- Open Access
Quantification of specific bindings of biomolecules by magnetorelaxometry
© Eberbeck et al; licensee BioMed Central Ltd. 2008
- Received: 05 July 2007
- Accepted: 11 March 2008
- Published: 11 March 2008
The binding reaction of the biomolecules streptavidin and anti-biotin antibody, both labelled by magnetic nanoparticles (MNP), to biotin coated on agarose beads, was quantified by magnetorelaxometry (MRX). Highly sensitive SQUID-based MRX revealed the immobilization of the MNP caused by the biotin-streptavidin coupling. We found that about 85% of streptavidin-functionalised MNP bound specifically to biotin-agarose beads. On the other hand only 20% of antibiotin-antibody functionalised MNP were specifically bound. Variation of the suspension medium revealed in comparison to phosphate buffer with 0.1% bovine serum albumin a slight change of the binding behaviour in human serum, probably due to the presence of functioning (non heated) serum proteins. Furthermore, in human serum an additional non-specific binding occurs, being independent from the serum protein functionality.
The presented homogeneous bead based assay is applicable in simple, uncoated vials and it enables the assessment of the binding kinetics in a volume without liquid flow. The estimated association rate constant for the MNP-labelled streptavidin is by about two orders of magnitude smaller than the value reported for free streptavidin. This is probably due to the relatively large size of the magnetic markers which reduces the diffusion of streptavidin. Furthermore, long time non-exponential kinetics were observed and interpreted as agglutination of the agarose beads.
- Surface Plasmon Resonance
- Binding Reaction
- Agarose Bead
- Relaxation Curve
- Analyte Molecule
The binding reaction between different biomolecules, e.g. antibody-protein or ligand-receptor coupling, is of great interest in traditional and in modern fields of biosciences, e.g. proteomics. For example, the kinetics of association and dissociation reactions enables the estimation of the affinity of biomolecules. This is useful for studies on drug efficiency or therapeutic drug monitoring .
The detection and quantification of antigenes, e.g. specific surface proteins of bacteria or malignant cells, or specific extraneous biomolecules, is performed by so-called immunoassays. In immunoassays, detection molecules, e.g. antibodies, bind specifically to the analyte to be quantified. Signal transducers which are linked to the detection molecules give a physically measurable signal.
In heterogeneous immunoassays, the unbound markers have to be washed out in order to get a signal from bound marked detection molecules, only. In homogeneous immunoassays the signal of the transducers changes as the result of the binding of the detection molecule, i.e. the amount of bound detection molecules can be measured in the presence of unbound ones by separating the two qualitatively different signals. Besides their high potential for automation, homogeneous immunoassays enable the measurement of the binding kinetics . Well-known examples of homogeneous assays are the Fluorescence Polarisation Immunoassay (FPIA)  and the Surface Plasmon Resonance (SPR) assay [4, 5]. In the case of FPIA the signal transducers are fluorophores changing the polarisation of the emitted light after a binding. In the SPR based assay, the detection molecules are attached to a solid surface acting as anchors for the analyte molecules. The binding increases the mass attached to the sensor surface leading to a change of the surface plasmon resonance frequency.
In this paper we investigate the quantification of the biotin-streptavidin and biotin-antibiotin-antibody bindings and its kinetics using MARIA. Biotin serves as the analyte and streptavidin and antibiotin-antibody have the function of detection molecules.
In MARIA, the detection molecules are labelled by Magnetic NanoParticles (MNP). These composites are the probes for the analyte molecules. The relaxation of the magnetic moment of the MNP after switching off an external field by their relaxation behavior is measured by MagnetoRelaXometry (MRX) . The relaxation signal depends on the binding state of the probes . MARIA provides the quantity of immobilised probes, i.e. the amount of bound biomolecules, in the presence of the unbound ones because these two signal contributions can be separated. Consequently, MARIA is a homogeneous immunoassay which needs no washing steps and the kinetics of the binding is easily accessible. Because the magnetic signal is not influenced by non-magnetic components of biological material, the binding behavior of an analyte can be investigated in different environments (e.g. water, serum or blood) with only one method by MARIA.
MARIA does not require a special geometry, so that standard vials can be used. Thus, it is possible to quantify biomolecules in a realistic environment, without severe sample alterations due to preparation.
Quantification of the binding
On the other hand, in the control sample, where MNP*SAV saturated with biotin was incubated with biotin agarose, the same relaxation signal as that of the reference sample of MNP*SAV without the biotin agarose target (Fig. 2) was obtained. This indicates the absence of unspecific binding, so that the binding between MNP*SAV and agarose can be attributed exclusively to the specific streptavidin-biotin coupling.
The binding behaviour of MNP*AB (antibiotin-antibody linked MNP) to biotin agarose was quantitatively different. Even after one day of incubation, only 25% of the MNP*AB were coupled to the targets (Fig. 4). We obtained the same result in the case of a 10 times lower concentration of MNP*AB. Apparently, 75% of the labels are not immobilized, even in the excess of target molecules. One explanation might be again that there are MNP-labels without properly coupled detection molecules. Obviously, in the case of MNP*AB the fraction of idle labels is much larger than in the case of MNP*SAV.
The control experiment for MNP*AB again exhibits a behaviour that is different from MNP*SAV. After incubation with a high excess of free biotin, part of MNP*AB are immobilized in the presence of biotin agarose, indicated by an increased relaxation time, while no change in relaxation was observed for the samples without biotin agarose (Fig. 4). To explain this behaviour we propose two hypotheses: (i) The MNP*AB bind to the agarose-beads non-specifically. (ii) The antibiotin antibodies bind readily to biotin being part of larger compartments, e.g. biotinylated proteins, but only modestly to free biotin . This causes the biotin, immobilised to agarose beads, to exchange the free biotin at the anti-biotin antibody.
The continuous measurement of the magnetic relaxation during the incubation time tI provides information about the binding kinetics. By fitting equation (16) to the relaxation curves, we obtain β(tI) the actual relative amount of bound MNP. From our data the binding time tb, which is defined as the time at which β(tb) = (1/(1 - 1/e)) βmax, where βmax is the amount of bound probes for t → ∞ in the saturation condition, was estimated to be tb = (9400 ± 1000) s and tb = (3600 ± 350) s for MNP*SAV and MNP*AB, respectively.
Values of binding time estimated from the binding curves β(tI) as well as the association rate constants calculated according (11), (12) and the association rate constant for free streptavidin, take from .
Association rate constant
MNP-concentration cP (nmol/1)
binding time tb (s)
eq. (11) ka
eq. (12) ka
Ref.  ka
9400 ± 1000
54 ± 9
270 ± 45
3600 ± 350
12 ± 2
60 ± 10
4400 ± 220
116 ± 20
580 ± 100
2700 ± 60
63 ± 2
315 ± 10
807 ± 100
55 ± 10
275 ± 50
As discussed in methodical section, we can calculate the association rate constants according to (11), which are listed in Table 1. With the obtained association rate constants equation 11 holds for cP,0 ≫ kd/ka,p = 10-12 , using kd ≈ 10-8 s-1 [12, 13]. This condition is fulfilled in all our experiments (Table 1).
In order to compare these values with those found for unlabelled streptavidin using SPR, we have first estimated the values for unlabelled streptavidin using (12). Assuming that the streptavidin molecules (SAV) have a "diameter" of about 10 nm we get a size ratio κ = rP/rSAV = 5 (mean diameter of the MNP*SAV is approximately 50 nm). Accordingly, the association rate constant for bare streptavidin becomes 3...6·105 depending on the agitation of the sample (Table 1). These values are one order below the reported association rate constants for streptavidin 5·106  and avidin 10·106 . Probably, this discrepancy is connected with the strong decrease of rotational diffusion (∝ ) of SAV due to its association with MNP, which is not taken into account in (12). Furthermore, there is an agglutination of the agarose beads which may cause a reduction of the binding kinetics.
The kinetics data β(tI) were well described by fitting a binding model (14) developed earlier for description the binding of charged MNP to oppositely charged latex spheres  (see appendix) (Fig. 4 and 5). However, there is a strong deviation from the expected exponential behavior (equation 10), represented by the dotted lines, especially for the non-agitated samples with the MNP*SAV probes (Fig. 4). Further, the obtained parameters seems to be far from the reality. For instance, the parameter αF, describing the fraction of binding active surface area of the agarose beads is only in the order of several percent.
We attribute this behavior to the agglutination of the agarose beads due to the binding of probes. This view is supported by the fact that agarose aggregates are visible with the eye after the binding reaction. This agglutination may also be responsible for the circumstance that the association rate "constant" depends on the concentration (Table 1).
Although the association constant of antibiotin-antibody to biotin Ka = 109  is much smaller than that of streptavidin (Ka ≈ 1015 ) and although the numbers of antibiotin-antibodies per probe seems to be less than that for streptavidin probes (see above), the kinetics of MNP*AB-biotin-agarose coupling is in the same range like that of MNP*SAV-biotin-agarose coupling (Table 1). We attribute this behavior to a lower degree of agglutination of biotin-agarose beads by MNP*AB probes, confirmed by visual observation of the aggregates, which are stronger developed in the MNP*SAV samples than in the MNP*AB samples. This we explain as follows: Only about 20% of the MNP*AB probes bind specifically (see above). Therefore, we guess that the fraction of MNP to which more than 1 antibody is attached in the right direction, is much smaller than in the case of MNP*SAV. Because solely these MNP having more than one detection molecule can provoke cross-linking among the agarose beads, there is a lower probability of agglutination of agarose beads by MNP*AB probes than by MNP*SAV probes. If agglutination takes place, many binding places becomes hidden quickly after start of the incubation. Thus, a slowing down of the binding kinetics accompanied by a non-exponential behavior can be understood.
Influence of the suspension medium
In this section we compare the binding of MNP-probes suspended in different media, namely BSA-Buffer (BSA-B), being PBS (phosphat buffered saline) with 0.1% BSA (bovine serum albumin), and human serum. Because we know that serum components can lead to additional agglutination effects in MNP-samples, probably due to active antibodies , we used also tempered serum. The serum was tempered at 60°C for 40 minutes leading to cancelling of this reason for agglutination .
Here, it was demonstrated that the relaxation behavior of MNP can be measured in different media, what was already done in . The data show, that the same results were obtained if the differences in the viscosity were taken into account.
Fraction of bound MNP*SAV2 to biotin-agarose beads after an incubation time tI in different suspension media estimated by fitting the MRX-curves by (2). The control sample means that SAV-molecules of the MNP*SAV2 are saturated with free biotin before incubation with analyte suspension.
Fraction of bound MNP
0.018 ± 0.006
0.054 ± 0.007
0.61 ± 0.04
0.005 ± 0.008
0.117 ± 0.012
0.61 ± 0.04
0.011 ± 0.008
0.114 ± 0.009
0.87 ± 0.06
The results obtained from the control samples show, that about 5% and 11% of the probes bind non-specifically in BSA-B and human serum, respectively. Because MNP*SAV shows no non-specific binding (Figure 1), we attribute the occurrence of the nonspecific binding in BSA-B to the changed batch of MNP-probes MNP*SAV2. However, serum components are obviously responsible for the enhancement of this non-specific binding of the MNP*SAV2 probes by about 6%. Note, that the MRX-curves of the control samples for serum and tempered serum are nearly identical. This means, that the non-specific binding is not related to the functioning of the serum proteins.
We presented a method for quantification of biomolecules in the form of a bead based magnetic relaxation immunoassay. In a conventional solid phase immunoassay the analyte is fixed on the surface of the reaction well. The area of this active surface of one well (96 well plate) is 1.5·10-4 m2. In our realised bead based assay the target surface area is about 1.5·10-3 m2 per well. The agarose beads and thus the target surface is more homogeneously distributed in the sample volume than in a solid phase system, where the analyte has to reach a surface coated with the detection molecules. Thus, in principle, in MARIA measurements in arbitrarily shaped volumes are possible.
Applying this method, we could quantify the binding of magnetically labelled streptavidin having a concentration of about 2 nmol/l with an accuracy of about 5% using a highly sensitive SQUID-measurement system. Given sensitivity was achieved by fitting a relaxation model to the relaxation data, whereby we could use the data of samples with fully immobilised MNP as a reference. By means of a control experiment we have shown that the probes were immobilised by specific streptavidin-biotin coupling or predominantly specific antibiotin-antibody-biotin coupling.
In the present assay design the analyte had to fixed to a relatively large bead enabling the detection by MRX. In order to quantify free analytes, the design has to be realised as a competition assay. I.e. the free analyte molecules compete with the bead based ones for the MNP-labelled detection molecules.
In the presented bead based binding assay the binding kinetics depends on the sample treatment during the incubation. In order to achieve reproducible kinetics, it is necessary to provide a controlled smooth sample stirring which prevents sedimentation of the larger beads.
Further, the size of the probes, i.e. MNP-detection molecule complexes, crucially determines the diffusion and hence the association rate constant. Presumably, the binding reaction is accompanied by agglutination processes affecting the binding kinetics. In order to estimate proper kinetics parameters binding experiments with an excess of probes have to be realised, suppressing the agglutination of agarose beads.
Obviously, the use of the large MNP as markers for biomolecules makes the estimation of the kinetics of the binding reaction difficult. However, the MRX method is suitable for a quantitative check of the functionalisation of MNP prepared for specific binding to an analyte. This is an important issue, because the research on systems of nanoparticles for diagnostic and therapeutical purposes is strongly increasing. For instance in tumor therapy and diagnostics (MRI) with MNP the focus tends from simple core shell MNP to functionalised (e.g. with an antibody) MNP which should find their target by specific binding . Therefore, the complex binding behavior which can be accompanied by nonspecific binding has to be measured in order to develop such particles or in order to check its quality by the users.
The bead based magnetic relaxation binding assay presented here (Fig. 1) has two peculiarities: (i) MNP that label the detection molecules have an overall diameter ranging from 15 nm to 60 nm or even more, i.e. in most cases the size of the marker is of the order or even larger than the size of the detection molecules. (ii) The analyte molecules are bound to beads being large in comparison to the markers. These two peculiarities make the signals of bound and unbound markers separable with high sensitivity. Furthermore, free analytes can be quantified by competition assay, i.e. the free analytes compete with the bead-associated ones for the binding sites of the probes.
Quantification of the binding by MRX
The measurement is performed using a procedure and a device described in detail by Matz et al . In short, a magnetising field of H = 2000 A/m is applied for t = 1 s. 450 μ s after switching off the field, a highly sensitive low-TC)-SQUID (Superconducting QUantum Interference Device) sensor measures the magnetic induction B(t) at a distance of 10 mm above the sample. The measurement time window is 450 μ s ≤ t ≤ 0.45 s. The output signals of SQUID sensors contain an unknown offset value Boffset. For visual comparison purposes, the offset of each measured relaxation curve B(t) was adjusted so that all relaxation curves coincide at the end of the measurement.
Note, that the relaxation signals can be measured also by high-TC-SQUIDs  or by fluxgate magnetometers . In the latter case the sensitivity is about 2 orders of magnitude lower, but there is no need for cost intensive cooling procedures. The relaxation behavior of MNP can also be measured with magneto-optical methods as described for example in .
The hydrodynamic diameter of the whole particle (including the shell) is denoted by dhyd and η is the dynamic viscosity of the fluid suspension being 10-3 Pa s for water. kB and T are the Boltzmann constant and the temperature, respectively. Note that the effective relaxation time τeff of unbound MNP is always shorter than that of immobilised MNP and obeys the equation .
to the measured relaxation curves. The difference between relaxation times of bound and unbound MNP crucially determines the accuracy by which the corresponding signals can be separated.
If the molecules to be quantified are comparatively small in comparison to the probes, i.e. the MNP-labelled detection molecules, then the binding of the analytes to the probes does not lead to a significant slowing down of the Brownian motion. But this slowing down is necessary for a sensitive quantification of the analyte. Therefore, in our preparation the analyte was coupled to agarose beads being much larger (d ≈ 5 μ m) than the probes. After the probes became bound to these analyte-beads via the detection molecules, the Brownian relaxation time of the probe-bead conjugates attains values of τB ≈ 400 s according to (1). This is orders of magnitude more than τB ≈ 2 ms which is measured for free probes (see below). Because this time is far beyond the upper limit of our observation time tm,max = 0.45 s, the MNP appear immobilized in our measurement. Thus, for the estimation of the amount of bound MNP by means of (2) we can use the relaxation curve of freeze dried MNP as the reference data for Bb(t).
Generally, one is interested in the binding kinetics between analyte and detection molecules. However, in marker based assays, the kinetics of the detection molecules including the marker is measured. (Note, that there are other assays working without markers e.g. SPR.) Caused by the markedly reduced diffusion of labelled streptavidin due to the large size of the MNP-marker in the present case, we expect a slower reaction than for assays which use smaller markers, e.g. dyes. This reduction has to be accounted for in order to compare our results with those of other methods.
The association rate and the dissociation rate constants ka,P and kd,P, respectively, describe the kinetics of the binding of the probes (MNP-detection molecule complex). The symbols ka and kd stands for the rate constants of the naked molecules alone.
Concentrations and size parameters of the probes and biotin-agarose beads.
Volume concentration of magnetite c V
Mean bead diameter nm
Stock susp. c pmol/1
Meas. samples c pmol/1
where tb is the binding time at which the (1-1/e) part of the number of bindings at saturation is realised.
where κ = rhyd,P/thyd. In this approximation the reduction of the rotational diffusion coefficient Drot ∝ was not taken into account. This latter effect should be strong only if the surface of MNP is sparsely covered by binding molecules.
We investigated the binding between biotin as the analyte and the detection biomolecules streptavidin and anti-biotin antibody using a bead based MARIA. As described above, the measurement signal is generated by immobilization of the MNP being the labels of streptavidin (SAV) and anti-biotin antibody (AB) by their binding to the biotin which is linked to agarose beads.
Biotin-agarose was purchased from Sigma-Aldrich (Germany), order No: B 0519 and has a binding capacity of 20–30 mg/ml avidin, i.e. 0.3–0.5 mmol/l. The diameter of the beads is about 5 μ m. Streptavidin and anti-biotin antibody, both labelled by MNP, were purchased from Miltenyi Biotec (Bergisch-Gladbach, Germany). We will refer to them further as MNP*SAV (Streptavidin-linked MicroBeads, order No: 130-048-102) and MNP*AB (Antibiotin-antibody-linked MicroBeads, order No: 130-090-485), respectively (Table 3). For the binding experiments in different media we used an other sample of MNP-labelled streptavidin, referred to as MNP*SAV2 (Streptavidin-linked MicroBeads, order No: 130-074-101).
The suspension media for the binding reactions are phosphate buffered saline (PBS) and human serum (Sigma-Aldrich, order No: B 0519) for the measurements of the influence of suspension medium.
The binding experiments were performed as follows: The biotin-agarose beads were washed 3 times with PBS to eliminate residues of free biotin which would saturate the MNP*SAV and MNP*AB probes. We diluted the stock suspension of biotin-agarose by a factor of 3 with PBS. The MNP*SAV were diluted with PBS by factors of 3 and 10; MNP*AB were diluted by factors of 10 and 100. For the MARIA-measurement we filled 100 μ l biotin-agarose in a polystyrene-well (BreakApart-wells, Nunc GmbH & Co.KG, Germany). Then, we added 50 μ l of the MNP*SAV or MNP*AB suspension. The final concentrations of MNP*SAV, MNP*AB and agarose beads in the 150 μ l measurement volume are listed in Table 3. After gently mixing we measured the magnetic relaxation.
Because the agarose have slightly higher density (ρ = 1.27 g/cm3) than water, the beads tend to sediment. However, because one measurement is done after about 5 s, this sedimentation does not effect the measurement significantly.
For the control experiment we incubated MNP*SAV and MNP*AB suspensions with free biotin with a concentration of c ≈ 30 μ mol/l for about 3 hours at room temperature (22°C). The high biotin excess should saturate the biotin binding sites of streptavidin and antibiotin-antibody. With this saturated suspensions we repeated the binding experiments as before. In order to measure the binding kinetics, we estimated the fraction of bound MNP*SAV and MNP*AB at different times tI after the incubation was launched by fitting (2) to the relaxation curves.
Because the size of the beads reaches the μ m-range and they have a slightly higher density than water, the beads tend to sediment due to gravity forces. Therefore, we investigated, how the treatment of the samples during the binding reaction determines the kinetics. In the first set of experiments, the samples were in rest between each single relaxation measurement. Only before each measurement, the samples were shaken once to obtain a homogeneous distribution of the agarose beads, because the measurement signal depends on the sample detector spacing. In the second set of experiments, the samples were rotated slowly between the measurements, providing a continuous stirring of the agarose.
In order to examine the influence of the suspension medium on the binding reaction, we repeated the binding experiments as described above substituting PBS by human serum.
Because of the sedimentation tendency of the agarose beads, the homogeneity of the sample gets lost after a couple of seconds. But due to the short measurement time of only 5 seconds, this has no impact to the given results. In the case of longer measurement cycles, e.g. short time kinetics measurement, there is a need of sample stirring preventing the sedimentation of the beads.
We describe the kinetics for the binding of magnetic probes to beads, β(tI), by a model, developed earlier for analysing the kinetics of the binding of electrically charged MNP to oppositely charged latex beads . The model bases on the diffusion driven collision theory of Smoluchowski . In this model only bindings between elements of different components, namely the probes denoted by P, and binding sites of the beads, denoted by B, are taken into account.
where αi is the collision parameter and DP is the diffusion constant of the probes. The total concentration of binding sites cB (0) which are accessible by ligands is related to that of the agarose beads by cB (0) = where dA and cA are the diameter and the concentration of the agarose beads, respectively. The dimensionless parameter αF represents the fraction of the surface area of the beads which can be covered by specific binding probes at most.
and the cross section area of the probes, , and the cross section of collision between probes and agarose beads, q = π (dP + dA)2, where dP is the overall diameter of the probes. DA is the diffusion constant of the agarose beads. The binding parameter αB describes the probability that a collision between probes and agarose results in a binding.
β(t)/βmax corresponds to cPB (t)/cP,0 in equation 10. βmax is the maximal fraction of probes which can bound to agarose beads. It is determined by the fraction of MNP which are grafted by detection molecules in the proper orientation making a binding possibly. If the dissociation rate constant kd is not negligibly, βmax is also determined by the position of the equilibrium of the reaction.
The research was supported by BMBF project Nanomagnetomedizin FKZ-13N9150.
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