micromachines

Article Configuration and Design of for Rapid and Precise Manipulation of Magnetic Beads in Biosensing Applications

Moshe Stern, Meir Cohen and Amos Danielli *

Faculty of Engineering, Bar-Ilan University, Ramat Gan 5290002, Israel; [email protected] (M.S.); [email protected] (M.C.) * Correspondence: [email protected]

 Received: 6 October 2019; Accepted: 13 November 2019; Published: 15 November 2019 

Abstract: Rapid and precise manipulation of magnetic beads on the nano and micro scales is essential in many biosensing applications, such as separating target molecules from background molecules and detecting specific proteins and DNA sequences in plasma. Accurately moving magnetic beads back and forth requires at least two adjustable magnetic field gradients. Unlike permanent , electromagnets are easy to design and can produce strong and adjustable magnetic field gradients without mechanical motion, making them desirable for use in robust and safe medical devices. However, using multiple magnetic field sources to manipulate magnetic beads presents several challenges, including overlapping magnetic fields, added bulk, increased cost, and reduced durability. Here, we provide a thorough analysis, including analytical calculations, numerical simulations, and experimental measurements, of using two electromagnets to manipulate magnetic beads inside a miniature glass cell. We analyze and experimentally demonstrate different aspects of the electromagnets’ design, such as their mutual influence, the advantages and disadvantages of different pole tip geometries, and the correlation between the electromagnets’ positions and the beads’ aggregation during movement. Finally, we have devised a protocol to maximize the magnetic forces acting on magnetic beads in a two- setup while minimizing the electromagnets’ size. We used two such electromagnets in a small footprint magnetic modulation biosensing system and detected as little as 13 ng/L of recombinant Zika virus antibodies, which enables detection of Zika IgM antibodies as early as 5 days and as late as 180 days post symptoms onset, significantly extending the number of days that the antibodies are detectable.

Keywords: magnetic tweezers; magnetic beads; biosensing; pole tip; Zika virus

1. Introduction Small spherical magnetic beads—usually consisting of a paramagnetic core embedded in a non-magnetic matrix, such as a polymer or quartz [1,2]—are widely used in bioanalysis and medical applications [2–6]. These applications include separating target molecules from background molecules [7–9], investigating molecular interactions inside living cells [5,10,11], directing neuronal migration and growth [12], detecting specific proteins and DNA sequences in plasma [13–16], and reducing background in opto-chemical sensing [17]. Many of these applications require accurate manipulation of the magnetic beads on the nano and micro scales. For example, Anker et al. (2003) developed magnetically modulated optical nanoprobes (MagMOONs) [17,18] that blink in response to rotating magnetic fields. Separating the signal of the blinking probe from the unmodulated background enables simple and sensitive detection of target analytes at low concentrations. Danielli et al. (2008) used a magnetic modulating biosensing (MMB) system to detect proteins and specific DNA sequences.

Micromachines 2019, 10, 784; doi:10.3390/mi10110784 www.mdpi.com/journal/micromachines Micromachines 2019, 10, 784 2 of 15

In MMB, the target molecules are captured by fluorescently labeled magnetic beads that are aggregated and manipulated in and out of an excitation beam, separating their signal from that of Raman scattering of water molecules and unbound fluorescently labeled probes [13–16]. To remotely manipulate magnetic beads, an external magnetic field is applied. A constant magnetic field can rotate the magnetic beads, and a magnetic field gradient exerts a force on the beads that can displace them. The design of external magnetic field sources affects the forces acting on the magnetic beads. In applications that involve separation of a target molecule from background molecules, a single magnetic field gradient source, e.g., a permanent , is used. The gradient pulls the magnetic beads, which are attached to the target molecules, onto the sample holder’s wall, and the rest of the sample is then washed out. However, a single magnet can only pull the magnetic beads, but not push them away [1]. Therefore, when precise manipulation of beads in space is required, several magnets are used. To manipulate magnetic beads along a straight line, in a plane, or in space, at least two, three, or six magnets are required, respectively [5,19]. The use of multiple magnetic field sources to manipulate magnetic beads presents several challenges, including overlapping magnetic fields, added bulk, increased cost, and reduced durability. In many lab-on-a-chip applications, permanent magnets are the most accessible source of a strong magnetic field [12,20]. However, to adjust the field strength and manipulate magnetic beads, permanent magnets have to be physically rotated or translated [17]. Alternatively, electromagnets, which convert electrical current into a magnetic field and allow rapid control of the field strength, can be turned on or off without mechanical movement [1,21] and thereby have less risk of malfunction. The simplest version of an electromagnet is a coiled conductive wire. Multiple coils that are formed in a cylindrical geometry construct a . When electrical current runs through the wire, a magnetic field is established in the direction of the solenoid’s axis. The magnetic field is concentrated into a nearly uniform field in the center of the solenoid and is weaker and diverges outside of the solenoid. To amplify the magnetic field, a magnetic core is positioned inside the solenoid. The cores, also called poles, are typically made of a soft ferromagnetic material (e.g., iron or -iron alloys) [1]. The manipulation of a single magnetic bead by either a single or by several electromagnets has been extensively analyzed [1,5,15,22]. However, manipulating multiple beads by using two electromagnets has yet to be explored. Moreover, recent publications have described the particular effectiveness of electromagnets with sharpened pole tips in manipulating magnetic beads [1,5,19,21,23]. A sharp pole tip induces higher forces on beads that are near the tip. To date, only basic cone [22] and parabolic [5] pole-tip shapes have been analyzed and experimentally tested. Here, we analyze and experimentally demonstrate these and other aspects of the beads’ manipulation, including the mutual influence of electromagnets, the advantages and disadvantages of different pole tip geometries, and the correlation between the position of the electromagnets and the beads’ aggregation during movement. Finally, we have devised a protocol to maximize the magnetic forces acting on magnetic beads in a two-electromagnet setup while minimizing the electromagnets’ size and power consumption. Using two electromagnets in a small footprint magnetic modulation biosensing system, we detected as little as 13 ng/L of recombinant Zika virus (ZIKV) antibodies, which enables detection of Zika IgM antibodies as early as 5 days and as late as 180 days post symptoms onset, significantly extending the number of days that the antibodies are detectable. [16].

2. Materials and Methods

2.1. Evaluating Different Pole Tip Shapes To evaluate different shapes of magnetic pole tips, we used a single electromagnet setup. In Figure1, the electromagnet’s mechanical dimensions are denoted by L, the length of the coil; w, the total winding area thickness; h, the distance from the coil to the pole’s tip (e.g., a parabolic pole tip with a curvature coefficient, β); D, the diameter of the magnetic pole; c, the core’s sleeve width; and d, the diameter of the wire (not including its insulating coating). Micromachines 2019, 10, 784 3 of 15 Micromachines 2019, 10, x FOR PEER REVIEW 3 of 15 Micromachines 2019, 10, x FOR PEER REVIEW 3 of 15

Figure 1. The geometry of an electromagnet with a parabolic pole tip. 𝐿L and w𝑤, length and width of Figure 1. The geometry of an electromag electromagnetnet with a parabolic pole pole tip. tip. 𝐿 and and ,𝑤, length length andand widthwidth ofof thethe windings windings area; area; 𝑑d,, wire diameter; D𝐷,, magnetic pole diameter; diameter; c𝑐,, corecore sleeve’ssleeve’s width; 𝛽β, parabolic the windings area; 𝑑, wire diameter; 𝐷, magnetic pole diameter; 𝑐, core sleeve’s width; 𝛽, parabolic curvature of the pole tip; and hℎ,, thethe distancedistance fromfrom the the coil coil edge edge to to the the pole’s pole’s tip. tip curvature of the pole tip; and ℎ, the distance from the coil edge to the pole’s tip We evaluated cylindrical magnetic poles𝐷=12.7 (D = 12.7 mm) with four different tip shapes: A flat, WeWe evaluatedevaluated cylindricalcylindrical magneticmagnetic polespoles ((𝐷=12.7 mm) mm) withwith fourfour differentdifferent tiptip shapes:shapes: AA flat,flat, aa a cone, a paraboloid, and a cube (Figure2). The magnetic field profile of each pole was simulated cone,cone, aa paraboloid,paraboloid, andand aa cubecube (Figure(Figure 2).2). TheThe magneticmagnetic fieldfield profileprofile ofof eacheach polepole waswas simulatedsimulated assuming an electromagnet with the following parameters: L =𝐿100 = mm,100 w =𝑤31.7 = mm,31.7 h = 35ℎ=35mm, assumingassuming anan electromagnetelectromagnet wiwithth thethe followingfollowing parameters:parameters: 𝐿 = 100 mm,mm, 𝑤 = 31.7 mm,mm, ℎ=35 d = 0.75𝑑mm = 0.75 (not including coating), and current I = 1 A. For𝐼=1 consistency, the tip of each magnetic pole mm,mm, 𝑑 = 0.75 mmmm (not(not includingincluding coating),coating), andand currentcurrent 𝐼=1 A.A. ForFor consistency,consistency, thethe tiptip ofof eacheach was set at (z, r) = (0, 0), and𝑧, the 𝑟 = distance0,0 from the coil edge to the pole tips was fixed at h = 35 mm. magneticmagnetic polepole waswas setset atat 𝑧, 𝑟 = 0,0,, andand thethe distancedistance fromfrom thethe coilcoil edgeedge toto thethe polepole tipstips waswas fixedfixed Toℎ=35 calculate the magnetic force acting on a magnetic bead as a function of the distance from the pole’s atat ℎ=35 mm. mm. ToTo calculatecalculate thethe magneticmagnetic forceforce actingacting onon aa magneticmagnetic beadbead asas aa functionfunction ofof thethe distancedistance tip along the electromagnet’s symmetry axis, we considered a magnetic bead (Dynabeads M-280 fromfrom thethe pole’spole’s tiptip alongalong thethe electromagnet’selectromagnet’s symmetrysymmetry axis,axis, wewe consideredconsidered aa magneticmagnetic beadbead (DynabeadsStreptavidin, M-280 Thermo Streptavidin, Fisher, Waltham, Thermo MA, Fisher, USA) Waltham, [24] whose MA, magneticUSA) [24] moment whose magnetic was saturated moment at (Dynabeads 13M-280 2Streptavidin, Thermo Fisher, Waltham, MA, USA) [24] whose m = 2 wass saturated1.8 10− atA m𝑚.=1.8∙10 A·m 2. was saturated· at · 𝑚 =1.8∙10 A·m .

Figure 2.2. COMSOLCOMSOL MultiphysicsMultiphysics®®simulations simulations of theof the magnetic magnetic force force profiles profiles of diff oferent different pole tip pole shapes. tip Figure 2. COMSOL Multiphysics® simulations of the magnetic force profiles of different pole tip shapes.The magnetic The magnetic force profiles force ofprofiles four pole of four tip shapes;pole tip( ashapes;) flat-top, (a) (flat-top,b) conical, (b) ( cconical,) parabolic, (c) parabolic, and (d) cubic. and shapes. The magnetic force profiles of four pole tip shapes; (a) flat-top, (b) conical, (c) parabolic, and (d)The cubic. color mapThe color of the map contour of the lines contour represents lines therepres magnitudeents the ofmagnitude the force, andof the the force, arrows and represent the arrows the (d) cubic. The color map of the contour lines represents the magnitude of the force, and the arrows representdirection ofthe the direction force. of the force. represent the direction of the force. 2.2. Analytical and Numerical Models of the Magnetic Force Acting on a Magnetic Bead 2.2.2.2. AnalyticalAnalytical andand NumericalNumerical ModelsModels ofof thethe MagneticMagnetic ForceForce ActingActing onon aa MagneticMagnetic BeadBead In general, magnetic beads’ movement in a fluid is mainly affected by the magnetic force and the In general, magnetic beads’ movement in a fluid is mainly affected by the magnetic force and dragIn force, general,Fdrag ,magnetic which, for beads’ a spherical movement particle, in isa fluid given is by mainly [1,2,9] affected by the magnetic force and the drag force, 𝐹, which, for a spherical particle, is given by [1,2,9] the drag force, 𝐹, which, for a spherical particle, is given by [1,2,9] = 𝐹Fdrag =6𝜋𝜂𝑟𝑣6πηrv (1)(1) 𝐹 =6𝜋𝜂𝑟𝑣 (1) where 𝜂 is the solution viscosity (e.g., 𝜂 = 8.9 4∙ 10 𝑃𝑎 ∙ 𝑠𝑒𝑐 in water), 𝑟 is the particle radius, and wherewhere η𝜂 is is the the solution solution viscosityviscosity (e.g.,(e.g., η𝜂= 8.9 = 8.910− ∙ 10 Pa 𝑃𝑎sec in ∙ water), 𝑠𝑒𝑐 in water),r is the𝑟 is particle the particle radius, radius, and andv is 𝑣 · · the𝑣 is is particle thethe particleparticle velocity. velocity.velocity. An AnAn accurate accurateaccurate model modelmodel of ofof the thethe beads’ beads’beads’ movement movementmovement in inin solution solutionsolution should shouldshould consider considerconsider both both forcesforces [15]. [[15].15]. However,However, However, thethe the purposepurpose purpose ofof of thisthis this paperpaper paper isis is toto to exploreexplore explore differentdifferent different aspectsaspects ofof electromagnets’electromagnets’ design,design, whichwhich mainlymainlymainly a affectsaffectsffects the thethe magnetic magneticmagnetic force forceforce acting actingacting on onon the thethe beads. beads.beads. Hence, Hence,Hence, our ourour simulation simulationsimulation focused focusedfocused on oncomparingon comparingcomparing the magneticthethe magneticmagnetic force in forceforce space inin for spacespace different forfor designs differentdifferent and designsdesigns configurations andand configurationsconfigurations of the electromagnets. ofof thethe electromagnets.electromagnets.

Micromachines 2019, 10, 784 4 of 15

To derive an analytical expression of the force acting on a magnetic bead, two assumptions were made. First, the bead is a single, zero-dimensional object. Second, the magnetic field surrounding the pole tip is sufficiently high that the bead’s magnetic moment is saturated. Without these assumptions, the magnetic moment of the bead becomes spatially-dependent rather than constant, and the calculation of the force is needlessly complicated. However, under these assumptions, the force acting on the bead depends simply on the bead’s moment and the magnetic field gradient at the bead’s specific location. Overall, the force, Fm, acting on a magnetic bead that has a saturated magnetic moment, ms, and is located at position z, r is given by (Supplementary Material, AppendixA):

1/2 →  2 2 Fm = (ms/ B ) (Br∂Br/∂r + Bz∂Bz/∂r) + (Br∂Br/∂z + Bz∂Bz/∂z) (2) | |

→ where B is the magnetic field, and Bz and Br are the scalar components of the magnetic field in the z and r directions. Simulations using COMSOL Multiphysics®magnetic field module showed that the magnetic moment of the bead used in our setup saturates around the pole tips (Supplementary Material, Figure S1). Moreover, the bead (2.8 µm in diameter) is much smaller than the 12.7 mm diameter of the electromagnetic pole. Therefore, in our setup both assumptions are valid.

2.3. Manipulation of Magnetic Beads Using a Two-Electromagnet Setup To manipulate magnetic beads back and forth along a straight line, two electromagnets that are facing each other are required. To analyze the characteristics of this manipulation, we used two 1 identical electromagnets, labeled A and B in Figure3, each having a parabolic pole tip ( β = 0.65 mm− ) and the following dimensions: L = 100 mm, w = 31.7 mm, h = 35 mm, D = 12.7 mm, c = 3 mm, and d = 0.75 mm. The number of turns was 3900, and the measured resistance was 24 ohms. To demonstrate and analyze the movement of magnetic beads, we used ~30,000 magnetic beads (Dynabeads M-280 Streptavidin, Thermo-Fischer, Waltham, MA, USA) mixed in phosphate buffered saline with Tween-20 buffer (PBST) and placed in a rectangular bottom-sealed borosilicate sample cell whose inner dimensions were 8 mm 0.4 mm 70 mm (Vitrocom, 2540, Boonton, NJ, USA). × × The sample cell was held between the electromagnets so that the beads could be manipulated along its narrow dimension (i.e., 0.4 mm). When the two electromagnets were alternately turned on and off, the magnetic beads moved periodically between them. The movement of the magnetic beads was imaged to the back plane of an objective lens (Newport, M-10 , 0.25NA, Newport, CA, USA) and × visualized using a CMOS camera (FLIR, GS3-U3-23S6M-C, Wilsonville, OR, USA).

2.4. Evaluating the Effects of Mutual in a Two-Electromagnet Setup When two or more electromagnets are used to manipulate magnetic beads, mutual magnetizing of the pole tips and the remnant magnetic fields of the ferromagnetic cores affect the forces acting on the magnetic beads. For example, in a two-electromagnet setup, when one of the electromagnets is active and the other is inactive, the beads are expected to move towards the active magnet. However, due to and the influence of the active electromagnet, the ferromagnetic core of the inactive electromagnet is magnetized, and it attracts nearby beads. In Figure4, when electromagnet A is active, the magnetic force along its symmetry axis decreases until it reaches zero at a point beyond half the distance to the inactive electromagnet B. Beyond this point, the magnetic force increases, but its direction changes towards the inactive electromagnet. Hence, although electromagnet B is inactive, beads that are in its proximity will be attracted to it rather than towards the active electromagnet A. Consequently, the distance over which the magnetic beads can be manipulated back and forth without being trapped by one of the electromagnets is smaller than the actual distance between the electromagnetic pole tips. Here, we defined this distance as the “working distance”, and it is calculated by subtracting the positions along the z-axis in which the force is zero (Figure4c). Micromachines 2019, 10, x FOR PEER REVIEW 4 of 15

To derive an analytical expression of the force acting on a magnetic bead, two assumptions were made. First, the bead is a single, zero-dimensional object. Second, the surrounding the pole tip is sufficiently high that the bead's magnetic moment is saturated. Without these assumptions, the magnetic moment of the bead becomes spatially-dependent rather than constant, and the calculation of the force is needlessly complicated. However, under these assumptions, the force acting on the bead depends simply on the bead's saturation moment and the magnetic field gradient at the bead’s specific location. Overall, the force, 𝐹 , acting on a magnetic bead that has a saturated magnetic moment, 𝑚, and is located at position 𝑧, 𝑟 is given by (Supplementary Material, Appendix A):

⁄ 𝐹 =𝑚⁄𝐵⃗𝐵𝜕𝐵⁄𝜕𝑟 +𝐵𝜕𝐵⁄𝜕𝑟 + 𝐵𝜕𝐵⁄𝜕𝑧 +𝐵𝜕𝐵⁄𝜕𝑧 (2) where 𝐵⃗ is the magnetic field, and 𝐵 and 𝐵 are the scalar components of the magnetic field in the 𝑧 and 𝑟 directions. Simulations using COMSOL Multiphysics® magnetic field module showed that the magnetic moment of the bead used in our setup saturates around the pole tips (Supplementary Material, Figure S1). Moreover, the bead (2.8 µm in diameter) is much smaller than the 12.7 mm diameter of the electromagnetic pole. Therefore, in our setup both assumptions are valid.

2.3. Manipulation of Magnetic Beads Using a Two-Electromagnet Setup To manipulate magnetic beads back and forth along a straight line, two electromagnets that are facing each other are required. To analyze the characteristics of this manipulation, we used two identical electromagnets, labeled A and B in Figure 3, each having a parabolic pole tip (𝛽 = 0.65 mm−1) and the following dimensions: 𝐿 = 100 mm, 𝑤 = 31.7 mm, ℎ=35 mm, 𝐷=12.7 mm, 𝑐= 3 mm, and 𝑑=0.75 mm. The number of turns was 3900, and the measured resistance was 24 ohms. To demonstrate and analyze the movement of magnetic beads, we used ~30,000 magnetic beads (Dynabeads M-280 Streptavidin, Thermo-Fischer, Waltham, MA, USA) mixed in phosphate buffered saline with Tween-20 buffer (PBST) and placed in a rectangular bottom-sealed borosilicate sample cell whose inner dimensions were 8 mm × 0.4 mm × 70 mm (Vitrocom, 2540, Boonton, NJ, USA). The sample cell was held between the electromagnets so that the beads could be manipulated along its narrow dimension (i.e., 0.4 mm). When the two electromagnets were alternately turned on and off, the magnetic beads moved periodically between them. The movement of the magnetic beads was Micromachines 2019, 10, 784 5 of 15 imaged to the back plane of an objective lens (Newport, M-10×, 0.25NA, Newport, CA, USA) and visualized using a CMOS camera (FLIR, GS3-U3-23S6M-C, Wilsonville, OR, USA).

Micromachines 2019, 10, x FOR PEER REVIEW 5 of 15

2.4. Evaluating the Effects of Mutual Magnetization in a Two-Electromagnet Setup When two or more electromagnets are used to manipulate magnetic beads, mutual magnetizing of the pole tips and the remnant magnetic fields of the ferromagnetic cores affect the forces acting on the magnetic beads. For example, in a two-electromagnet setup, when one of the electromagnets is active and the other is inactive, the beads are expected to move towards the active magnet. However, due to remanence and the influence of the active electromagnet, the ferromagnetic core of the inactive electromagnet is magnetized, and it attracts nearby beads. In Figure 4, when electromagnet A is active, the magnetic force along its symmetry axis decreases until it reaches zero at a point beyond half the distance to the inactive electromagnet B. Beyond this point, the magnetic force increases, but its direction changes towards the inactive electromagnet. Hence, although electromagnet B is inactive, beads that are in its proximity will be attracted to it rather than towards the active electromagnetFigure 3. Experimental ExperimentalA. Consequently, setup setup theof of two distance electromagnets over which wi with theth parabolicmagnetic pole-tips beads can that be aremanipulated positioned back and oppositeforth without eacheach other.other. being TheThe trapped sample sample cell bycell isone is positioned positioned of the betweenelec betweentromagnets the the poles poles usingis smallerusing a sample a samplethan holder the holder andactual anand XYZdistance an betweenXYZtranslational thetranslational electromagnetic stage. stage. The The movement pole movement tips. of Here, the of magneticthe we magnetic defined beads beads this in thedistance in the cell cell is as imaged is theimaged “working to theto the back backdistance”, plane plane of and an objective lens and visualized using a CMOS camera. it is calculatedof an objective by subtractinglens and visualized the positions using a CMOSalong thecamera. z-axis in which the force is zero (Figure 4c).

Figure 4. The magnetic force profile profile of two electromagnets positioned opposite each other. Simulated magnetic fieldfield profile profile when when (a )( electromagneta) electromagnet A (bottom) A (bottom) is active is active and electromagnet and electromagnet B (top) isB inactive,(top) is andinactive, conversely, and conversely, (b) when (b electromagnet) when electromagnet A (bottom) A (bottom) is inactive is in andactive electromagnet and electromagnet B (top) B is (top) active. is = 1 Theactive. distance The distance between between the parabolic the parabolic pole tips (βpole0.65 tipsmm (𝛽=0.65− ) is 3 mm.mm− The1) is contour3 mm. linesThe contour represent lines the magnituderepresent the of magnitude the force, and of the the force, arrows an representd the arrows its direction.represent (itsc) Thedirection. working (c) The distance working is defined distance as theis defined distance as between the distance the positionsbetween the along positions the z-axis, alon ing whichthe z-axis, the magneticin which forcethe magnetic is zero. force is zero. First, we simulated the correlation between the working distance and different parameters, such as First, we simulated the correlation between the working distance and different parameters, such the distance between pole tips, the pole tip’s parabolic curvature, and the electric signal profile. as the distance between pole tips, the pole tip's parabolic curvature, and the electric signal profile. To To correlate the working distance and the distance between the pole tips, we assumed that the parabolic correlate the working distance and the distance between the pole tips, we assumed that the parabolic curvature of the tips was β = 0.65 mm 1. To correlate the working distance and the pole tips’ parabolic curvature of the tips was 𝛽 = 0.65 −mm−1. To correlate the working distance and the pole tips’ curvature, we assumed that the distance between the pole tips was 3 mm. For the correlation between parabolic curvature, we assumed that the distance between the pole tips was 3 mm. For the the working distance and the electric signal profile, we assumed that the distance between the pole correlation between the working distance and the electric signal profile, we assumed that the distance tips was 3 mm and the parabolic curvature of the tips was β = 0.25, 0.65, and 0.85 mm 1. In addition, between the pole tips was 3 mm and the parabolic curvature of the tips was 𝛽= 0.25,− 0.65, and 0.85 we assumed that the electromagnets were activated by two square waves, with a 50% duty cycle and mm−1. In addition, we assumed that the electromagnets were activated by two square waves, with a a 180 phase shift between them. The peaks of the square waves were 36 V, and the valleys ranged 50% duty◦ cycle and a 180° phase shift between them. The peaks of the square waves were 36 V, and between 0 V to 36 V. Therefore, the ratio between the voltages of the electromagnets, V /V , ranged the valleys ranged− between 0 V to −36 V. Therefore, the ratio between the −voltages2 1 of the from 0 to 1. For each correlation study, we calculated the magnetic force along the z-axis between the electromagnets, −𝑉⁄𝑉, ranged from 0 to 1. For each correlation study, we calculated the magnetic electromagnets’ pole tips and derived the working distance. force along the z-axis between the electromagnets’ pole tips and derived the working distance. Second, we experimentally validated the correlation between the working distance and the Second, we experimentally validated the correlation between the working distance and the distance between the pole tips. We placed the magnetic poles (β = 0.65 mm 1) 3 mm and 4 mm apart distance between the pole tips. We placed the magnetic poles (𝛽 = 0.65 mm−−1) 3 mm and 4 mm apart and imaged the beads’ movement inside rectangular glass cells that had various inner widths, ranging from 0.4 mm to 0.8 mm (Vitrocom, 2540, 4905, 4806, 4707, 4608). The electromagnets were activated by two square waves, with an amplitude of 36V, a 50% duty cycle, and a 180° phase shift between them.

Micromachines 2019, 10, 784 6 of 15 and imaged the beads’ movement inside rectangular glass cells that had various inner widths, ranging from 0.4 mm to 0.8 mm (Vitrocom, 2540, 4905, 4806, 4707, 4608). The electromagnets were activated by two square waves, with an amplitude of 36V, a 50% duty cycle, and a 180◦ phase shift between them. Third, we explored how the magnetic beads move between two electromagnets with parabolic pole tips. When the two electromagnets, positioned opposite each other, were placed in proximity, the magnetic beads moved along a narrow line on the z-axis between the pole tips. This movement resembled an hourglass with a narrow neck. To evaluate the correlation between the width of the neck and the distance between the pole tips, we placed a bottom-sealed borosilicate sample cell with an inner width of 0.6 mm (Vitrocom, 4806, Boonton, NJ, USA) between two electromagnets with parabolic pole 1 tips (β = 0.65 mm− ). Using XYZ translational stages, we changed the distance between the pole tips from 1 mm to 7 mm. For each distance, the beads’ movement was recorded, and the width of the neck was measured.

2.5. Optimizing Magnetic Forces in a Two-Electromagnet Setup To maximize the magnetic force of an electromagnet while minimizing its physical dimensions and power consumption, we calculated the tradeoff between the winding area width, w, and the diameter of the pole, D. Based on the physical constraints of the setup, one can determine the total diameter of the electromagnet, S, which is defined as:

S = D + 2w + 2c (3) where c is the core sleeve’s width. For three fixed total diameters of the electromagnet (S = 45, 50, and 55 mm), we simulated the magnetic force acting on a magnetic particle located along the symmetry axis at z = 2 mm from the parabolic pole tip as a function of the winding area width. The core sleeve’s width was assumed to be 3 mm (i.e., c = 3 mm), and the electromagnet parameters were set at 1 L = 100 mm, h = 35 mm, d = 0.75 mm, β = 0.65 mm− , and I = 1 A.

2.6. Preparing the MMB IgM anti-Zika NS1 Dose Response To demonstrate the use of two optimally designed electromagnets in a biosensing application, we measured increasing concentrations of recombinant ZIKV antibodies (Human IgM anti-Zika NS1 monoclonal antibodies, MAB12123, Native Antigen) in an MMB system (Supplementary Material, AppendixB). The MMB system uses a 532 nm laser module (Thorlabs, CPS532, Newton, NJ, USA), working at 0.25 mW. A dichroic mirror (Semrock, BrightLine Di02-R532, Rochester, NY, USA) diverts the excitation beam to an objective lens (Newport, M-10 , 0.25NA, Newport, CA, USA), × which focuses the beam to a 150 µm spot size on a rectangular, borosilicate sample cell. The cell contains the fluorescently tagged beads and has inner dimensions of 8 mm 0.4 mm 70 mm (Vitrocom, W2540, × × Boonton, NJ, USA). The emitted fluorescence is collected using the same objective lens, passed through the dichroic mirror and two emission filters (Semrock, FF03-575/25, Rochester, NY, USA), and detected by a digital camera (FLIR, GS3-U3-23S6M-C, Wilsonville, OR, USA). Two electromagnets, positioned 3 mm apart (one on each side of the glass sample cell), apply an alternating magnetic field gradient to the sample, causing the magnetic beads to aggregate and move together in a periodic lateral motion in and out of the laser beam. The modulation frequency of the electromagnets was set to 1 Hz. While the beads are moving, the laser beam remains fixed, causing the beads to form an “on” signal when they are in the laser beam and an “off” signal when they 1 have moved out of the laser beam. The new electromagnets have parabolic pole tips (β = 0.85 mm− ) and the following parameters: L = 50 mm, w = 20 mm, D = 9 mm, h = 15 mm, d = 0.81 mm, c = 3 mm, and I = 1.4 A. For each measurement, a sequence of 600 images is acquired over a period of 12 seconds. The grey value from the laser beam area of each image is integrated and the peak-to-peak voltage differences over time are calculated and averaged. Micromachines 2019, 10, 784 7 of 15

To validate the analytical performance of the new MMB system with the two small footprint electromagnets, we measured the same concentrations of recombinant ZIKV antibodies using a previous version of the MMB system. The standard MMB system, which was extensively analyzed [6,13–16], uses the relatively bulky and power consuming electromagnets.

3.Micromachines Results 2019, 10, x FOR PEER REVIEW 7 of 15

3.1.3.1. Evaluating Evaluating Di Differentfferent Pole Pole Tip Tip Shapes Shapes FigureFigure5 presents5 presents the the magnetic magnetic field field force force along alon theg the electromagnet’s electromagnet’s symmetry symmetry axis axis for for di differentfferent polepole tip tip shapes. shapes. AtAt lessless thanthan 0.170.17 mmmm fromfrom thethe polepole tip,tip, the highest magnetic force is is generated generated by by a aconic conic pole tip. At At a distance between 0.17 mmmm andand 7.57.5 mm,mm, thethe highesthighest magnetic magnetic force force is is generated generated byby a a parabolic parabolic pole pole tip. tip. AtAt aa distancedistance overover 7.57.5 mmmm fromfrom the pole’s tip, a flat-top flat-top pole tip tip generates generates a aslightly slightly higher higher magnetic magnetic force force than than any any of of the the other other pole pole tip tip shapes. shapes. At a At relatively a relatively long long distance distance from fromthe pole the pole tips tips(e.g., (e.g., over over 3 mm), 3 mm), the magnetic the magnetic forces forces generated generated by a by cubic a cubic pole pole tip and tip and a parabolic a parabolic pole poletip tipare aresimilar. similar. However, However, at ata arelatively relatively short short di distancestance (e.g., (e.g., less less than 3 mm),mm), thethe magneticmagnetic force force generatedgenerated by by a a parabolic parabolic pole pole tip tip is is up up to to 10-fold 10-fold higher higher than than that that of of a a cubic cubic pole pole tip tip (Figure (Figure5). 5).

Figure 5. The magnetic force as a function of the distance from the pole’s tip for various magnetic pole tips.Figure Inset: 5. The The magnetic magnetic force force as as a a function function of of the the distance distance from from the the pole’s pole’s tip tip fo forr various a conic magnetic pole tip and pole atips. parabolic Inset:pole The tip.magnetic force as a function of the distance from the pole’s tip for a conic pole tip and a parabolic pole tip. 3.2. Characteristics of Magnetic Beads Manipulation and Mutual Magnetization in a Two-Electromagnet Setup 3.2. Characteristics of Magnetic Beads Manipulation and Mutual Magnetization in a Two-Electromagnet Figure6 depicts the characteristics of the working distance in a two-electromagnet system. Setup The working distance significantly lengthens when the distance between the pole tips increases (FigureFigure6a). In 6 addition, depicts the for acharacteristics fixed distance of between the working the pole distance tips, the in workinga two-electromagnet distance becomes system. larger The whenworking the parabolicdistance significantly coefficient, β lengthens, increases when (Figure the6b). distance The broadening between the of pole the workingtips increases distance (Figure as a6a). function In addition, of the parabolicfor a fixed coe distancefficient between saturates the at po approximatelyle tips, the workingβ = 0.85. distance becomes larger when the Theparabolic correlation coefficient, between 𝛽, increases the working (Figure distance 6b). The and broadening the ratiobetween of the working the voltages distance of theas a electromagnetsfunction of the is parabolic depicted incoefficient Figure6c. saturates When the atvoltage approximately of the inactive 𝛽=0.85. electromagnet, V2, is inverted (i.e., insteadThe correlation of 0 V during between its inactive the working phase, itdistance receives and a negative the ratio voltage), between the the working voltages distance of the canelectromagnets be broadened. is Thedepicted working in Figure distance 6c. reaches When itsthe maximum voltage of value the (3inactive mm,the electromagnet, distance between 𝑉 , is theinverted pole tips) (i.e., when instead the of ratio 0 V betweenduring its the inactive amplitudes phase, of it the receives inactive a negative electromagnet voltage), and the the working active electromagnetdistance can be is 0.6–0.9broadened. (i.e., TheV / Vworking= 0.6 –distance0.9). The reaches ratio for its which maximum the working value distance(3 mm, the reaches distance its − 2 1 maximumbetween the varies pole for tips) diff whenerent the parabolic ratio between coefficients. the amplitudes When the ratioof the between inactive the electromagnet voltages increases and the further,active theelectromagnet working distance is 0.6–0.9 drops (i.e., until −𝑉 it⁄ becomes𝑉 = 0.6– zero 0.9). when The theratio negative for which amplitude the working of the inactivedistance electromagnetreaches its maximum equals the varies positive for different amplitude parabolic of the active coefficients. electromagnet When the (i.e., ratioV between/V = 1). the voltages − 2 1 increases further, the working distance drops until it becomes zero when the negative amplitude of

the inactive electromagnet equals the positive amplitude of the active electromagnet (i.e., −𝑉⁄𝑉 = 1).

Micromachines 2019, 10, 784 8 of 15 Micromachines 2019, 10, x FOR PEER REVIEW 8 of 15

Figure 6. Characteristics of the working distance for a system of two electromagnets with parabolic Figure 6. Characteristics of the working distance for a system of two electromagnets with parabolic pole tips that are positioned opposite each other. (a) The working distance as a function of the distance pole tips that are positioned opposite each other. (a) The working distance as a function of the distance between the pole tips (β = 0.65). (b) The working distance as a function of the parabolic coefficient, between the pole tips (𝛽 = 0.65). (b) The working distance as a function of the parabolic coefficient, β (the distance between the pole tips is 3 mm). (c) The working distance as a function of the ratio 𝛽 (the distance between the pole tips is 3 mm). (c) The working distance as a function of the ratio between the voltages of the electromagnets (all β units are in [1/mm], and the distance between the pole between the voltages of the electromagnets (all 𝛽 units are in [1/mm], and the distance between the tips is 3 mm). pole tips is 3 mm). The correlation between the working distance and the distance between the pole tips was validated experimentally.The correlation When between the distance the betweenworking the distance two parabolic and the pole distance tips (β =between0.65) was the 4 mm,pole thetips beads was couldvalidated be manipulated experimentally. inside When a 0.5 the mm distance wide cuvette between (Figure the two7a). parabolic However, pole when tips the (𝛽 inner = 0.65 width) was of 4 themm, cuvette the beads was could 0.7 mm, be themanipulate beads wered inside trapped a 0.5 on mm the wide cuvette’s cuvette walls (F andigure could 7a). However, not be manipulated when the frominner sidewidth to of side the (Figure cuvette7 b).was When 0.7 mm, the the distance beads we betweenre trapped the twoon the parabolic cuvette’s pole walls tips and was could 3 mm, not thebe manipulated beads could befrom manipulated side to side inside (Figure a 0.4 7b). mm When wide the cuvette, distance but notbetween inside the a 0.5 two mm parabolic or wider pole cuvette tips (Supplementarywas 3 mm, the beads Material, could Movie be manipulated S1). These inside experimental a 0.4 mm findingswide cuvette, match but well not with inside the a COMSOL0.5 mm or Multiphysicswider cuvette® (Supplementarysimulation results Material, (Figure Movie6a). S1). These experimental findings match well with the COMSOL Multiphysics® simulation results (Figure 6a).

Micromachines 2019, 10, 784 9 of 15 MicromachinesMicromachines 20192019,, 1010,, xx FORFOR PEERPEER REVIEWREVIEW 99 ofof 1515

FigureFigure 7.7. ExperimentalExperimentalExperimental demonstrationdemonstration demonstration ofof of thethe the workingworking working distandistan distancecece inin aa in systemsystem a system ofof twotwo of electromagnetselectromagnets two electromagnets withwith parabolicwithparabolic parabolic polepole tips poletips ((𝛽=0.65 tips𝛽=0.65 (β =)) 0.65 thatthat) are thatare positionedpositioned are positioned 44 mmmm 4 mmoppositeopposite opposite eacheach each other.other. other. ((aa)) MagneticMagnetic (a) Magnetic beadsbeads beads cancan becanbe manipulatedmanipulated be manipulated fromfrom from sideside side toto sideside to side inin inaa 0.50.5 a 0.5 mmmm mm widewide wide glassglass glass cuvette.cuvette. cuvette. ((b (bb)) ) MagneticMagnetic Magnetic beadsbeads beads cannotcannot be be manipulatedmanipulated from from sideside toto sideside inin aa 0.70.7 mmmm widewide glassglass cuvette.cuvette.

FigureFigure8 8 8shows showsshows the thethe correlation correlationcorrelation between betweenbetween the widththethe widtwidt of thehh ofof beads’ thethe beads’beads’ aggregate aggregateaggregate and the distanceandand thethe betweendistancedistance betweenthebetween pole tips. thethe polepole When tips.tips. the WhenWhen pole tips thethe pole arepole located tipstips areare relatively locatelocatedd relativelyrelatively far from each farfar fromfrom other eacheach (e.g., otherother 7 mm (e.g.,(e.g., apart), 77 mmmm the apart),apart), beads themovethe beadsbeads in a movemove chain-shaped inin aa chain-shapedchain-shaped structure (Figurestructurestructure8a). (Figure(Figure These 8a).8a). swarms TheseThese are swarmsswarms not aggregated areare notnot aggregatedaggregated to form a to cloudto formform or aa cloudacloud single oror aggregate. aa singlesingle aggregate.aggregate. When the WhenWhen pole thethe tips polepole are tipstips closer areare to closercloser each toto other eacheach (e.g., otherother 4 (e.g.,(e.g., mm apart),44 mmmm apart),apart), the beads thethe beads movebeads moveasmove a single asas aa single aggregatesingle aggregateaggregate in a narrow inin aa narrownarrow line between lineline betwbetw theeeneen glass thethewalls glassglass (Figure wallswalls (Figure(Figure7a). The 7a).7a). width TheThe ofwidthwidth the beads ofof thethe beadsaggregatebeads aggregateaggregate as a function asas aa functionfunction of the distanceofof thethe distancedistance between bebetween thetween pole thethe tips polepole is depictedtipstips isis depicteddepicted in Figure inin 8FigureFigureb. 8b.8b.

Figure 8. The correlation between the width of the aggregate and the distance between the pole tips. Figure(a) The 8. 8.width TheThe correlationof correlation the beads’ between betweenaggregate the the widthwhen width manipulaof the of theaggregted aggregate ateby twoand and electromagnetsthe thedistance distance between with between parabolic the pole the poletips.pole (tips.tipsa) The ( (𝛽a )width The = 0.65 width of) that the of beads’are the positioned beads’ aggregate aggregate 7 whenmm whenopposite manipula manipulated eachted byother two by (the electromagnets two cuvette’s electromagnets width with is withparabolic 0.6 parabolicmm). pole (b) tipspoleExperimental ( tips𝛽 (=β 0.65= )measurements 0.65that) are that positioned are positionedof the 7width mm 7 mmofopposite the opposite aggr eachegate eachother as othera (thefunction (thecuvette’s cuvette’sof the width distance width is 0.6 between is mm). 0.6 mm). (theb) Experimental(poleb) Experimental tips. measurements measurements of the of the width width of ofthe the aggr aggregateegate as as a afunction function of of the the distance distance between between the pole tips. 3.3. Optimizing Magnetic Forces in a Two-Electromagnet Setup

Micromachines 2019, 10, 784 10 of 15

Micromachines 2019, 10, x FOR PEER REVIEW 10 of 15 3.3. Optimizing Magnetic Forces in a Two-Electromagnet Setup Micromachines 2019, 10, x FOR PEER REVIEW 10 of 15 WhenWhen thethe totaltotal diameterdiameter ofof thethe electromagnetelectromagnet isis fixedfixed (e.g.,(e.g., duedue toto physicalphysical constraintsconstraints ofof thethe system),system),When there the is istotal a a tradeoff tradeo diameterff betweenbetween of the the electromagnet the winding winding area areais width, fixed width, (e.g.,𝑤, wand ,due and the to thediameter physical diameter ofconstraints the of pole, the pole, 𝐷of. ThetheD. system),Themagnetic magnetic there force is force at a tradeoff𝑧=2 at z mm= between2 asmm a function as the a functionwinding of the windingarea of the width, winding area 𝑤 width, and area theof width electromagnets diameter of electromagnets of the with pole, different 𝐷. with The magneticditotalfferent diameters totalforce diametersat is 𝑧=2depicted mm is indepicted as Figu a functionre 9. in For Figure of a the fixed9 winding. Fortotal a diameter fixedarea width total of diameterofthe electromagnets electromagnet, of the electromagnet, with the magneticdifferent totaltheforce magnetic diameters is maximized force is depicted isby maximized using in Figuthe optimal byre 9. using For combinatio a the fixed optimal totaln ofdiameter combination the pole’s of the diameter of electromagnet, the pole’s and diameterthe windingthe magnetic and area the forcewindingwidth. is Formaximized area example, width. by For when using example, the the total optimal when diameter the combinatio total of diameter the nelectromagnet of ofthe the pole’s electromagnet diameteris 55 mm, isand the 55 mm,themagnetic winding the magnetic force area is width.forcemaximized is For maximized example, for 𝑤=20 for whenw mm= the20 and mm total 𝐷=9 and diameterD mm= 9 (assuming mmof th (assuminge electromagnet 𝑐=3c mm).= 3 mm). is 55 mm, the magnetic force is maximized for 𝑤=20 mm and 6.5𝐷=9 mm (assuming 𝑐=3 mm). mm 6.5 6 mm mmmm 6 mm 5.5 mm

5.5 5

5 4.5 Force [pN] Force 4.5 Force [pN] Force 4

4 3.5

3.5 3 14 16 18 20 22 24 3 w [mm] 14 16 18 20 22 24 w [mm] Figure 9. The magnetic force acting on a magnetic particle located at 𝑧=2 mm from an Figureelectromagnet 9.9.The The magnetic withmagnetic a parabolic force force acting poleacting on tip a as magneticon a functia magnetic particleon of the locatedparticle electromagnet’s atlocatedz = 2 mm at winding from𝑧=2 an areamm electromagnet width.from Foran electromagnetwitha fixed a parabolictotal diameter with pole a parabolic tipof the as aelectromagnet, function pole tip ofas thea functi𝑆, electromagnet’s the onmagnetic of the electromagnet’s force winding is maximized area winding width. by using Forarea a thewidth. fixed optimal total For adiametercombination fixed total of thediameter of electromagnet,𝐷, the of pole’s the electromagnet, diameter,S, the magnetic and 𝑆 ,𝑤 forcethe, the magnetic is winding maximized force area byis width. maximized using theThe optimal core by using sleeve’s combination the widthoptimal ofis combinationDassumed, the pole’s to be diameter,of 3 𝐷 mm., the andpole’sw, thediameter, winding and area 𝑤, width. the winding The core area sleeve’s width. width The iscore assumed sleeve’s to bewidth 3 mm. is 3.4. MMBassumed IgM to anti-Zikabe 3 mm. NS1 Dose Response Results 3.4. MMB IgM anti-Zika NS1 Dose Response Results 3.4. MMBThe dose IgM responseanti-Zika curvesNS1 Dose of the Response IgM antibodies Results in the small footprint MMB system (“New MMB”) The dose response curves of the IgM antibodies in the small footprint MMB system (“New and the standard MMB system (“MMB”) are depicted in Figure 10. The limits of detection, calculated MMB”)The anddose the response standard curves MMB ofsystem the IgM (“MMB”) antibodi arees de inpicted the small in Figure footprint 10. The MMB limits system of detection, (“New as three standard deviations from the blank measurement, are 13 ng/L and 25 ng/L with dynamic MMB”)calculated and as the three standard standard MMB deviations system (“MMB”)from the blankare de measurement,picted in Figure are 10. 13 The ng/L limits and 25of detection,ng/L with ranges of 2-logs and 3-logs, respectively. calculateddynamic ranges as three of standard2-logs and deviations 3-logs, respectively. from the blank measurement, are 13 ng/L and 25 ng/L with dynamic ranges of 2-logs and 3-logs, respectively.

Figure 10. Dose responses of recombinant human IgM anti-Zika NS1 usinga small footprint MMB Figure 10. Dose responses of recombinant human IgM anti-Zika NS1 using a small footprint MMB system (“New MMB”) and a standard MMB system (“MMB”). Figuresystem 10. (“New Dose MMB”) responses and ofa strecombinantandard MMB human system IgM (“MMB”). anti-Zika NS1 using a small footprint MMB 4. Discussionsystem (“New MMB”) and a standard MMB system (“MMB”). 4. Discussion Efficient manipulation of magnetic beads heavily depends on the strength and structure of the 4. Discussion magneticEfficient field manipulation sources. Electromagnets of magnetic provide beads heavil strongy anddepends adjustable on the magnetic strength fields,and structure and their of lack the ofmagnetic mechanicalEfficient field manipulation movementsources. Electromagnets makes of magnetic them less providebeads susceptible heavil strongy dependsand to mechanical adjustable on the magnetic malfunctionstrength andfields, thanstructure and permanent their of lackthe magneticmagnets.of mechanical Threefield sources.movement key factors Electromagnets makes affect the them performance provideless suscepti stro ofng electromagnets:ble and to mechanicaladjustable (1) magnetic themalfunction magnetic fields, propertiesthan and permanent their of lack the ofmagnets. mechanical Three movement key factors makes affect them the performance less suscepti ofble electromagnets: to mechanical malfunction1) the magnetic than properties permanent of magnets.the electromagnet’s Three key factors pole affectmaterial the performance(e.g., magnetization of electromagnets: saturation 1) theand magnetic maximum properties relative of thepermeability), electromagnet’s which affectpole thematerial maximum (e.g., magnetic magnetization field and thesaturation response timeand ofmaximum the electromagnet, relative permeability), which affect the maximum magnetic field and the response time of the electromagnet,

Micromachines 2019, 10, 784 11 of 15 electromagnet’s pole material (e.g., magnetization saturation and maximum relative permeability), which affect the maximum magnetic field and the response time of the electromagnet, (2) the electromagnet’s physical parameters (e.g., winding area length and width, core diameter, wire diameter, current), and (3) the pole’s tip shape, which affects the strength and direction of the magnetic field near the pole tip. For example, the sharper the pole tip, the higher the magnetic field gradient near the tip. In applications that require high magnetic field gradients at very short distances from the pole tip (e.g., tens to a few hundred micrometers) [5,19], a conic pole tip is preferable. In applications that require high magnetic field gradients over a long range of distances from the pole tip (e.g., from a few hundred micrometers to several millimeters [14], a parabolic pole tip is preferred. At a long distance from the pole tip (e.g., inside blood vessels) [25], a flat-top pole tip, which is the easiest to produce, is sufficient. When two or more electromagnets are used to manipulate magnetic beads in space, the mutual influence of the magnetic fields dictates the maximum working distance over which magnetic beads can be manipulated without being trapped by one of the electromagnets. To enable precise manipulation of magnetic beads over a large area, increasing the working distance is desirable. Here, we showed that, for parabolic pole tips, the working distance can be broadened by increasing the parabolic curvature. However, above a certain parabolic curvature (e.g., β = 0.85), further broadening of the working distance is negligible. Significant broadening of the working distance (e.g., for applications that require transportation of magnetic beads over a long distance) can also be achieved by increasing the distance between the pole tips. Nevertheless, increasing the distance between the pole tips increases the total size of the device, reduces the magnetic field forces in both the z and r axas, and consequently modifies the shape of the beads’ aggregate. For example, when the parabolic pole tips are located away from each other, the magnetic beads move in chain-shaped clusters and do not form a cloud or a single aggregate. In some biosensing applications [6,14,15], the movement of the beads as a single aggregate is critical to achieving high repeatability between measurements. For a fixed distance between two identical electromagnets with parabolic pole tips, the working distance can be adjusted by changing the ratio between the maximum voltages of the two electromagnets. For example, when the distance between the poles is 3 mm and the parabolic curvature is β = 0.65, the working distance reaches its maximum value (3 mm) if the ratio between the voltages of the electromagnets is V /V = 0.7. − 2 1 In many lab-on-a-chip applications, physical constraints limit certain mechanical parameters, such as the length of the electromagnet, L, its total diameter, S, and the distance from the coil to the pole’s tip, h. When the total diameter of the electromagnet, S, and the core sleeve’s width, c, are fixed, there is a tradeoff between the winding area width, w, and the diameter of the core, D. Here, to minimize the size of an MMB system, we produced two electromagnets, each with a length of L = 50 mm and a total diameter of S = 55 mm. According to our simulation (Figure9), the magnetic force is maximized for w = 20 mm and D = 9 mm (assuming c = 3 mm). These electromagnets, which are approximately 21% smaller in volume than the previous version [6], produced sufficient magnetic force to aggregate magnetic beads and manipulate them from side to side in a small footprint MMB system. The analytical sensitivity of the new MMB system (13 ng/L) is on par with the standard MMB system. According to recent studies [16], this limit of detection enables detection of Zika IgM antibodies as early as 5 days and as late as 180 days post symptoms onset, significantly extending the number of days that the antibodies are detectable. It should be noted that the smaller dynamic range of the new MMB system is explained by the lack of additional neutral density filter before the camera. Thus, at a high concentration of target molecules, the strong fluorescent signal saturated the camera. This problem can be solved using a shorter exposure time whenever the camera saturates.

5. Conclusions Here, we provide a thorough analysis, including analytical calculations, numerical simulations, and experimental measurements, of using one or two electromagnets to manipulate magnetic beads. Micromachines 2019, 10, 784 12 of 15

In general, the magnetic field gradient of an electromagnet, and subsequently the force acting on magnetic beads, can be significantly maximized for a specific application by carefully selecting the pole material and the tip’s shape. In addition, the shape of the beads’ aggregate and the distance over which they can be manipulated highly depends on both the position of the electromagnets relative to each other and their relative voltage. In a two-electromagnet setup, to maximize the magnetic force acting on magnetic particles while maintaining the electromagnets’ minimal size and power consumption requirements, the following protocol can be used. First, based on power consumption constraints, select the maximum wire current, I, and the corresponding wire diameter, d. Second, based on the mechanical constrains, select the length of the electromagnet, L, its total diameter, S, and the distance from the coil to the pole’s tip, h. Third, to maximize the magnetic force, select the optimal pairing of the core diameter, D, and the winding area width, w. Then, based on the application and the distance between the pole tip and magnetic particles, select the pole material, shape, and curvature coefficient.

Supplementary Materials: The following are available online at http://www.mdpi.com/2072-666X/10/11/784/s1, Figure S1: The area between two electromagnets in which the magnetic moment of the M-280 beads saturates. Movie S1: The correlation between the working distance and the distance between the pole tips. Author Contributions: Methodology, M.C.; software, M.S.; formal analysis, M.S.; resources, M.C.; writing—original draft preparation, M.S.; writing—review and editing, A.D.; supervision, A.D. Funding: This work was supported by the Israel Science Foundation (ISF), grants 2152/15 and 1142/15. Acknowledgments: The authors thank Yasha Nikulshin from the Department of Bar-Ilan University for his technical assistance. James Ballard provided an editorial review of the manuscript. Conflicts of Interest: The authors declare no conflict of interest.

Appendix A

The magnetic force acting on a single magnetic bead, with a magnetic moment, m→, in an applied magnetic field, →B, is [26,27]: → → → F m = (m→(B) B). (A1) ∇ · When the magnetic field is high, the magnetic moment saturates and becomes spatially constant:

m→ = msBˆ (A2) where ms is the magnetic bead’s saturation magnetization. Substituting Equation (A2) into Equation (A1) yields [28]: → → F m = msBˆ B. (A3) ·∇ The magnetic field gradient can be represented as a tensor:    ∂rBr ∂rBφ ∂rBz    →B =  1 B 1 B 1 B   r ∂φ r r ∂φ φ r ∂φ z . (A4) ∇   ∂zBr ∂zBφ ∂zBz

When the magnetic field is applied using an electromagnet with a cylindrical symmetry, the tensor can be reduced to: ! ∂ B ∂ B →B = r r r z . (A5) ∇ ∂zBr ∂zBz Substituting Equation (A6) into Equation (A3) yields: ! → ∂rBr ∂rBz →   F m = msBˆ = (ms/ B ) Br∂rBr + Bz∂rBz Br∂zBr + Bz∂zBz . (A6) · ∂zBr ∂zBz | | · Micromachines 2019, 10, 784 13 of 15

Hence, the magnitude of the magnetic field is:

Micromachines 2019, 10, x FOR PEER REVIEW 13 of 15 1/2 → →  2 2 Fm = F m = (ms/ B ) (Br∂rBr + Bz∂rBz) + (Br∂zBr + Bz∂zBz) . (A7) Micromachines 2019, 10, x FOR| PEER| REVIEW| | · 13 of 15

Figure S1. The area between two electromagnets in which the magnetic moment of the M-280 beads Figure A1. The area between two electromagnets in which the magnetic moment of the M-280 beads saturates. The spatial distribution of the magnetic field surrounding two electromagnets with saturates.Figure S1. The The spatial area between distribution two ofelectromagnets the magnetic fieldin wh surroundingich the magnetic two electromagnets moment of the with M-280 parabolic beads parabolic pole tips (𝛽=0.65) that are located 3 mm opposite each other. The contours represent the polesaturates. tips ( βThe= 0.65 spatial) that distribution are located 3of mm the opposite magnetic each field other. surrounding The contours two represent electromagnets the magnetic with magnetic field magnitude. The magnetic moment of the M-280 beads saturates at an external field fieldparabolic magnitude. pole tips The (𝛽=0.65 magnetic) that moment are located of the 3 mm M-280 opposite beads each saturates other. at The an externalcontours fieldrepresent strength the strength above 0.3 (marked with a thick blue line). Therefore, the magnetic moment of the abovemagnetic 0.3 Teslafield (markedmagnitude. with The a thick magnetic blue line). moment Therefore, of the theM-280 magnetic beads moment saturates of at the an magnetic external beads field magnetic beads saturates when the beads are located less than 2 mm from the pole tips. saturatesstrength above when the0.3 beadsTesla are(marked located with less a than thick 2 mmblue from line). the Therefore, pole tips. the magnetic moment of the magnetic beads saturates when the beads are located less than 2 mm from the pole tips.

Figure A2. Movie S1. The correlation between the working distance and the distance between the pole Movie S1. The correlation between the working distance and the distance between the pole tips. tips. When the distance between the two parabolic pole tips (β = 0.65) is 3 mm, the working distance is When the distance between the two parabolic pole tips (β = 0.65) is 3 mm, the working distance is ~0.4 ~0.4Movie mm, S1 i.e.,. The beads correlation can be manipulated between the inside working a 0.4 distance mm wide and cuvette the distance (left), but between not inside the a 0.5pole mm tips. or mm, i.e., beads can be manipulated inside a 0.4 mm wide cuvette (left), but not inside a 0.5 mm or widerWhen cuvettethe distance (right). between the two parabolic pole tips (β = 0.65) is 3 mm, the working distance is ~0.4 wider cuvette (right). mm, i.e., beads can be manipulated inside a 0.4 mm wide cuvette (left), but not inside a 0.5 mm or Appendixwider cuvette B (right). Appendix B Each MMB IgM anti-Zika assay consisted of ~25,000 tosylactivated magnetic beads (M-280, Thermo FisherAppendixEach Scientific, MMBB Waltham,IgM anti-Zika MA, assay USA), consisted which were of pre-conjugated~25,000 tosylactivated to the Zika magnetic NS1-suriname beads (M-280, strain Thermo Fisher Scientific, Waltham, MA, USA), which were pre-conjugated to the Zika NS1-suriname (TheEach Native MMB Antigen IgM Company, anti-Zika UK)assay using consisted Thermo of Fishers’ ~25,000 standard tosylactivated coupling magnetic procedures. beads The (M-280, beads strain (The Native Antigen Company, UK) using Thermo Fishers' standard coupling procedures. The wereThermo incubated Fisher Scientific, for one hour Waltham, at room MA, temperature USA), which with were human pre-conjugated IgM anti Zika to the NS1 Zika in concentrationsNS1-suriname beads were1 2 incubated3 4 for5 one6 hour7 at room temperature with human IgM anti Zika NS1 in ofstrain 0, 10 (The, 10 Native, 10 , 10 Antigen, 10 , 10Company,, and 10 UK)ng/ L.using The Thermo initial incubation Fishers' standard was followed coupling by procedures. incubation with The concentrations of 0, 101, 102, 103, 104, 105, 106, and 107 ng/L. The initial incubation was followed by abeads fluorescently were incubated labeled detection for one antibodyhour at (Anti-Humanroom temperature IgM (µ with-chain human specific)-Biotin, IgM anti Sigma–Aldrich Zika NS1 in incubation with a fluorescently labeled detection antibody (Anti-Human IgM (µ-chain specific)- Ltd.,concentrations Israel). After of 0, a second101, 102 wash,, 103, 10 the4, beads105, 10 were6, and incubated 107 ng/L. withThe initial R-Phycoerythrin-Streptavidin incubation was followed (The by Biotin, Sigma–Aldrich Ltd., Israel). After a second wash, the beads were incubated with R- Jacksonincubation Lab., with USA). a fluorescently To remove unbound labeled detectiondetection antibodies,antibody (Anti-Human a single buffer IgM replacement (µ-chain wasspecific)- done Phycoerythrin-Streptavidin (The Jackson Lab., USA). To remove unbound detection antibodies, a Biotin, Sigma–Aldrich Ltd., Israel). After a second wash, the beads were incubated with R- single buffer replacement was done after the final incubation. The final solution was then loaded into Phycoerythrin-Streptavidin (The Jackson Lab., USA). To remove unbound detection antibodies, a a borosilicate glass cuvette and measured in the MMB system. The number of repetitions of the blank single buffer replacement was done after the final incubation. The final solution was then loaded into measurement was six (𝑛=6). The number of repetitions for all other concentrations was three (𝑛= a borosilicate glass cuvette and measured in the MMB system. The number of repetitions of the blank 3). The limit of detection (LoD) for each set of experiments was calculated as three standard measurement was six (𝑛=6). The number of repetitions for all other concentrations was three (𝑛= 3). The limit of detection (LoD) for each set of experiments was calculated as three standard

Micromachines 2019, 10, 784 14 of 15 after the final incubation. The final solution was then loaded into a borosilicate glass cuvette and measured in the MMB system. The number of repetitions of the blank measurement was six (n = 6). The number of repetitions for all other concentrations was three (n = 3). The limit of detection (LoD) for each set of experiments was calculated as three standard deviations over the blank measurement. The reaction buffer solution was a mixture of phosphate buffered saline (PBS 1), 1 mg/ml of bovine × serum albumin (VWR, Rodnor, PA, USA), and 0.05% of Tween-20 (Sigma–Aldrich, St. Louis, MO, USA).

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