- Email: [email protected]
An easily constructed, inexpensive device for dot blotting
ANALYTICAL BIOCHEMISTRY Analytical Biochemistry 370 (2007) 115–117 www.elsevier.com/locate/yabio
Notes & Tips
An easily constructed, inexpensive device for dot blotting Chihiro Kondo, Seigo Nakano, Takahiro Suzuki, Takao Kanamori
*
Department of Biochemistry, School of Dentistry, Aichi-Gakuin University, Chikusa-ku, Nagoya 464-8650, Japan Received 19 April 2007 Available online 24 May 2007
Dot blotting is a technique in which proteins or nucleic acids are immobilized in dots on a blotting matrix [1]. This technique is simple and has been applied for quantification and analysis of macromolecules [2–5]. It is especially useful for handling highly diluted samples because they can be applied repetitively and concentrated in dots. Several devices are commercially available for preparing uniformly focused reproducible dots. They are, however, relatively expensive and sometimes cause problems such as leakage of samples and resultant appearance of smudges. Here we report a new, simple, inexpensive, and leak-free device for dot blotting. It is easily constructed in-house and allows reproducible transfer of molecules onto polyvinylidene difluoride (PVDF),1 nitrocellulose, and nylon membranes without the use of a vacuum pump. Fig. 1A shows a schematic overview of our device for dot blotting. Its major part was made of a rectangular acrylic plate (36 · 320 · 2 mm). At the center of this plate, a tapered window (top 10 · 10 mm, bottom 8 · 8 mm) was opened (a hole 8 mm in diameter was bored first and then deformed with files). On either side of the plate, two small acrylic plates (36 · 10 · 2 mm each) were glued in parallel at a 12-mm interval (dichloromethane was used as a glue). Each pair of small acrylic plates was designed to retain a steel weight (see below). Another small rectangular acrylic plate (36 · 20 · 3 mm) was prepared. At the center of this plate, a tapered hole (upper diameter 5.5 mm, lower diameter 4.0 mm) was bored (a hole 4.0 mm in diameter was bored first and then the upper part was enlarged with a drill of larger diameter). A trace amount of adhesive (ZERO, Sekisui, Tokyo, Japan) was applied to the edge surrounding the lower orifice, to which an O-ring (outer diameter 5.2 mm, inner diameter 1.8 mm) was attached. The smaller *
Corresponding author. Fax: +81 52 752 5988. E-mail address: [email protected] (T. Kanamori). 1 Abbreviations used: PVDF, polyvinylidene difluoride; BSA, bovine serum albumin. 0003-2697/$ - see front matter 2007 Elsevier Inc. All rights reserved. doi:10.1016/j.ab.2007.05.015
plate (O-ring side down) was placed under the window of the larger one and fixed with vinyl adhesive tape. A steel weight (12 · 12 · 215 mm, 240 g) was then set on either side of the device. Before the device was used for dot blotting, a PVDF membrane (Immobilon-PSQ, Millipore, Bedford, MA, USA) of an appropriate size was ruled into 6-mm squares with a soft pencil, wetted with methanol, and rinsed with a solution suitable for the subsequent procedure. A nitrocellulose membrane (Trans-Blot Transfer Medium, 0.45 lm, Bio-Rad, Hercules, CA, USA) and a nylon membrane (Hybond-N+, GE Healthcare, Buckinghamshire, UK) were also treated as described for the PVDF membrane except that the former two membranes were not prewetted with methanol. In this work, Tris-buffered saline (20 mM Tris–HCl [pH 7.5] containing 150 mM NaCl) was used as a rinsing solution for the PVDF and nitrocellulose membranes, and 10 mM Tris–HCl (pH 8.0) containing 1 mM EDTA was used for the nylon membrane. Three sheets of filter paper (no. 2, Advantec, Tokyo, Japan) were stacked on a sheet of Saran Wrap (Asahikasei, Tokyo, Japan) and saturated with the rinsing solution for the intended membrane. The wetted membrane to be used was placed on the filter paper stack, and air bubbles below the membrane were removed. The excess solution in the paper stack was absorbed into dry paper. The dot-blotting device assembled was now placed on a blotting membrane so that the O-ring was positioned at the center of a square. A sample was loaded into the well enclosed by the O-ring, which was pressed against the membrane with the aid of the weights (Fig. 1B). Care was taken not to touch the membrane with the pipette tip. The well had a capacity of approximately 10 ll, and care was also taken so that the sample did not overflow the O-ring. When large volumes of samples were applied, they were repetitively loaded in small portions. In this work, 50 lg/ml bovine serum albumin (BSA) in Tris-buffered saline was used as a model sample for the PVDF and nitrocellulose
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Fig. 1. Schematic illustration of the device for dot blotting. (A) Overview. An enlarged illustration of the central portion of the device is shown in the inset placed at the upper left. (B) Cross section. In both panels A and B, parts are marked as follows: 1, acrylic plate with a window and weight retainers; 2, acrylic plate with a hole; 3, O-ring; 4, steel weights; 5, blotting matrix on which a grid was drawn; 6, filter paper; 7, Saran Wrap; 8, sample; 9, bench top; 10, vinyl tape. For detailed presentation of several portions, the illustration is not drawn to scale.
membranes, and 10 lg/ml plasmid DNA (pBluescript II KS(+), Stratagene, La Jolla, CA, USA) in 10 mM Tris– HCl (pH 8.0) containing 1 mM EDTA was used for the nylon membrane. When 10 ll of each sample was applied to the well in one portion, it usually was absorbed within 30 s. If the sample absorption was slow, the solution in the paper stack was further removed with dry paper. When the sample was completely absorbed, the membrane-rinsing solution (10 ll) was added to the well and allowed to be absorbed. This step ensured complete sample transfer and prevented potential sample carryover. The device was then moved to another square for the next sample application, and the procedure was repeated until all of the samples were applied. Adequate moisture of the filter paper stack was maintained for at least 1 h without the addition of the solution. When the sample application was finished, the membrane was briefly washed with H2O and subjected to subsequent treatment. In this work, the PVDF and nitrocellulose membranes were stained for protein with Reactive Brown 10 [6], and the nylon membrane was stained for DNA for 30 min in 0.0015% Nile Blue in H2O and destained in 50% ethanol. The latter procedure is based on the reported method for staining of DNA in agarose and polyacrylamide gels [7]. Resultant membranes were scanned with a model GT-7600S flatbed scanner (Epson, Tokyo, Japan) connected to a Power Macintosh 7600/ 132 microcomputer (Apple, Cupertino, CA, USA), and images were subjected to densitometric analysis using the public domain software NIH Image 1.62 (written by Wayne Rasband, National Institutes of Health, Bethesda, MD, USA), with values being presented as means and standard deviations. Fig. 2 shows dots formed with our device. It provided uniformly focused, smudge-free dots on PVDF (Fig. 2A),
Fig. 2. Dots prepared with the device introduced in this report. (A) PVDF membrane. (B) Nitrocellulose membrane. (C) Nylon membrane. For panels A and B, dots were prepared by the application of 10, 2 · 10, and 3 · 10 ll of 50 lg/ml BSA and were visualized with Reactive Brown 10. Under each dot, its protein content is shown. For panel C, dots were prepared by the application of 10, 2 · 10, and 3 · 10 ll of 10 lg/ml pBluescript II KS(+) and were visualized with Nile Blue. Under each dot, its DNA content is shown.
nitrocellulose (Fig. 2B), and nylon (Fig. 2C) membranes. Reactive Brown 10, which was used for staining of protein, gave a higher background level for the PVDF membrane than for the nitrocellulose membrane; however, it stained protein on the PVDF membrane more intensely than that on the nitrocellulose membrane. The dots on the nylon membrane contained some white spots. It is likely that these white spots are due to the property of the membrane; we have observed similar spots on the use of several membranes of the supported type (Hybond-N+ is a membrane of this type). In separate experiments, multiple dots were formed on the three membranes; each dot was prepared by two applications of 10 ll of 50 lg/ml BSA or 10 lg/ ml pBluescript II KS(+). Densitometric analysis of the stained membranes indicated that the dot areas were 8.86 ± 0.11 mm2 (n = 6) for the PVDF membrane, 8.90 ± 0.07 mm2 (n = 6) for the nitrocellulose membrane, and 8.48 ± 0.19 mm2 (n = 6) for the nylon membrane. Optical density values above the background within the dots were 0.096 ± 0.003 (n = 6) for the PVDF membrane, 0.052 ± 0.002 (n = 6) for the nitrocellulose membrane, and 0.046 ± 0.003 (n = 6) for the nylon membrane (data not shown). Thus, it was confirmed that the device provided reproducible dots. Nitrocellulose and nylon membranes can be used for blotting without prewetting; however, blotting onto the dry membranes provided nonuniform dots owing to rapid absorption of samples and cannot be recommended. The washing of the well after each sample application (described above) seems unnecessary in most cases because little of the sample remained in the well; we observed little carryover effect when the washing was omitted. Another inexpensive homemade device was reported previously by others [8]. Here half-cut p200 tips were used as tanks for samples. They were placed upside down (cut side up) on a blotting membrane with the aid of a tip support (a stack of filter paper was placed under the membrane in advance). The device was designed so that the
Notes & Tips / Anal. Biochem. 370 (2007) 115–117
rims of the multiple tips were pressed firmly against the membrane through the tip support. Because we needed an inexpensive dot-blotting device, we tried to make one according to the previous report. The construction, however, was not easy for us; preparation of the tip support was difficult because multiple parallel holes needed to be drilled in a thick (1–2 cm) acrylic plate (the thickness was required to avoid the deformation of the plate). After several attempts, we reached a new design reported here (Fig. 1). The device could be made of acrylic plates 2 to 3 mm in thickness that were easily processed. Only one tapered hole needed to be bored carefully in an acrylic plate for retaining an O-ring and for easy sample application. The dimensions of the window opened in another acrylic plate were essentially arbitrary, and no precise work was required. We made the whole device at a cost of less than $20 without professional help. It has been used, without inconvenience, for preparation of dots that are subjected to immunostaining (sample volumes for dot blotting 10– 40 ll). When many samples with larger volumes are subjected to dot blotting, a device with multiple large wells might be more convenient than ours. In addition to the ease of construction, the dot-blotting device introduced here has several other advantages. The design with only one sample-loading well allows easy observation of the sample in the well, facilitates sample application, decreases the possibility of including air bubbles, and consequently guarantees reproducible dots. The device requires no vacuum, and it is easy to keep the blotting membrane wet during the procedure. The one-well design with an O-ring provides a tightly sealed sampling space, effectively preventing leakage of the sample loaded. Because the device can be moved freely after application of each sample, dots can be prepared in any number and in any arrangement. If the O-ring and its retainer are
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replaced appropriately, the device can also provide dots in another size. The device is easily disassembled and cleaned. When the applicability of the dot-blotting technique to some work is assessed, an easily constructed, inexpensive blotting device is required. It seems likely that the device reported here meets such a requirement and facilitates the use of the dot-blotting technique for quantification and analysis of macromolecules. Acknowledgment This work was supported in part by grants-in-aid from Aichi-Gakuin University. References [1] J.M. Gershoni, Blotting, in: T.E. Creighton (Ed.), Encyclopedia of Molecular Biology, vol. 1, John Wiley, New York, 1999, pp. 301– 303. [2] C. Costanzi, D. Gillespie, Fast blots: Immobilization of DNA and RNA from cells, Methods Enzymol. 152 (1987) 582–587. [3] R. Jahn, W. Schiebler, P. Greengard, A quantitative dot-immunobinding assay for proteins using nitrocellulose membrane filters, Proc. Natl. Acad. Sci. USA 81 (1984) 1684–1687. [4] G. Rijksen, B.A. van Oirschot, G.E. Staal, A nonradioactive dot-blot assay for protein tyrosine kinase activity, Anal. Biochem. 182 (1989) 98–102. [5] M. Guttenberger, V. Neuhoff, R. Hampp, A dot-blot assay for quantitation of nanogram amounts of protein in the presence of carrier ampholytes and other possibly interfering substances, Anal. Biochem. 196 (1991) 99–103. [6] C.R. Yonan, P.T. Duong, F.N. Chang, High-efficiency staining of proteins on different blot membranes, Anal. Biochem. 338 (2005) 159–161. [7] Y.I. Yang, H.Y. Hong, I.S. Lee, D.G. Bai, G.S. Yoo, J.K. Choi, Detection of DNA using a visible dye, Nile Blue, in electrophoresed gels, Anal. Biochem. 280 (2000) 322–324. [8] R. Barbieri, G. Duro, M.A. Costa, V. Izzo, Simple and inexpensive dot-blot apparatus, Anal. Biochem. 216 (1994) 461–462.
Notes & Tips
An easily constructed, inexpensive device for dot blotting Chihiro Kondo, Seigo Nakano, Takahiro Suzuki, Takao Kanamori
*
Department of Biochemistry, School of Dentistry, Aichi-Gakuin University, Chikusa-ku, Nagoya 464-8650, Japan Received 19 April 2007 Available online 24 May 2007
Dot blotting is a technique in which proteins or nucleic acids are immobilized in dots on a blotting matrix [1]. This technique is simple and has been applied for quantification and analysis of macromolecules [2–5]. It is especially useful for handling highly diluted samples because they can be applied repetitively and concentrated in dots. Several devices are commercially available for preparing uniformly focused reproducible dots. They are, however, relatively expensive and sometimes cause problems such as leakage of samples and resultant appearance of smudges. Here we report a new, simple, inexpensive, and leak-free device for dot blotting. It is easily constructed in-house and allows reproducible transfer of molecules onto polyvinylidene difluoride (PVDF),1 nitrocellulose, and nylon membranes without the use of a vacuum pump. Fig. 1A shows a schematic overview of our device for dot blotting. Its major part was made of a rectangular acrylic plate (36 · 320 · 2 mm). At the center of this plate, a tapered window (top 10 · 10 mm, bottom 8 · 8 mm) was opened (a hole 8 mm in diameter was bored first and then deformed with files). On either side of the plate, two small acrylic plates (36 · 10 · 2 mm each) were glued in parallel at a 12-mm interval (dichloromethane was used as a glue). Each pair of small acrylic plates was designed to retain a steel weight (see below). Another small rectangular acrylic plate (36 · 20 · 3 mm) was prepared. At the center of this plate, a tapered hole (upper diameter 5.5 mm, lower diameter 4.0 mm) was bored (a hole 4.0 mm in diameter was bored first and then the upper part was enlarged with a drill of larger diameter). A trace amount of adhesive (ZERO, Sekisui, Tokyo, Japan) was applied to the edge surrounding the lower orifice, to which an O-ring (outer diameter 5.2 mm, inner diameter 1.8 mm) was attached. The smaller *
Corresponding author. Fax: +81 52 752 5988. E-mail address: [email protected] (T. Kanamori). 1 Abbreviations used: PVDF, polyvinylidene difluoride; BSA, bovine serum albumin. 0003-2697/$ - see front matter 2007 Elsevier Inc. All rights reserved. doi:10.1016/j.ab.2007.05.015
plate (O-ring side down) was placed under the window of the larger one and fixed with vinyl adhesive tape. A steel weight (12 · 12 · 215 mm, 240 g) was then set on either side of the device. Before the device was used for dot blotting, a PVDF membrane (Immobilon-PSQ, Millipore, Bedford, MA, USA) of an appropriate size was ruled into 6-mm squares with a soft pencil, wetted with methanol, and rinsed with a solution suitable for the subsequent procedure. A nitrocellulose membrane (Trans-Blot Transfer Medium, 0.45 lm, Bio-Rad, Hercules, CA, USA) and a nylon membrane (Hybond-N+, GE Healthcare, Buckinghamshire, UK) were also treated as described for the PVDF membrane except that the former two membranes were not prewetted with methanol. In this work, Tris-buffered saline (20 mM Tris–HCl [pH 7.5] containing 150 mM NaCl) was used as a rinsing solution for the PVDF and nitrocellulose membranes, and 10 mM Tris–HCl (pH 8.0) containing 1 mM EDTA was used for the nylon membrane. Three sheets of filter paper (no. 2, Advantec, Tokyo, Japan) were stacked on a sheet of Saran Wrap (Asahikasei, Tokyo, Japan) and saturated with the rinsing solution for the intended membrane. The wetted membrane to be used was placed on the filter paper stack, and air bubbles below the membrane were removed. The excess solution in the paper stack was absorbed into dry paper. The dot-blotting device assembled was now placed on a blotting membrane so that the O-ring was positioned at the center of a square. A sample was loaded into the well enclosed by the O-ring, which was pressed against the membrane with the aid of the weights (Fig. 1B). Care was taken not to touch the membrane with the pipette tip. The well had a capacity of approximately 10 ll, and care was also taken so that the sample did not overflow the O-ring. When large volumes of samples were applied, they were repetitively loaded in small portions. In this work, 50 lg/ml bovine serum albumin (BSA) in Tris-buffered saline was used as a model sample for the PVDF and nitrocellulose
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Fig. 1. Schematic illustration of the device for dot blotting. (A) Overview. An enlarged illustration of the central portion of the device is shown in the inset placed at the upper left. (B) Cross section. In both panels A and B, parts are marked as follows: 1, acrylic plate with a window and weight retainers; 2, acrylic plate with a hole; 3, O-ring; 4, steel weights; 5, blotting matrix on which a grid was drawn; 6, filter paper; 7, Saran Wrap; 8, sample; 9, bench top; 10, vinyl tape. For detailed presentation of several portions, the illustration is not drawn to scale.
membranes, and 10 lg/ml plasmid DNA (pBluescript II KS(+), Stratagene, La Jolla, CA, USA) in 10 mM Tris– HCl (pH 8.0) containing 1 mM EDTA was used for the nylon membrane. When 10 ll of each sample was applied to the well in one portion, it usually was absorbed within 30 s. If the sample absorption was slow, the solution in the paper stack was further removed with dry paper. When the sample was completely absorbed, the membrane-rinsing solution (10 ll) was added to the well and allowed to be absorbed. This step ensured complete sample transfer and prevented potential sample carryover. The device was then moved to another square for the next sample application, and the procedure was repeated until all of the samples were applied. Adequate moisture of the filter paper stack was maintained for at least 1 h without the addition of the solution. When the sample application was finished, the membrane was briefly washed with H2O and subjected to subsequent treatment. In this work, the PVDF and nitrocellulose membranes were stained for protein with Reactive Brown 10 [6], and the nylon membrane was stained for DNA for 30 min in 0.0015% Nile Blue in H2O and destained in 50% ethanol. The latter procedure is based on the reported method for staining of DNA in agarose and polyacrylamide gels [7]. Resultant membranes were scanned with a model GT-7600S flatbed scanner (Epson, Tokyo, Japan) connected to a Power Macintosh 7600/ 132 microcomputer (Apple, Cupertino, CA, USA), and images were subjected to densitometric analysis using the public domain software NIH Image 1.62 (written by Wayne Rasband, National Institutes of Health, Bethesda, MD, USA), with values being presented as means and standard deviations. Fig. 2 shows dots formed with our device. It provided uniformly focused, smudge-free dots on PVDF (Fig. 2A),
Fig. 2. Dots prepared with the device introduced in this report. (A) PVDF membrane. (B) Nitrocellulose membrane. (C) Nylon membrane. For panels A and B, dots were prepared by the application of 10, 2 · 10, and 3 · 10 ll of 50 lg/ml BSA and were visualized with Reactive Brown 10. Under each dot, its protein content is shown. For panel C, dots were prepared by the application of 10, 2 · 10, and 3 · 10 ll of 10 lg/ml pBluescript II KS(+) and were visualized with Nile Blue. Under each dot, its DNA content is shown.
nitrocellulose (Fig. 2B), and nylon (Fig. 2C) membranes. Reactive Brown 10, which was used for staining of protein, gave a higher background level for the PVDF membrane than for the nitrocellulose membrane; however, it stained protein on the PVDF membrane more intensely than that on the nitrocellulose membrane. The dots on the nylon membrane contained some white spots. It is likely that these white spots are due to the property of the membrane; we have observed similar spots on the use of several membranes of the supported type (Hybond-N+ is a membrane of this type). In separate experiments, multiple dots were formed on the three membranes; each dot was prepared by two applications of 10 ll of 50 lg/ml BSA or 10 lg/ ml pBluescript II KS(+). Densitometric analysis of the stained membranes indicated that the dot areas were 8.86 ± 0.11 mm2 (n = 6) for the PVDF membrane, 8.90 ± 0.07 mm2 (n = 6) for the nitrocellulose membrane, and 8.48 ± 0.19 mm2 (n = 6) for the nylon membrane. Optical density values above the background within the dots were 0.096 ± 0.003 (n = 6) for the PVDF membrane, 0.052 ± 0.002 (n = 6) for the nitrocellulose membrane, and 0.046 ± 0.003 (n = 6) for the nylon membrane (data not shown). Thus, it was confirmed that the device provided reproducible dots. Nitrocellulose and nylon membranes can be used for blotting without prewetting; however, blotting onto the dry membranes provided nonuniform dots owing to rapid absorption of samples and cannot be recommended. The washing of the well after each sample application (described above) seems unnecessary in most cases because little of the sample remained in the well; we observed little carryover effect when the washing was omitted. Another inexpensive homemade device was reported previously by others [8]. Here half-cut p200 tips were used as tanks for samples. They were placed upside down (cut side up) on a blotting membrane with the aid of a tip support (a stack of filter paper was placed under the membrane in advance). The device was designed so that the
Notes & Tips / Anal. Biochem. 370 (2007) 115–117
rims of the multiple tips were pressed firmly against the membrane through the tip support. Because we needed an inexpensive dot-blotting device, we tried to make one according to the previous report. The construction, however, was not easy for us; preparation of the tip support was difficult because multiple parallel holes needed to be drilled in a thick (1–2 cm) acrylic plate (the thickness was required to avoid the deformation of the plate). After several attempts, we reached a new design reported here (Fig. 1). The device could be made of acrylic plates 2 to 3 mm in thickness that were easily processed. Only one tapered hole needed to be bored carefully in an acrylic plate for retaining an O-ring and for easy sample application. The dimensions of the window opened in another acrylic plate were essentially arbitrary, and no precise work was required. We made the whole device at a cost of less than $20 without professional help. It has been used, without inconvenience, for preparation of dots that are subjected to immunostaining (sample volumes for dot blotting 10– 40 ll). When many samples with larger volumes are subjected to dot blotting, a device with multiple large wells might be more convenient than ours. In addition to the ease of construction, the dot-blotting device introduced here has several other advantages. The design with only one sample-loading well allows easy observation of the sample in the well, facilitates sample application, decreases the possibility of including air bubbles, and consequently guarantees reproducible dots. The device requires no vacuum, and it is easy to keep the blotting membrane wet during the procedure. The one-well design with an O-ring provides a tightly sealed sampling space, effectively preventing leakage of the sample loaded. Because the device can be moved freely after application of each sample, dots can be prepared in any number and in any arrangement. If the O-ring and its retainer are
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replaced appropriately, the device can also provide dots in another size. The device is easily disassembled and cleaned. When the applicability of the dot-blotting technique to some work is assessed, an easily constructed, inexpensive blotting device is required. It seems likely that the device reported here meets such a requirement and facilitates the use of the dot-blotting technique for quantification and analysis of macromolecules. Acknowledgment This work was supported in part by grants-in-aid from Aichi-Gakuin University. References [1] J.M. Gershoni, Blotting, in: T.E. Creighton (Ed.), Encyclopedia of Molecular Biology, vol. 1, John Wiley, New York, 1999, pp. 301– 303. [2] C. Costanzi, D. Gillespie, Fast blots: Immobilization of DNA and RNA from cells, Methods Enzymol. 152 (1987) 582–587. [3] R. Jahn, W. Schiebler, P. Greengard, A quantitative dot-immunobinding assay for proteins using nitrocellulose membrane filters, Proc. Natl. Acad. Sci. USA 81 (1984) 1684–1687. [4] G. Rijksen, B.A. van Oirschot, G.E. Staal, A nonradioactive dot-blot assay for protein tyrosine kinase activity, Anal. Biochem. 182 (1989) 98–102. [5] M. Guttenberger, V. Neuhoff, R. Hampp, A dot-blot assay for quantitation of nanogram amounts of protein in the presence of carrier ampholytes and other possibly interfering substances, Anal. Biochem. 196 (1991) 99–103. [6] C.R. Yonan, P.T. Duong, F.N. Chang, High-efficiency staining of proteins on different blot membranes, Anal. Biochem. 338 (2005) 159–161. [7] Y.I. Yang, H.Y. Hong, I.S. Lee, D.G. Bai, G.S. Yoo, J.K. Choi, Detection of DNA using a visible dye, Nile Blue, in electrophoresed gels, Anal. Biochem. 280 (2000) 322–324. [8] R. Barbieri, G. Duro, M.A. Costa, V. Izzo, Simple and inexpensive dot-blot apparatus, Anal. Biochem. 216 (1994) 461–462.