Transport efficiency of biofunctionalized magneticparticles tailored by surfactant concentration

Meike Reginka,∗,†,‡ Hai Hoang,† Ozge Efendi,¶ Maximilian Merkel,†,‡ RicoHuhnstock,†,‡ Dennis Holzinger,† Kristina Dingel,§,‡ Bernhard Sick,§,‡ Daniela

Bertinetti,¶ Friedrich W. Herberg,∗,¶ and Arno Ehresmann†,‡

†Institute of Physics and Center for Interdisciplinary Nanostructure Science and Technology(CINSaT), University of Kassel, Heinrich-Plett-Strasse 40, D-34132 Kassel (Germany)

‡Artificial Intelligence Methods for Experiment Design (AIM-ED), Joint Lab Helmholtzzentrumfur Materialien und Energie, Berlin (HZB) and Kassel University, cc Gregor Hartmann,

Hahn-Meitner Platz 1, 14109 Berlin, Germany¶Institute of Biology and Center for Interdisciplinary Nanostructure Science and Technology

(CINSaT), University of Kassel, Heinrich-Plett-Strasse 40, D-34132 Kassel (Germany)§Intelligent Embedded Systems, University of Kassel, Wilhelmshoher Allee 71-73, D-34121

Kassel (Germany)

E-mail: reginka@uni-kassel.de; herberg@uni-kassel.de

Abstract

Controlled transport of surface functionalizedmagnetic beads in a liquid medium is a central re-quirement for the handling of captured biomolec-ular targets in microfluidic lab-on-chip biosen-sors. Here, the influence of the physiological liq-uid medium on the transport characteristics offunctionalized magnetic particles and on the func-tionality of the coupled protein is studied. Theseaspects are theoretically modeled and experimen-tally investigated for prototype superparamagneticbeads, surface functionalized with green fluores-cent protein immersed in buffer solution with dif-ferent concentrations of a surfactant. The modelreports on the tunability of the steady-state parti-cle substrate separation distance to prevent theirsurface sticking via the choice of surfactant con-centration. Experimental and theoretical averagevelocities are discussed for a ratchet like particlemotion induced by a dynamic external field super-posed on a static locally varying magnetic fieldlandscape. The developed model and experimentmay serve as a basis for quantitative forecastson the functionality of magnetic particle transport

based lab-on-chip devices.

Keywords

particle transport, magnetic bead, exchange bias,IBMP, magnetic field landscape, biofunctionaliza-tion, green fluorescent protein (GFP), Lab-on-chip(LOC), surface forces

Lab-on-a-chip1 tests are in the focus of med-ical diagnostics, where disease-relevant biomark-ers may be detected in human body fluids (e.g.blood serum, urine). For these systems, mag-netic micro- or nanobeads (in the following syn-onymously referred to as particles) are discussedto play a key role for single to few molecule de-tection. In on-chip biosensors, functionalized par-ticles may cover functionalities like stirring, ana-lyte capturing, transport, and detection,2–5 wherefor the latter they may serve as labels for mag-netic sensing technologies like magnetoresistiveelements.6–10 Precise bead motion control there-fore is the basis for these functionalities.3–5 Cor-responding actuation concepts for superparamag-

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netic beads (SPBs) are based on magnetic thinfilm systems which are topographically11 or mag-netically patterned12–15 into designed micromag-netic elements for SPB guidance by magneticstray field tracks.10,16 The tracks can, e.g., beachieved by moving domain walls13,17 or by thedesign of asymmetric magnetic potentials, com-monly referred to as magnetic ratchets.9,18

Hence, dynamically transforming the SPBs’magnetic potential energy landscape by the appli-cation of periodic external magnetic fields leadsto their directed transport as the beads followthe shifted energy minima.11,12 Although the localstray field strengths originating from these mag-netic domain configurations are not very strong,they possess high field gradients which causehigh transport velocities in external fields below2 kA/m.12 For the design of the described mag-netic stray field landscapes from the magnetic ortopographic patterns towards specific propertiesof the SPB transport, micromagnetic simulationsare frequently used to estimate the magnetic po-tential energy of the individual beads and, thus,allow for the prediction of their motion.7,11,12,19

Although it is obvious that the SPBs’ motionin liquid environment is governed mainly by theforce exerted by the magnetic potential energylandscape and consequently the drag force,12,20

there are multiple hidden factors influencing themotion that have not been profoundly consideredso far. Interestingly, the impact of surface forcesbetween magnetic beads and substrate surface hasonly been discussed for non-functionalized SPBsin water,20 however, they determine the colloidalstability and the sticking probability to the sub-strate surface of the SPBs and define, therefore,the necessary conditions for a SPB transport in therespective liquid. Although most transport con-cepts presented in past work have been performedin pure water,10,11,13,16 in realistic devices, proteinsfunctionalizing the SPB surface e.g. as capturemolecules would denaturate therein. This necessi-tates the use of physiological liquid environments,i.e. buffer solutions, that preserve the correct pro-tein structure which in turn directly determinesthe protein function. The physical characteristicsof these physiological solutions are rather differ-ent from the ones of pure water, particularly theirviscosities, permittivities, the ionic strengths and

m

x

yz

tPMMAz‘b

OO

OO

O-O

O-O

DS-

GFP

Figure 1: Sketch of the prototype system for theinvestigation of the colloidal stability and surfaceadhesion of superparamagnetic core-shell particleswith biochemically immobilized green fluorescentprotein (GFP), not drawn to scale. The sub-strate consists of a parallel stripe magnetic domainpattern with in-plane opposing magnetizations inadjacent domains covered by a polymeric spacerlayer. The liquid environment of the particle isa physiological buffer (indicated by red and blueions +/-) to guarantee protein stability, while thecolloidal stability is realized via specific surfactantconcentrations (DS-).

consequently the dependence of the surfaces’ elec-trochemical potentials on the distance to the sur-face. This directly affects the surface forces whichare mediated by the chosen dispersion medium.Hence, the dispersion medium does not only serveas a passive carrier liquid but plays an importantrole in the colloidal stability and for the surfacesticking probability of the particles. As the deli-cate balance of surface forces, buoyancy, gravita-tion and magnetic forces determines the equilib-rium separation between the beads and betweenbead and substrate, the described properties mustbe taken into account when aiming at bead trans-port without sticking and agglomeration. In pastwork, individual routines have been established toexperimentally minimize agglomeration and ad-sorption of particles to the substrate surface: Thedistance between particle and magnetic layer hasbeen increased by the introduction of a spacerlayer7,11–14,20 which at the same time modifiesthe surface potential with the choice of mate-rial. This lowers the attractive magnetic forces

2

and modifies the surface forces. Moreover, sur-factants have been added in a specific concentra-tion to reduce particle agglomeration and surfaceadhesion.19,21,22 In these approaches, the individ-ually chosen parameters are usually restricted tothe specific setup - consisting of the magnetic sub-strate, the SPB type, the immobilized proteins andthe liquid - complicating a comparison of the stud-ied transport concepts.

In order to understand the transport of bio-functionalized superparamagnetic beads (BSPBs)through physiologically relevant liquids morequantitatively, the current work describes a modelto predict particle velocities for a prototype trans-port technology, where BSPBs are actuated byexternal magnetic field pulses superposed on peri-odic magnetic stray field field landscapes.12 Thisresults in a transport of BSPBs in steps fromdomain wall to domain wall of the underlying to-pographically flat magnetic pattern (s. fig. 1)with characteristic average bead velocities withinthe transport steps.

This model includes a series of factors affectingthe particle, from the distance dependent mag-netic stray fields to the impact of surfactants onthe viscous properties of the liquid and the sur-face forces determining the particle substrate dis-tance. The model represents a basis to deviseoptimum conditions for the transport of BSPBsvia the choice of surfactant and its concentration,the design of the magnetic stray field landscapesand the respective spacer thickness and substratesurface material. In figure 1, the model systemfor this study is depicted, where the GFP mut2structure (PDB code: 6GQG23) image was gen-erated using the PyMOL Molecular Graphics Sys-tem. The magnetic stray field landscape is fab-ricated according to ref. 12 and as a spacer a700 nm thick layer of bio-compatible poly(methylmethacrylate) (PMMA) was spin coated onto themagnetic thin film system. As prototype BSPBswe chose to immobilize the green fluorescent pro-tein (GFP) on the surface of SPBs with a nominaldiameter of 1 µm (see exp. methods section).

GFP functionalized BSPBs are not only advan-tageous for particle tracking by the GFP fluo-rescence, but GFP itself is a sensitive probe forthe detection of denaturation processes caused bythe surrounding medium. The denaturation of

GFP would lead to an unfolding of its beta-barrelstructure23 such that its spectral properties willchange.24 Moreover, its stability is comparable toproteins like antibodies, which are well-establishedhigh-affinity capture molecules for biomoarker de-tection.25 For the current experiments we variedthe surface forces systematically by the concen-tration of the amphiphilic surfactant sodium do-decyl sulfate (SDS), of which data is well avail-able,24,26–29 in phosphate buffered saline (PBS).The average BSPB transport velocity (within theabove mentioned steps of the stepwise transport)has then been determined as a function of SDSconcentration and at the same time the protein’sfunction has been monitored by the remaining flu-orescence over time scales of days. Using the ex-periments in comparison to the model it is pos-sible to determine parameter spaces for realisticlab-on-chips using magnetic particles.

Model

Magnetic field landscape - The magnetic fieldlandscape (MFL) over an exchange biased thinfilm patterned into magnetic parallel stripe do-mains with head-to-head and tail-to-tail domainconfiguration30 (see fig. 1) has been modeled us-ing the object oriented micromagnetic framework(OOMMF) package.31 The magnetic stray fieldlandscape (MFL) with components Hx(x , y , z)and Hz(x , y , z) was afterwards computed as thesuperposition of the magnetic fields from all mag-netic moments obtained from the simulation indipole approximation. Due to the stripes’ parallelgeometry, the transport is independent of the ycoordinate. The magnetic field landscape deter-mined in this way (more details given in Suppl.)can similarly be determined for other kinds of pat-terned magnetic substrates.

Steady-state distance - The forces which arerelevant for the theoretical description of magneticbead transport in the model system are sketchedin figure 2. The two vertical axes in this depic-tion account for the fact that the individual forcesare exerted either at the particle surface or atits center. The steady-state distance z ′b betweenthe lowermost part of the BSPB and the PMMAsurface, i.e. the bottom of the microfluidic con-

3

tPMMA

z‘b

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z‘

x

z

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Fm(x,z,t)Fd(z‘)

FvdW(z‘)Fel(z‘)

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zb

PMMAcapping

FMAFM

bu�er�magnetic

layer stack

Figure 2: Sketch of the relevant forces on aBSPB (indicating the GFP surface functionaliza-tion in light green and the magnetic core in brown)for the theoretical description. Along the verti-cal axis, the electrostatic (Fel(z ′)), van-der-Waals

(FvdW(z ′)) and magnetic force (~Fm(z)ez) are in-dicated from which balance the steady-state dis-tance is derived. The distance dependent forcesdetermining the particle velocity are pointing hor-izontally: the drag force (~Fd(z ′)) and the time

dependent magnetic force (~Fm(x , z , t)) which ac-tuates the bead. The magnetic substrate consistsof a buffer layer, an EB bilayer (antiferromag-net + ferromagnet) which is covered by a cap-ping layer of the thickness tcl. Please note, thatz = z ′ + tcl + tPMMA, with the spacer thicknesstPMMA.

tainer, results from balancing the magnetostaticforce Fm(z) and the surface forces (commonly re-ferred to as DLVO forces, after the names of Der-jaguin, Landau, Verwey, Overbeek32,33), namelythe electrostatic force Fel(z ′) and the van-der-Waals force FvdW(z ′). Gravitation and buoyancyare neglected in the present calculations, becausethey are both in the range of 10−15 N, which isorders of magnitude smaller than the other namedforces. The separation z ′b between the surfaces re-sults in a distance between the BSPB’s center andthe ferromagnetic layer of zb = z ′b +tcl +tPMMA +rwith tcl being the thickness of the magnetic thinfilm system’s capping layer, tPMMA the thicknessof the PMMA spacer, and r being the particle’shydrodynamic radius. The magnetostatic force iscalculated by the gradient of the magnetic poten-

tial energy Ub:12

~Fm(x , z) = −~∇Ub

= −µ0(~mb(x , z) · ~∇) · ~Heff(x , z)(1)

where ~Heff(x , z) is the effective magnetic field,which is the superposition of the homogenous ap-plied field ~Hext and the magnetic stray field of themagnetically patterned substrate ~HMFL(x , z), µ0 isthe vacuum permeability and ~mb(x , z) the mag-netic moment of the BSPB which was calculatedin point dipole approximation by the Langevinfunction (see Suppl.).34 For the steady-state dis-tance between particle and substrate surface onlythe vertical component of the magnetic force isrelevant, i.e. ~Fm(z)·ez. The required field gradienthas been determined from the z-dependent mag-netic stray field values above the stripe domainpattern (equation 1, Suppl.). The values deter-mined above the domain wall centers (averagedalong the long stripe axis) have then been fittedto the function Hz,fit(z) = a+b ·zc . The magneticforce was subsequently calculated for the effectivemagnetic field ~Heff(z)·ez = Hz,fit(z)+Hext,z, whereHext,z is the z-component of the externally appliedmagnetic field.

The distance dependent electrostatic force as apart of the surface forces is described by20

Fel(z ′) =2πεrε0 · r · κ

1− exp(−2κz ′)· [2ζbζs · exp(−κz ′)

± (ζ2b + ζ2

s ) · exp(−2κz ′)]

(2)

with the permittivity εrε0 of the liquid mediumand the zeta potentials ζb and ζs of the BSPBand the substrate surface, respectively. We usethe zeta potentials as an approximation for sur-face potentials as the latter can not be experi-mentally obtained. Hence, we also use the hy-drodynamic rather than the nominal radius. Theforce can be calculated either using the lower signin equation 2 assuming a constant potential or us-ing the upper sign, which corresponds to the con-stant surface charge density assumption. Whileit is known that neither of the two quantities re-mains constant during the approach of both sur-faces,35 the two approaches can be used as lim-iting cases. The electrostatic force furthermore

4

depends on the Debye-Huckel inverse double-layerthickness

κ =

√2000 · NA · e2 · I

εrε0 · kBT(3)

with the Avogadro constant NA, Boltzmann’s con-stant kB, the temperature T and the elementarycharge e. As κ depends on the ionic strength ofthe liquid I = 1/2

∑i ci · z2

i , the strong influenceof the concentration ci as well as the valency zi ofeach ion species i in the given dispersion mediumon the electrostatic force becomes obvious. Forthe present model, all ions of the buffer and thesurfactant in the chosen concentrations need to beconsidered which yields I =172 mM for the PBSbuffer without additional SDS. Calculating Fel(z ′)requires furthermore a value for the sphere’s hy-drodynamic radius (r =(614±22) nm) and its zetapotential (see fig. 5), which were experimentallyobtained for the utilized BSPBs in PBS via dy-namic light scattering. The given uncertainties aresingle standard deviations from the mean value ofthe measurements. For each surfactant concen-tration, εr of the dispersion medium PBS as wellas ζs for PMMA were estimated from computa-tional as well as experimental results.26 Note thatthis is an approximation since the values extractedfrom the cited article are based on a pH of 7 andan ionic strength of 100 mM, while we worked atpH=7.4 and at ionic strengths above 170 mM.While the electrostatic force is repulsive for samezeta potential signs as it is the case in our experi-ment, the van-der Waals force FvdW as the secondDLVO force, is attractive.36 Under considerationof the hydrodynamic radius and the Hamaker con-stants for the involved materials the distance de-pendence of FvdW between a sphere and a planewas determined (see Suppl.).

After balancing the three forces Fm(z), Fel(z ′)and FvdW(z ′) for a particle positioned above a do-main wall, the derived steady-state distance z ′bwith an uncertainty from Gaussian error propaga-tion can be used to theoretically predict the par-ticle’s trajectory during a transport experiment.

Particle trajectory & steady-state velocity- The forces governing the transport velocity arethe position (x ,z) dependent magnetostatic forceFm causing the bead’s actuation and the z ′ depen-

dent drag force Fd exerted by the liquid. For themagnetic actuation, equation 1 will then be eval-uated for the x-component of the motion. As weuse parallel stripe domains along the y directionthe potential is flat along y such that dU/dy = 0.In order to correctly describe Heff(x , z , t) and con-sequently mb, the magnetic field landscape is cal-culated in the determined distance zb and the ex-ternal field Hext(x , z , t) is described in its tempo-ral evolution during the experiment. The appliedtrapezoidal magnetic field pulses in x and z direc-tion used in this study cause a dynamic transfor-mation of the bead’s potential energy landscapewhich drives their step wise transport.12 The op-posing drag force

Fd(x , z ′) = 6 ·π · r ·ηl(cSDS) · fd(z ′) ·~vb(x , z ′) (4)

is given by Stokes law for low Reynolds numbers,since they represent the utilized microfluidic de-vice in good approximation. Here, r is the beadradius, fd is the distance dependent drag forcecoefficient and ηl is the liquid’s viscosity, whichin our case is surfactant dependent.37 The SDSconcentration dependence of the viscosity ηl wasdetermined by a linear fit from the experimentaldata of ref. 26. In the following we only inspectthe average steady-state velocity for one motionstep, since the time interval for the bead’s accel-eration is with 1 µs much smaller than all relevanttimescales for the presented experiments and cantherefore be neglected.12 By balancing Fd(x , z ′b)and Fm(x , zb) at a given time t, the spatial de-pendence of the BSPB’s momentary steady-statevelocity

~vb(x , z ′, t) = −µ0(~mb(x , z , t) · ~∇) · ~Heff(x , z , t)

6 · π · r · ηl · fd(z ′)(5)

can be calculated.12,20 When applying this ap-proach to transport concepts with accelerationphases in the temporal resolution of the exper-iment the equation of motion has to be solvedrather than utilizing this force balancing ap-proach.38 Due to the position dependent en-ergy landscape, ~vb(x , z ′, t) varies along the bead’spath. Performing the calculation of ~vb(x , z ′, t) foreach time interval ∆t = 10 µs during the trans-port experiment we can construct the step like

5

particle trajectory xb(ti+1) = xb(ti)+~vb(xb,i , z , ti)·∆t + xrw. The distance xrw is added in orderto account for the bead’s Brownian motion (see.Suppl.).

For a comparison of the simulated trajectorieswith positional data of the particles experimentallydetermined from microscopic videos via a trackingprocedure,39 mean step velocities for both datasets have been calculated in the same way. Asthe experimental data has been partly noisy, itwas not possible to determine the particle veloci-ties from the derivatives of the determined particlepositions. Instead, the observed trajectories havebeen modeled by fitting a Gaussian error func-tion to each step of the trajectory x(t). The ve-locity was deduced from the function’s derivative,which possesses by definition the shape of a nor-mal distribution. The mean step velocity v BSPB

was evaluated as the average velocity within theregion around the maximum in which the valuesare above 50 % of the function’s maximum (see.Supplementary). For the simulations, this pro-cedure was also applied for the upper and lowerboundaries of zb derived from Gaussian error prop-agation in order to estimate the velocity’s uncer-tainty for one step. This uncertainty together withthe standard deviation from 5 averaged transportstep simulations will be considered as an uncer-tainty in the evaluation (see fig. 5).

Results and Discussion

Magnetic stray field landscape - In figure 3the x and z component of the magnetic stray fieldemerging from the parallel-stripe domains with in-plane head-to-head and tail-to-tail magnetizationconfigurations is shown as a result of the OOMMFsimulations. The field is shown for a distanceabove the ferromagnetic layer of zb=1.328 µm,which is the steady-state distance between theparticle and the magnetic domain pattern at thelateral location of a domain wall. The inflectionpoints in the magnetic stray field’s x componentand the maxima and minima of the z compo-nent coincide at the positions of the domain walls,therefore determining the potential energy minimaof the magnetic beads. The stray field gradientalong z above the domain wall in superposition

x-length /µm

y-le

ngth

/µm

H /k

A/m

HzHx

Figure 3: Top: The computed magnetic strayfield components Hx and Hz in the xy -plane atzb=1.328 µm above the exchange biased stripe ar-ray. This distance corresponds to the steady-statedistance zb of the BSPB in PBS for cSDS = 1 wt%.The white arrows indicate the average remanentmagnetization direction in the individual stripesseparated by domain walls (dashed black). Bot-tom: respective line plot of the magnetic strayfield components averaged along the y coordinate.

with the externally applied field Hext,z was subse-quently used for the determination of the z com-ponent of the magnetic force for the steady-statedistance evaluation in combination with the inter-play of the surface forces that both depend on thedistance and the surfactant concentration in mul-tiple ways.

Steady-state-distance & transport veloc-ities - The interplay of forces will be discussedfor BSPBs immersed in phosphate buffered saline(PBS) with an ionic strength of about 0.15 Mwith a variation of the surfactant concentration(cSDS = [0, 0.01, 0.1, 1, 10] wt%) in comparisonto a plain SPB in water that was not previouslyfunctionalized with GFP. The sum of the magneticforce and the van-der-Waals force between parti-cle and substrate surface is attractive (see fig. 2),and it is displayed together with its uncertaintyin figure 4. On the other hand, the electrostaticforce causes the repulsion of the particle. The twolimiting cases of the calculated repulsive force arealso shown in Fig.4. For all forces, the uncertain-ties were considered by a Gaussian error propaga-

6

ba) b)

Figure 4: Absolute values of the repulsive and attractive forces between bead and substrate. The sumof the magnetic and the van-der-Waals forces (solid blue) is attractive. The two cases of either constantpotential (− in eq. 2, solid dark green) or constant charge density (+, dashed dark green) for theelectrostatic force are repulsive. The shaded areas in blue and dark green depict the correspondinguncertainties. While the left panel (a) depicts the force situation for a non-functionalized SPB in water,the graphs in the right panel (b) show the respective forces for BSPBs in PBS under the given SDSconcentration. Note the different scales for the force and the distance. The vertical short-dashed linesindicate the steady-state distances for the two limiting cases of the calculated electrostatic force. Thepale rose shaded area represents the uncertainty range for the equilibrium distance, derived from theintersections of the forces’ error margins. When two dotted lines are given, the intersections do notcoincide for the two limiting cases of the repulsive force, hence an averaged steady-state distance wasdetermined.

tion. When the beads are immersed in the liquidduring the experiment, they sediment first due togravity and soon due to the additional attractivemagnetic force until they reach a region (aroundz ′b=6.4 nm for BSPB in PBS) in which the van-derWaals interaction dominates the attraction. Ap-proaching now even smaller distances, the steady-state distance z ′b is reached when the repulsiveforce balances the attractive forces, which is indi-cated by the dashed vertical lines in figure 4. Inthe case that the two limiting cases for the cal-culated electrostatic force do not coincide, twodashed lines are given and the average value istaken as the effective steady-state distance. Simi-larly, the respective error margins of z ′b are derivedfrom the crossing of the forces’ uncertainties de-picted as shaded regions, where the outer bound-aries of both cases (+/−) were taken. While weretrieve an averaged steady-state distance of theSPB in water at z ′b =148.5 nm within the errormargins [0, 309] nm, the separation between aBSPB and a PMMA surface in PBS has been cal-culated to be much smaller, i.e. is at z ′b =1.3 nm

within the error margins of [0,2.3] nm. This valueis even smaller than the typical surface roughnessof spin coated PMMA, which was experimentallydetermined to be in the range of 2 nm.40 Un-der these conditions it is very likely that beadswill stick to the PMMA surface. Moreover, asthe van der Waals force dominates for small dis-tances, for the interaction among the beads, thevan der Waals and electrostatic forces in PBS donot cancel each other for finite particle - particledistances. In this case the colloidal particle systemis not stable, with BSPBs forming agglomerateswith others in their vicinity. This corresponds tothe experimental findings, where the BSPBs couldnot be actuated to perform full transport steps butwere seen immobile or wiggling around a position,while some also formed agglomerates.

The interplay of the zeta potential, the permit-tivities and the ionic strength of the medium suchas the used buffer, PBS, mimicking a physiolog-ical environment strongly influences the electro-static force. Dynamic light scattering has beenused to determine the zeta-potentials ζb of the

7

beads. They had been negative for all experimen-tal cases (fig. 5a) due to the carboxylic function-alization of the SPBs and the fact that GFP hasits isoelectric point (4.6-5.4)41 below the presentpH value of 7.4. On the other hand, the absolutevalue |ζb| of a BSPB in PBS is with 15 mV con-siderably smaller than |ζb| of a SPB in water with69 mV, which is due to electrochemical shieldingby the ions in the buffer. Secondly, the Debyelength 1/κ as a measure for the extension of theelectrochemical double layer was determined to be0.74 nm for PBS (see eq. 3), while 1/κ =100 nmis usually approximated for water as a mediumdue to ionic impurities.42 In order to avoid particleadhesion on the PMMA surface, SDS as an am-phiphilic species was added in different concentra-tions, where the adsorption of the alkyl chain sideof dodecyl sulfate anions (DS-) on the surfaces inthe system causes a change of the electrochem-ical double layer associated with these surfaces,i.e. increases their negative charge density. Thisresults in increasing absolute zeta potential val-ues for increased surfactant concentration, as canbe seen in the experimental data as well as in lit-erature (see fig. 5).26 (A possible contribution ofso-called non-DLVO forces to the steady-state dis-tance consideration is assumed to be negligible inour system, since the beads’ surface is hydrophilic(mostly negatively charged GFP on the BSPBs atour pH / COO- terminated SPBs) and the PMMAsurface is partly hydrophobic, so that neither at-tractive hydrophobic nor repulsive hydration forcesare expected to contribute.) Under the addition ofdifferent concentrations of SDS, a transport wasexperimentally achieved, which was in agreementwith the SDS concentration dependent computedsteady-state distances. The received values for z ′bextracted from the force curves in figure 4 withthe respective errors were subsequently used forthe step velocity computation and are given infigure 5 b). The increasing absolute zeta poten-tials cause an increase of the steady-state distancefor SDS concentrations of up to 0.5 wt%. How-ever, z ′b drops beyond this concentration becausethe course of Fel becomes steeper with the in-crease of the Debye length κ due to the solutions’ionic strength for higher cSDS. Correspondingly,the results for the mean step velocities v BSPB ob-tained via the model as well as in the concluded

a)

b)

c)

d)

Figure 5: Effects of the surfactant concentrationon the transport of BSPBs. a) Zeta potential val-ues ζs of the PMMA substrate26 and ζb of the pre-pared BSPBs experimentally obtained by dynamiclight scattering. b) Steady-state separations z ′bbetween the substrate surface and the BSPBs de-rived from the force evaluation (fig. 4). c) Av-erage number of steps nsteps evaluable from thetransport videos. d) Experimental results and the-oretical values of the mean step velocities v BSPB

during BSPB transport at room temperature. TheSDS concentration dependent progression of theviscosity ηl taken from ref.26 is drawn with therespective axis on the right.

experiments are also presented as a function ofthe SDS concentration. Note, that the given ve-locities are averaged experimental values includingacceleration and deceleration phases of evaluabletransport steps, disregarding the number of beadssticking to the surface. As a measure for the trans-port efficiency, we furthermore plot the averagednumber of evaluable steps nsteps per SDS concen-tration in figure 5, while for each concentration 10to 14 videos were recorded at different times af-ter the biochemical coupling of GFP with a fixedparticle concentration in the dispersion (see fig.6).

Although the velocity of a BSPB at a SDS con-

8

centration of 0.01 wt% with a steady-state dis-tance of z ′b = 1.8 nm (error margins [0,2.7] nm)was theoretically obtained to be around 223 µm/sit can be expected that this value is too high.Firstly, because the z-distance lower error marginis zero, which speaks for the particle being ad-hered. Secondly, because the distance of 1.8 nmis still smaller than the surface roughness of spincoated PMMA,40 similar to the case of BSPBs inPBS without surfactant. Hence, the particles willpossibly not be able to move in this close proxim-ity as it was also seen in the experiments. Accord-ingly, the number of successfully evaluated stepsas a measure for the quality of the transportationin this SDS concentration of 0.01 wt% is only 7 %of the steps evaluated for the concentration of0.1 wt%. This low transport efficiency gives riseto a large experimental uncertainty of the step ve-locity v BSPB = (87±76) µm/s. For increased SDSconcentrations the transport efficiency increasesresulting in reduced error margins.

An explanation for the deviation between modeland experiment could be a systematic error byoverestimating the magnetic force that arises fromthe approximations made during the simulationof the magnetic layer properties. Particularly,the step-like transition between the simulated do-mains with opposing exchange bias field was pre-viously shown to yield an overestimated chargedensity in the domain wall and consequently ahigher magnetic stray field strength.43,44 This re-sults in the calculation of too high step velocities,although the steady-state distance will be unaf-fected for BSPBs as it is in the van der Waalsdominated distance regime of some nm. (A rea-son for the stray field overestimation is that theslope of the resist mask walls during the ion bom-bardment patterning together with the scatteringof ions are expected to cause a gradual change ofanisotropy rather than an abrupt transition.44)

Nevertheless, the step velocity trend is qualita-tively captured by the model: When increasingcSDS from 0.1 to 1 wt% the theoretical velocitydrops from 226 µm/s to 195 µm/s, firstly dueto the enhanced separation zb causing a loss inMFL strength and consequently a reduced actu-ating magnetic force and secondly because of thedrag force increase caused by the enhanced vis-cosity at this SDS concentration (see right axis

of figure 5d). For cSDS =10 wt%, the reducedparticle-MFL separation again enhances the mag-netic force, however the effect of the enhancedviscosity is even stronger which causes the theo-retical step velocity to be reduced to 108 µm/s.From both the experimental and theoretical re-sults, there seems to be an optimum SDS con-centration between 0.1 and 1 wt%. Accordingly,experiments with 0.1 wt% SDS gave the maxi-mum for the average number of evaluable steps inthe respective videos. This is valid for the modelsystem presented in this study and will vary forother combinations of magnetic bead, buffer so-lution, surfactant as well as spacer thickness andon the magnetic domain pattern used for the ac-tuation.Protein Stability - Since the critical concentra-tion for micellation (CMC) of SDS in water is8 mM = 0.23 wt% and is expected to be lower inour buffer,45 we would assume to observe a reduc-tion of the fluorescence intensity because globaland cooperative unfolding occurs around the CMCand results in a rapid denaturation.27,28 However,non-immobilized GFP was also previously shownfunctional above the CMC which underpins itshigh stability:24,29 While a relative fluorescenceabove 85 % at a SDS concentration of 0.5 wt% forpH values above 7.5 is reported at room temper-ature,29 the relative fluorescence was lowered to∼40 % at elevated temperatures of 50 ◦C.24 In or-der to investigate the surfactant’s influence on thestability of the immobilized protein, the BSPBswere stored in the same media that we used forthe transport experiments at room temperatureand the fluorescence was qualitatively tested ina fluorescence microscope while the simultaneoustransport indicated a remained colloidal stability.At all chosen points in the time frame of 8 days,a fluorescence of the beads was detected for eachstorage medium and simultaneously the transportproperties were evaluated via the mean step ve-locities as described earlier. As depicted in figure6, we observed no significant changes in the meanstep velocity for cSDS = [0.1, 1, 10] wt% indicat-ing a preserved colloidal stability and it can beexpected that the steady-state distance betweenBSPB and PMMA surface remained constant forall transport experiments. For particles in PBS at0.01 wt% SDS it has not been possible to deter-

9

Figure 6: Experimentally obtained mean step ve-locities of GFP-functionalized BSPBs in buffermedia with different concentrations of SDS atroom temperature depending on the time afterthe BSPBs had been transferred to the respec-tive storage buffer subsequent to the GFP func-tionalization. For each transport experiment, thefluorescence was simultaneously qualitatively de-tected indicating no unfolding of GFP for all stor-age times.

mine a trend due to the small number of evaluabletransport steps causing larger uncertainties thanfor the other concentrations. These findings are incorrespondence with the simulated small steady-state distance and the respective uncertainty forthis buffer medium for which the transport proper-ties may vary depending on slight variations of theexperimental conditions, e.g. environmental tem-perature or the position on the PMMA-coveredmicromagnetic array. Furthermore, we accountthe remained GFP functionality at SDS concentra-tions of up to 10 wt%, which is considerably higherthan in the reports of non-immobilized GFP,24,29

to an entropic effect due to the immobilizationwhich hinders the unfolding of the protein. Hence,fewer unfolded conformations are available for thebound protein, which enhances the stability.46

Conclusions

We have theoretically and experimentally stud-ied the influence of different surfactant concentra-

tions on the transport of GFP functionalized su-perparamagnetic beads in PBS mimicking physio-logical conditions, because experimentally no ac-tuation in pure buffer was possible. Therefore,the particles’ steady-state velocities and the num-ber of evaluable transport steps were investigatedas a measure for the transport behavior. Ourbead actuation concept combines a topograph-ically flat and magnetically structured substratewith external magnetic field pulses. The intro-duced theoretical model represents not only themagnetic and the drag force acting on a parti-cle at any given distance but also addresses theinfluence of surface forces in order to accuratelypredict the equilibrium bead-substrate separationdistance in dependence of the surfactant concen-tration. The steady-state distance is an indispens-able key information when simulating a bead’s tra-jectory and velocity. The experimentally receivedtrend for particle velocities as well as the transportefficiency measured via the number of evaluabletransport steps matches the predicted tendencywhere the mobility is enhanced within a certainrange of the surfactant concentration, which isfor the presented system 0.1 to 1 wt% sodiumdodecyl sulfate (SDS). The presented model canbe applied to other bead transport concepts whenthe governing forces can be determined. More-over, we demonstrated the effect of SDS on thetransport efficiency over the timescale of 8 days,in which transportation remains successful, whilecoincidentally the fluorescence was qualitativelyobserved to remain. This indicates a preservedprotein stability over days which can possibly beexplained entropically by the reduced number ofunfolded states due to the immobilization and pro-motes GFP as a candidate for similar studies dueto its stability. The possibility to forecast condi-tions where particle agglomeration and their ad-hesion to the substrate are avoided together withthe boundary condition of preserved protein func-tionality renders the presented model as basis forfuture lab-on-a-chip explorations.

We conclude that optimizing the transportationmechanism for non-functionalized beads in waterand expecting the same transportation yield sub-sequent to the protein immobilization is a mis-leading approach for the design of a biosensinglab-on-chip unit. Instead, it is inevitable that the

10

optimization of the biofunctionalized beads’ prop-erties, the properties of the liquid medium andthe adaption of the transport characteristics goeshand in hand.

Experimental Methods

Preparation of BSPB - His tagged green fluo-rescent protein (GFP) mut 247 was overexpressedin E. coli BL21 DE3 RIL cells after inductionwith 1 mM IPTG over night at RT using the ex-pression vector pET15b. Cells were harvested(7,000 xg, 10 min) and stored at -20◦C un-til further processed. Cells were homogenizedin TRIS-buffer (50 mM Tris(hydroxymethyl)-aminomethanhydrochlorid pH 8.0, 300 mM NaCl)plus EDTA-free protease inhibitor (cOmpleteTM,Roche) and lysed by French press (Thermo IEC).Lysates were centrifuged (40,000 xg, 45 min).Supernatant was passed through 0.45 mm sterilePVDF Rotilabo1-syringe filters (Roth) and ap-plied to metal affinity chromatography (Protino1Ni-NTA column 1 mL, Macherey-Nagel) usingan FPLC system (Akta) at 4◦C . Unspecificallybound proteins were removed with a 20 mM imi-dazole step, followed by elution of the His-taggedprotein with an imidazole gradient (20 mM –500 mM) in TRIS-buffer. Elution fractions (70mM – 350 mM imidazole) were pooled accordingto their absorbance at 280 nm followed by ex-tensively dialysed against PBS-buffer (phosphatebuffered saline: 140 mM NaCl, 10 mM NaH2PO4

pH 7.4, 2.7 mM KCl, 1.8 mM KH2PO4). Proteinconcentration was determined using absorbanceat 488 nm (lmax) and the concentration calcu-lated using an estimated extinction coefficient of55,000 g/mol. Protein purity was controlled byCoomassie-stained SDS-PAGE.48 GFP was solubleand stable, aliquots were stored at -20◦C . Dyn-abeads (Dynabeads® MyOne™Carboxylic Acid,ThermoFisher Scientific) conjugation was carriedout in principal according to the suppliers’ proto-col.49 Briefly, 75 µL of beads (10 mg/mL) werewashed two times with cold (0 °C) 0.01 M NaOHand once with 50 mM MES-buffer (25 mM 2-(N-morpholino)ethanesulfonic acid pH 6.4). Beadswere separated after each step with a magneticapparatus for 3 min. After discarding the super-

natant, the mixture was sonicated after insertingnew solution for 20 s to maintain a homoge-nous solution. Beads were activated with 25 mMN-hydroxysuccinimide (NHS, Sigma Aldrich)and 25 mM N-ethyl-N’-(dimethylaminopropyl)-carbodiimide (EDC, Sigma Aldrich) in MES withslow continuous shaking at RT for 30 min. Af-ter discarding the supernatant, the beads werewashed twice with MES-buffer. GFP was dilutedwith PBS-buffer to a total concentration of 1,10, 30, 60, 100 µM and added to the activatedbeads. As a negative control, coupling in absenceof His-GFP was carried out. The beads were incu-bated on a shaker with slow constant speed at RTfor 30 min. The conjugated beads were washedtwice with MES-buffer plus 0.2 wt% Tween. Forquenching non-reacted activated groups, a solu-tion of 50 mM ethanolamine was added and incu-bated at RT for 15 min, followed by two washingsteps with PBS-buffer plus 0.01 wt% Tween. Thefluorescence intensities of the BSPBs were mea-sured in a CLARIOstar® microplate reader. Beadsuspensions were diluted 1:50 and transferred toblack 384 well plates (Brand). As a reference200 nM GFP in PBS-buffer pH 7.4 was used.Each measurement was carried out in triplicateapplying the well scan method (settings: 15 x15 scanmatrix, 2 mm width, 8 flashes per scanpoint). For excitation and emission determina-tion optical filters (BMG LABTECH) were used(Ex. 482-16 nm, Em.: 530-40 nm, Dichroic: LP504 nm). From the comparison of the chosenGFP concentrations we determined the maximumin the relative fluorescence intensity for an initialGFP concentration of 60 µM (s. Supplementaryfig. S4), which was subsequently used for thefabrication of BSPBs for transport experiments.Fractions of the BSPB suspension were trans-ferred to the storage and transport media, namelyPBS solutions with the SDS concentrations 10,1, 0.1, 0.01 and 0 wt%, and stored in the samebuffer at room temperature afterwards.Preparation of micromagnetic array - Themagnetic substrate we used for the actuation is anexchange bias layer system with artificial parallelstripe magnetic domains with head-to-head andtail-to-tail magnetization orientations in adjacentdomains (figure 1). This layer stack with the com-position Cu10nm/Ir17Mn30nm

83 /Co70Fe10nm30 /Ta10nm

11

was fabricated by rf sputter deposition and fieldcooled as described by Holzinger et al.12 Theartificial parallel stripe domains were fabricatedby ion bombardment induced magnetic pattern-ing (IBMP)50,51 using a home-built Penning ionsource. For this procedure, a lithographicallydeposited 700 nm thick photoresist (AZ1505, Mi-crochemicals) parallel stripe structure (5 µm widewith a periodicity of 10 µm) served as a shadowmask for the ion bombardment. 10 keV He+-ionbombardment was performed with an ion fluencyof 2.2 · 1015 ions/cm2 in an applied magnetic fieldof 64 kA/m antiparallel to the initial EB direction.The bombarded EB system showed a magnetiza-tion reversal superposed of two hysteresis loopscorresponding to the adjacent artificial magneticdomains with the absolute values of the oppos-ing exchange bias fields |HEB,L| = 12±1 kA/m(HC,L = 5±1 kA/m) and |HEB,R| = 7±1 kA/m(HC,R = 3±1 kA/m). After the removal of thephotoresist, a 700 nm thick layer of PMMA wascoated on top of the EB layer system serving asa spacer unit.Transport experiments - A microfluidic cham-ber corresponding to a fluid container volumeof ∼3 µl was fabricated from Parafilm M and amicroscopy glass slide. For the experiments sus-pensions of BSPBs [130 µg/ml (1:75 from stock)]in PBS buffer with SDS concentrations cSDS be-tween 0 and 10 w% were prepared. After loadingthe chamber with the respective particle suspen-sion, it was placed between two solenoid pairs forthe creation of trapezoidal magnetic field pulsesperpendicular (z) and parallel (x) to the samplesurface plane (see fig. 1).12 The plateau mag-netic fields were chosen to be Hx,max = 2.4 kA/m(Hz,max = 4.0 kA/m), while the rise and fall hadan alteration rate of vH =3.2 ·106 A/(m s). Themagnetic field pulses for both directions were sup-plied at a frequency of ωext = 1.25 Hz, while theoscillations of Hz advanced Hx by π/2. The par-ticle trajectories during this transport performedat room temperature were recorded via an opti-cal microscope setup (40x optical magnification)equipped with a high-speed camera operated at aframe rate of 1000 fps (Optronis CR450 x2) andsubsequently analyzed with the tracking softwareAdaPT developed for particle tracking.39

BSPB properties - The same suspensions were

used to obtain the hydrodynamic radius and thezeta potential of the BSPBs in a triplicate viadynamic light scattering with the Zetasizer NanoZS90 (Malvern) at room temperature subsequentto 1 min ultrasonication.

Acknowledgement The authors thank theCenter for Interdisciplinary Nanostructure Scienceand Technology (CINSaT) at Kassel universitypromoting cross-disciplinary communication andresearch, project ”‘MASH”’ supported by an in-ternal grant of Kassel university. Moreover, weacknowledge the participation of J. Ruhl in trans-port experiments.

Supporting Information Avail-able

Additional information for the model part, aboutthe coupling efficiency of GFP and the evaluationof particle velocities is given.

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15

Supporting Information:

Transport efficiency of biofunctionalized magnetic

particles tailored by surfactant concentration

M. Reginka,∗ H. Hoang, O. Efendi, M. Merkel, Rico Huhnstock, D. Holzinger,

K. Dingel, B. Sick, D. Bertinetti, F. W. Herberg,∗ and A. Ehresmann

E-mail: reginka@physik.uni-kassel.de; herberg@uni-kassel.de

Magnetic field landscape calculation - The patterned exchange biased thin film with

head to head and tail to tail domain configurationS1 was modeled using the object oriented

micromagnetic framework (OOMMF) package.S2 Since the pattern has been fabricated by keV

He ion bombardment, the magnetic properties differ in the adjacent domain types.S3 Thus, for

the saturation magnetization of the unbombarded domains an experimentally determined value

is used while this value needs to be decreased for the bombarded stripes.S4 Furthermore, the

ferromagnet’s uniaxial anisotropy is reduced accordingly and the relative changes were taken into

account.S5 The exchange bias as the responsible anisotropy for the pinned magnetization direction

of each stripe domain was accounted for in the OOMMF simulations by a fixed Zeeman term

with exchange bias fields determined by magneto-optical Kerr measurements for each domain

type. The sign of the Zeeman term has been inverted for the different stripe domain regions in

order to appropriately implement the chosen head-to-head and tail-to-tail domain configuration.

From the resulting magnetization values for the mesh elements of volume Vi = (5 nm)3 in the

chosen grid (x = 20 µm, y = 10µm) the magnetic moment for each element i was calculated

as mx = Mx · Vi . The magnetic stray field landscape (MFL) at the position ~r = (x , y , z) with

S-1

arX

iv:2

103.

1393

4v1

[co

nd-m

at.s

oft]

25

Mar

202

1

components Hx(~r) and Hz(~r) was afterwards computed as the superposition of the magnetic fields

from all magnetic moments obtained from the simulation in dipole approximation:

~H(~r) =1

4π

∑

i

3(~R · ~mi) ~R

|~R |5− ~mi

|~R |3(1)

where ~R = ~r − ~ri is the distance vector between the observer position ~r and the position of the

dipole (or here the mesh element) ~ri.S6

Modeling a Trajectory Including Browninan Motion - We described this random walk

under the assumption of an infinite liquid environment as

xrw =

√∆t

kBT

3πηlfd(z)· arand (2)

where arand is a random value sampled from a Gaussian distribution with a mean of 0 and a

variance of 1.

The magnetic moment of a SPB - The latter can be described in point particle approxi-

mation by the Langevin functionS7

~mb(x , z) = ms ·[

coth(b · ~Heff(x , z))

−(

1

b · ~Heff(x , z)

)] (3)

where for the average saturation magnetic moment ms a value of 2.45 ·10−14 Am2 calculated

from the vendor’s informationS8,S9 was used and the Langevin parameter b =1.05·10−4 m/A was

taken from experimental data provided in ref. S10.

Van der Waals Forces - The distance dependence of FvdW between a sphere and a plane

writes asS11

FvdW(z ′) = −AH,123 · r6z ′2

(1

1 + 14z ′/lret

)(4)

with the hydrodynamic radius r of the sphere, the Hamaker constant AH,123 describing the in-

S-2

teraction of the bead of material 1 and a substrate of material 2 in a liquid medium 3 via the

relative permittivities εr,i and the optical refractive indices ni of the respective material/medium

i . For the calculations AH,123 according to refs. S12 and S13 with the respective values for ni and

εr,i of the materials 1 and 2, namely PMMA and polystyrene as an estimate for the BSPBs.S13

The associated uncertainty is expected to be insignificant since the range of AH,123 from 1.2 to

1.8 ·10−20 J for the different surfactant concentrations used in the present experiments are in

the range of Hamaker constants of proteins reported in literature (0.8 to 2.0·10−20 J).S14,S15 For

the dispersion medium PBS the same SDS dependent values for εr,3 as for the calculation of Fel

were taken.S16 When approaching distances z ′b smaller than the radius of the sphere - like in this

work-, retardation effects, which are reflected by the term in brackets, can be neglected.

Evaluation of experimental data - From the recorded videos we evaluated the beads’

trajectory via a tracking procedure. For this purpose, we used the particle tracking software

AdaPT [Ref], which fulfills tracking in two subsequent steps: Locating the particles in the re-

spective frames with subpixel accuracy and linking the extracted x-y coordinates into probable

trajectories. The result of the tracking procedure is displayed in Fig. S1.

Figure S1: Left: exemplary video frame. Right: Output figure from tracking procedure. Alltrajectories of a video (8.1 s) in which the magnetic field sequence theoretically induced 20 stepsfor each particle.

S-3

Steady-state velcoities - As the tracked positional information of the beads from the videos

can be noisy due to lighting conditions and the spatial resolution of the microscopic unit, we

decided not to determine the momentary velocity for each frame from the numerical derivative.

Instead, a Gaussian error function was fitted to each step within the observed trajectory x(t),

where the velocity was deduced from the function’s derivative, which possesses by definition

the shape of a normal distribution. In order to compare the experimental and the theoretical

findings, we proceeded with both types of trajectory in the same manner. Next, the mean step

velocity was evaluated as the average velocity within the region around the maximum in which the

values are above 50 % of the function’s maximum. From the trajectories simulated via balancing

magnetic and drag force during transportation time for different SDS concentrations, we deduced

this method from the comparison with the momentary velocity and its average value for v >

60 µm/s.

Figure S2: Evaluation of mean step velocity via error function fit to the large step within thesimulated trajectory.

Figure S3: Simulated momentary steady-state velocities. Comparison between the momentaryvelocity, its mean value above a threshold of 60 µm/s (grey shaded region) and the result fromthe error function fit evaluation with the respective error.

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Coupling efficiency - Prior to the transportation experiments the coupling protocol for

the biofunctionalization of SPBs with GFP was tested. While varying the concentration of GFP

added to the suspension of beads and coupling reagents, we determined relative fluorescence

intensities. Consequently, we chose a GFP concentration for coupling of 60 µM for all subsequent

biofunctionalizations for the transport experiments.

Figure S4: Determination of coupling efficiency in dependency of the protein concentration duringthe coupling process. Different concentrations of GFP, ranging from 1 µM up to 100 µM,were incubated with activated beads. After coupling, the GFP-fluorescence was measured with100 % set to the fluorescence of a 200 nM GFP solution. Measurements from three independentcouplings (white circles, black triangles and grey squares) with 10 points were measured for eachcoupling.

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