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Updated: August 17, 2005

N A N O P R O B E S     E - N E W S

Vol. 6, No. 8          August 17, 2005

In this Issue:

This monthly newsletter is to inform you about techniques to improve your immunogold labeling, highlight interesting articles and novel applications of metal nanoparticles, and answer your questions. We hope you enjoy it and find it useful; as always, let us know if we can improve anything.

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Nanogold® as an AFM Label

Because atomic force microscopy (AFM) does not require a vacuum environment, it offers the opportunity to look at the structure of single molecules under aqueous buffer, an advantage over 'dry' techniques such as X-ray crystallography and electron microscopy. We have previously reported the use of small gold particles for AFM applications: In 2004, Collins and group used small gold nanoparticles formulated as [Au55]+ or [Au70]+ as attachment sites for histidine affinity tagged (nitrilotriacetic acid, or NTA-Ni(II)-modified) green fluorescent protein (pHAT-GFP) and Human Oncostatin M; and in 2001, Fritzsche and co-workers used oligonucleotides tagged with gold nanoparticles to localize target sequences adsorbed to gold surfaces.

Hussain and co-workers now describe the use of Nanogold® as a label for AFM use, detected and imaged using phase imaging. This group used high-resolution AFM to study the role of the platelet integrin AlphaIIABeta3 in platelet adhesion, activation, and aggregation at the subendothelium and at protein-coated synthetic biomaterials. Interactions between AlphaIIABeta3 and both protein and peptide ligands for the receptor were imaged under physiological conditions.

To directly image the ligand-receptor interactions, AlphaIIABeta3 receptors were reconstituted into a supported lipid bilayer formed on a mica surface in the AFM fluid cell assembly, and subsequently activated with Mn2+. Fibrinogen - the natural protein ligand for the integrin - and a Nanogold-labeled peptide ligand (an RGD-containing heptamer) were infused into the AFM fluid cell, incubated with the reconstituted and activated receptors, then imaged under buffer.

Mono-Sulfo-N-hydroxysuccinimido Nanogold (MW 15,000) was conjugated to RGD-containing peptide according to the procedure supplied by Nanoprobes. The peptides were reacted with Mono-Sulfo-N-hydroxysuccinimido Nanogold for 1 hour at room temperature in HEPES buffer (pH 7.5). A 20- to 40- fold stoichiometric excess of peptide over Nanogold molar concentration was used to ensure that Nanogold acted as the limiting reagent and was conjugated as completely as possible, thus making separation of the Nanogold conjugate from unreacted peptide the principal purification requirement (see the following article for a discussion on how to separate Nanogold conjugates). Unconjugated peptide was separated from Nanogold-labeled peptide using gel exclusion chromatography over a prepacked PD-10 column with Sephadex G25 M, having a size exclusion limit of 5 kDa. 0.02 M Sodium phosphate buffer with 150 mM sodium chloride, pH 7.4, was used to elute the concentrated reaction mixture. The conjugate was collected as the first peak, pale yellow-brown in color, and the subsequent colorless collection samples were discarded.

For AFM, all images were collected using a MultiMode atomic force microscope with a Nanoscope IIIa controller. An E scanner (max scan size ~ 14 micrometers x 14 micrometers 4 micrometers) and high aspect ratio carbon tips on triangular Si3N4 cantilevers (spring constant ~ 0.6 N/m) were used to obtain images of the samples. All images were first-order flattened prior to analysis to remove sample tilt, and were collected using the fluid tapping mode; this measures topography by intermittently contacting the surface with the tip, thereby reducing lateral forces that can damage soft samples. Tip oscillation frequency was approximately 10 kHz. Gold particles were located using the phase signal, which generates contrast by differences in mechanical properties across the sample.

Height images illustrating topographical features showed the integrin reconstituted in the bilayer. Fibrinogen molecules binding to the receptors were easily observed in the height images. Fibrinogen showed its characteristic trinodular structure, and occasionally bridging integrin receptors; it was observed to bind to integrins at the D-domain, consistent with the location of the gamma-chain dodecapeptide, while fibrinogen-bridging integrins bound to receptors on opposite sides of the protein, consistent with a 2-fold axis of symmetry. The peptide ligands were not visible in height images; however, phase images, which map the mechanical properties, detected the Nanogold labels and demonstrated the presence of peptide ligands bound to the receptors.

The results demonstrate the ability of high-resolution AFM techniques to directly visualize single ligand/receptor interactions in a dynamic and physiologically relevant environment, and establish a framework for fundamental studies of both single protein/receptor interactions during normal pathological processes as well as biomaterial surface-induced thrombosis.


Hussain, M. A.; Agnihotri, A.; Siedlecki, C. A.: AFM imaging of ligand binding to platelet integrin alphaIIb-beta3 receptors reconstituted into planar lipid bilayers. Langmuir, 21, 6979-6986 (2005).

More information:

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Best Ways to Separate Nanogold® Conjugates

This is a frequent subject of technical questions, so a review of how to go about separating Nanogold® conjugates from impurities - and how to set up your labeling reaction so that the separation is as easy as possible - is in order. This includes: Gel electrophoresis and dialysis are discussed in previous articles.

Considerations for effective separation

  • Purity: which impurities must be removed?

    Is the complete removal of one of the unreacted reagents critical for your experiment? For example, if you are using gold to quench molecular beacons, then even very small amounts of unconjugated fluorescently labeled oligonucleotide may compromise the fluorescence properties of your product, so you need to ensure that these are completely removed. If you are labeling in order to solve the structure of a protein or large protein complex, removal of unconjugated gold may be critical; but if you are making an antibody conjugate to label a cell surface antigen, the presence of small amounts of unattached gold may not be a problem as they can be easily washed off after staining.

    If it is critical that your product does not contain one of the unreacted starting materials, plan to use an excess of the other to ensure that the critical one reacts to completion, and no unreacted form remains after conjugation. For example, if you are labeling molecular beacons, use a 5-fold to 10-fold excess of gold even if they are smaller than the Nanogold, to ensure that all the oligonucleotide reacts.

  • Separation method: which reagent is more easily separated?

    How do you plan to separate the conjugate? If you know which method you will use when you plan your reaction, you can set up the reaction stoichiometry using an excess of the reagent that is more easily separated from the conjugate using this method.

    In our experience, gel filtration liquid chromatography, which works by separating molecules by size, is the most effective and reliable method for separating Nanogold conjugates. Our product information and instructions are optimized for this method: this means that generally, we recommend performing the conjugation reaction using an excess of the smaller of the two reagents, so that the larger one is limiting and reacts completely. For example, we recommend using excess gold when labeling antibodies, but excess biomolecule if you are labeling a smaller peptide. It is easier to separate the unreacted smaller reagent by gel filtration, because of the greater relative size difference between it and the conjugate.

    For molecules that are close to Nanogold in size, small excesses (two-fold to five-fold) work best because they allow better resolution of overlapping peaks. For example, if you are labeling a large oligonucleotide (20 bases or more) that is larger than Nanogold, the gold label should be present in excess; if you are labeling a smaller oligonucleotide that is smaller that the gold label (10 bases or fewer), use an excess of the oligonucleotide.

    However, if you know you will be using a different method - such as gel electrophoresis or reverse-phase chromatography - then check to see which reagent is more easily separated, and set up your labeling reaction accordingly. For example, if you plan to purify a smaller labeled oligonucleotide by gel electrophoresis and know that the labeled and unlabeled oligonucleotide run very close together, while the gold is well separated, use an excess of the gold, so that the oligonucleotide is the limiting reagent and completely labeled. Sometimes it is worth running control separations with small quantities of the unlabeled biomolecule and unconjugated gold first, so that you can identify and separate unreacted starting materials.

  • What equipment and resources are available? If you don't have a full chromatography system, check alternatives

    If you know that your conjugate is readily separated by gel filtration liquid chromatography, but you don't have a liquid chromatography system available, you may be able to use gravity columns or spin columns instead. See the section on alternative separation methods, below.

Gel filtration: media selection guide

We have found that the following media work well for gel filtration of different Nanogold-labeled conjugates:

Biomolecule Suggested Gels MW separation range
Antibodies: whole IgG
Medium - large proteins (MW 30,000 - 300,000)
Superose-12 (Pharmacia)
Pre-packed columns or bulk media.
1,000 - 300,000
Antibodies: Fab' fragments
Small - medium proteins (MW 10,000 - 50,000)
Superdex-75 (Pharmacia)
Pre-packed columns or bulk media.
3,000-70,000 (globular proteins)
Large proteins and protein complexes (MW 100,000 - 1,000,000) Superose-6 (Pharmacia)
Pre-packed columns or bulk media.
5,000 - 500,000
Very large proteins and protein complexes (MW 200,000 - 5,000,000) A-1.5m (Bio-Rad)
Available in coarse, medium or fine grades.
10,000 - 1,500,000 (globular proteins)
Small proteins and peptides, oligonucleotides (MW 7,000 and smaller) Superdex-Peptide (Pharmacia)
Pre-packed columns or PG-30 bulk media.
100 - 7,000
Substrate analogs and other small molecules (MW 2,000 and smaller) GH-25 desalting gel (contact Millipore). Exclusion limit: 3,000
Substrate analogs and other small molecules (MW 3,000 and smaller) Sephadex G-25 (Pharmacia)
Hi-Trap columns or Bulk media.
Exclusion limit: 5,000

These are suggestions that have worked well in our laboratories. You may find it worthwhile to check our separation section in our Guide to Gold Cluster Labeling, or the Pharmacia gel filtration selection guide for other gel filtration media, or products from other manufacturers, before proceeding.

Alternatives: spin and gravity columns

We have received quite a few questions about spin columns. While we have not tried these, a number of columns are commercially available that contain similar gel filtration media to those recommended for liquid chromatography, and these may work well for the separation or purification of Nanogold conjugates.

Some media with appropriate fractionation ranges and exclusion limits are shown below:

Biomolecule Media MW fractionation range Exclusion limit
Antibodies: whole IgG and Fab' fragments
Small - medium proteins
Microspin® Sephacryl S-200 HR
(GE Health Sciences (Amersham Pharmacia))
5,000 - 250,000 (Globular proteins)
1,000 - 80,000 (dextrans)
30 bp
Antibodies: IgG and larger molecules
Large proteins
Microspin® Sephacryl S-300 HR
(GE Health Sciences (Amersham Pharmacia))
10,000 - 1,500,000 (Globular proteins)
2,000 - 400,000 (dextrans)
118 bp
Antibodies: whole IgG and Fab' fragments
Medium - large proteins
Microspin® Sephacryl S-400 HR
(GE Health Sciences (Amersham Pharmacia))
20,000 - 8,000,000 (Globular proteins)
10,000 - 2,000,000 (dextrans)
271 bp
Removal of smaller molecules from Nanogold conjugates.
Desalting or removal of excess cross-linking reagents
Bio-Spin / Micro Bio-Spin P-6
Exclusion limit 6,000 (Globular proteins) Not given
Removal of Nanogold and smaller molecules from larger conjugates Bio-Spin / Micro Bio-Spin P-30
Exclusion limit 40,000 (Globular proteins) Not given

Gravity columns, such as the disposable PD10 columns from GE Healthcare (formerly Amersham Pharmacia), can be used for desalting and removal of small molecules such as cross-linkers; although we have not tested them, it is possible that they may be used to separate excess small molecules (such as small peptides or substrate analogs) from Nanogold conjugates after labeling.

Other chromatographic separation methods

Reverse-phase chromatography and gel electrophoresis for oligonucleotides

There are some systems where the molecules are better separated by differences in properties such as hydrophobicity or charge rather than size, and for these, other chromatographic methods - although less well established than gel filtration - may be better.

One such case is oligonucleotides, particularly if the oligonucleotide to be labeled is close to Nanogold in size. We have found that reverse-phase chromatography can be helpful for separating labeled oligonucleotides from both gold particles and from unlabeled oligonucleotides. Separation of unlabeled oligonucleotide, unconjugated gold, and conjugate may be achieved using a butyl column, eluted with a gradient of 0 to 70% acetonitrile in 0.1 M triethylammonium acetate buffer at pH 7. Other methods that may be useful include hydrophobic interaction chromatography (HIC) and ion exchange.

Gel electrophoresis has also been used to separate labeled oligonucleotides, as described by Dubertret and co-workers. This is helpful in applications such as molecular beacon preparation, in which it is critical that one component of the mixture be limiting whether or not it is the smaller of the two. For effective detection of labeled oligonucleotides, divide the reaction mixture in two, and run two gels in parallel. Treat one with a standard DNA stain such as ethidium bromide: this will visualize the location of DNA-containing species. Develop the second using silver enhancement with LI Silver. This will visualize the Nanogold. Compare the silver enhanced and ethidium bromide stained gels: if the same band is stained using both treatments, it is labeled oligonucleotide. An application note on our web site describes the detection of Nanogold-labeled molecules in gel in more detail. In addition, our Guide to Gold Cluster Labeling includes detailed discussions of how to get the best out of conjugation and separation procedures.


Dubertret, B., Calame, M., and Libchaber, A.; Single-mismatch detection using gold-quenched fluorescent oligonucleotides. Nat. Biotechnol., 19, 365-370 (2001).

Ion exchange chromatography and hydrophobic interaction chromatography

These methods may be useful for separating gold-labeled proteins from both unconjugated gold and unlabeled protein. We have found, for example, that hydrophobic interaction chromatography, in which a gradient of decreasing salt concentration is used with an alkylated or phenylated resin, may be used to separate undecagold or Nanogold-labeled proteins from unlabeled proteins.


Hainfeld, J. F.: Undecagold-antibody method. In Colloidal Gold: Principles Methods, and Applications, M. A. Hayat (Ed.), San Diego, Academic Press; Vol. 2, pp. 413-429 (1989).

Please let us know if you need advice or assistance on the best methods for your labeling reaction. We will be glad to advise.

More information:

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Correlative Double Immunoelectron Microscopy and Double Immunofluorescence

We have reported in the past on the difficulties that fluorescence quenching by large particles presents to efforts to carry out correlative fluorescent and gold labeling using either larger gold labels, or using different sized gold labels to distinguish multiple sites. Albrecht and group have developed several novel approaches to this problem, and presented another at the recent Microscopy and Microanalysis 2005 meeting: the use of primary antibodies conjugated with 6 nm particles of different metals, distinguished by electron spectroscopic imaging, combined with secondary antibodies conjugated with different fluorophores.

In previous presentations, this group had shown that conjugating both a 5 nm gold particle and a fluorescent label to a single IgG molecule resulted in almost complete fluorescence quenching. However, when a 6 nm gold particle was conjugated to a secondary antibody and a fluorescently labeled tertiary probe was used with the gold-labeled primary, fluorescence intensities up to 50 % of those found with fluorescently labeled secondaries were found, sufficient for effective fluorescent imaging. However, when larger gold-labeled probes were used, fluorescence quenching even with this arrangement was still too high. In order to distinguish multiple sites at electron microscopic resolution, this group therefore turned to using similarly sized particles of different metals that may be differentiated spectroscopically.

[Correlative double immunofluorescence and EM labeling scheme (41k)]

left: Effect on fluorescence intensity for fluorescently labeled secondary antibody bound to 6 nm gold-labeled primary (top), and fluorescent and 6 nm gold-labeled primary antibody. right: schematic showing labeling of myosin with 6 nm gold and Cy5 (Z bands) and labeling of alpha-actinin with 6 nm palladium and Cy2 (I and A bands).

Correlative labeling was carried out as shown above. The authors prepared 6 nm colloidal particles of gold and palladium using conventional reductive methods, and conjugated these respectively to mouse anti-myosin and goat anti-alpha-actinin primary antibodies. These were then detected with donkey anti-mouse conjugated with Cy3 (emission maximum at 552 nm), and donkey anti-goat IgG conjugated to Cy2 (emission maximum at 492 nm), respectively for fluorescence observation. Correlative double immunolabeling was carried out on 70nm Epon sections of skeletal muscle tissue; before labeling, these were etched using sodium or potassium ethoxide to reduce antigenic masking. The colloidal metal labels were distinguished by Electron Spectroscopic Imaging (ESI).

By light microscopy, the signal pattern of the Cy3 signal showed the known distribution of myosin in the A band of muscle tissue. In contrast, the Cy2 signal displayed a narrow banded pattern, corresponding to the well-known presence of alpha-actinin in the Z lines. In the electron microscope, the colloidal gold and colloidal palladium were distinguished by ESI using a Leo 912 energy filtering transmission electron microscope equipped with an Omega filter. Images were formed using inelastically scattered electrons of specific energy losses associated with specific elemental compositions; the three window method was used for extrapolation of background, with two images taken at energy losses before and one image at the maxima of gold and palladium. The distribution of the filtered signals for each element was also found to reflect the known distribution of myosin and alpha-actinin. This approach may be extended to particles of other compositions, enabling multiple correlative labeling; it is limited only by the resolution of electron spectroscopic imaging, which currently requires at least a 3 - 5 nm particle for detection.


Kandela, I. K.; Bleher, R., and Albrecht, R. M.: Correlative Immunolabeling on Etched Epon Samples. Microsc. Microanal., 11 (Suppl. 2),; Price, R.; Kotula, P.; Marko, M.; Scott, J. H.; Vander Voort, G. F.; Nanilova, E.; Mah Lee Ng, M.; Smith, K.; Griffin, P.; SMith, P., and McKernan, S. (Eds.), Cambridge University Press, 1098CD (2005).

Correlative fluorescent and immunogold labeling may by achieved using the FluoroNanogold line of combined fluorescent and gold labeled Fab' conjugates available from Nanoprobes, which are the only commercially available conjugates with both labels and are available with the very bright Alexa Fluor® 488 and 594 labels developed by Molecular Probes. These may be enlarged using silver enhancement or gold enhancement for differentiation in the electron microscope.

More information:

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Triple EM Immunolabeling: Gold, Palladium and Platinum

In the same session, Bleher and co-workers extended the application of differentiating labeling by composition to a triple immunoelectron microscopy labeling system, using 6 nm colloidal gold, platinum and palladium particles, detected and imaged by energy filtering transmission electron microscopy (EFTEM). This approach has several advantages over the conventional method of labeling multiple targets with different sized colloidal gold particles:

  • Because the different labels are the same size, performance variations due to probe or label size (penetration, antigen access, and labeling density) are reduced or eliminated. Penetration overall is improved because the need for one of more large colloidal gold probes is removed, potentially allowing improved fixation and better morphological preservation.

  • More different particle compositions than sizes may be distinguished, thus allowing a greater number of targets to be visualized in the same image.

  • If different labeling sites are located close together, labeling one may further restrict access to the other, and this may result in poor or no labeling if one of the sites is labeled with larger particles.

  • Labeling resolution is the same for all labels. For high-resolution work, the inherently lower resolution from the larger sizes of colloidal gold is no longer a factor.

6 nm colloidal gold was prepared by white phosphorus reduction of tetrachloroaurate, 6 nm colloidal platinum by a modified citrate/tannic acid reduction of tetrachloropalladate, and 6 nm platinum particles by the enlargement of gold cores by reductive platinum deposition. These were then conjugated to anti-alpha-actinin, anti-actin, and anti-myosin antibodies respectively using conventional procedures. Conjugation ratios of protein to metal particles were optimized using isotherms at a pH slightly above that of the protein isoelectric pH, and conjugates separated by ultracentrifugation. For the test system, skeletal muscle was used, as described in the previous article: it provides a well-characterized system in which the distributions of several different targets are well-known and easily distinguished.

Multiple labeling could be achieved in a single labeling step using a mixture of the three conjugates. Metal labels were identified using a LEO 912 EFTEM equipped with an Omega energy filter by electron spectroscopic imaging (ESI). For ESI, inelastically scattered electrons with element specific energy losses were selectively used for imaging to generate elemental distribution maps. The three windows method, in which two images are taken at energy losses below the element specific energy loss maximum to extrapolate the background signal which is then subtracted from the third image at the maximum element specific energy loss, was used to remove background signal for each element. Gold labeling (Anti-alpha-actinin) was found exclusively at Z-lines, whereas palladium (anti-actin) and platinum (anti-myosin) were localized within in the I- and A-Bands, or A-Bands only, respectively.

These results confirm that this is an effective method for multiple labeling at the electron microscope level, although it does require specialized instrumentation, and the resolution is not quite as high as that obtained with standard transmission electron microscopy optics.


Bleher, R.; Meyer, D. A., and Albrecht, R. M.: High Resolution Multiple Labeling for Immuno-EM applying Metal Colloids and Energy Filtering Transmission Electron Microscopy (EFTEM). Microsc. Microanal., 11 (Suppl. 2),; Price, R.; Kotula, P.; Marko, M.; Scott, J. H.; Vander Voort, G. F.; Nanilova, E.; Mah Lee Ng, M.; Smith, K.; Griffin, P.; SMith, P., and McKernan, S. (Eds.), Cambridge University Press, 1100CD (2005).

Nanogold®, particularly if used with differential silver or gold enhancement, or in conjunction with peroxidase/DAB staining, can also be effective for double labeling. The use of Fab'-Nanogold conjugates, which are smaller than unlabeled IgG molecules, reduces probe size, allowing better penetration and antigen access combined with visualization using conventional electron optics.

More information:

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Nanoprobes Adds Space and Staff

Nanoprobes is currently expanding its operations in Yaphank, New York, approximately doubling our office and laboratory space. We also welcome three new staff members, who bring specific skills that will enable us to expand our research, product and application development activities: Andrew Thelian, an electron microscopist; Michael O'Connor, a Research Assistant in nanotechnology and cancer therapy; and Meliza Cruz, a Research Assistant in nanotechnology product development. We thank all our customers, and look forward to providing even more and better products and services from our expanded facilities.

More information:

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Other Recent Publications

Continuing our theme of multiple labeling, Albrecht and co-workers describe the multiple labeling by shape as well as by composition, using the observation that different compositions tend to produce particles with different shapes and morphology. Four different platelet epitopes were labeled using two sizes of round colloidal gold particles, together with umbonate ("popcorn-shaped") colloidal palladium particles, and faceted colloidal palladium particles which appear in the transmission electron microscope as mixtures of triangles, cubes, pentagons, and hexagons. Modifications to an ascorbic acid reduction procedure were used to produce either umbonate or faceted palladium particles with average diameters of 18 nm or 15 nm respectively; these could then be conjugated to antibodies using conventional procedures.


Meyer, D. A.; Oliver, J. A., and Albrecht, R. M.: A Method for the Quadruple Labeling of Platelet Surface Epitopes for Transmission Electron Microscopy. Microsc. Microanal., 11 (Suppl. 2),; Price, R.; Kotula, P.; Marko, M.; Scott, J. H.; Vander Voort, G. F.; Nanilova, E.; Mah Lee Ng, M.; Smith, K.; Griffin, P.; SMith, P., and McKernan, S. (Eds.), Cambridge University Press, 142 (2005).

New methods for recognizing and evaluating the extent of colocalization of different fluorophores are described by Agnati and group in the current Journal of Histochemistry and Cytochemistry. This study introduces image analysis methods to identify locations that exhibit the highest association of two fluorophores, and characterize their distribution pattern. These methods were applied to the analysis of the cotrafficking of adenosine A2A and dopamine D2 receptors belonging to the G proteincoupled receptor family, visualized by means of fluorescence immunocytochemistry in Chinese hamster ovary cells after agonist treatment. These procedures have a significant advantage in that they are largely insensitive to the need for similar staining intensity with the two fluorophores. The new procedures comprise image processing, visualization, and analysis of colocalized events, using covariance and multiply methods and evaluation of the identified colocalization patterns. The covariance method also may enable the quantitative characterization of anticorrelated patterns of intensities, while the multiply method allows immediate detection of colocalized clusters with a high concentration of labeling. The present methods offer a new and sensitive approach to detecting and quantitatively characterizing strongly associated fluorescence events, such as those generated by receptorreceptor interaction, and their distribution patterns.


Agnati, L. F.; Fuxe, K.; Torvinen, M.; Genedani, S.; Franco, R.; Watson, S.; Nussdorfer, G. G.; Leo, G., and Guidolin D.: New Methods to Evaluate Colocalization of Fluorophores in Immunocytochemical Preparations as Exemplified by a Study on A2A and D2 Receptors in Chinese Hamster Ovary Cells. J. Histochem. Cytochem., 53, 941-953 (2005).

In a recent Science article, Hopkins and collaborators report an alternative method for preparing 5 - 15 nm diameter nanowires: sputtering gold onto suspended duplex DNA. These wires become superconducting at low temperatures, and because the wires are very thin, comparable to the DNA molecules themselves, they are susceptible to thermal fluctuations typical for one-dimensional superconductors. They were found to exhibit a nonzero resistance over a broad temperature range, and could be used to fabricate structures. Pairs of such DNA nanowires were found to exhibit resistance oscillation, making them a superconducting quantum interference device (SQUID). Resistance oscillations different to the usual Little-Parks oscillations were found, and the authors provide a quantitative explanation that takes into account strong phase gradients created in the leads by the applied magnetic field.


Hopkins, D. S.; Pekker, D.; Goldbart, P. M, and Bezryadin, A.: Quantum interference device made by DNA templating of superconducting nanowires. Science, 308, 1762-1765 (2005).

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