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Saharia J, Bandara YMNDY, Kim MJ. Investigating protein translocation in the presence of an electrolyte concentration gradient across a solid-state nanopore. Electrophoresis 2022; 43:785-792. [PMID: 35020223 DOI: 10.1002/elps.202100346] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/27/2021] [Revised: 11/19/2021] [Accepted: 12/22/2021] [Indexed: 12/21/2022]
Abstract
Electrolyte chemistry plays an important role in the transport properties of analytes through nanopores. Here, we report the translocation properties of the protein human serum transferrin (hSTf) in asymmetric LiCl salt concentrations with either positive (Ctrans /Ccis < 1) or negative chemical gradients (Ctrans /Ccis > 1). The cis side concentration was fixed at 4 M for positive chemical gradients and at 0.5 M LiCl for negative chemical gradients, while the trans side concentration varied between 0.5 to 4 M which resulted in six different configurations, respectively, for both positive and negative gradient types. For positive chemical gradient conditions, translocations were observed in all six configurations for at least one voltage polarity whereas with negative gradient conditions, dead concentrations where no events at either polarity were observed. The flux of Li+ and Cl- ions and their resultant cation or anion enrichment zones, as well as the interplay of electrophoretic and electroosmotic transport directions, would determine whether hSTf can traverse across the pore.
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Affiliation(s)
- Jugal Saharia
- Department of Mechanical Engineering, Southern Methodist University, Dallas, TX, USA
| | - Y M Nuwan D Y Bandara
- Department of Mechanical Engineering, Southern Methodist University, Dallas, TX, USA.,Department of Bioengineering, University of California, Riverside, CA, USA
| | - Min Jun Kim
- Department of Mechanical Engineering, Southern Methodist University, Dallas, TX, USA
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2
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Bandara YMNDY, Saharia J, Karawdeniya BI, Kluth P, Kim MJ. Nanopore Data Analysis: Baseline Construction and Abrupt Change-Based Multilevel Fitting. Anal Chem 2021; 93:11710-11718. [PMID: 34463103 DOI: 10.1021/acs.analchem.1c01646] [Citation(s) in RCA: 17] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
Solid-state nanopore technology delivers single-molecule resolution information, and the quality of the deliverables hinges on the capability of the analysis platform to extract maximum possible events and fit them appropriately. In this work, we present an analysis platform with four baseline fitting methods adaptive to a wide range of nanopore traces (including those with a step or abrupt changes where pre-existing platforms fail) to maximize extractable events (2× improvement in some cases) and multilevel event fitting capability. The baseline fitting methods, in the increasing order of robustness and computational cost, include arithmetic mean, linear fit, Gaussian smoothing, and Gaussian smoothing and regressed mixing. The performance was tested with ultra-stable to vigorously fluctuating current profiles, and the event count increased with increasing fitting robustness prominently for vigorously fluctuating profiles. Turning points of events were clustered using the dbscan method, followed by segmentation into preliminary levels based on abrupt changes in the signal level, which were then iteratively refined to deduce the final levels of the event. Finally, we show the utility of clustering for multilevel DNA data analysis, followed by the assessment of protein translocation profiles.
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Affiliation(s)
- Y M Nuwan D Y Bandara
- Department of Electronic Materials Engineering, Research School of Physics, Australian National University, Canberra, Australian Capital Territory 2601, Australia
| | - Jugal Saharia
- Department of Mechanical Engineering, Southern Methodist University, Dallas, Texas 75275, United States
| | - Buddini I Karawdeniya
- Department of Electronic Materials Engineering, Research School of Physics, Australian National University, Canberra, Australian Capital Territory 2601, Australia
| | - Patrick Kluth
- Department of Electronic Materials Engineering, Research School of Physics, Australian National University, Canberra, Australian Capital Territory 2601, Australia
| | - Min Jun Kim
- Department of Mechanical Engineering, Southern Methodist University, Dallas, Texas 75275, United States
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3
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Saharia J, Bandara YMNDY, Karawdeniya BI, Hammond C, Alexandrakis G, Kim MJ. Modulation of electrophoresis, electroosmosis and diffusion for electrical transport of proteins through a solid-state nanopore. RSC Adv 2021; 11:24398-24409. [PMID: 34354824 PMCID: PMC8285365 DOI: 10.1039/d1ra03903b] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/19/2021] [Accepted: 07/03/2021] [Indexed: 01/01/2023] Open
Abstract
Nanopore probing of molecular level transport of proteins is strongly influenced by electrolyte type, concentration, and solution pH. As a result, electrolyte chemistry and applied voltage are critical for protein transport and impact, for example, capture rate (CR), transport mechanism (i.e., electrophoresis, electroosmosis or diffusion), and 3D conformation (e.g., chaotropic vs. kosmotropic effects). In this study, we explored these using 0.5–4 M LiCl and KCl electrolytes with holo-human serum transferrin (hSTf) protein as the model protein in both low (±50 mV) and high (±400 mV) electric field regimes. Unlike in KCl, where events were purely electrophoretic, the transport in LiCl transitioned from electrophoretic to electroosmotic with decreasing salt concentration while intermediate concentrations (i.e., 2 M and 2.5 M) were influenced by diffusion. Segregating diffusion-limited capture rate (Rdiff) into electrophoretic (Rdiff,EP) and electroosmotic (Rdiff,EO) components provided an approach to calculate the zeta-potential of hSTf (ζhSTf) with the aid of CR and zeta potential of the nanopore surface (ζpore) with (ζpore–ζhSTf) governing the transport mechanism. Scrutinization of the conventional excluded volume model revealed its shortcomings in capturing surface contributions and a new model was then developed to fit the translocation characteristics of proteins. Figure shows hSTf protein translocating through a solid-state nanopore under an applied electric field and the resulting current traces. The transport mechanism is determined by the interplay of electrophoretic and electroosmotic force.![]()
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Affiliation(s)
- Jugal Saharia
- Department of Mechanical Engineering, Southern Methodist University Dallas TX 75275 USA
| | - Y M Nuwan D Y Bandara
- Department of Mechanical Engineering, Southern Methodist University Dallas TX 75275 USA
| | - Buddini I Karawdeniya
- Department of Mechanical Engineering, Southern Methodist University Dallas TX 75275 USA
| | - Cassandra Hammond
- Department of Mechanical Engineering, Southern Methodist University Dallas TX 75275 USA
| | - George Alexandrakis
- Department of Bioengineering, University of Texas at Arlington Arlington TX 76019 USA
| | - Min Jun Kim
- Department of Mechanical Engineering, Southern Methodist University Dallas TX 75275 USA
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Bouteiller M, Dupont C, Bourigault Y, Latour X, Barbey C, Konto-Ghiorghi Y, Merieau A. Pseudomonas Flagella: Generalities and Specificities. Int J Mol Sci 2021; 22:ijms22073337. [PMID: 33805191 PMCID: PMC8036289 DOI: 10.3390/ijms22073337] [Citation(s) in RCA: 31] [Impact Index Per Article: 10.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/08/2021] [Revised: 03/22/2021] [Accepted: 03/22/2021] [Indexed: 12/21/2022] Open
Abstract
Flagella-driven motility is an important trait for bacterial colonization and virulence. Flagella rotate and propel bacteria in liquid or semi-liquid media to ensure such bacterial fitness. Bacterial flagella are composed of three parts: a membrane complex, a flexible-hook, and a flagellin filament. The most widely studied models in terms of the flagellar apparatus are E. coli and Salmonella. However, there are many differences between these enteric bacteria and the bacteria of the Pseudomonas genus. Enteric bacteria possess peritrichous flagella, in contrast to Pseudomonads, which possess polar flagella. In addition, flagellar gene expression in Pseudomonas is under a four-tiered regulatory circuit, whereas enteric bacteria express flagellar genes in a three-step manner. Here, we use knowledge of E. coli and Salmonella flagella to describe the general properties of flagella and then focus on the specificities of Pseudomonas flagella. After a description of flagellar structure, which is highly conserved among Gram-negative bacteria, we focus on the steps of flagellar assembly that differ between enteric and polar-flagellated bacteria. In addition, we summarize generalities concerning the fuel used for the production and rotation of the flagellar macromolecular complex. The last part summarizes known regulatory pathways and potential links with the type-six secretion system (T6SS).
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Affiliation(s)
- Mathilde Bouteiller
- LMSM, Laboratoire de Microbiologie Signaux et Microenvironnement, EA 4312, Normandy University, Université de Rouen, 27000 Evreux, France; (M.B.); (C.D.); (Y.B.); (X.L.); (C.B.); (Y.K.-G.)
- SFR NORVEGE, Structure Fédérative de Recherche Normandie Végétale, FED 4277, 76821 Mont-Saint-Aignan, France
| | - Charly Dupont
- LMSM, Laboratoire de Microbiologie Signaux et Microenvironnement, EA 4312, Normandy University, Université de Rouen, 27000 Evreux, France; (M.B.); (C.D.); (Y.B.); (X.L.); (C.B.); (Y.K.-G.)
- SFR NORVEGE, Structure Fédérative de Recherche Normandie Végétale, FED 4277, 76821 Mont-Saint-Aignan, France
| | - Yvann Bourigault
- LMSM, Laboratoire de Microbiologie Signaux et Microenvironnement, EA 4312, Normandy University, Université de Rouen, 27000 Evreux, France; (M.B.); (C.D.); (Y.B.); (X.L.); (C.B.); (Y.K.-G.)
- SFR NORVEGE, Structure Fédérative de Recherche Normandie Végétale, FED 4277, 76821 Mont-Saint-Aignan, France
| | - Xavier Latour
- LMSM, Laboratoire de Microbiologie Signaux et Microenvironnement, EA 4312, Normandy University, Université de Rouen, 27000 Evreux, France; (M.B.); (C.D.); (Y.B.); (X.L.); (C.B.); (Y.K.-G.)
- SFR NORVEGE, Structure Fédérative de Recherche Normandie Végétale, FED 4277, 76821 Mont-Saint-Aignan, France
| | - Corinne Barbey
- LMSM, Laboratoire de Microbiologie Signaux et Microenvironnement, EA 4312, Normandy University, Université de Rouen, 27000 Evreux, France; (M.B.); (C.D.); (Y.B.); (X.L.); (C.B.); (Y.K.-G.)
- SFR NORVEGE, Structure Fédérative de Recherche Normandie Végétale, FED 4277, 76821 Mont-Saint-Aignan, France
| | - Yoan Konto-Ghiorghi
- LMSM, Laboratoire de Microbiologie Signaux et Microenvironnement, EA 4312, Normandy University, Université de Rouen, 27000 Evreux, France; (M.B.); (C.D.); (Y.B.); (X.L.); (C.B.); (Y.K.-G.)
- SFR NORVEGE, Structure Fédérative de Recherche Normandie Végétale, FED 4277, 76821 Mont-Saint-Aignan, France
| | - Annabelle Merieau
- LMSM, Laboratoire de Microbiologie Signaux et Microenvironnement, EA 4312, Normandy University, Université de Rouen, 27000 Evreux, France; (M.B.); (C.D.); (Y.B.); (X.L.); (C.B.); (Y.K.-G.)
- SFR NORVEGE, Structure Fédérative de Recherche Normandie Végétale, FED 4277, 76821 Mont-Saint-Aignan, France
- Correspondence:
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Lee JS, Oviedo JP, Bandara YMNDY, Peng X, Xia L, Wang Q, Garcia K, Wang J, Kim MJ, Kim MJ. Detection of nucleotides in hydrated ssDNA via 2D h-BN nanopore with ionic-liquid/salt-water interface. Electrophoresis 2021; 42:991-1002. [PMID: 33570197 DOI: 10.1002/elps.202000356] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/03/2020] [Revised: 01/20/2021] [Accepted: 01/30/2021] [Indexed: 02/03/2023]
Abstract
Accomplishing slow translocation speed with high sensitivity has been the most critical mission for solid-state nanopore (SSN) device to electrically detect nucleobases in ssDNA. In this study, a method to detect nucleobases of ssDNA using a 2D SSN is introduced by considerably reducing the translocation speed and effectively increasing its sensitivity. The ultra-thin titanium dioxide coated hexagonal boron nitride nanopore was fabricated, along with an ionic-liquid 1-butyl-3-methylimidazolium hexafluorophosphate/2.0 M KCl aqueous (cis/trans) interface, for increasing both the spatial and the temporal resolutions. As the ssDNA molecules entered the nanopore, a brief surge of electrical conductivity occurred, which was followed by multiple resistive pulses from nucleobases during the translocation of ssDNA and another brief current surge flagging the exit of the molecule. The continuous detection of nucleobases using a 2D SSN device is a novel achievement: the water molecules bound to ssDNA increased the molecular conductivity and amplified electrical signals during the translocation. Along with the experiment, computational simulations using COMSOL Multiphysics are presented to explain the pivotal role of water molecules bound to ssDNA to detect nucleobases using a 2D SSN.
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Affiliation(s)
- Jung Soo Lee
- Applied Science Program, Lyle School of Engineering, Southern Methodist University, Dallas, TX, USA
| | - Juan Pablo Oviedo
- Department of Materials Science and Engineering, The University of Texas at Dallas, Richardson, TX, USA
| | | | - Xin Peng
- Department of Materials Science and Engineering, The University of Texas at Dallas, Richardson, TX, USA.,Department of Physical Chemistry, University of Science and Technology, Beijing, P. R. China
| | - Longsheng Xia
- Department of Electrical Engineering, The University of Texas at Dallas, Richardson, TX, USA
| | - Qingxiao Wang
- Department of Materials Science and Engineering, The University of Texas at Dallas, Richardson, TX, USA
| | - Kevin Garcia
- Department of Materials Science and Engineering, The University of Texas at Dallas, Richardson, TX, USA.,Monterrey Institute of Technology and Higher Education, Mexico City, Mexico
| | - Jinguo Wang
- Department of Materials Science and Engineering, The University of Texas at Dallas, Richardson, TX, USA
| | - Min Jun Kim
- Applied Science Program, Lyle School of Engineering, Southern Methodist University, Dallas, TX, USA.,Deparment of Mechanical Engineering, Southern Methodist University, Dallas, TX, USA
| | - Moon Jae Kim
- Department of Materials Science and Engineering, The University of Texas at Dallas, Richardson, TX, USA.,Simmons Comprehensive Cancer Center, University of Texas Southwestern Medical Center, Dallas, TX, USA
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Saharia J, Bandara YMNDY, Karawdeniya BI, Alexandrakis G, Kim MJ. Assessment of 1/f noise associated with nanopores fabricated through chemically tuned controlled dielectric breakdown. Electrophoresis 2021; 42:899-909. [PMID: 33340118 DOI: 10.1002/elps.202000285] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/21/2020] [Revised: 11/21/2020] [Accepted: 12/14/2020] [Indexed: 02/01/2023]
Abstract
Recently, we developed a fabrication method-chemically-tuned controlled dielectric breakdown (CT-CDB)-that produces nanopores (through thin silicon nitride membranes) surpassing legacy drawbacks associated with solid-state nanopores (SSNs). However, the noise characteristics of CT-CDB nanopores are largely unexplored. In this work, we investigated the 1/f noise of CT-CDB nanopores of varying solution pH, electrolyte type, electrolyte concentration, applied voltage, and pore diameter. Our findings indicate that the bulk Hooge parameter (αb ) is about an order of magnitude greater than SSNs fabricated by transmission electron microscopy (TEM) while the surface Hooge parameter (αs ) is ∼3 order magnitude greater. Theαs of CT-CDB nanopores was ∼5 orders of magnitude greater than theirαb , which suggests that the surface contribution plays a dominant role in 1/f noise. Experiments with DNA exhibited increasing capture rates with pH up to pH ∼8 followed by a drop at pH ∼9 perhaps due to the onset of electroosmotic force acting against the electrophoretic force. The1/f noise was also measured for several electrolytes and LiCl was found to outperform NaCl, KCl, RbCl, and CsCl. The 1/f noise was found to increase with the increasing electrolyte concentration and pore diameter. Taken together, the findings of this work suggest the pH approximate 7-8 range to be optimal for DNA sensing with CT-CDB nanopores.
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Affiliation(s)
- Jugal Saharia
- Department of Mechanical Engineering, Southern Methodist University, Dallas, TX, USA
| | - Y M Nuwan D Y Bandara
- Department of Mechanical Engineering, Southern Methodist University, Dallas, TX, USA
| | - Buddini I Karawdeniya
- Department of Mechanical Engineering, Southern Methodist University, Dallas, TX, USA
| | | | - Min Jun Kim
- Department of Mechanical Engineering, Southern Methodist University, Dallas, TX, USA
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7
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Karawdeniya BI, Bandara YMNDY, Khan AI, Chen WT, Vu HA, Morshed A, Suh J, Dutta P, Kim MJ. Adeno-associated virus characterization for cargo discrimination through nanopore responsiveness. NANOSCALE 2020; 12:23721-23731. [PMID: 33231239 PMCID: PMC7735471 DOI: 10.1039/d0nr05605g] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Solid-state nanopore (SSN)-based analytical methods have found abundant use in genomics and proteomics with fledgling contributions to virology - a clinically critical field with emphasis on both infectious and designer-drug carriers. Here we demonstrate the ability of SSN to successfully discriminate adeno-associated viruses (AAVs) based on their genetic cargo [double-stranded DNA (AAVdsDNA), single-stranded DNA (AAVssDNA) or none (AAVempty)], devoid of digestion steps, through nanopore-induced electro-deformation (characterized by relative current change; ΔI/I0). The deformation order was found to be AAVempty > AAVssDNA > AAVdsDNA. A deep learning algorithm was developed by integrating support vector machine with an existing neural network, which successfully classified AAVs from SSN resistive-pulses (characteristic of genetic cargo) with >95% accuracy - a potential tool for clinical and biomedical applications. Subsequently, the presence of AAVempty in spiked AAVdsDNA was flagged using the ΔI/I0 distribution characteristics of the two types for mixtures composed of ∼75 : 25% and ∼40 : 60% (in concentration) AAVempty : AAVdsDNA.
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D Y Bandara YMN, Saharia J, Karawdeniya BI, Hagan JT, Dwyer JR, Kim MJ. Beyond nanopore sizing: improving solid-state single-molecule sensing performance, lifetime, and analyte scope for omics by targeting surface chemistry during fabrication. NANOTECHNOLOGY 2020; 31:335707. [PMID: 32357346 DOI: 10.1088/1361-6528/ab8f4d] [Citation(s) in RCA: 25] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Solid-state nanopores (SSNs) are single-molecule resolution sensors with a growing footprint in real-time bio-polymer profiling-most prominently, but far from exclusively, DNA sequencing. SSNs accessibility has increased with the advent of controlled dielectric breakdown (CDB), but severe fundamental challenges remain: drifts in open-pore current and (irreversible) analyte sticking. These behaviors impede basic research and device development for commercial applications and can be dramatically exacerbated by the chemical complexity and physical property diversity of different analytes. We demonstrate a SSN fabrication approach attentive to nanopore surface chemistry during pore formation, and thus create nanopores in silicon nitride (SiNx) capable of sensing a wide analyte scope-nucleic acid (double-stranded DNA), protein (holo-human serum transferrin) and glycan (maltodextrin). In contrast to SiNx pores fabricated without this comprehensive approach, the pores are Ohmic in electrolyte, have extremely stable open-pore current during analyte translocation (>1 h) over a broad range of pore diameters ([Formula: see text]3- ∼30 nm) with spontaneous current correction (if current deviation occurs), and higher responsiveness (i.e. inter-event frequency) to negatively charged analytes (∼6.5 × in case of DNA). These pores were fabricated by modifying CDB with a chemical additive-sodium hypochlorite-that resulted in dramatically different nanopore surface chemistry including ∼3 orders of magnitude weaker Ka (acid dissociation constant of the surface chargeable head-groups) compared to CDB pores which is inextricably linked with significant improvements in nanopore performance with respect to CDB pores.
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Affiliation(s)
- Y M Nuwan D Y Bandara
- Department of Mechanical Engineering, Southern Methodist University, Dallas, TX 75275, United States of America
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Tang J, Rogowski LW, Zhang X, Kim MJ. Flagellar nanorobot with kinetic behavior investigation and 3D motion. NANOSCALE 2020; 12:12154-12164. [PMID: 32490471 DOI: 10.1039/d0nr02496a] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Wirelessly controlled nanorobots have the potential to perform highly precise maneuvers within complex in vitro and in vivo environments. Flagellar nanorobots will be useful in a variety of biomedical applications, however, to date there has been little effort to investigate essential kinetic behavior changes related to the geometric properties of the nanorobot and effects imparted to it by nearby boundaries. Flagellar nanorobots are composed of an avidin-coated magnetic nanoparticle head (MH) and a single biotin-tipped repolymerized flagellum that are driven by a wirelessly generated rotating magnetic field. Nanorobots with different MHs and flagellar lengths were manually guided to perform complex swimming trajectories under both bright-field and fluorescence microscopy visualizations. The experimental results show that rotational frequency, handedness of rotation direction, MH size, flagellar length, and distance to the bottom boundary significantly affect the kinematics of the nanorobot. The results reported herein summarize fundamental research that will be used for the design specifications necessary for optimizing the application of helical nanorobotic devices for use in delivery of therapeutic and imaging agents. Additionally, robotic nanoswimmers were successfully navigated and tracked in 3D using quantitative defocusing, which will significantly improve the efficiency, function, and application of the flagellar nanorobot.
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Affiliation(s)
- Jiannan Tang
- Department of Mechanical Engineering, Lyle School of Engineering, Southern Methodist University, Dallas, TX 75275, USA.
| | - Louis William Rogowski
- Department of Mechanical Engineering, Lyle School of Engineering, Southern Methodist University, Dallas, TX 75275, USA.
| | - Xiao Zhang
- Department of Mechanical Engineering, Lyle School of Engineering, Southern Methodist University, Dallas, TX 75275, USA.
| | - Min Jun Kim
- Department of Mechanical Engineering, Lyle School of Engineering, Southern Methodist University, Dallas, TX 75275, USA.
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Qiao L, Slater GW. Capture of rod-like molecules by a nanopore: Defining an "orientational capture radius". J Chem Phys 2020; 152:144902. [PMID: 32295359 DOI: 10.1063/5.0002044] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Both the translational diffusion coefficient D and the electrophoretic mobility μ of a short rod-like molecule (such as dsDNA) that is being pulled toward a nanopore by an electric field should depend on its orientation. Since a charged rod-like molecule tends to orient in the presence of an inhomogeneous electric field, D and μ will change as the molecule approaches the nanopore, and this will impact the capture process. We present a simplified study of this problem using theoretical arguments and Langevin dynamics simulations. In particular, we introduce a new orientational capture radius, which we compare to the capture radius for the equivalent point-like particle, and we discuss the different physical regimes of orientation during capture and the impact of initial orientations on the capture time.
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Affiliation(s)
- Le Qiao
- Department of Physics, University of Ottawa, Ottawa, Ontario K1N 6N5, Canada
| | - Gary W Slater
- Department of Physics, University of Ottawa, Ottawa, Ontario K1N 6N5, Canada
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