# Asynchronous Magnetic Bead Rotation (AMBR) Microviscometer for Label-Free DNA Analysis

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## Abstract

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## 1. Introduction

## 2. Experimental Section

#### 2.1. Reagents

#### 2.2. Viscosity Measurement

**Figure 1.**Asynchronous magnetic bead rotation (AMBR) microviscometer. (

**a**) A schematic experimental set-up of an AMBR microviscometer. 1: perpendicular Helmholtz coils for rotating field generation; 2: liquid to be measured; 3: magnetic bead; 4: inverted microscope objective. (

**b**) Observed bead rotation frequency vs. field driving frequency. Below 9 Hz the bead rotation frequency matches that of the field; above 9 Hz, the bead rotates asynchronously, with frequency decreasing as the driving frequency increases. (

**c**) Viscosity measurement of glycerol/water mixture solutions. The graph compares AMBR results in a magnetic field with 100 Hz driving frequency to published values and conventional (Ubbelohde) viscometer measurements of the same liquid. (

**d**) AMBR microviscometer linear response to viscosity in prepared solutions of glycerol/water at 100 Hz driving frequency. Error bars represents standard deviation among three measurements.

#### 2.3. Preparation of Digestion Reaction Samples

#### 2.4. Preparation of PCR Samples

#### 2.5. Gel Electrophoresis

## 3. Results and Discussion

#### 3.1. Calibration of AMBR Viscometer

_{m}is the volume of the bead’s magnetic content (i.e., the magnetic nanoparticles embedded in the bead), B is the strength of the driving magnetic field, and µ

_{0}is the permeability of free space. The torque due to the viscous drag can be expressed as,

**Figure 2.**Reproducibility of AMBR viscosity measurements at 100 Hz driving frequency. (

**a**) Rotation period measurement of 20 independent beads in the same solution plotted against the optically measured bead size of each bead. (

**b**) The rotation periods of two examples of 45 µm beads observed over time in the same solution. The rotation periods are calculated over a 12 s period and plotted in the graph. The average values are for 17 sequential observations

#### 3.2. Viscosity Measurement of DNA Aqueous Solutions

_{0}(1 + C[η]), where η

_{0}is the viscosity of the solvent and [η] is the intrinsic viscosity of the DNA product. This equation gives a linear correlation between the viscosity and the macromolecule concentration. The intrinsic viscosity increases with the molecular weight of dsDNA, and this correlation has been documented [15],

**Table 1.**Rotation periods and viscosities of lambda DNA EcoRI digest solutions at different DNA concentrations measured by AMBR microviscometer. The expected ranges of viscosities are calculated, assuming only the longest or shortest piece of DNA is present.

Experimental Results | Expected Range | |||
---|---|---|---|---|

DNA Conc. (g/L) | Rotation Period (s) | Viscosity (cP) | Min Viscosity (cP) | Max Viscosity (cP) |

0.00 | 2.40 ± 0.24 | 0.90 ± 0.05 | 0.89 | 0.89 |

0.02 | 2.70 ± 0.64 | 0.96 ± 0.14 | 0.94 | 1.07 |

0.05 | 3.12 ± 0.62 | 1.06 ± 0.14 | 1.02 | 1.34 |

0.09 | 3.87 ± 0.21 | 1.22 ± 0.05 | 1.15 | 1.78 |

0.19 | 5.86 ± 0.49 | 1.67 ± 0.11 | 1.41 | 2.67 |

0.35 | 9.52 ± 1.53 | 2.48 ± 0.34 | 1.85 | 4.18 |

**Figure 3.**DNA measurement using AMBR microviscometer. (

**a**) Viscosities of lambda DNA EcoRI digest solutions at different concentrations, as measured by AMBR microviscometer. The green area indicates the expected range of the viscosity calculated theoretically, assuming that only the longest (top range) or only the shortest (bottom range) DNA fragment size is present. Error bars represent standard deviation among 10 beads in one measurement. (

**b**) Measurement of bead rotation period of pre- and post-digestion samples of lambda DNA by AMBR microviscometer. The field driving frequency is 150 Hz. The error bars show the standard deviation among 10 beads in each measurement. (

**c**) Measurement of viscosity by bead rotation period in PCR reactions sampled every 5 cycles, starting from the 6th cycle. PCR reactions with initial DNA amounts of 0 ng, 0.05 ng, 5 ng, 55 ng, and 250 ng are shown. The reaction volumes are 50 µL each. The field driving frequency is 150 Hz, and the PCR product size is 4500 bp. Each point represents the mean value, observing ten beads. (

**d**) Fluorescent signal intensities of the PCR product (4500 bp band) observed on a electrophoresis gel for the same samples measured in (

**c**).

#### 3.3. Measurement of DNA Reaction Progression

## 4. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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## Appendix

**Figure A1.**Images of the bead rotation at time 0,

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_{4}T,

^{1}/

_{4}T,

^{3}/

_{4}T and T for 45 µm beads at 100 Hz driving frequency, where T is the bead rotation period. While the commercial beads look spherical and symmetrical by eye, the software can tell the subtle difference in shape and surface smoothness of the beads, so as to determine the bead rotation periods.

**Figure A2.**Calibration curves of 45µm bead at different driving frequencies.

**A**: 30 Hz;

**B**: 100 Hz;

**C**: 200 Hz;

**D**: 250 Hz. The critical frequency is at 10–15 Hz. The error bars represent the standard deviation among ten different beads in one measurement. The calibration curves yield good linearity consistently at frequencies away from the critical frequency, i.e., from 100 Hz to 250 Hz.

## Analysis of Figure A3

**Figure A3.**Calibration curves at 100 Hz using beads of different sizes.

**A**: 7.6 µm;

**B**: 16 µm;

**C**: 45 µm. Error bars represents standard deviation among 10 beads in one measurement.

**Figure A4.**Plot of reaction cycle number versus log of initial DNA amount for the qPCR measurement by AMBR method. Error bars represent the uncertainty due to the AMBR measurement of every five cycles.

© 2014 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

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**MDPI and ACS Style**

Li, Y.; Burke, D.T.; Kopelman, R.; Burns, M.A.
Asynchronous Magnetic Bead Rotation (AMBR) Microviscometer for Label-Free DNA Analysis. *Biosensors* **2014**, *4*, 76-89.
https://doi.org/10.3390/bios4010076

**AMA Style**

Li Y, Burke DT, Kopelman R, Burns MA.
Asynchronous Magnetic Bead Rotation (AMBR) Microviscometer for Label-Free DNA Analysis. *Biosensors*. 2014; 4(1):76-89.
https://doi.org/10.3390/bios4010076

**Chicago/Turabian Style**

Li, Yunzi, David T. Burke, Raoul Kopelman, and Mark A. Burns.
2014. "Asynchronous Magnetic Bead Rotation (AMBR) Microviscometer for Label-Free DNA Analysis" *Biosensors* 4, no. 1: 76-89.
https://doi.org/10.3390/bios4010076