For the immunometric assay described herein DDM128N nanoparticles (Meito Sangyo, Japan) were selected. They are composed of a maghemite core and a carboxydextran shell. In addition to mean size and size distribution measurements by measurements of the magneto-optical relaxation of ferrofluids (MORFF) and dynamic light scattering measurements (photon correlation spectroscopy, PCS), particles were characterized by PCS measurements with respect to their stability, as determined by the zeta potential in diverse media [water, phosphate buffer 10 mM pH 7.4, phosphate buffered saline (PBS) and human plasma].

Since MNPs possess a wide size distribution they were separated in different size fractions by magnetic fractionation. This was done by means of an adjustable electromagnet (Bruker, Germany) and MACS LS columns (Miltenyi Biotec, Germany). For the next preparation steps only MNPs of the largest fraction with a mean hydrodynamic diameter of about 55 nm were utilized.

Functionalization of the particles was achieved by reductive amination. As functionalization agent streptavidin (IBA GmbH, Germany) was applied as it forms extremely stable complexes with biotin. Subsequently one of the interaction partners can be biotinylated and than easily connected with the streptavidinated MNPs [13,14]. Furthermore, direct coupling of protein interaction partners on MNPs by the periodate method was successful as well. Here, biotinylated polyclonal anti-IGF-1 antibody (US Biologicals, USA) was conjugated with the manufactured streptavidin-MNPs. For this purpose, 50 μg of the antibody were diluted in 6 mL PBS under sterile working conditions followed by the dropwise addition of 500 μL of the streptavidin-MNPs. After incubation for 2 h at 4 °C, 100 μg biotin were added in order to saturate the remaining streptavidin binding sites. After another hour, MNPs were washed via a MACS LS column in a static magnetic field.

The binding affinity between antigen (A) and antibody (B) is usually described with association and dissociation rate constants k_a and k_d, or with the equilibrium constant K_D. These quantities are defined by: (5) K D = k d k a = c A c B c A B ,where c_A and c_B denotes the concentration of unbound interaction partners and c_AB the bound ones. These concentrations cannot be measured directly in our experimental setup; instead the binding reaction can be characterized by the rate and end value of particle growth caused by the aggregation of MNPs. In order to calculate the kinetic parameters a model of chain-like aggregation of the particles was developed. Antibody loaded MNPs are linked via the antigen molecules to chains of the form …-[A-A]-[B-B]-[A-A]-[B-B]-…. Two antibodies B on the same MNP are symbolized by [B-B], whereas [A-A] denotes the antigen molecule with two binding sites (epitopes) A. From the known antigen amount added to antibody sensors and the increase in particle size during the interaction the unknown parameters can be estimated using theoretical concepts of stepwise polymerization. A more detailed description of our model is given in [14].

Relating the normalized mean particle diameter in steady state (90 – 120 min incubation time) D S S = d ¯ S S / d 1 S S (d^SS₁ – diameter of a single MNP) to the weight-average of chain length distribution the equation: (6) c A , 0 ⋅ 2 D S S ( D S S ) 2 − 1 = c B , 0 + K D c B , 0 + 1 c B , 0 ⋅ c A , 0with c_A,0 being the epitope concentration and c_B,0 the antibody binding sites on MNP at the reaction start can be obtained.

For the scaled plot suggested here, the mean diameters d̄^SS, determined by the exponential fit (Equation 1) of the relaxation signals of various antigen concentrations under steady state conditions, have to be normalized by the initial value d^SS₁ to obtain D^SS. Plotting the quantity: (7) y = c A , 0 ⋅ 2 D S S ( D S S ) 2 − 1against the respective antigen concentrations c_A,0 a linear regression in form of y = ax + b can be performed.

The equilibrium constant K_D and the antibody concentration c_B,0 result from the regression parameters as: (8) c B , 0 = 1 b 2 , K D = a b − 1 b 2 .

The mean hydrodynamic diameter of the original ferrofluid is about 45 nm. For the application in immunological analyses DDM128N was fractionated into five fractions by magnetic fractionation. Since only the largest particles give a sufficient relaxation signal, the particles of this fraction were used. In Figure 3 size distributions of the original and the largest fraction of DDM128N are depicted. The mean hydrodynamic diameter of the last is about 55 nm.

The zeta potential as a stability marker generated by PCS in different media averaged out at -35 mV in water, -29 mV in phosphate buffer pH 7.4 10 mM, -27 mV in 0.9% NaCl solution, -0.4 mV in PBS and -2.3 mV in 10% human plasma. Stability of the particle suspension decreases with increasing ion and protein concentrations due to the electrostatic interference of repulsive forces between MNPs.

In Figure 4 the increase in the hydrodynamic diameter as a consequence of the addition of antigen to antibody sensors is depicted. The hydrodynamic diameters of aggregates developing during the interaction were determined by the monoexponential fit (Equation 1). Over a period of 120 min concentrations of 6.6 nM and higher IGF-1 generated an aggregate size growth up to 1.5-fold of the original particle size. As the diameter increases fast during the first 30 min, a slower part follows. Control experiments include the incubation of antibody sensors with BSA in order to exclude unspecific binding. In this case, MNP diameters remained constant. Steady state conditions are achieved within 90 – 120 min.

Among the qualitative determination of the IGF-1/anti-IGF-1 binding reaction in form of the binding assays the kinetic aspects received priority. The knowledge of interaction rates and affinities facilitate the identification and characterization of antibodies and other proteins, e.g. in high throughput screening methods in search of new drugs, where affinity methods are applied [20].

The equilibrium constant K_D was determined by creating a scaled plot. In contrast to the usual immunoassay techniques, where the fractions of bound and free reaction partners can be presented in a linearized plot (e.g. Scatchard plot), these quantities are not directly ascertainable with this method.

The known parameters total antigen concentration and particle size increase due to the formation of aggregates are included in the data evaluation. The model acts on the assumption of the formation of a chain like topology of particle aggregates. Up to trimers the involved MNPs have no alternative for aggregate formation. With the formation of tetramers the possibility of branching is given. That means that the developed model is only valid for small reaction conversions.

In Figure 5 the scaled plot for the interaction between IGF-1 and its antibody is depicted as the conversion parameter y versus the concentration of IGF-1 epitopes. The conversion parameter is composed of the underlying steady state diameters averaged from diameters at t = 90 - 120 min and the epitope concentration. The equilibrium constant K_D was calculated as described in Section 2.3. and totals 70 nM. The antibody loading on MNPs c_B,0 was estimated as 78 nM.

The formation of MNP chains is already described in literature. Chantrell et al. [21] demonstrated chain formation under influence of an external magnetic field. However, also without magnetic fields chain like aggregates due to magneto-statical interactions are described by Klokkenburg et al. [22]. Although protein binding plays the important role in aggregate formation in this contribution magnetic dipole-dipole interaction cannot be excluded.

A further prerequisite for the model validity is that only two antibody binding sites on each MNP are involved in the binding process as well as two epitopes per antigen. Former investigations concerning the determination of effective binding sites on functionalized MNPs result in the calculation of 1 – 10 binding sites assuming a particle core diameter of 10 nm [14]. Thus, the assumption of two binding sites is in the right size range.

Modelling of the aggregate formation plays also an important role. We assume an additive increase in diameters, i.e. dimers possess the twofold diameter of monomers, etc. Today we are not able to substantiate the actual aggregate topology. For a further clarification of the aggregate relaxation behaviour additional investigations are required enabling a more concise description of the aggregate behaviour, e.g. size exclusion chromatography ore magnetic fractionation.

The equilibrium constant describing the affinity between antigen and antibody was also determined by other workgroups with different immunometric methods. Manes et al. [23] calculated a K_D of 0.1 – 100 nM for IGF-1 and monoclonal antibodies on the basis of BIAcore™ SPR interaction analyses. Another group determined equilibrium constants of 0.01 – 0.15 nM for the interaction between monoclonal anti-IGF-1 antibodies and an IGF-1-analogue (LR3-IGF-1) by ELISA [24]. SPR analysis and also ELISA are methods based on interactions on solid surfaces. First of all MORFF is representing a solution based method, though immobilization of antibodies on MNPs constrains the free movement of proteins. At least a comparison with results from SPR analysis is possible. Day and colleagues [25] obtained comparable kinetic data from SPR, isothermal titration calorimetry and stopped flow fluorescence, whereas the last two methods are solution based. Furthermore, the dextran surface of the SPR sensor chip is not a rigid and solid system, but rather a swollen gel matrix, which enables some degree of diffusional rotation of proteins. Binding constants determined by SPR are very sensitive of potential artefacts produced by mass transport, non-specific binding and avidity effects [26], which require a very accurate and time-consuming sample preparation. The topology of interactions should be present previous to the experiments in order to evaluate the data correctly with evaluation procedures provided by the BIAcore™ software.

Due to the utilization of a polyclonal antibody it is supposable that the K_D determined by MORFF differs from that in literature. A polyclonal antibody is a blend of diverse antibody subtypes with different affinities. We used a polyclonal antibody in our method for demonstration purposes. For detection of kinetics with immunoassays, i.e. using antibodies, concrete data for K_D are rarely; in fact affinity ranges are given (e.g. in [23]). This is due to the numerous method evaluation factors, which cannot be directly influenced. Therefore, the estimation of the order of magnitude of K_D is satisfying.

For a prospective utilization in an every day lab routine the method described herein was validated according the ICH tripartite guidelines [27] for MNPs as well as for the analyzed protein system. Concerning the particle concentration the MORFF technology offers a limit of detection (LOD) of 100 fmol·mL^-1 particles [14]. Meanwhile other methods offer higher sensitivity regarding particle detection; however, our method is more robust and does not require magnetic shielding [28, 29]. Furthermore the LOD of the analyzed antigen IGF-1 was determined. Ideally, it should be below the physiological and pathological concentrations. In table 1 concentrations of human IGF-1 and the LOD are demonstrated.

The results demonstrate that at present we are able to determine adequate physiological and pathological IGF-1 concentrations with the method described herein. IGF-1 is detected by other workgroups mainly by radioimmunoassays, fluorescence immunoassays, chemiluminescence immunoassays or ELISAs. The LOD of these immunoassays is between 0.1 and 100 ng/mL [34,35]. A major problem of these immunoassays is the interference of IGF-1 with IGF-1 binding proteins (IGFBP), which also appear in plasma samples. Beside elimination of IGF-1/IGFBP-complexes with acidification processes or acid-ethanol extraction, the addition of IGF-2 is now the method of choice to circumvent this problem. IGF-2 binds to IGFBP to the same degree as IGF-1 and blocks binding sites on IGFBP for IGF-1, which then can be analyzed undisturbed with high specific antibodies [12]. Of course this is of major relevance for the sample preparation of the magneto-optical immunoassay described herein. In future experiments, an adequate IGF-2 amount as a sample adjuvant has to be evaluated in order to specify the exact IGF-1 concentration.

In principle the LOD of both, MNPs and protein systems can be decreased by optimization of the cuvette geometry concerning the sample volume. A volume of 10 μL would be enough to ensure the propagation of the laser beam. Furthermore, the application of more appropriate MNPs offering high shape anisotropy, a narrow size distribution and sufficiently large magnetic cores would result in higher signals.