore measured from the plot is indicated on the plot; the inset shows the change in current between the two states as a function of voltage. (c) Variation in the conductance with the position of the protein. The shaded region from −10 to 10 nm represents the hourglass shape of the pore. The dotted line represents the open pore conductance when no protein is present in the system. The conductance drop predicted from equation (2) is shown as the blue solid line. (d) The drop in pore conductance for different numbers of proteins inside the pore. With one protein inside the pore, the current is averaged over the three configurations shown in figures 1(c) (ii), (iii) and (vi). Similarly for two proteins inside the pore, the current is averaged over the three configurations shown in figures 1(c) (ix), (x) and (xi). The system with three proteins inside the pore is shown in figure 1(c) (xii).
3. Results and discussion
first equilibrated in the NPT ensemble at atmospheric pressure with zero applied field before production runs at constant temperature. For the latter simulations, the thermostat was only applied to the SiN atoms and not the protein or solvent. As explained in the introduction, we used two different simulation methods to characterize the electrical response of the protein and pore system. In the first set of simulations, the protein or proteins were held at fixed positions within the pore, as shown in figure 1(c). In this case, the center of mass of the α-carbon atoms on the protein backbone was constrained using a harmonic spring of force constant 5 kcal mol−1 Å−2 . As the constraint was only applied to the center of mass it did not disturb the internal dynamics of the protein. Following this, we used the nonequilibrium SMD technique to pull the molecule through the pore at fixed velocity, vp along the z-axis. Pulling velocities in the range 2–128 nm ns−1 were used. To measure the instantaneous ionic current, I (t), the displacement of ions was monitored from snapshots of the system taken at fixed intervals. The current was then calculated as 1 X I (t) = qi [z i (t + 1t) − z i (t)], (1) 1t L
3.1. Protein at fixed positions within the pore
In this section we consider different configurations of the protein within the pore and the response of the ionic current to the applied external voltage. For a given steady state ionic current, I , and external voltage, V , the conductance can be calculated from Ohm’s law: G = I /V . The conductance captures information about the configuration of the protein in relation to the pore that we can use to characterize the translocation process. For instance, it should be possible to relate the magnitude of the drop in G to the size and shape of the translocating object. Following equilibration, we performed simulations of duration 1 ns. At the start of these simulations, the external electric field was applied causing the ionic current to flow. In figure 2(a), I (t) is shown for an applied voltage of 5 V for both open and occupied pores corresponding to states (i) and (ii) in figure 1(c). In both cases I (t) relaxes within 0.2 ns to a steady state value indicated by the dashed lines. Partially blocking the pore with the protein leads to a clearly discernible difference in the steady state value, I¯, as measured by averaging I (t) over the final 0.5 ns of the simulation trajectory. The magnitude of the peak-to-peak noise will depend on the duration of the sampling window during which current is averaged. For our simulations, this duration is 5 ps, but in experiment it will typically be of order microseconds. The thermal noise observed experimentally will therefore be less noticeable than seen in these simulations.
i∈pore
where L is the thickness of the membrane; qi and z i are the charge and z coordinate of the ith ion; and 1t is the time interval (5 ps for these simulations). For the simulation parameters described above, we performed bulk simulations of the electrolyte with an external field to measure its conductivity, finding a value 9.2 S m−1 . This can be compared with a reference value of 10.5 S m−1 [28]. 3
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Independent simulations for voltages in the range −5 V to +5 V are combined in figure 2(b) again corresponding to states (i) and (ii). Although this voltage range is considerably larger than that typically employed in experiments we find that I¯(V ) is linear across the range of voltages studied, and we are able to use linear regression to calculate the conductance for both states, finding the open pore conductance to be G (i) = 31.8 ± 0.2 nS and the conductance for a pore with the protein at its center to be G (ii) = 26.4 ± 0.3 nS. The difference between the two values of I¯(V ) is shown in the figure inset. Differences in conductance of the order of 5.4 nS have been measured experimentally [2, 3]. For voltages of 1 and 2 V, the average current was measured with the protein held at various positions along the pore axis (states (ii) to (vii) in figure 1(c)). The values of G from these simulations are compiled in figure 2(c) and compared with open pore conductance indicated by the dashed line. For positions outside the pore and up to the pore entrance, G is unchanged by the presence of the protein, only falling once the center of the protein is actually inside the pore. The minimum value of G is found at the center of the pore where the ratio of the pore and protein cross-sectional areas is lowest. Good agreement in the profile of G is found for both of the applied voltages. For very high concentrations of protein in the external reservoir, multiple translocation events can occur simultaneously. We can perform virtual experiments to test the additivity of the conductance change in this situation and simulated combinations of one, two and three proteins held at z = 0, ±6.5 nm as illustrated in configurations (ii), (iii), (vi) and (ix)–(xii) in figure 1(c). The resulting change in conductance from the open pore situation is shown in figure 2(d). As can be seen, the conductance drop is proportional to the number of proteins inside the pore, but is non-additive: the conductance drop increases by roughly a factor of 2 when the number of proteins is increased from one to three. The results of figure 2 can be interpreted in terms of a framework that, while simple, gives estimates of the pore conductivity that are of the same order of magnitude as those seen experimentally [29]. The effective resistance of an arbitrarily shaped pore can be estimated from 1 1 R= = G σ
Z
L/2 −L/2
dz + Racc , A(z) − A0 (z)
Figure 3. Results from protein translocation simulations with an
applied voltage 2 V for the pulling velocities 2, 64 and 128 nm ns−1 : (a) root mean squared deviation (RMSD) of the protein backbone compared with the initial conformation; (b) radius of gyration Rg ; (c) percentage of the protein residues forming β sheets, while the protein is pulled through the pore. The shaded region from −10 to 10 nm indicates the region that the protein is within the pore.
p where α = (D 2 − d 2 )/d, and d and D are the neck and entrance diameters of the pore. The second term in the above equation is the contribution from the access resistance [31]. The open pore conductance measured from simulations, 31.8 nS, is in agreement with the conductance 30.8 nS calculated using equation (3) with σ = 9.2 S m−1 . To compare the predictions of equation (2) with our simulation results, we consider a pore with identical dimensions and a spherical analyte with diameter 7 nm. This is plotted as the thick blue curve on figure 2(c) and shows reasonable quantitative agreement with the calculated simulation results. Again, this demonstrates that the principal determinant of the total current through the pore is related to the cross-sectional area that is available for ions to flow through. When the translocating object is at the center of the hourglass pore, this area is at its minimum value and the change in conductance is largest. We can also use the formula to predict the conductance change for pores occupied with multiple proteins, plotted as the diamonds in figure 2(d). In this case, the basic non-additive trend is conserved, but the conductance drop is consistently under predicted for two or more proteins.
(2)
where σ is the bulk conductivity of the electrolyte, Racc is the access resistance of the pore, and A(z) and A0 (z) are the cross-sectional areas of the hourglass shape pore and analyte at position z. The above expression does not take into account the variation in electric field and inhomogeneities in ion density that can affect the resistance. It also does not include the effects of surface charge, though expressions do exist to take this into account [30]. For an hourglass shape nanopore, the open pore resistance derived from equation (2) is Rhg =
4L 1 1 arctan(α) + , 2 σD σπd α
3.2. Steered translocation of proteins through the nanopore
In section 2 we measured the pore ionic current for situations where the protein was held fixed in position. We now move on to examine the stability and dynamics of the protein during translocation in a series of simulations that artificially guide the protein through the pore at an accelerated rate. Unless otherwise stated, the following simulations were performed with an external potential difference of 2 V. We first address the issue of conformational stability and the choice of an appropriate steering velocity, vp , that keeps the streptavidin tetramer intact. In figures 3(a)–(c) we
(3) 4
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Figure 4. Results from protein translocation simulations with an applied voltage of 2 V. (a) Force on the protein along the axial direction. (b) Force divided by vp . (c) Angle between the protein principal axis and the z-axis for two repetitions of steering simulations with vp = 2 and 4 nm ns−1 . (d) Ionic current through the pore. The red and black dotted lines indicate the open and protein occupied currents for a voltage of 2 V from figure 2(b); the black points indicate the data from figure 2(c). In all figures, the shaded region represents the position of the pore.
plot for representative steering simulations: the root mean squared deviation (RMSD); the radius of gyration, Rg ; and the proportion of residues that are in β-sheet structures. The RMSD measures the deviation in the conformation of the protein at time t from a reference structure, and is calculated through: v u N u1 X (ref) 2 RMSD(t) = t ri0 (t) − ri , (4) N
of the order of microseconds, several orders of magnitude longer than the forced translocations that we simulate here. We can estimate the extent to which we introduce inertial flows within the fluid through the Reynolds number, Re, which we estimate to be 0.05 for vp = 2 nm ns−1 . While this is reasonably low, it will certainly be the case that significantly higher pulling velocities will change the nature of fluid flow within the pore. From the steering simulations, we are able to retrieve the force, f(z), applied to the protein at each position along the translocation path. This is plotted in figure 4(a) for velocities in the range 2–64 nm ns−1 . The overall force increases for larger pulling velocities and some fine structure can be seen in each curve: the force increases as the protein approaches the pore entrance; gradually decreases while the protein translocates through the pore; and finally returns to the bulk value after the protein exits. If we assume an overdamped equation of motion for the protein center of mass of the form vz = f z /γ (z) + 0(t), where 0(t) is a thermal noise term, then we can calculate the position dependent friction, γ (z), plotted in figure 4(b). For intermediate values of vp there is reasonable collapse of the data onto a single curve. However, at lower pulling velocities the effects of thermal noise tend to dominate and the agreement is less clear. The gradual decrease in γ (z) while the protein passes through the pore is perhaps difficult to explain. In figure 4(c) we plot the angle between the protein principal axis and the z-axis for two repetitions of steering simulations at 2 and 4 nm ns−1 . We define this axis from the smallest eigenvector of the protein moment of inertia. In all simulations, the protein is started in a set orientation based on original x-ray crystal structure. During
i=1
where the sum runs over a subset of the atoms in the protein; we choose the α-carbon atoms on the protein backbone. The (ref) coordinates ri and ri0 (t) are the position of the ith atom in the reference structure and a copy of the simulation structure from (ref) time t that has been aligned against ri respectively. Along with Rg , the RMSD remained relatively constant for all but the highest velocity with which we steered the protein through the pore. For vp = 128 nm ns−1 , shown by the blue curve in the figure, Rg and the RMSD increase steadily throughout the simulation. The change in the secondary structure content indicates that this is at least partly due to internal changes in the conformation of each monomer from the streptavidin tetramer. A change in the quaternary structure of the molecule could also be a contributing factor. For this system we can conclude that steering velocities below 64 nm ns−1 will not lead to unnatural deformation of the protein during translocation. However, a further constraint that we have in performing simulations that accelerate the system dynamics is a requirement not to introduce any unnatural flows within the fluid. Typical experimental translocation times are 5
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translocation, we find that the protein reorients so that the long axis is aligned with the pore axis, reducing the translational drag coefficient. Finally, in figure 4(d), the ionic current through the nanopore is shown for different steering simulations and compared with the results from section 3.1. We find that I (z) has a similar profile for both the static and steered simulations, though the current calculated in the steering simulations tends to underestimate the magnitude of the change in current. Agreement is best for lower values of vp where the perturbation on the electrolyte surrounding the protein will be lower.
of this work to consider biomolecule specific surface functionalization, the effects of protein conformational changes, or changes in device shape and fabrication techniques. Acknowledgments
This research was supported by a Victorian Life Sciences Computation Initiative (VLSCI) grant number VR0224 on its Peak Computing Facility at the University of Melbourne, an initiative of the Victorian Government, Australia. References
4. Conclusion
[1] Niedzwiecki D J, Iyer R, Borer P N and Movileanu L 2013 Sampling a biomarker of the human immunodeficiency virus across a synthetic nanopore ACS Nano 7 3341–50 [2] Han A, Sch¨urmann G, Mondin G, Bitterli R A, Hegelbach N G, de Rooij N F and Staufer U 2006 Sensing protein molecules using nanofabricated pores Appl. Phys. Lett. 88 093901 [3] Fologea D, Ledden B, McNabb D S and Li J 2007 Electrical characterization of protein molecules by a solid-state nanopore Appl. Phys. Lett. 91 539011 [4] Plesa C, Kowalczyk S W, Zinsmeester R, Grosberg A Y, Rabin Y and Dekker C 2013 Fast translocation of proteins through solid state nanopores Nano Lett. 13 658–63 [5] Mohammad M M, Prakash S, Matouschek A and Movileanu L 2008 Controlling a single protein in a nanopore through electrostatic traps J. Am. Chem. Soc. 130 4081–8 [6] Rotem D, Jayasinghe L, Salichou M and Bayley H 2012 Protein detection by nanopores equipped with aptamers J. Am. Chem. Soc. 134 2781–7 [7] Kowalczyk S W, Kapinos L, Blosser T R, Magalh˜aes T, van Nies P, Lim R Y H and Dekker C 2011 Single-molecule transport across an individual biomimetic nuclear pore complex Nature Nanotechnol. 6 433–8 [8] Yusko E C, Johnson J M, Majd S, Prangkio P, Rollings R C, Li J, Yang J and Mayer M 2011 Controlling protein translocation through nanopores with bio-inspired fluid walls Nature Nanotechnol. 6 253–60 [9] Cressiot B, Oukhaled A, Patriarche G, Pastoriza-Gallego M, Betton J-M, Auvray L, Muthukumar M, Bacri L and Pelta J 2012 Protein transport through a narrow solid-state nanopore at high voltage: experiments and theory ACS Nano 6 6236–43 [10] Freedman K J, Haq S R, Edel J B, Jemth P and Kim M J 2013 Single molecule unfolding and stretching of protein domains inside a solid-state nanopore by electric field Sci. Rep. 3 1638 [11] Kowalczyk S W, Hall A R and Dekker C 2010 Detection of local protein structures along DNA using solid-state nanopores Nano Lett. 10 324–8 [12] Stoloff D H and Wanunu M 2013 Recent trends in nanopores for biotechnology Curr. Opin. Biotechnol. 24 699–704 [13] Howorka S and Siwy Z S 2012 Nanopores as protein sensors Nature Biotechnol. 30 506–7 [14] Miles B N, Ivanov A P, Wilson K A, Doˇgan F, Japrung D and Edel J B 2013 Single molecule sensing with solid-state nanopores: novel materials, methods, and applications Chem. Soc. Rev. 42 15–28 [15] Oukhaled A, Bacri L, Pastoriza-Gallego M, Betton J-M and Pelta J 2012 Sensing proteins through nanopores: fundamental to applications ACS Chem. Biol. 7 1935–49
We have investigated a computational model for sensing protein translocations through nanopores. Using this model, we have studied the interaction and translocation of streptavidin through a SiN nanopore. While the system was relatively small, the pore diameter and length are representative of possible experimental systems. We have applied two simulation strategies—examining proteins at fixed positions and protein translocations using SMD—to characterize the pore conductance and protein motion inside the pore. In the static protein simulations we found a linear dependence of the ionic current through the pore with variation in the external applied voltage. By changing the position of the protein within the pore, we were able to identify the non-cylindrical profile of the pore through the changing ionic current: for a protein at the pore entrance, the change in current was negligible; in the center of the pore, the protein takes up a larger fraction of the cross-sectional area of the pore and the change is maximized. Good quantitative agreement was found in comparing the results of simulations with a simple theory of ionic pore conductance. We also considered situations in which multiple proteins occupied the pore simultaneously. In this case, the change in current was not an integer multiple of the pore occupancy. This observation may hamper the ability to cleanly interpret ionic current traces in experimental systems for high concentrations of proteins in the reservoir. Since the typical translocation time is several orders of magnitude slower than timescales that are accessible in atomistic molecular dynamics simulations, we used SMD to guide proteins through the pore on a timescale of up to 10 ns. For lower translocation velocities we found that the protein was conformationally stable and were able to monitor the changes in the force required to pull the protein at a constant velocity. We interpret these changes in terms of the friction coefficient of the protein due to its confinement within the pore. Combining together the position dependence of the friction coefficient and current drop allows us to build a model of the current trace of a typical device: arrival of proteins at the pore entrance can be modeled as a Poisson process dependent only on the concentration of proteins in the reservoir and their diffusion coefficient; the actual translocation can then be modeled as a simple one-dimensional Langevin process. Studies such as this yield valuable information on the overall device properties of nanopore devices used for biosensor applications. It is of great interest to broaden the scope 6
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[16] Wanunu M 2012 Nanopores: a journey towards DNA sequencing Phys. Life Rev. 9 125–58 [17] Healy K 2007 Nanopore-based single-molecule DNA analysis Nanomedicine 2 459–81 [18] Luan B, Peng H, Polonsky S, Rossnagel S, Stolovitzky G and Martyna G 2010 Base-by-base ratcheting of single stranded DNA through a solid-state nanopore Phys. Rev. Lett. 104 06 [19] Luan B, Afzali A, Harrer S, Peng H, Waggoner P, Polonsky S, Stolovitzky G and Martyna G 2010 Tribological effects on DNA translocation in a nanochannel coated with a self-assembled monolayer J. Phys. Chem. B 114 17172–6 [20] Luan B, Wang D, Zhou R, Harrer S, Peng H and Stolovitzky G 2012 Dynamics of DNA translocation in a solid-state nanopore immersed in aqueous glycerol Nanotechnology 23 455102 [21] Kong C Y and Muthukumar M 2005 Simulations of stochastic sensing of proteins J. Am. Chem. Soc. 127 18252–61 [22] Gumbart J and Schulten K 2006 Molecular dynamics studies of the archaeal translocon Biophys. J. 90 2356–67 [23] Lee P-H, Helms V and Geyer T 2012 Coarse-grained Brownian dynamics simulations of protein translocation through nanopores J. Chem. Phys. 137 145105
[24] Javidpour L, Tabar M R R and Sahimi M 2009 Molecular simulation of protein dynamics in nanopores. II. Diffusion J. Chem. Phys. 130 085105 [25] Kal L, Skeel R, Bhandarkar M, Brunner R, Gursoy A, Krawetz N, Phillips J, Shinozaki A, Varadarajan K and Schulten K 1999 NAMD2: greater scalability for parallel molecular dynamics J. Comput. Phys. 312 283–312 [26] MacKerell A D Jr et al 1998 All-atom empirical potential for molecular modeling and dynamics studies of proteins J. Phys. Chem. B 102 3586–616 [27] Humphrey W, Dalke A and Schulten K 1996 VMD: visual molecular dynamics J. Mol. Graph. 14 33–8 [28] Haynes W M 2010 CRC Handbook of Chemistry and Physics 93rd edn (Boca Raton, FL: CRC Press) [29] DeBlois R W 1970 Counting and sizing of submicron particles by the resistive pulse technique Rev. Sci. Instrum. 41 909 [30] Smeets R M M, Keyser U F, Krapf D, Wu M-Y, Dekker N H and Dekker C 2006 Salt dependence of ion transport and DNA translocation through solid-state nanopores Nano Lett. 6 89–95 [31] Hall J E 1975 Access resistance of a small circular pore J. Gen. Physiol. 66 531–2
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Sensing of protein molecules through nanopores: a molecular dynamics study
This content has been downloaded from IOPscience. Please scroll down to see the full text. 2014 Nanotechnology 25 155502 (http://iopscience.iop.org/0957-4484/25/15/155502) View the table of contents for this issue, or go to the journal homepage for more
Download details: IP Address: 138.100.4.44 This content was downloaded on 05/01/2015 at 14:22
Please note that terms and conditions apply.
Nanotechnology Nanotechnology 25 (2014) 155502 (7pp)
doi:10.1088/0957-4484/25/15/155502
Sensing of protein molecules through nanopores: a molecular dynamics study Sridhar Kumar Kannam1 , Sung Cheol Kim1 , Priscilla R Rogers1 , Natalie Gunn1 , John Wagner2 , Stefan Harrer1 and Matthew T Downton2 1
IBM Research Australia, 204 Lygon Street, 3053 Carlton, Victoria, Australia IBM Research Collaboratory for Life Sciences—Melbourne, Victorian Life Sciences Computation Initiative, The University of Melbourne, Victoria, 3010, Australia 2
E-mail: [email protected] Received 1 December 2013, revised 28 January 2014 Accepted for publication 13 February 2014 Published 20 March 2014
Abstract
Solid-state nanopores have been shown to be suitable for single molecule detection. While numerous modeling investigations exist for DNA within nanopores, there are few simulations of protein translocations. In this paper, we use atomistic molecular dynamics to investigate the translocation of proteins through a silicon nitride nanopore. The nanopore dimensions and profile are representative of experimental systems. We are able to calculate the change in blockade current and friction coefficient for different positions of the protein within the pore. The change in ionic current is found to be negligible until the protein is fully within the pore and the current is lowest when the protein is in the pore center. Using a simple theory that gives good quantitative agreement with the simulation results we are able to show that the variation in current with position is a function of the pore shape. In simulations that guide the protein through the nanopore we identify the effect that confinement has on the friction coefficient of the protein. This integrated view of translocation at the nanoscale provides useful insights that can be used to guide the design of future devices. Keywords: nanopores, protein sensing, biomolecular detection, biosensors (Some figures may appear in colour only in the online journal)
1. Introduction
patch-clamp apparatus. Analytes, such as proteins, which are of similar size as the pore can then be placed in the solution and will be detected if they pass through the pore by a transient drop in the measured ionic current. Translocation events are typically characterized by the magnitude of the change in the current and its duration. Specificity for a particular molecule can be conferred by functionalizing the surface of the pore with an appropriate, assay specific coating, though there are alternatives. Niedzwiecki et al used highly specific RNA aptamers that bind to a target protein to detect its presence [1]. The combined aptamer and protein complex is too large to pass through the nanopore in their experiments leading to a change in the rate of translocation events. Silicon nitride (SiN) nanopores are frequently used in biomolecular detection due to their manufacturability and robustness. Han et al demonstrated the detection of BSA proteins [2], while Fologea and coworkers estimated the
Over the past decade, DNA sequencing using nanopore technology has received great interest due to its ability to probe the molecular details of single strands of DNA. Research in this area is still vigorous due to the obvious potential for creating a new generation of sequencing technologies that are rapid, cheap and ubiquitous. However, there is also great scope for generating new biosensors that do not rely on precise control and electronic sensing of molecules, but have much simpler designs based around surface functionalization and the long established technique of resistive pulse sensing. The principle on which these devices work is straightforward. A pore with size in the range 5–50 nm is drilled through a thin membrane and then submerged within an electrolyte. An external voltage applied across the membrane drives an ionic current through the pore that can be detected using a 0957-4484/14/155502+07$33.00
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change in the effective charge of BSA with variation in the pH of the solution [3]. Using the same pore, they also found a larger current drop was associated with the larger fibrinogen molecule. Plesa et al found anomalous translocation rates for small proteins due to their shorter translocation times and lower signal to noise ratio [4]. New designs have been developed which utilize functionalization of the pore or electrostatic trapping [5–8]. Several other studies have been carried out to study protein structure, conformation and folding using nanopores [9–11]. Reviews of sensing proteins and single molecules can be found in [12–17]. Simulation studies of biomolecular translocation through nanopores have focused attention on nucleic acids. Luan et al have investigated the control of single-stranded DNA in solidstate nanopores using electrostatic traps, pore coating and solvent viscosity [18–20]. Using coarse-grained modeling and Langevin dynamics, Kong and Muthukumar studied protein sensing in the α-hemolysin nanopore [21]. They investigated the effect of length and anchoring position of polyethylene glycol which is used to functionalize the pore. Gumbart and Schulten characterized the SecYEβ translocon by translocating alanine and leucine helices using MD simulations, demonstrating the flexibility of SecYEβ as a channel to conduct molecules [22]. Coarse-grained models have also been used to investigate the translocation and diffusion of small proteins in nanopores [23, 24]. The scope and breadth of previous work has to a certain extent been limited by the scale of simulations that can be attempted. In the following work, we use atomistic molecular dynamics simulations to investigate the translocation of a test protein through a solid-state nanopore that has a non-cylindrical profile. We measure the ionic current for several different situations in which one or more proteins are held at static positions within the pore. From this we extract the geometric dependence of the pore conductance on protein position. This is interpreted in terms of a commonly used framework for calculating the pore conductance adapted to a non-cylindrical pore. We then investigate the translocation of proteins through the pore. Since experimental translocation timescales are not currently accessible to atomistic molecular dynamics simulation we use the steered molecular dynamics (SMD) technique to guide proteins through the pore at an accelerated rate. After establishing a range of steering velocities that leave the protein conformationally stable, we examine the position dependent friction coefficient and the reorientation of the protein within the pore. Combining static and dynamic simulation protocols in this way allows us to create a picture of both the response of the pore ionic current to the presence of a protein and the change in the dynamics of the protein during its confinement within the pore.
Figure 1. Schematic representations of the systems studied. (a) The
SiN nanopore (gray) and protein (red, white, blue, green) are depicted in space-filling representations. The pore length is 20 nm, and has the hourglass profile shown with minimum and maximum diameters of 10 and 12.5 nm. The surface of the water box is shown in space-filling representation and potassium and chlorine atoms are shown as yellow and blue spheres (for clarity only 10% of the ions are shown). (b) The secondary and quaternary structure of streptavidin; the four monomers are represented in different colors. (c) Representations of the different systems studied where we have varied the position of the proteins and the number of proteins inside the pore. Only the SiN nanopore and the proteins are shown. (i) open pore, (ii)–(vii) one protein in the system, (ix)–(xi) two proteins inside the pore, and (xii) three proteins inside the pore.
aligned with the z-axis. For a test protein we use streptavidin (pdb access code: 1sws), a 52.8 kDa tetrameric molecule that has a radius of gyration of 2.2 nm. A secondary structure representation of the protein that shows its fold is shown in figure 1(b) with the four monomers given different colors. The pore and protein were solvated in 1 M aqueous potassium chloride solution and a hexagonal prism shaped periodic box was used with fluid reservoirs of 10 nm thickness on either side of the pore. Approximately 4700 atoms of each ion type were added to match the desired electrolyte density and ensure zero net charge for the entire system. Atomistic simulations that considered the interactions between all of the atoms in the simulation were performed using the NAMD molecular dynamics package [25] with the CHARMM force field [26] and the TIP3P water model; VMD was used for visualization and analysis [27]; a cut-off of 1.2 nm was used for non-bonded short-ranged interactions; and simulations were performed at a temperature of 295 K using a Langevin thermostat. In all cases, configurations were
2. Simulation details
The simulated pore consists of a SiN membrane of length 20 nm with the hourglass profile shown in figure 1(a). The pore diameter is 10 nm at its thinnest point and 12.5 nm at the pore entrance and exit. The origin of our coordinate system is placed at the center of the pore and its long axis is 2
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Figure 2. Results from static protein simulations. (a) Typical ionic current traces for open and protein occupied pores at voltage 5 V. The dotted lines represent the average current during the final 0.5 ns of simulation time. (b) Current as a function of voltage for open and protein occupied pores. The conductance of the pore measured from the plot is indicated on the plot; the inset shows the change in current between the two states as a function of voltage. (c) Variation in the conductance with the position of the protein. The shaded region from −10 to 10 nm represents the hourglass shape of the pore. The dotted line represents the open pore conductance when no protein is present in the system. The conductance drop predicted from equation (2) is shown as the blue solid line. (d) The drop in pore conductance for different numbers of proteins inside the pore. With one protein inside the pore, the current is averaged over the three configurations shown in figures 1(c) (ii), (iii) and (vi). Similarly for two proteins inside the pore, the current is averaged over the three configurations shown in figures 1(c) (ix), (x) and (xi). The system with three proteins inside the pore is shown in figure 1(c) (xii).
3. Results and discussion
first equilibrated in the NPT ensemble at atmospheric pressure with zero applied field before production runs at constant temperature. For the latter simulations, the thermostat was only applied to the SiN atoms and not the protein or solvent. As explained in the introduction, we used two different simulation methods to characterize the electrical response of the protein and pore system. In the first set of simulations, the protein or proteins were held at fixed positions within the pore, as shown in figure 1(c). In this case, the center of mass of the α-carbon atoms on the protein backbone was constrained using a harmonic spring of force constant 5 kcal mol−1 Å−2 . As the constraint was only applied to the center of mass it did not disturb the internal dynamics of the protein. Following this, we used the nonequilibrium SMD technique to pull the molecule through the pore at fixed velocity, vp along the z-axis. Pulling velocities in the range 2–128 nm ns−1 were used. To measure the instantaneous ionic current, I (t), the displacement of ions was monitored from snapshots of the system taken at fixed intervals. The current was then calculated as 1 X I (t) = qi [z i (t + 1t) − z i (t)], (1) 1t L
3.1. Protein at fixed positions within the pore
In this section we consider different configurations of the protein within the pore and the response of the ionic current to the applied external voltage. For a given steady state ionic current, I , and external voltage, V , the conductance can be calculated from Ohm’s law: G = I /V . The conductance captures information about the configuration of the protein in relation to the pore that we can use to characterize the translocation process. For instance, it should be possible to relate the magnitude of the drop in G to the size and shape of the translocating object. Following equilibration, we performed simulations of duration 1 ns. At the start of these simulations, the external electric field was applied causing the ionic current to flow. In figure 2(a), I (t) is shown for an applied voltage of 5 V for both open and occupied pores corresponding to states (i) and (ii) in figure 1(c). In both cases I (t) relaxes within 0.2 ns to a steady state value indicated by the dashed lines. Partially blocking the pore with the protein leads to a clearly discernible difference in the steady state value, I¯, as measured by averaging I (t) over the final 0.5 ns of the simulation trajectory. The magnitude of the peak-to-peak noise will depend on the duration of the sampling window during which current is averaged. For our simulations, this duration is 5 ps, but in experiment it will typically be of order microseconds. The thermal noise observed experimentally will therefore be less noticeable than seen in these simulations.
i∈pore
where L is the thickness of the membrane; qi and z i are the charge and z coordinate of the ith ion; and 1t is the time interval (5 ps for these simulations). For the simulation parameters described above, we performed bulk simulations of the electrolyte with an external field to measure its conductivity, finding a value 9.2 S m−1 . This can be compared with a reference value of 10.5 S m−1 [28]. 3
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Independent simulations for voltages in the range −5 V to +5 V are combined in figure 2(b) again corresponding to states (i) and (ii). Although this voltage range is considerably larger than that typically employed in experiments we find that I¯(V ) is linear across the range of voltages studied, and we are able to use linear regression to calculate the conductance for both states, finding the open pore conductance to be G (i) = 31.8 ± 0.2 nS and the conductance for a pore with the protein at its center to be G (ii) = 26.4 ± 0.3 nS. The difference between the two values of I¯(V ) is shown in the figure inset. Differences in conductance of the order of 5.4 nS have been measured experimentally [2, 3]. For voltages of 1 and 2 V, the average current was measured with the protein held at various positions along the pore axis (states (ii) to (vii) in figure 1(c)). The values of G from these simulations are compiled in figure 2(c) and compared with open pore conductance indicated by the dashed line. For positions outside the pore and up to the pore entrance, G is unchanged by the presence of the protein, only falling once the center of the protein is actually inside the pore. The minimum value of G is found at the center of the pore where the ratio of the pore and protein cross-sectional areas is lowest. Good agreement in the profile of G is found for both of the applied voltages. For very high concentrations of protein in the external reservoir, multiple translocation events can occur simultaneously. We can perform virtual experiments to test the additivity of the conductance change in this situation and simulated combinations of one, two and three proteins held at z = 0, ±6.5 nm as illustrated in configurations (ii), (iii), (vi) and (ix)–(xii) in figure 1(c). The resulting change in conductance from the open pore situation is shown in figure 2(d). As can be seen, the conductance drop is proportional to the number of proteins inside the pore, but is non-additive: the conductance drop increases by roughly a factor of 2 when the number of proteins is increased from one to three. The results of figure 2 can be interpreted in terms of a framework that, while simple, gives estimates of the pore conductivity that are of the same order of magnitude as those seen experimentally [29]. The effective resistance of an arbitrarily shaped pore can be estimated from 1 1 R= = G σ
Z
L/2 −L/2
dz + Racc , A(z) − A0 (z)
Figure 3. Results from protein translocation simulations with an
applied voltage 2 V for the pulling velocities 2, 64 and 128 nm ns−1 : (a) root mean squared deviation (RMSD) of the protein backbone compared with the initial conformation; (b) radius of gyration Rg ; (c) percentage of the protein residues forming β sheets, while the protein is pulled through the pore. The shaded region from −10 to 10 nm indicates the region that the protein is within the pore.
p where α = (D 2 − d 2 )/d, and d and D are the neck and entrance diameters of the pore. The second term in the above equation is the contribution from the access resistance [31]. The open pore conductance measured from simulations, 31.8 nS, is in agreement with the conductance 30.8 nS calculated using equation (3) with σ = 9.2 S m−1 . To compare the predictions of equation (2) with our simulation results, we consider a pore with identical dimensions and a spherical analyte with diameter 7 nm. This is plotted as the thick blue curve on figure 2(c) and shows reasonable quantitative agreement with the calculated simulation results. Again, this demonstrates that the principal determinant of the total current through the pore is related to the cross-sectional area that is available for ions to flow through. When the translocating object is at the center of the hourglass pore, this area is at its minimum value and the change in conductance is largest. We can also use the formula to predict the conductance change for pores occupied with multiple proteins, plotted as the diamonds in figure 2(d). In this case, the basic non-additive trend is conserved, but the conductance drop is consistently under predicted for two or more proteins.
(2)
where σ is the bulk conductivity of the electrolyte, Racc is the access resistance of the pore, and A(z) and A0 (z) are the cross-sectional areas of the hourglass shape pore and analyte at position z. The above expression does not take into account the variation in electric field and inhomogeneities in ion density that can affect the resistance. It also does not include the effects of surface charge, though expressions do exist to take this into account [30]. For an hourglass shape nanopore, the open pore resistance derived from equation (2) is Rhg =
4L 1 1 arctan(α) + , 2 σD σπd α
3.2. Steered translocation of proteins through the nanopore
In section 2 we measured the pore ionic current for situations where the protein was held fixed in position. We now move on to examine the stability and dynamics of the protein during translocation in a series of simulations that artificially guide the protein through the pore at an accelerated rate. Unless otherwise stated, the following simulations were performed with an external potential difference of 2 V. We first address the issue of conformational stability and the choice of an appropriate steering velocity, vp , that keeps the streptavidin tetramer intact. In figures 3(a)–(c) we
(3) 4
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Figure 4. Results from protein translocation simulations with an applied voltage of 2 V. (a) Force on the protein along the axial direction. (b) Force divided by vp . (c) Angle between the protein principal axis and the z-axis for two repetitions of steering simulations with vp = 2 and 4 nm ns−1 . (d) Ionic current through the pore. The red and black dotted lines indicate the open and protein occupied currents for a voltage of 2 V from figure 2(b); the black points indicate the data from figure 2(c). In all figures, the shaded region represents the position of the pore.
plot for representative steering simulations: the root mean squared deviation (RMSD); the radius of gyration, Rg ; and the proportion of residues that are in β-sheet structures. The RMSD measures the deviation in the conformation of the protein at time t from a reference structure, and is calculated through: v u N u1 X (ref) 2 RMSD(t) = t ri0 (t) − ri , (4) N
of the order of microseconds, several orders of magnitude longer than the forced translocations that we simulate here. We can estimate the extent to which we introduce inertial flows within the fluid through the Reynolds number, Re, which we estimate to be 0.05 for vp = 2 nm ns−1 . While this is reasonably low, it will certainly be the case that significantly higher pulling velocities will change the nature of fluid flow within the pore. From the steering simulations, we are able to retrieve the force, f(z), applied to the protein at each position along the translocation path. This is plotted in figure 4(a) for velocities in the range 2–64 nm ns−1 . The overall force increases for larger pulling velocities and some fine structure can be seen in each curve: the force increases as the protein approaches the pore entrance; gradually decreases while the protein translocates through the pore; and finally returns to the bulk value after the protein exits. If we assume an overdamped equation of motion for the protein center of mass of the form vz = f z /γ (z) + 0(t), where 0(t) is a thermal noise term, then we can calculate the position dependent friction, γ (z), plotted in figure 4(b). For intermediate values of vp there is reasonable collapse of the data onto a single curve. However, at lower pulling velocities the effects of thermal noise tend to dominate and the agreement is less clear. The gradual decrease in γ (z) while the protein passes through the pore is perhaps difficult to explain. In figure 4(c) we plot the angle between the protein principal axis and the z-axis for two repetitions of steering simulations at 2 and 4 nm ns−1 . We define this axis from the smallest eigenvector of the protein moment of inertia. In all simulations, the protein is started in a set orientation based on original x-ray crystal structure. During
i=1
where the sum runs over a subset of the atoms in the protein; we choose the α-carbon atoms on the protein backbone. The (ref) coordinates ri and ri0 (t) are the position of the ith atom in the reference structure and a copy of the simulation structure from (ref) time t that has been aligned against ri respectively. Along with Rg , the RMSD remained relatively constant for all but the highest velocity with which we steered the protein through the pore. For vp = 128 nm ns−1 , shown by the blue curve in the figure, Rg and the RMSD increase steadily throughout the simulation. The change in the secondary structure content indicates that this is at least partly due to internal changes in the conformation of each monomer from the streptavidin tetramer. A change in the quaternary structure of the molecule could also be a contributing factor. For this system we can conclude that steering velocities below 64 nm ns−1 will not lead to unnatural deformation of the protein during translocation. However, a further constraint that we have in performing simulations that accelerate the system dynamics is a requirement not to introduce any unnatural flows within the fluid. Typical experimental translocation times are 5
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translocation, we find that the protein reorients so that the long axis is aligned with the pore axis, reducing the translational drag coefficient. Finally, in figure 4(d), the ionic current through the nanopore is shown for different steering simulations and compared with the results from section 3.1. We find that I (z) has a similar profile for both the static and steered simulations, though the current calculated in the steering simulations tends to underestimate the magnitude of the change in current. Agreement is best for lower values of vp where the perturbation on the electrolyte surrounding the protein will be lower.
of this work to consider biomolecule specific surface functionalization, the effects of protein conformational changes, or changes in device shape and fabrication techniques. Acknowledgments
This research was supported by a Victorian Life Sciences Computation Initiative (VLSCI) grant number VR0224 on its Peak Computing Facility at the University of Melbourne, an initiative of the Victorian Government, Australia. References
4. Conclusion
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We have investigated a computational model for sensing protein translocations through nanopores. Using this model, we have studied the interaction and translocation of streptavidin through a SiN nanopore. While the system was relatively small, the pore diameter and length are representative of possible experimental systems. We have applied two simulation strategies—examining proteins at fixed positions and protein translocations using SMD—to characterize the pore conductance and protein motion inside the pore. In the static protein simulations we found a linear dependence of the ionic current through the pore with variation in the external applied voltage. By changing the position of the protein within the pore, we were able to identify the non-cylindrical profile of the pore through the changing ionic current: for a protein at the pore entrance, the change in current was negligible; in the center of the pore, the protein takes up a larger fraction of the cross-sectional area of the pore and the change is maximized. Good quantitative agreement was found in comparing the results of simulations with a simple theory of ionic pore conductance. We also considered situations in which multiple proteins occupied the pore simultaneously. In this case, the change in current was not an integer multiple of the pore occupancy. This observation may hamper the ability to cleanly interpret ionic current traces in experimental systems for high concentrations of proteins in the reservoir. Since the typical translocation time is several orders of magnitude slower than timescales that are accessible in atomistic molecular dynamics simulations, we used SMD to guide proteins through the pore on a timescale of up to 10 ns. For lower translocation velocities we found that the protein was conformationally stable and were able to monitor the changes in the force required to pull the protein at a constant velocity. We interpret these changes in terms of the friction coefficient of the protein due to its confinement within the pore. Combining together the position dependence of the friction coefficient and current drop allows us to build a model of the current trace of a typical device: arrival of proteins at the pore entrance can be modeled as a Poisson process dependent only on the concentration of proteins in the reservoir and their diffusion coefficient; the actual translocation can then be modeled as a simple one-dimensional Langevin process. Studies such as this yield valuable information on the overall device properties of nanopore devices used for biosensor applications. It is of great interest to broaden the scope 6
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[16] Wanunu M 2012 Nanopores: a journey towards DNA sequencing Phys. Life Rev. 9 125–58 [17] Healy K 2007 Nanopore-based single-molecule DNA analysis Nanomedicine 2 459–81 [18] Luan B, Peng H, Polonsky S, Rossnagel S, Stolovitzky G and Martyna G 2010 Base-by-base ratcheting of single stranded DNA through a solid-state nanopore Phys. Rev. Lett. 104 06 [19] Luan B, Afzali A, Harrer S, Peng H, Waggoner P, Polonsky S, Stolovitzky G and Martyna G 2010 Tribological effects on DNA translocation in a nanochannel coated with a self-assembled monolayer J. Phys. Chem. B 114 17172–6 [20] Luan B, Wang D, Zhou R, Harrer S, Peng H and Stolovitzky G 2012 Dynamics of DNA translocation in a solid-state nanopore immersed in aqueous glycerol Nanotechnology 23 455102 [21] Kong C Y and Muthukumar M 2005 Simulations of stochastic sensing of proteins J. Am. Chem. Soc. 127 18252–61 [22] Gumbart J and Schulten K 2006 Molecular dynamics studies of the archaeal translocon Biophys. J. 90 2356–67 [23] Lee P-H, Helms V and Geyer T 2012 Coarse-grained Brownian dynamics simulations of protein translocation through nanopores J. Chem. Phys. 137 145105
[24] Javidpour L, Tabar M R R and Sahimi M 2009 Molecular simulation of protein dynamics in nanopores. II. Diffusion J. Chem. Phys. 130 085105 [25] Kal L, Skeel R, Bhandarkar M, Brunner R, Gursoy A, Krawetz N, Phillips J, Shinozaki A, Varadarajan K and Schulten K 1999 NAMD2: greater scalability for parallel molecular dynamics J. Comput. Phys. 312 283–312 [26] MacKerell A D Jr et al 1998 All-atom empirical potential for molecular modeling and dynamics studies of proteins J. Phys. Chem. B 102 3586–616 [27] Humphrey W, Dalke A and Schulten K 1996 VMD: visual molecular dynamics J. Mol. Graph. 14 33–8 [28] Haynes W M 2010 CRC Handbook of Chemistry and Physics 93rd edn (Boca Raton, FL: CRC Press) [29] DeBlois R W 1970 Counting and sizing of submicron particles by the resistive pulse technique Rev. Sci. Instrum. 41 909 [30] Smeets R M M, Keyser U F, Krapf D, Wu M-Y, Dekker N H and Dekker C 2006 Salt dependence of ion transport and DNA translocation through solid-state nanopores Nano Lett. 6 89–95 [31] Hall J E 1975 Access resistance of a small circular pore J. Gen. Physiol. 66 531–2
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