- Open Access
A multiplexed magnetic tweezer with precision particle tracking and bi-directional force control
© The Author(s). 2017
- Received: 8 August 2017
- Accepted: 22 November 2017
- Published: 2 December 2017
In the past two decades, methods have been developed to measure the mechanical properties of single biomolecules. One of these methods, Magnetic tweezers, is amenable to acquisition of data on many single molecules simultaneously, but to take full advantage of this "multiplexing" ability, it is necessary to simultaneously incorporate many capabilities that have been only demonstrated separately.
Our custom built magnetic tweezer combines high multiplexing, precision bead tracking, and bi-directional force control into a flexible and stable platform for examining single molecule behavior. This was accomplished using electromagnets, which provide high temporal control of force while achieving force levels similar to permanent magnets via large paramagnetic beads.
Here we describe the instrument and its ability to apply 2–260 pN of force on up to 120 beads simultaneously, with a maximum spatial precision of 12 nm using a variety of bead sizes and experimental techniques. We also demonstrate a novel method for increasing the precision of force estimations on heterogeneous paramagnetic beads using a combination of density separation and bi-directional force correlation which reduces the coefficient of variation of force from 27% to 6%. We then use the instrument to examine the force dependence of uncoiling and recoiling velocity of type 1 fimbriae from Eschericia coli (E. coli) bacteria, and see similar results to previous studies.
This platform provides a simple, effective, and flexible method for efficiently gathering single molecule force spectroscopy measurements.
- Single molecule force spectroscopy
- Magnetic tweezer
Single molecule force spectroscopy (SMFS) has become a powerful tool for investigating the force dependence of biological phenomenon including, but not limited to, biological bonds [1–3],viscoelastic cell properties , DNA stretching , and motor proteins [6, 7]. However, traditional SMFS methods of atomic force microscopy, optical trap, and biomembrane force probe obtain data at slow rates, usually acquiring a single measurement at a time. Since some studies require hundreds to thousands of measurements to accurately model force dependence, such as the stochastic process of biological binding , gathering statistically sufficient data via traditional SMFS methods can take a prohibitively long time.
The smallest detectable change in the height of a bead is referred to as the spatial resolution and determines the lower limit of biological length changes that can be detected. The spatial resolution in basic MT’s is estimated using the depth of field and is on the order of several microns . However, by implementing high-precision particle tracking algorithms, the spatial resolution can be improved to ~1 nm [13–15], greatly expanding the biological questions that can be addressed [9, 11, 16–22]. The use of magnets both below and above the chamber allows beads to be pulled toward and away from the functionalized surface . This bi-directional force control allows greater control of the contact time of the beads with the surface, and as will be shown, can be used to increase the precision of force estimations on the beads. To our knowledge, a MT combining the three capabilities of multiplexing, precision bead tracking, and bidirectional force control has not been demonstrated.
Here we describe a multiplexed MT with precision bead tracking and bi-directional force control (MMTB) and characterize its capabilities. Because high forces of up to 100 pN are desired for many studies, and pose unique challenges for multiplexing with electromagnets, we describe use of the MMTB to obtain this force range. To achieve these high forces, large paramagnetic beads with high magnetic content were used. These beads showed significant bead to bead force variation, which can prohibit the accurate estimation of force dependent properties. To address this challenge, we developed a novel technique for precisely determining forces on beads with heterogeneous magnetic content, which reduced the coefficient of variation of force from 27% to 6%. We then used the MMTB to examine the uncoiling and recoiling velocities of E. coli fimbriae under a wide range of forces. Finally, we discuss the tradeoffs when optimizing a MT for multiplexing versus spatial precision.
Bead size, model, and manufacturer data for beads used in experiments
Bead Size (μm)
Dynabead m-280 streptavidin
Thermo Fisher Scientific, Waltham, MA
Spherotech Inc., Lake Forest, IL
Bangs Laboratories UM4CN
Bangs Laboratories Inc., Fishers, IN
Spherotech Inc., Lake Forest, IL
Chamber slides (Fisherbrand Microscope Cover Glass, 24 × 60 × 1.5, Fisher Scientific, Waltham, MA) were placed in Acetone for 3 min before being rinsed with ethanol and water. A 100 μl droplet of fimbria in 0.02% bicarbonate buffer (1.5 μg/ml) was added to center of the bottom slides and incubated for 2 h at room temperature. A 100 μl droplet of 0.2% PBS-BSA was added to the center of the top slides and incubated at room temperature for 1 h. Bottom slides were rinsed with 0.2% PBS-BSA three times. Chambers were then assembled with double sided tape and 40 μl of 0.2% PBS-BSA was injected into the chamber via a 100 μl pipet. Chambers were covered and stored overnight at 4 °C.
To separate beads by density, differential centrifugation was used similarly to a method used to isolate cellular organelles of different density. Briefly, 5 ml of 1.5 M NaCl (S271–1, Fisher Chemical, Fair Lawn, NJ) was added to a Nalgene 50 ml polypropylene centrifugation tube (3119–0050, Thermo Fisher Scientific, Waltham, MA). 45 ml of a mixture of Percoll (p1644, Sigma Aldrich, St. Louis, MO) and water was added to the tube to obtain a density of 1.09 g/ml. Paramagnetic beads were washed 3 times in PBS, and added to the Percoll solution. This solution was then spun at 30,000 x g for 30 min. A thumbtack was used to create a hole in the bottom of the centrifugation tube, and the solution was drained into 1 ml aliquots. Because Percoll forms a gradient during spinning, both the percent Percoll and the spinning conditions can be adjusted to spread magnetic beads as broadly as possible for maximum separation.
Preparation of beads for Fimbrial uncoiling experiments
In order to bind mannose-BSA to beads, 0.1 mL of 7.8 μm paramagnetic beads were washed two times in 1 mL of MES hydrate (M8250-25G, Sigma Aldrich, St. Louis, MO) with a pH of 4.5–7.5. After the second wash, the pellet was resuspended in 1 mL of MES hydrate and vortexed for 10 s. 10 mg of N-Cyclohexyl-N′-(2-morpholinoethyl) carbodiimide methyl-p-toluenesulfonate (C106402-5G, Sigma Aldrich, St. Louis, MO) was added to the beads. The beads were then vortexed for 10 s, and rotated at room temperature for 15 min. Beads were then washed two times in PBS, and resuspended in 1 mL of the same. The PBS was replaced with 1 mL of 100 mg/ml mannose-BSA (D-Mannose-BSA, NGP-1108, Dextra Laboratories, UK) in PBS and the solution was rotated at room temperature for 2 h. Beads were then washed in 1 mL of 35 mM glycine (Bio-rad Laboratories, Hercules, CA) in water with 0.2% BSA (A3059-100G, Sigma Aldrich, St. Louis, MO) and rotated at room temperature for 30 min. Beads were then washed and resuspended in 0.2% PBS-BSA and stored at 4 °C.
Fimbria were purified from E. coli using magnesium precipitation as described previously .
Description and characterization of the MMTB
The MMTB has four electromagnetic poles: two above and two below a chamber containing paramagnetic beads suspended in buffer (Fig. 1b). The design and orientation of these magnets is similar to those described by Snook and Guilford . Each electromagnetic pole consists of a 6.6 mm diameter Mu-metal rod (GoodFellow, Coraopolis, PA) with the tip shaped to maximize the gradient of the magnetic field . This was achieved by using a taper angle of 33 degrees, with a perpendicular cut near the tip such that the cross sectional area of the flat tip of the rod is reduced by a factor of 40 when compared to its untapered area (Fig. 1c). The Mu-metal rods are encased in spools with several hundred turns of 26 AWG copper wire wound around them. The upper poles are placed very near to the top surface of the chamber, with a separation distance between the poles of ~1 mm. The lower poles, due to spatial constraints below the chamber, are spaced ~7 mm apart and ~3 mm below the chamber. This reduces the magnetic field that pulls beads down, but suffices.
By applying a voltage potential across the coils using two identical power supplies (1697, BK Precision, Yorba Linda, CA), a magnetic field gradient acts to pull the beads in the upward (upper magnet) or downward (lower magnet) direction. In practice, the lower magnet is first used to pull the beads to the bottom, functionalized surface. The current to the lower magnet is then turned off and the current to the upper magnet turned on, and the beads are pulled away from the bottom surface at a force controlled by the magnetic field. This cycle of pulling the beads toward and away from the bottom surface is known as a “pull”. A high speed camera (GT1910, Allied Vision, Exton, PA) is mounted to an inverted microscope (Eclipse TI-E, Nikon, Melville, NY) and used to acquire images of the beads at rates of up to 100 Hz, using either a 0.45 NA 20× or 0.55 NA 40× objective. The use of objectives with longer working distances and low NA’s is due to spatial constraints below the chamber caused by the lower magnet. With the 20× objective, 40 7.8 μm diameter beads or 120 2.8 μm diameter beads can fit in the field of view (528 × 297 μm), with enough space between beads to allow bead tracking i.e. diffraction patterns do not overlap (see Bead Tracking). Multiplexing can be further increased using non-random tether techniques .
A custom Labview program (National Instruments Corporation, Austin, TX) is used to provide synchronous control of the microscope, power supplies, and camera. The Labview program allows the camera and power supply settings to be adjusted in real time, or a time-based script can be used to ensure repeatability between pulls. This flexibility is beneficial when measuring bond lifetimes: one may use a high frame rate to examine the rupture of short-lived bonds, and then switch to a lower frame rate to examine the rupture of long-lived bonds, thus avoiding collecting superfluous amounts of data. Using the Labview program, we found that it takes ~40 ms to switch from one current level to another (data not shown), similar to the findings by Snook and Guilford .
To estimate the tracking accuracy of the MMTB over long distances, we tracked several beads under force as the beads traversed the axial distance of the chamber(~78 μm) under 0.6 amps of current. We then compared this to the chamber height, as measured by focusing on beads that were stuck to the top and bottom of the chamber and noting the microscope objective position. The difference in objective position was then multiplied by 1.33 to account for the refractive index mismatch. The tracked bead displacement was within a few percent of the chamber height with an error of 2.9 ± 0.5% (SEM) for 7.8 μm beads. This demonstrates that our system is capable of accurately tracking beads over long distances, an important ability when estimating the force on beads (described in Force Calibration).
To examine the effect of objective properties and bead size on spatial resolution we determined the spatial resolution for beads of different sizes using a 0.45 NA 20× and a 0.55 NA 40× objective while using a single reference bead (Fig. 3b). At 20×, the resolution was similar for the 2.8–7.8 μm beads but increased dramatically for the 11 μm beads. At 40×, the resolution was a relatively constant 18–30 nm for all bead sizes. Considering the twofold higher magnification objective results in a four-fold reduced field of view and throughput, the small improvement in resolution may be unwarranted for most experiments. Also, since the resolution of beads ranging from 2.8–7.8 μm was similar, the choice of bead size should be based on the desired force range and level of multiplexing: larger beads can achieve higher forces, but fewer can be tracked simultaneously.
Considering that our average chamber height was approximately 78 μm, this estimation of lambda was used for estimating forces on 2.8 μm and 5.3 μm beads, where the position of the bead was assumed to be in the middle of the chamber (b = 39 μm). Because bead velocities were typically measured in the middle third of the chamber, we estimate that this approximation yielded an error in force of less than 5%. For the larger 7.8 μm and 11 μm beads, b/r was less than <15, and therefore the second surface had an effect on the bead velocity. In this case, λ was estimated using the tables and figures created by Ganatos, Pfeffer, and Weinbaum . Estimations of λ in the middle third of the chamber ranged from 1.04 for 2.8 μm beads to 1.35 for 11 μm beads. It should be noted that taller chambers would minimize the need to compensate for surface effects when calibrating force even with larger beads.
To assess the magnetic field gradient variation in the chamber along the z-dimension, we examined the velocity of beads at two different heights of the chamber. Because the velocity of beads near the chamber walls are highly nonlinear due to the effect of the chamber walls, we examined the change in bead velocities at positions in the chamber where the velocities (and thus forces) were more stable: when the beads were at z-positions 25% and 75% the height of the chamber. Examining the velocity of fifteen 7.8 um beads measured on two separate days, we found that the velocity of the beads at a z-position of 75% of the chamber height is 1.11 ± .02 (SEM) times that of the beads at 25% of the chamber height. This increase is unsurprising as the beads are slightly closer to the magnets at the 75% height. Since this change in height is the same as when beads are on the surface compared to when they are halfway across the chamber (where the force is calibrated), we expect the forces measured at the halfway point to be within 11% of the forces at the surface. This potential 11% force error is very similar to the force accuracy of other SMFS instruments .
Expanding on this force data, the smallest upward force that can be applied using the MMTB is about 2 pN with 2.8 μm beads (data not shown), and is limited by the lowest applicable current of our power supply of 0.02 Amps. This force is about five times smaller than the smallest applicable force using an atomic force microscope , and could be further decreased by using a more versatile power supply or increasing the space between the magnetic pole tips. Similarly, the largest force that can be applied with the MMTB is about 260 pN with 11 μm beads at 0.6 Amps (Fig. 4b). This force is ~2.5 fold higher than the maximum applicable force with an optical trap . This 130-fold force range with commercially available beads encompasses the forces usually seen when investigating biological phenomena [1–3, 5]. Furthermore, the linear relationship between force and current over the working range of forces in the MMTB (see Fig. 4a), combined with the ability to program any desired change in current, provides time-dependent force control without the need for a feedback loop. Together, the biologically relevant force range and simple mechanism for manipulating force makes the MMTB a versatile instrument for acquiring constant force measurements.
To test the bead to bead force variation, we determined the coefficient of variation (COV) in force of 7.8 μm beads at 0.1 amps. This resulted in a COV of 27% for “Stock” beads: beads directly from the manufacturer’s container (Fig. 5b, Stock). We hypothesized that this high value was due to inconsistent amounts of magnetic material across the bead population, which would manifest in different bead densities. To test this hypothesis, we separated beads by density using Percoll (p1644, Sigma Aldrich, St. Louis, MO) to create a centrifugal density gradient. We then extracted a small portion of beads from the middle of the density gradient and examined the COV. The separated beads had a 12% COV (Fig. 5b, Separated), less than half the COV of the stock beads.
Application of MMTB for single molecule force measurements
To demonstrate specific adhesion, beads that did not have covalently bound Mannose-BSA were pulled from the fimbria-coated surface at either 60 or 100 pN. These negative control pulls had less than 1% (SEM = 0.2%) adhesion on average, while the average for beads with Mannose-BSA had 23% (SEM = 5%) of beads adhered to the surface. This demonstrates that the vast majority of adhesive events were bound specifically to the fimbrial tips. Based on the net 22% adhesion rate, a Poisson distribution predicts that 12% of attached beads formed multiple attachments .
To ensure that measured velocities were due to fimbrial uncoiling and not reorientation of long fimbriae, we used atomic force microscope imaging to measure the lengths of the fimbriae, which were found to have an average native length of 0.43 ± 0.15 μm with no fimbriae longer than 0.8 μm (N = 39 samples). We then disregarded any measurements that had bead displacements of less than 1.5 μm during the 5 s uncoiling pulls, or during the 2 s 100 pN force for the recoiling pulls. This eliminated any measurements in which fimbriae changed orientation to an upright position without uncoiling, since it is very unlikely that any single fimbria had a length greater than 1.5 um in the native state. Because uncoiling typically extends fimbria to ten times their native length , many uncoiled fimbria met this criteria. We also required at least a 225 nm bead displacement during the fimbrial recoiling velocity measurements, which ensured that all measurements were beyond position noise (~75 nm for this experiment).
Advantages of MMTB
Our MMTB with its unique combination of multiplexing, precision bead tracking, and bi-directional force control was able to efficiently gather single-molecule uncoiling and recoiling velocities over a wide range of forces. Without any of the three aforementioned capabilities, this study would have been significantly more difficult.
The multiplexing ability of the MMTB decreased the experimental time needed to acquire the data. In this case, the decrease was not large over traditional methods. Most of our pulls lasted only 6 s for the actual pull plus 60 s to replace the beads in the chamber, and provided an average of more than 30 measurements per pull, or 0.45 measurements per second. To run a similar experiment with traditional SMFS instruments, there would only be 1 measurement for every 6 s pull, or 0.17 measurements per second. We therefore estimate the MMTB acquired data ~2.7 times faster than traditional SMFS instruments for this experiment. The major limitation on efficiency in this experimental was that detached beads aggregate under the influence of the magnetic field, so beads cannot be reused for multiple pulls, requiring the minute-long bead replacement after each pull cycle. For long pulls where efficiency is most critical, this additional time is well worth it to provide multiplexing. However, for short pulls of less than 1 s, high efficiency would require improvements such as creation of regular arrays with microcontact printing , a microfluidic device for rapid bead replacement, and/or an experimental design that eliminates complete detachment of beads from surface.
Multiplexed SMFS systems have been demonstrated with other MT’s [11, 12], and alternative methods including acoustic force spectroscopy , centrifugal force spectroscopy , nanophotonic traps , optoelectronic tweezers , AFM cantilever arrays , optical tweezer arrays , and DNA curtains . However most of these systems lack key attributes of the MMTB including the ability to change force quickly , precision bead tracking , bidirectional force control (and thus the use of force correlation) , and application of large forces . The multiplexing arrays of optical tweezers or AFM cantilevers do not allow independent position control or force control through feedback loops, so do not apply uniform force conditions to all elements of the array [40, 41]. Other methods have issues with local heating [38, 43], or use high optical intensities that can damage biological specimens [39, 44]. MT’s therefore provide the most flexible multiplexed platform for biological measurements at this time.
For MT’s without precision bead tracking, the spatial resolution is estimated as the depth of field and is on the order of several microns . Since the fimbriae typically uncoiled to lengths of <8 μm, the uncoiling velocities would have been inaccurate or even undetectable without tracking. However, even without using reference beads or time averaging, our spatial resolution of 75 nm was sufficient to accurately determine the uncoiling velocities in this study.
The ability to quickly change the bead force was imperative in estimating recoiling velocities. Because the recoiling velocities were quite rapid, there was a limited time at which the force-dependent velocity could be measured. Since we wanted to measure the dependence of this recoiling velocity on force, the force on the beads had to be set quite quickly, otherwise the fimbria would have completely recoiled before the new force level was attained. This was achievable with electromagnets where a new steady-state force was reached in ~40 ms, but would be more difficult with permanent magnets because a precise and fast shift in position would be required.
Finally, our novel force correlation method, which required the use of the lower magnet, allowed force estimations of tethered beads with greatly improved precision. An alternative method for estimating bead forces uses the Brownian motion of the tethered bead and requires a known tether length and a significant amount of bead position data . This method would have been difficult to implement for the recoiling pulls since the fimbria length was dependent on the bead force, and the bead force was changed every 1–2 s resulting in few data points at each force (Fig. 7b). Our method can be used for virtually any type of experimental design with the MT. Use of the lower magnet to bring the beads into contract with the reactive surface also provides higher temporal control of contact time than does the use of gravitational settling.
Optimization of MMTB for different purposes
Here we specifically designed and optimized the MMTB for efficiently gathering mechanical measurements of single molecules or molecular complexes. This necessitated both multiplexing and precision bead tracking, but prevents either of these capabilities from being maximized. However, others in the field may have need of instruments that emphasize other applications of SMFS, and we offer the following guidance for those considering building their own MT.
To maximize the multiplexing ability of the MT, as many beads as possible should be fit into the field of view. This can be achieved by using a camera with a large field of view in combination with a low magnification objective and small beads. Such a setup does come with drawbacks. First, cameras with large field of views often have low frame rates. This frame rate reduction combined with the low magnification objective decreases the maximum spatial precision . Also, obtaining a uniform magnetic field gradient over a large area requires either more space between the magnetic poles or a less tapered pole tip (for electromagnets) , which reduces the maximum bead force that can be achieved. This is compounded by the desire to use small beads, which typically have a lower applied force than larger beads, due to the smaller amount of magnetic content.
Conversely, maximum spatial precision requires a high magnification objective and a camera with a high frame rate and small pixel area. Such cameras tend to have smaller fields of view, which together with the higher magnification reduces the multiplexing factor. For very high speed cameras, a stronger light source may be required for proper illumination, of which superluminescent diodes are an option . Due to the smaller field of view, a smaller area of uniform magnetic field gradient will suffice, allowing the magnetic poles to be placed closer together, or a more tapered electromagnetic pole tip to be used. These magnetic pole setups can obtain larger maximum bead forces when compared to the multiplexing setup. Finally, since current bead tracking algorithms assume a spherical shaped particle, beads with a very uniform shape will be required to maximize spatial precision. With such a setup, spatial precisions of 0.1 nm at 100 Hz have been demonstrated .
The preceding paragraphs have shown the spectrum of capabilities of the MT: maximizing multiplexing and throughput on one end, and maximizing spatial precision and bead force on the other. Our MMTB is a hybrid of these two extremes: capable of enough spatial precision to detect many biological phenomena [20, 31, 47, 48], while multiplexing to a degree that dramatically increases the throughput of many SMFS experiments. This increased throughput, the biggest advantage of the MT over other SMFS instruments, increases the scope and complexity of questions that can be addressed using SMFS. We hope that this article is a useful guide for others in the field that may be interested in developing or optimizing their own MT.
We would like to thank Dr. Alberto Aliseda and Dr. Nathan Sniadecki for their valuable advice on the movement of beads near surfaces. We would also like to thank Dr. Charles Asbury for his insightful comments in regards to SMFS methods.
Availability of data and materials
The datasets used and/or analysed during the current study are available from the corresponding author on reasonable request.
KCJ modified the design of the MMTB, wrote and/or optimized all the software related to the MMTB, collected all data in this work (with the exception of fimbria native lengths), and did the majority of writing of this manuscript. EC conceived initial concepts and design for the MMTB, and built the first iteration of the instrument. RK wrote the first iteration of the bead tracking code. HM was involved in the initial design and calibration of the MMTB. JV examined the native lengths of fimbriae using atomic force microscopy. WT provided guidance about the design of the MMTB and experimentation strategy while continuously providing biophysical expertise. WT was the primary editor for this manuscript. All authors read and approved the final manuscript.
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