Determination of the binding reaction between avidin and biotin by relaxation measurements of magnetic nanoparticles

Determination of the binding reaction between avidin and biotin by relaxation measurements of magnetic nanoparticles

Journal of Magnetism and Magnetic Materials 194 (1999) 62—68 Determination of the binding reaction between avidin and biotin by relaxation measuremen...

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Journal of Magnetism and Magnetic Materials 194 (1999) 62—68

Determination of the binding reaction between avidin and biotin by relaxation measurements of magnetic nanoparticles R. Ko¨titz  *, W. Weitschies , L. Trahms, W. Brewer, W. Semmler Institut fu( r Diagnostikforschung GmbH an der Freien Universita( t Berlin, Spandauer Damm 130, D-14050 Berlin, Germany Physikalisch-Technische Bundesanstalt, Abbestra}e 2 - 12, D-10587 Berlin, Germany Freie Universita( t Berlin, Arnimallee 14, D-14195 Berlin, Germany

Abstract The binding between avidin and biotinylated magnetic iron oxide nanoparticles can be monitored by means of magnetic relaxation measurements. The resultant signal, caused by particle aggregates, has Brownian and Ne´el components. The time constant and amplitude of Brownian relaxation were determined by a fit algorithm which also yielded Ne´el amplitudes proportional to the avidin content of the samples.  1999 Elsevier Science B.V. All rights reserved. Keywords: Biological binding reaction; Brownian relaxation; Ne´el relaxation

1. Introduction Magnetic nanoparticles coupled with biological substances have gained a variety of biomedical applications, mostly based on their strong magnetic moment. The utilisation of magnetic field gradients for the application of magnetic forces on the particles is well established for magnetic separation techniques. Recently, a novel technique for the sensitive binding specific quantification of biological binding processes has been introduced [1], where magnetic nanoparticles are used as labels for biological substances. This new approach involves the

direct measurement of the relaxation of the magnetisation, generated by the magnetic moments of the nanoparticles, with sensitive sensors like superconducting quantum interference devices (SQUIDs). In this new type of magnetic immunoassay the analyte — that is the biological substance to be detected — was incubated onto a solid phase. The aim of the present study was to evaluate this relaxation technique for the direct detection of a biological binding reaction in a homogeneous liquid phase.

2. Theoretical background * Corresponding author. Fax: #49-30-30390499; e-mail: [email protected]

An ensemble of magnetic nanoparticles, suspended in a carrier liquid is also known as a

0304-8853/99/$ — see front matter  1999 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 8 8 5 3 ( 9 8 ) 0 0 5 8 0 - 0

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magnetic fluid. An external magnetic field H tends to align the microscopic magnetic mo  ments of the nanoparticles and hence produces a macroscopic magnetisation of the sample. After switching off the magnetic field, the moments of the magnetic nanoparticles return to equilibrium which is reflected by a decay of the magnetisation. This relaxation process can be accomplished by two different mechanisms, the so called Ne´el relaxation and Brownian relaxation. Brownian relaxation [2] is due to rotational diffusion of the particle in the carrier liquid with a relaxation time of q

"3»g/k¹, (1)  where » is the hydrodynamic volume of the particle including a possible coating with biological components, g the dynamic viscosity of the carrier liquid, k the Boltzmann constant and ¹ the absolute temperature. Ne´el relaxation [3] is caused by the reorientation of the magnetisation vector inside the magnetic nanoparticles against an energy barrier *E. The time constant of this process is given by

Fig. 1. Comparison of the dependence of Brownian, Ne´el and effective relaxation time on the core diameter of spherical magnetic nanoparticles. Assumptions: coat thickness 15 nm, K"20 kJ/m, ¹"300 K. The Brownian relaxation times are calculated for hydrodynamic particle sizes. The time window is determined by the measurement setup.

q

"q exp(*E/k¹), (2) ,&   where q is usually quoted as 10\ s and  *E"K»(1!h) for a system of uniaxial noninteracting particles with an anisotropy field H and h"H /H . In real systems of magnetic

 nanoparticles there is always a distribution of energy barriers due to a distribution of the magnetic anisotropy constants K (caused by crystalline and predominantly shape anisotropy) as well as of the core volumes of the particles ». In general both mechanisms contribute to the relaxation process and the faster relaxation process dominates the resultant effective relaxation time given by q q , . q " (3)  q #q , In Fig. 1 the Brownian, Ne´el and effective relaxation times are plotted against the core diameter of magnetic nanoparticles. Here, spherical particles of magnetite with an anisotropy constant of K" 20 kJ/m are assumed, that are stabilised with

a coat of 15 nm thickness and suspended in water (g"10\ N s/m). Therefore, a core diameter of e.g. 20 nm corresponds to a hydrodynamic diameter of 50 nm. It is evident, that the Ne´el relaxation time depends much stronger on the particle size than the Brownian relaxation time q . Fur thermore, q is shorter than the observed time  window over the displayed range of diameters relevant for well dispersed particles. Therefore, free particles do not contribute to the relaxation signal in the selected time window. However, if particles are immobilised and the Brownian mechanism is thereby inhibited, the effective relaxation is only due to the Ne´el mechanism. Then within the selected time window, Ne´el relaxation of particles within a certain narrow range of sizes can be observed. Thus by using particles of appropriate size as labels for biological components, magnetic nanoparticle relaxation provides a binding specific signal. The inset of Fig. 1 shows a double logarithmic plot of the Brownian relaxation time against an

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extended range of hydrodynamic diameters. It demonstrates, that objects of a hydrodynamic size of some 100 nm yield Brownian relaxation times within the observed time window. For objects bigger than approximately 2 lm q becomes even  longer than the observed time window, which means that Ne´el relaxation becomes the only relevant process. Objects of this size can be formed e.g. by biochemically induced aggregation of magnetic nanoparticles. This means, that using particles of appropriate size a binding specific Ne´el relaxation signal can be obtained if the binding reaction yields sufficiently large aggregates of nanoparticles. For the evaluation of the signals obtained from such measurements knowledge of the time dependence of the relaxation signal is of importance. Ne´el, Brownian and effective relaxation of an ensemble of identical particles are described by an exponential decay with time: M(t)"M(t"0) exp(!t/q).

(4)

Relaxation in real systems is usually non-exponential, due to the superposition of different relaxation times. In the case of Ne´el relaxation, the distribution of energy barriers of a system of magnetic nanoparticles leads to a time dependent magnetisation given by [4]

 

t M(t)"M & ln 1#  ,  , t

(5)

where the characteristic time t depends on the  magnetisation time t and H . For the case of



 weak magnetising fields [5] t "t . 

 For Brownian relaxation has been shown, that due to the comparatively weak dependence of the time constant on the hydrodynamic particle size the model of a single exponential decay may be used, which yields an estimate of the mean Brownian relaxation time [6].

four specific binding sites for biotin. Therefore, the binding reaction can result in a crosslink of the reaction components. Biotinylated iron oxide particles (BIOP) were prepared by biotinylation of dextran coated magnetic iron oxide particles with median core- and hydrodynamic diameters of 12 and 50 nm, respectively. For this purpose, 2 mg of NaIO were added  to 2 ml of a colloidal solution of the nanoparticles (50 mmol Fe/l) in 100 mmol/l citrate buffer at pH 5.0. The colloidal solution was stirred in the dark for 30 min. The nanoparticles were separated by gel filtration (Sephadex PD 10, 100 mmol/l phosphate buffered saline pH 7.4). 1.9 mg of biotinamidocaproyl hydrazide (Sigma, Germany) were added to the activated nanoparticles and the colloidal solution was stirred for further 12 h in the dark. Thereafter, the magnetic nanoparticles were purified by magnetic separation using 100 mmol/l phosphate buffered saline pH 7.4 with added 0.1% Tween 20 (PBST). The mean hydrodynamic particle diameter of the magnetically separated biotinylated nanoparticles was about 80 nm as determined by laser light scattering. The final nanoparticle concentration was about 0.5 mmol Fe/l. To 450 ll of this BIOP sample defined amounts of avidin were added stepwise. The amount of magnetic nanoparticles remains constant for all measurements. 1 min after each addition of avidin the sample was positioned in a self shielding twin coil [5] and magnetised with 1.6 kA/m for 1 s. After switching off the magnetising field, the relaxation of the magnetic induction B was measured in the time window between t "5 ms and t "1000 ms using    a dc-SQUID-Magnetometer [7] in a magnetically shielded environment [8]. During the entire experiment the sample was kept at room temperature.

4. Results and discussion 3. Materials and methods As an experimental system we chose the binding reaction between avidin, which is a protein derived from egg yolk and biotin, which is a small molecule, also known as vitamin H. The avidin molecule has

Fig. 2 shows a comparison of the relaxation signals measured for the different amounts of added avidin. Before addition of avidin the BIOP showed no relaxation signal within the observed time window. This is expected from Fig. 1, since their

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Fig. 3. Schematic depiction of aggregates caused by the binding reaction between biotinylated iron oxide particles and avidin.

Fig. 2. Relaxation signals of biotinylated iron oxide particles (BIOP) after stepwise addition of avidin. The values in the legend correspond to the total amount of avidin. All measurements were taken after magnetisation with 1.6 kA/m for 1 s.

Brownian relaxation time is less than 100 ls and shorter than the starting time of the measurement. This observation is in accordance with previous studies on the relaxation of stable magnetic fluids [6,9]. Furthermore, it indicates that the BIOP themselves do not form larger aggregates and do not adsorb onto the wall of the sample container, since both effects would lead to Ne´el relaxation [1]. Reference samples with added bovine serum albumin (not shown in Fig. 1) yielded no relaxation signal, which proves that the addition of a protein that does not bind specifically with biotin does not change the relaxation behaviour of the BIOP within the observed time. As Fig. 2 further shows, a relaxation signal can be observed for all samples after addition of avidin. The amplitude of the relaxation signal increases with the amount of avidin added to the sample. This is caused by an increasing fraction of magnetic nanoparticles contributing to the relaxation signal in the observed time window. The relaxation signal arises from avidin induced specific aggregation of the BIOP as schematically depicted in Fig. 3. The

Fig. 4. Relaxation signal of biotinylated iron oxide particles after addition of a total amount of 10 lg avidin and curve fit according to Eq. (5).

unbound BIOP particles remain free and do not contribute to the signal. The amount of aggregation can be estimated from an analysis of the time dependence of the measured data. Fig. 4 shows the relaxation signal of the sample with the highest investigated avidin content of 10 lg. The measured relaxation is well described by a fit according to Eq. (5). This indicates that the relaxation in the observed time

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Fig. 5. Relaxation signal of biotinylated iron oxide particles after addition of a total amount of 2 lg avidin and curve fits according to Ne´el, Brownian and superimposed relaxation processes according to Eq. (6).

window is only due to the Ne´el mechanism. It may be explained by the formation of large particle clusters. This measurement was reproduced in intervals of several minutes with the result of unchanged relaxation signals. This indicates that the binding reaction between avidin and biotin was already completed at the time of the first measurement. As a typical example for the samples of a lower avidin content Fig. 5 shows the relaxation signal of the sample containing 2 lg avidin. Evidently, Eq. (5) applicable for pure Ne´el relaxation, does not describe the relaxation of this sample. Also a curve fit assuming pure Brownian relaxation using a single exponential decay is unsatisfactory. This suggests, that within the observed time window both relaxation processes contribute to the signal. The simplest model is a superposition of a Ne´el and a Brownian component:

 

t *B(t)"B & ln 1#   , t

#B exp(!t/q ).   

(6)

Fig. 6. Relaxation amplitude *B as a function of the total amount of added avidin.

As indicated in Fig. 5 this model function fits the measurement well. It was successfully applied to the data of all samples with an avidin content of less than 10 lg. As a result of the fit procedure values for the amplitude of the Ne´el process B ´ and the  , amplitude B and the time constant q of    the Brownian relaxation are obtained. It can be concluded from this analysis, that the investigated samples can be subdivided into at least three different fractions: a first fraction consists of free unbound BIOP with a Brownian relaxation time shorter than the observed time window. A second fraction of aggregates with a moderate size of approximately 400 nm yields a Brownian relaxation time within the observed time window. The third fraction consists of aggregates bigger than approximately 2 lm where due to their size the Brownian mechanism is practically inhibited and which consequently relax by the Ne´el mechanism. In order to study the effect of the addition of avidin on the relaxation signal, in a first approach the effective relaxation amplitude *B"B(t )!   B(t ) was determined. In Fig. 6 *B is plotted  against the total amount of added avidin. The effective relaxation amplitude is proportional to the

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Fig. 7. Brownian relaxation time obtained by fit according to Eq. (6) as a function of the total amount of added avidin. Inset: Amplitude of Brownian relaxation obtained by the same fit as a function of the total amount of added avidin. The straight line is the linear regression of the data.

amount of avidin for small amounts of added avidin but clearly deviates from linearity for the 10 lg avidin sample. *B contains the contributions of the Brownian as well as the Ne´el relaxation components which are now evaluated separately on the basis of a fit according to Eq. (6). As the inset of Fig. 7 shows, the Brownian relaxation amplitude is proportional to the amount of avidin in the interval between 100 ng and 2 lg. Since the relaxation of the 10 lg avidin sample is due to Ne´el, its Brownian relaxation amplitude is negligible. This indicates that there is no more fraction of aggregates with a moderate size of approximately 400 nm. In Fig. 7 the Brownian relaxation time of the aggregates is plotted against the total amount of avidin. The data show a trend towards longer Brownian relaxation times for increasing amounts of avidin. This could be explained by an increase of the hydrodynamic size of the avidin-BIOP conjugates assuming an unchanged viscosity of the carrier liquid. Since due to its negligible amplitude the Brownian relaxation time can not be determined

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Fig. 8. Amplitude of Ne´el relaxation obtained by fit according to Eq. (6) as a function of the total amount of added avidin. The straight line is the linear regression of the data.

for the 10 lg avidin sample, the parameters of Brownian relaxation yield information only for a limited range of avidin concentrations. However Fig. 8 shows that the amplitude of Ne´el relaxation is proportional to the amount of avidin over the entire investigated range. Hence this parameter is best suited for the quantification of the avidin content of the sample.

5. Conclusions and summary We have shown, that the magnetic nanoparticle relaxation technique yields binding specific signals for a system of biotin and avidin in a homogenous liquid phase. The addition of avidin to biotinylated magnetic nanoparticles leads to crosslinking and hence to particle aggregates. The resultant complex relaxation signal has Brownian and Ne´el components. Assuming a superposition of both components a fit algorithm yielded the parameters of both relaxation processes. The time constant and amplitude of the Brownian relaxation depend on the

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amount of avidin present in the sample over a limited range of avidin concentrations. The amplitude of the Ne´el relaxation is proportional to the amount of avidin over the entire investigated range. This study demonstrates for the first time that using appropriate binding components, magnetic nanoparticle relaxation measurements can be applied for the analysis of binding systems in a homogenous phase. References [1] W. Weitschies, R. Ko¨titz, T. Bunte, L. Trahms, Pharm. Pharmacol. Lett. 7 (1997) 5.

[2] P. Debye, Polar Molecules, Chemical Catalog Company, New York, 1929. [3] L. Ne´el, Ann. Geophys. 5 (1949) 99. [4] R.W. Chantrell, S.R. Hoon, B.K. Tanner, J. Magn. Magn. Mater. 38 (1983) 133. [5] D.V. Berkov, R. Ko¨titz, J. Phys.: Condens. Matter 8 (1996) 1257. [6] R. Ko¨titz, W. Weitschies, L. Trahms, W. Semmler, J. Magn. Magn. Mater. 198 (1999), in press. [7] H. Koch, R. Cantor, D. Drung, S.N. Erne´, K.P. Matthies, M. Peters, T. Ryha¨nen, H.J. Scheer, H.D. Hahlbohm, IEEE Trans. Magn. 27 (1991) 2793. [8] S.N. Erne´, H.D. Hahlbohm, H.J. Scheer, Z. Trontelj, in: S.N. Erne´, H.D. Hahlbohm, H. Lu¨bbig (Eds.), Biomagnetism, de Gruyter, Berlin, 1981 p. 79. [9] R. Ko¨titz, P.C. Fannin, L. Trahms, J. Magn. Magn. Mater. 149 (1995) 42.