WO2010041178A1

WO2010041178A1 - Biosensor system and method for determining the properties of a magnetic particle

Info

Publication number: WO2010041178A1
Application number: PCT/IB2009/054312
Authority: WO
Inventors: Xander J.A. Janssen; Ben De Clercq; Menno W.J. Prins; Leonardus J. Van Ijzendoorn; J. M Van Noorloos
Original assignee: Koninklijke Philips Electronics N.V.
Priority date: 2008-10-06
Filing date: 2009-10-02
Publication date: 2010-04-15

Abstract

Biosensor system and method for determining properties of a particle bounded to a surface reacting to a magnetic field. The method for determining properties of a particle bound to a surface reacting to a magnetic field, comprising the steps of: (a) determining an angular reference referring to a particular orientation of the bonded particle, (b) sequentially applying at least two different magnetic fields to the bonded particle or applying one rotating field to the bonded particle; (c) measuring an angular velocity, and an angular value relating to the orientation of the bonded particle; and (d) determining a magnetic characteristic or a binding characteristic of the bonded particle from said angular velocity, angular value and angular reference.

Description

Biosensor system and method for determining the properties of a magnetic particle

FIELD OF THE INVENTION

The invention relates to a method for determining properties of a particle bound to a surface.

BACKGROUND OF THE INVENTION Analyses of micro fluids are usually carried out by means of a lab-on-a-chip system for medical, life-science, forensic and environmental applications.

Various analytical procedures to detect an analyte (so-called a target) in a test sample are known. Targets may for example be proteins, nucleic acids, cells, cell fractions, drugs, hormones, etc. For example, immunoassays use the mechanisms of the immune system, wherein a capture element (e.g. antibody or antigen) is capable of specifically binding to the analyte. The capture elements may be for example attached to a sensing surface and the analytes present in a fluidic sample. Capture elements may be capture moieties which can for example be nucleic acids, proteins or peptides, macro molecules, small molecules, etc. The specific reaction mechanism between the capture elements and the analytes is used to determine the presence or concentration of the antigen in a test sample.

Furthermore it is well known to bind the analyte of interest with a detectable label in order to quantify the interactions between capture elements - analytes at or in the vicinity of the sensing surface. Common labels are, for example, fluorescent and chemiluminescent molecules, colored particles (dyes) radioisotopes, or magnetic labels.

Magnetic labels are particularly used in biological assays to detect the presence or quantity of an analyte. The use of magnetic labels as, for example, magnetic particles or magnetic beads, has several advantages. The magnetic particles can be manipulated by applying a magnetic field such that the analytical procedure can be both accelerated and improved. A further advantage of using magnetic labels is that there is no magnetic background signal in a biological test sample that would otherwise disturb the detection of the magnetic particles.

A first generation of magnetic biosensors is based on the detection of bound magnetic particle labels on a sensor surface (via analytes/capture elements), which are indicative of the mere presence and/or concentration of analytes in solution. Before detection, the labeled analytes are magnetically manipulated by first applying a magnetic force towards the sensor surface (on which capture elements are bounded) in order to attract the analytes to the sensor surface and therefore facilitate the bindings with the capture elements, and applying consecutively a magnetic force away from the sensor surface so as to expel the analytes unbounded to the sensor surface and perform accordingly a washing step. The detection may then be performed by using different techniques, such as for example optical or magnetic ones.

In WO2005/111596, it is proposed an improved biosensor provided with means for generating a magnetic torque to bonded magnetic particles and measuring a parameter (e.g. angular position) determining their rotational freedom. By doing so, it is possible to remove from the measurement some artifacts.

However, the reliability of said parameter measurement has still to be improved, so as to have a more accurate and thorough interpretation of the measured data, in particular the influence of the environment has to be taken into account.

SUMMARY OF THE INVENTION

So as to improve the situation, an idea of the invention is to measure the influence of the binding of a particle with respect to its response to a magnetic field as well as the inherent specific magnetic properties of the particle itself to enable an improved sensibility, speed, specificity, and/or functionality of a biosensor.

More specifically an idea is to determine the magnetic torque and/or magnetic moment and/or binding characteristics (e.g. mechanical torque) of a magnetic particle attached/bound to a surface when a magnetic field is applied, so as to calibrate the measurement. A particular goal may be to determine the torsional spring constant. A particular problem solved by the invention is to make these determinations for an assay in which many magnetic particles are biologically bound to a sensor surface., and therefore find a way of measuring many particles at the same time.

Furthermore, it has to been noticed that the bound particles have generally different equilibrium orientations of their permanent magnetic moments and/or magnetic anisotropy axes, and the mechanical and magnetic torques depend accordingly on these orientations. If these differences are not taken into account, the next measurements/calculations may be therefore significantly erroneous. The invention proposes also a method of calibrating the particles in order to solve this problem.

Another particular problem solved by the invention is that there are two unknowns in the calculations: (i) the magnetic torque properties of the particles, and (ii) the torsional spring constants of the biological tethers.

The aforementioned objects are achieved and the aforementioned problems are solved with the method and the biosensor system of the present invention.

According to the present invention, a method for determining properties of a (e.g. biological) particle bound (e.g. biochemically or physically) to a surface is provided reacting to a magnetic field. The method comprises a determination of a angular reference of the bonded particle (method step (a)). Further, a sequential application of at least two different magnetic fields to the bonded particle or of a rotating field is carried out (method step (b)), and the angular velocity and an angular value relating to the orientation of the bonded particle are measured (method step (c)). Finally a magnetic characteristic or a surface binding characteristic of the bonded particle is determined from said angular velocity, angular value and angular reference (method step(d)).

The angular value of the particle may, for example, be the zero-torque orientation of the bonded particle. The zero-torque orientation is the rotational orientation of the particle in the absence of an applied magnetic field. At this orientation, the total torsion energy in the biochemical moiety bound to the sensor surface has a minimum value. In the case of a torque generated by a permanent magnetic moment in the particle, the "orientation of the particle" is generally meant to be the orientation of the permanent magnetic moment of the particle. In an alternative embodiment, the angular reference is a non-zero torque orientation. This embodiment may allow determining the magnitude of the magnetic moment of the particle, provided that mechanical parameters (e.g. elastic constraints) are previously known.

In an alternative embodiment, the angular reference of step (a) is the phase lag between the orientation of the particle and the orientation of an applied magnetic field when the torque is maximum, and the angular value of step (c) is a phase lag between the orientation of the particle and the orientation of the applied magnetic field. The said phase lag of step (a) may be determined by applying a rotating field and identifying the first maximum torque. This angular reference can therefore be determined rapidly.

Different magnetic fields are magnetic fields differing from each other with respect to their absolute value and/or their orientation and/or their helicity. A magnetic field may be a static magnetic field, a rotating magnetic field, or a combination thereof. In case of at least two magnetic fields to be applied, the two magnetic fields may be rotating magnetic fields, wherein the second magnetic field is the reversed first rotating magnetic field.

Reversing rotating magnetic fields may be rotating magnetic fields, wherein the rotational orientation of the first field is "flipped" in order to apply the second field.

In an embodiment, two different magnetic fields can be static fields with two different orientations (e.g. to derive the static magnetic moment of the particle, or the moment induced by anisotropy) or dynamic fields with different helicities (e.g. to derive the high-frequency induced moment), or a combination thereof. The angular velocity and the angular value of step (c) may be measured in the

"vicinity" of the angular reference of the bonded particle (e.g. a zero-torque orientation of the particle) means to measure at an angular orientation (see, for example, θi and/or Θ3 in Fig. 4) of the particle moment which is lower, in absolute value, than 90°, and particularly lower than 45°, with respect to the angular reference of the particle. In a particular embodiment, the measuring may be carried out if the bonded particle passes through or is located at the zero-torque orientation. In another particular embodiment, the measuring may be carried out if the particle is close to the zero-torque orientation, e.g. at an angle +δi (i.e. at a first side of the angular reference) and an angle -δ₂ (i.e. at a second side of the angular reference) with respect to the zero-torque orientation of the particle, wherein the range of +δi to -δ₂ is covered by the maximum angular range as indicated above, and wherein the absolute values of δi and δ₂ are preferably equal.

An advantage of sequentially applying magnetic torques with an opposite sign via the application of magnetic fields is that the particle passes with a non-zero angular velocity through the zero-torque orientation of the particle. At that zero-torque angle, the velocity is minimally dependent on the potential torsion energy of the (biochemical) binding, i.e. the velocity is minimally dependent on the elastic stiffness of the moiety/molecule. In a particular embodiment, the first of the two magnetic fields in step (b) is applied so as to attract the orientation of the bonded particle into a first angular direction, and the second of the two magnetic fields in step (b) is applied so as to attract the orientation of the bonded particle into a second angular direction opposite the first angular direction.

In doing so, and if the particle exhibits a permanent moment, the orientation of the permanent magnetic moment in the particle may be determined by observing the particle rotation and/or orientation, for example, as a function of the orientation of the applied field. In particular, the field orientation which does not change the particle orientation (in particular, i.e. the field orientation at which the torque is zero) coincides with the orientation of the (static) permanent magnetic moment.

In a particular embodiment, step (c) is performed after applying the first magnetic field according to step (b), and/or (an additional) step (c) is performed after applying the second magnetic field according to step (b). In a further particular embodiment, step (c) is performed at a first angular orientation of the bonded particle when the second magnetic field is applied. In this case, the first and second angular orientations of the bonded particle may have opposite signs with respect to the angular reference, and/or may have the same absolute value.

For example, by measuring the angular velocity of the particle sequentially attracted by the magnetic fields at two, e.g. equal, angles on both sides of the angular reference of the particle, the permanent magnetic moment of the particle can be determined as further explained in the "detailed description of embodiments" below.

In a particular embodiment, the method further comprises pre-determination of an angular orientation of the magnetic fields to be applied, with respect to the angular reference of the particle.

For example, the orientation of the particle may qualitatively be determined by finding the magnetic field orientation which does not modify the particle orientation (the zero-torque orientation). Based on this qualitative determination of the orientation of the permanent magnetic moment of the particle, the at least two magnetic fields may be applied at particular angles with respect to the angular reference. Such a predetermination of the angles is advantageous, since the whole measuring process may become more accurate and faster, if the orientation of the fields to be applied is well- chosen with respect to the angular reference.

In a particular embodiment, the pre-determined angle between the orientation of the first magnetic field and the angular reference (in particular, the zero-torque orientation of the particle) is positive, and the angle between the orientation of the second magnetic field and the zero-torque orientation of the particle is negative. Further, the absolute value of the pre-determined angle between the orientation of the first magnetic field and the zero-torque orientation of the particle and the absolute value of the predetermined angle between the orientation of the second magnetic field and the zero- torque orientation of the particle may be equal. Furthermore, the pre-determined angle between the orientation of the first magnetic field and the zero-torque orientation of the particle may be +θ, and the angle between the orientation of the second magnetic field and the zero-torque orientation of the particle may be -θ. In a particular embodiment, the pre-determined angle between the orientations of the at least two magnetic fields may be zero. In a particular embodiment, the two magnetic fields in step (b) are a first and second rotating magnetic field rotating according to opposite angular directions. In a further particular embodiment, the second rotating magnetic field is applied by reversing the first rotating magnetic field.

For example, in order to produce a rotating magnetic field, a device according to Fig. 3 may be used. It schematically shows four coils with which a homogeneous and rotating magnetic field at the centre of the four pole tips can be produced. Each coil is connected by an electronic circuit to a function generator generating a sine function. The field is rotated by setting a phase shift to each coil with respect to the others. Therefore, oppositely placed coils will have a phase shift of 180° (absolute value), whereas adjacent coils will have a phase shift of 90° (absolute value): In clockwise direction, the four coils have a phase shift of 0°, 270°, 180°, 90°, respectively. Such a configuration will result in a counter clockwise rotation seen from above in Fig. 3.

In a further particular embodiment, each of the first and second rotating magnetic fields has a rotating frequency lower than, greater than or equal to the breakdown frequency of the particle.

For example, if a rotating magnetic field is applied to a magnetic particle, the particle rotates with a frequency equal to the field frequency, up to a certain maximum rotation frequency for the particle, called the breakdown frequency. For field frequencies higher than the breakdown frequency, the average rotation frequency of the particle decreases for increasing field frequency. Hence, the breakdown frequency is the maximum rotation frequency that a particle can reach. It is reached when the magnetic torque is maximal.

In a particular embodiment, the two magnetic fields are static magnetic fields, and wherein the first of the two magnetic fields is oriented on a first side of the angular reference, and the second of the two magnetic fields is oriented on a second side of the angular reference. In a particular embodiment, the absolute value of the angle between the orientation of the first magnetic field and the angular reference and the absolute value of the angle between the orientation of the second magnetic field and the angular reference are similar, and the magnetic moment of the particle is calculated thereafter in step (d) based on the angular velocities of the particle measured at these two angles in step (c). For example, by applying the magnetic fields on two sides of the angular reference, the measurements may be carried out when the particle passes through the zero-torque orientation so that the permanent magnetic moment of the particle can be determined (see also discussion of the first embodiment below in section "detailed description of embodiments"). In a particular embodiment, the magnetic moment of the particle is calculated in step (d) by applying in step (b) two rotating magnetic fields having different magnitudes and by performing step (c) for the two fields at a same angular orientation of the particle.

Torsional torque of the bonded particle may calculated in step (d) after having calculated the magnetic moment of the particle. The torsional constant of the bonded particle may be calculated in step (d) after having calculated the magnetic moment of the particle.

In a particular embodiment, the method further comprises providing a fluid sample including a magnetizable or magnetic particle onto the sensor surface. In a particular embodiment, the particle binds to the sensor surface via a biochemical binding.

For example, the biological interactions may be investigated on a Biotin- Streptavidin system. This system involves a strong non-covalent biological bond. In particular, Bio tin may be immobilized on a sensor surface (made, for example, of glass and/or cyclo-olefm (co)polymers, polyethylene, polystyrene, polycarbonate, or polymethylmetacrylate) by means of Biotinylated Bovine Serum Albumin (Biotin- BSA), which is a protein that typically contains eight Biotin molecules on its surface. For example, a solution of 1 mg/ml BSA, from which 0,05% of the molecules are Biotin-BSA, in Phosphate Buffered Saline (PBS) may by incubated on a glass coverslide for 24 hours. After incubation, the coverslides are washed in PBS and dried in a nitrogen flow. A fluid chamber may be made, e.g. a closed cylindrical cell with the biologically activated surface at one end of the cylinder. A fluid with magnetic particles is entered into the chamber, e.g. a 10 μl drop of 10Ox diluted Dynabeads M280 solution in PBS with 0,05% Tween20 added. During incubation, the Streptavidin-coated beads get in contact with the Biotin-coated surface, driven by diffusion, gravitational forces and/or magnetic forces. After incubation, unbound particles may be removed from the surface, e.g. by gravitational forces, magnetic forces and/or fluidic shear forces.

The bond between the particle and the surface is preferably a biochemical bond, and the method of the invention further comprises a step of determining whether the biochemical bond is specific or non-specific. The method of the invention may further comprise the implementation of similar and simultaneous steps (a) through (d) for other particles bound to the surface.

In a particular embodiment, the method further comprises a determination of a permanent or induced magnetic moment of the particle on the basis of the measured angular velocity and/or angular orientation of the particle.

The above determination of the magnetic moment of a particle may be advantageous, since an accurate determination of an applied torque and a correct interpretation of data require the knowledge of the mechanical torque applied by the magnetic particle attached to a surface. Further, the torque properties can also depend on the orientation at which the particle is bound to the surface, particularly when the torque is generated by a static moment and/or a magnetic anisotropy. According to the present invention, a biosensor system for carrying out the above method of the invention is provided. The system comprises a sensor surface adapted to biochemically bind at least one particle thereon and field-generating means. The field-generating means may generate the sequence of the magnetic fields or a rotating field and are operated by controlling means. Further, the biosensor system comprises measuring means to detect the angular velocity of the particle and the angular value relating to the bonded particle orientation. Moreover the biosensor system comprises processing means for determining the angular reference, and a magnetic characteristic or a binding characteristic of the particle from said angular velocity and angular value and from the angular reference. For example, the processing means may be a processor for evaluating the signal received from the measuring means. In particular, the signal may be a data signal comprising the measured values and/or a signal merely indicating that a pre-determined threshold for the velocity and/or angular value relating to the orientation of the particle is achieved. In one embodiment, the processing means may assign a particular property of the particle (for example, the presence of a permanent magnetic moment or an induced magnetic moment, or the binding stiffness) to a particular signal received from the measuring means and may display such a result on a monitor and/or further transmit the result to a printer or a further processor. In an embodiment, the processing means may comprise or may be connected to a storage device for storing the data or the data signal or the signal received from the measuring means.

In a particular embodiment, the biosensor system further comprises a chip having a sensor surface, wherein the chip and/or the sensor surface comprises the field- generating means.

A chip of the biosensor system may comprise a container or reservoir for receiving a fluid test sample containing the magnetic particle. Usually, the chip may have at least one plane base area, particularly a rectangular or circular or elliptical base area . The base area functions as a sensor surface at which the particle may be analyzed by detection procedures. Preferably, the chip or at least the plane base area of the chip is made, for example, from cyclo-olefm (co)polmers, polyethylene, polystyrene, polycarbonate, or polymethylmetacrylate, which enables cost-effective manufacturing and also enables an optical analysis of the test sample. A chip may contain or may receive magnetic or magnetizable particles.

"Magnetic" or "magnetizable" particles are influenced by the application of a magnetic field and are magnetically responsive. For example, these particles are attracted or repulsed or rotated or have a detectable magnetic susceptibility or induction. These particles may be beads or labels, or a combination thereof. The particles can be adapted for facile detection of particle orientation, e.g. have a non-spherical shape or material property. The particles are adapted to bind to a target moiety. Such a binding can occur directly or via a specific binding member or capture moiety, as, for example, a protein captured by an antibody.

In particular, the magnetization of superparamagnetic particles has a preferential direction, called the easy axis, determined by the orientation of the crystal lattice and the shape of the grain. Such a dependency of magnetic properties with respect to the easy axis is called magnetic anisotropy.

In a particular embodiment, the magnetic fields have different pre-determined orientations and/or different pre-determined magnitudes and/or pre-determined helicities within the sequence generated by the field-generating means. In a particular embodiment, the controlling means is adapted to actuate the sequential generation of static magnetic fields having different orientations and/or magnitudes, and reversing rotating magnetic fields, and wherein the controlling means is adapted to actuate the generation of a sequential combination of a static magnetic field and/or a rotating magnetic field.

As already discussed above, reversing rotating magnetic fields are rotating magnetic fields, wherein the rotational orientation of the first field is "flipped" in order to apply the second field.

For example, the field-generating means may be controlled by the controlling means to generate magnetic fields which have specific properties dependent on the particles to be analyzed. In one embodiment, the magnitude of a magnetic field may be different for different particles to be probed, or it may be advantageous to apply magnetic fields having specific helicities for determining the magnetic properties of a particular particle. Hence, the controlling means may be adapted to adjust the field- generating means so as to apply, for example, pre-determined magnitudes of magnetic fields, dependent on the (e.g. inherent) properties of the particle. In a particular embodiment, the measuring means is adapted to measure at a predetermined angular orientation of the particle moment relative to the angular reference of the particle. For example, the angular orientation of a particle attracted by a magnetic field at which orientation the measurements of the, e.g., angular velocity is to be carried out, may be specified prior to the measuring and depending on the particle's properties. In one embodiment, the measurement means may be adjusted to measure at that specified (pre-determined) orientation.

In a particular embodiment, the field-generating means comprises a two- dimensional current wire arrangement and/or at least two electromagnetic units, wherein the magnetic field strength of each electromagnetic unit is separately changeable by electrical control. As, for example, shown in Fig. 2, a chip of a biosensor system may be provided with current wires. In a particular embodiment, the wires may each be 1 - 5 μm, more particularly 3 μm, wide and 0,1 - 0,5 μm, particularly 0,3 μm, thick. In one embodiment, a magnetic particle may be suspended in a fluid sample and provided onto the sensor surface of the chip, for example, a sensor surface of gold. As, for example, shown in Fig.3, there may be an arrangement of at least two, particularly four, electromagnetic units for generating a sequence of magnetic fields as discussed above. Each of the electromagnetic units may comprise a core and a current coil. In particular, the core may be made of (or comprises) a magnetically soft material, such as a composite of nickel, cobalt and iron or a low carbon soft iron as an outer shell, and/or a composite of cobalt, vanadium and iron as an inner core, for example, covered by an outer shell. As an example, a shell composite of 29% nickel, 17% cobalt and 54% iron may be used, as well as an inner core composite of 50% cobalt, 2% vanadium and 48% iron.

Further, the present invention provides a computer program product comprising one or more computer readable media having computer executable instructions for performing the steps of the above-described method and particular embodiments of the method.

For example, the computer program product may be transmitted over a local or wide area telecommunications network. In one embodiment, the invention also provides a machine readable data storage device storing the computer program product. BRIEF DESCRIPTION OF THE DRAWINGS

Fig. 1 schematically shows a particle bound to a surface via biochemical moiety and actuated by magnetic fields;

Fig. 2 schematically shows a cross section of a chip with current wires (Fig. 2a) and a top view of the crossed wires (Fig. 2b);

Fig.3 schematically shows a top view of field-generating means with four electromagnets;

Fig.4 schematically shows a sequence for measuring the permanent magnetic moment of a particle bound to a surface; and Fig. 5 schematically depicts how determining the equilibrium position of a magnetic bead elastically bonded to a surface.

Fig. 6 shows the theoretical angular value of a bead bonded to a surface over time, when a rotating magnetic field is applied.

Fig. 7A and 7B are diagramms of the angular orientation over time of a magnetic bead bonded to a surface via a G-IgG biochemical bond, exposed to a rotating magnetic field with a frequency of 20OmHz and a magnitude of 22 mT. Prior to the bonding, the beads of Fig. 7A were incubated with an IgG concentration of 50 nM and the beads of Fig. 7B were incubated with an IgG concentration of 1000 nM.

Fig. 8 is a diagram showing the measured elastic torque of the beads of Fig.7A and Fig. 7B.

Fig. 9 is a diagram showing the measured torsional constant of the beads of Fig.7A and Fig. 7B computed according to a method of the invention.

DETAILED DESCRIPTION OF EMBODIMENTS Generalities

Fig. 1 schematically shows a particle bound to a surface via a biochemical moiety. The particle may be actuated by a magnetic field and monitored (e.g. by optical detection). The actuation and monitoring allow to determine how the particle is bound to the surface (e.g. by single or by multiple binding, specific or non-specific binding) and/or to derive specific information of the biochemical moiety (e.g. the strength of binding and/or the rotational properties). The invention is focused on studying the response of a magnetic particle bonded to a surface via a biochemical bond when a magnetic field is applied to the system.

Particulary, by applying a magnetic field in the plane of the surface, it is possible to exert a torque on the magnetic bead and hence on the biochemical bonds. By studying the angular displacement of the bead in the plane of the surface, information can thus be obtained on the characteristics of the biological complex such as its stiffness. The feasibility of the application of a magnetic torque on superparamagnetic beads has been reported in several studies.

Superparamagnetic beads may consist of a non-magnetic shell (e.g. made of polystyrene) filled with magnetite grains. These beads are commercially available (e.g.

Dynabeads M-270 or M-280 from Dynal Biotech ASA which have a diameter of about

2.8 μm). The grains may be essentially ferrimagnetic and have a size distribution ranging from a diameter of 6 to 12 nm. The orientation of the grain's easy axis is random so that the net magnetization of the total ensemble of grains in a superparamagnetic bead is considered as zero. However, this symmetry can be broken by an external magnetic field and the bead has a total net magnetization in the direction of the external magnetic field.

Magnetic torque:

The response of the magnetization M of a superparamagnetic bead to an external magnetic field B is similar to the behaviour of a paramagnetic material. For a low magnitude magnetic field (typically a few mT for Dynal® beads) the magnetization of the superparamagnetic bead is given by

M = χB , where χ is the magnetic susceptibility. The magnetic torqueτ^* _m on a bead with a magnetic moment μ due to the presence of a magnetic field B is given by τ_m = μ xB = μBsmφ . Here φ refers to the angle between the direction of the magnetic moment μ and the magnetic field B. The applied magnetic torque results in physical rotation of the bead around an axis perpendicular to the bonding surface, until the direction of the bead's magnetic moment has aligned with the magnetic field. However, in the case of a superparamagnetic bead the angle between the direction of the magnetic moment and the magnetic field is equal φ = 0 by definition. It can therefore be concluded that it is impossible to apply a magnetic torque on a superparamagnetic bead that behaves truly paramagnetic. Nevertheless, apart from that induced magnetic moment in the direction of the external magnetic field, it has been demonstrated the some magnetic beads may also have a small magnetic permanent moment which is fixed in a certain direction within the bead.

The rotation of superparamagnetic beads in a fluid induced by applying a rotating magnetic field was illustrated by Schellekens and Janssen [Schellekens, A. J., Magnetic rotation of superparamagnetic beads, Bachelor Thesis, Eindhoven University of Technology (2007); Janssen, X.J.A., Schellekens, A.J., Van Ommering, K., Van IJzendoorn, L.J., Prins, M.W.J., Biosens. Bioelectron. 24 (2009), 1937-1941]. It was shown that the beads rotate with the same angular velocity as the rotating magnetic field for low field frequencies. However, by gradually increasing the field frequency it was found that at a certain field frequency the bead is not able to follow the magnetic field any longer leading to a drop in average rotation frequency of the bead. The field frequency at which the drop in rotation frequency occurs is denoted as the breakdown frequency /_M . For field frequencies above the breakdown frequency, the bead cannot follow the field any longer leading to a decrease in rotation frequency. Preferably, the method according to the invention would be implemented below f_bd . The value of f_bd depends at least on the torque-generating magnetic moment of the particle, the size of the magnetic field, and on the size of the particle. For the commercial micrometer-sized Dynal beads used in the experiments, typical values of f_bd are a few tens of Hz. In biological assay preparation, the magnetic beads are then bonded to a target

(e.g. protein, antigens, DNA,etc), via different techniques depending on the applications. For example, the target may be covalently coupled to the bead via carboxyl groups coated on each bead (commercially available).

Then, in a second step the complexes (each comprising the magnetic beads attached to a corresponding target) may be attracted towards a sensor surface on which some capture elements have been fixed. These capture elements have been chosen to specifically bind with the complexes. In a particular embodiment several kinds of capture elements may be present on the sensing surface in order to capture different kinds of targets (this is the multiplexed solution). The result is that the magnetic beads are biochemically bonded to the surface.Apart from the magnetic torque when applying a magnetic field, the magnetic bead is submitted to two additional torques: - The viscosity torque

The elastic torque

Viscosity torque: In the case the beads are located in a fluid, the rotating beads also experiences a viscosisty torque due to the hydrodynamic drag which is opposed to the rotation of the bead and is given by

τ_Mro = -8πηi?³ ^- .

dθ /dt is the angular velocity of the bead represented by a vector pointing out of the plane of rotation. Furthermore, η is the dynamical viscosity of the particular fluid

(η = 10^~3 Pa-s for water) and R corresponds to the bead radius.

The viscous term has been approximated by the bulk drag, but can be extended by additional drag terms (e.g. due to the presence of a surface, or due to drag-generating materials on or near the surface).

Elastic torque: To first order, the elastic property of a particle-to-surface binding - in particular of a binding generated by a biochemical moiety between particle and surface - can be approximated as a torsion spring: τ = - kQ (l) with τ the torque of the biochemical moiety, k its spring constant, and θ the angle over which the particle is rotated away from its equilibrium position (i.e. the zero-torque orientation). This torque increases when the bead is pulled from its equilibrium position. One of the goals of this invention is determining the torsion constant k(Q) of a biological complex. k(θ) can be determined using several different methods some of which will be discussed in this section.

The equation of motion when applying a magnetic field is given by: μ X B - kθ - SπηR³ — = 0 dt ₍₂₎ with the magnetic moment (μ), the magnetic field (B), the orientation of the particle with respect to a reference angle (θ), the viscosity of the fluid (η) and the radius of the particle (R). We note that the torsional spring constant might depend on the angular orientation i.e. k = k(θ). If a rotating magnetic field with a frequency below the breakdown frequency is applied to a bonded bead, the equation of motion becomes: dθ μB sin(ωf - θ) - kθ - SπηR³ — = 0 dt ₍3) with ω the angular velocity of the field.

Fig. 6 depicts the bead behavior in such a rotating field. The particle follows the rotating field (slope of the forward section 1) until the torque due to the spring constant is equal to the magnetic torque (maximum 3). When the field rotates further, the bead rotates backward (vertical section 2 of the curve). Another cycle of increasing angle is then repeated. Note that exact shape of the curve of the angular orientation as a function of time depends on the spring constant k and its dependency on the angular orientation.Due to the possible variabilities in the alignment of the magnetic moments of particles (e.g. the orientation of the permanent moment, or the axis of easy magnetization) with respect to the elastic bonds, the measurements and interpretation of the measurements may vary significantly from one bead to another one. A method of bead-dependent calibration is therefore necessary. To summarize , the invention takes into account that a biochemical attachment hinders and/or limits the motional and orientational freedom of the particle, and thereby complicates the calibration/determination process, since the rotational motion of the particle is hindered by the torque generated by the biochemical binding, the torque being at least partly caused by the deformation of the biochemical moiety between particle and surface. Further, the torque properties can depend on the orientation at which the particle is bound to the surface, particularly when the torque is generated by a static moment and/or an anisotropy of susceptibility.

Furthermore, the calibration/determination method according to the invention needs to be rapid and accurate in the presence of thermal fluctuations.

Examples of Equipment and Method used for measurement. Magnetic source

Fig. 2a schematically shows a cross section of a chip 10 of a biosensor system with current wires 11-12. In a particular embodiment, the wires 11-12 may each be 1 - 5 μm, more particularly 3 μm, wide and 0,1 - 0,5 μm, particularly 0,3 μm, thick. The wires 11-12 are perpendicular one to the other and electricall y insultaed one to the other thanks to a dielectric layer 14 (e.g. made of Si₃N₄). The wiresl l-12 / dielectric layer 14 are formed on a substrate 13 (e.g. made of Si). A magnetic particle 50 is bounded onto the sensor surface 15 of the chip 10 via a biochemical bond 51.

Fig. 2b schematically shows a top view of the crossed wires 11-12 of Fig. 2a. In a particular embodiment, a rotating magnetic field with an angular velocity ω/ may be applied to the particle 50 by running currents through the two wires 11-12 which are 90 degrees out of phase.

Fig. 3 schematically shows a top view of another field-generating means 60 of a biosensor system. The field-generating means 60 may be four electromagnet units 70. Generally, currents flowing through the coils 90 may generate time-dependent magnetic fields with a controlled orientation and magnitude. In particular, the core 80 of the coils may be made of (or comprises) a soft material, such as a composite of nickel, cobalt and iron as an outer shell, and/or a composite of cobalt, vanadium and iron as an inner core and/or low carbon soft iron, for example, covered by an outer shell. In a particular embodiment, a shell composite of 29% nickel, 17% cobalt and 54% iron may be used, as well as an inner core composite of 50% cobalt, 2% vanadium and 48% iron.

This four-magnets configuration 60 may be a quadrupole unit adapted to provide a magnetic field gradient at the sensor surface, such as the quadrupole disclosed in EP08166797. This unit may be arranged below the sensor surface, allowing the volume above the sensor surface to be free - this might be useful for providing on top of the sensor surface a detector (e.g. an optical detector). In a particular embodiment, the core of each electromagnet have a sloped pole tip, the normal of the sloped surface being directed towards the sensor surface, so as to obtain more parallel magnetic field at the sensor surface (avoiding therefore beads clustering). These magnetic sources are controlled to generate rotating magnetic fields and/or flipped magnetic fields, and optionally the possiblity to change the magnitude and/or the frequency of the applied magnetic field. Detection

The detection may be magnetic (e.g. using GMR) as disclosed in WO2005/111596.

Alternatively or in combination, the detection may be optical by using a microscope, a high-speed camera (e.g. at a frame rate of 30 fps, or preferably higher, since a higher frame rate gives a better angular resolution at a given rotation frequency of the bead) and imaging tools.

The angular orientation of the rotating beads as a function of time is preferably analyzed with a computer algorithm. A recorded movie of a rotating bead consists of a sequence of images which can be interpreted as a series of snapshots of the rotating bead. For each image in the sequence the algorithm basically calculates the angle that the bead has rotated with respect to the first image. For each image the program normalises the intensity of the pixels within a chosen region of interest, assigning a value 1 to the pixel with the maximum intensity. Subsequently, all pixels with an intensity below a certain set threshold intensity are collected and the centre of the bead is found by averaging the minimum and maximum x and y coordinates of the collected pixels. Subsequently, the cartesian image of the bead may be converted to a polar image of the bead for all images in the sequence where the centre of the bead is taken as the origin. It should be noted that the bead might slightly translate. Therefore, the centre of the bead may be determined for every image in the sequence. The rotation of the bead around the origin, corresponds to a shift in the polar angle of the polar image. Each polar image in the sequence is then correlated with the first image. A shift in the maximum of the correlation function corresponds to a shift in the polar angle corresponding to the rotation angle of the bead with respect to the first image. In this way it is possible to compute the angle covered by the bead in the time span between a particular image and the first image in the sequence. By doing so, the algorithm computes the angular displacement of the bead as a function of time. With such kind of method motions of a large number of magnetic beads bonded to a surface can be measured simultaneously.

Method for determining properties of a particle bound to a sensor surface This method according to the invention comprises the following steps:

(a) determining a angular reference of the particle bound to the sensor surface,

(b) sequentially applying at least two different magnetic fields to the particle or applying one rotating magnetic field; and (c) measuring the angular velocity and an angular value relating to the orientation of the bonded particle; (d) determining a magnetic characteristic or a surface binding characteristic from said angular velocity, angular value and the angular reference. Determining an angular reference of bonded beads According to a first embodiment, the reference of step (a) may be the zero- torque orientation of the bead (i.e. when no magnetic and no thermal torque is applied to the bead).

The zero-torque orientation may be determined by different ways. A first method may consist in referencing the mean orientation of the beads when no magnetic field is applied. This mean orientation should be the zero-torque orientation.

An alternative method may comprise applying successive rotating fields in two opposite directions (Fig. 5). In both situations the bead will follow the field until the maxium angle is identified (see Fig. 6 for illustration, reference "3"). This maximum angle is reached when the angle between the magnetic moment of the bead and the magnetic field is 90 degrees. The first rotating magnetic field is firstly applied until maximum angles (CC₁ ) of the beads have been identified, then a second rotating magnetic field (having the same magnitude and the same frequency as those of the first rotating field) is applied to the opposed orientation until the maximum angles (a.2) have been identified. The couple of maximum values can be identified by analyzing the movement of the beads (i.e. beads do not follow the rotating field anymore and then revert backwards suddenly). At these two maximum values the angle of the first and second magnetic fields are respectively measured with respect to a frame of reference (θ_ref), which may be the plane of the sensor surface. The zero-torque position of the bond (θo) with respect to the frame of reference is now deduced from the two orientations of the magnetic field i.e. θo = (ai-a2)/2. According to a second embodiment, the reference of step (a) is found by applying a rotating field, from the maximum-torque orientation 3 of the particle as depicted in Fig. 6, 7A, 7B. The maxium-torque orientation 3 (OrG_1113x ) is the orientation of the particle between the forward motion 1 and the backward motion 2 of the particle (as already explained; Fig. 6, 7A, 7B). For a particle with a permanent magnetic moment, at the maximum-torque orientation the angular value between the magnetic moment of the particle and the applied magnetic field corresponds to 90 degrees:

<_*W - θ_max = π/2 ).

This angular value is the angular reference according to this second embodiment. From this angular value, any phase lag (O_fleldt -Q can be calculated for every previous measured orientation of the particle in the forward section 1 of the curve by going backwards in time from the maximum-torque orientation 3 (G_1113x ) into any given points of the forward section 1 preceding the maximum-torque orientation 3 (Fig. 6, 7A, 7B). So, at θ, ω_fιeldt_γ - θ = {ω_fιeldt_γ - θ) + (ω_fιeldt₂ - θ_max ) - (ω_fιeldt₂ - θ_max ) which can be rewritten as follows:

<«Wi - θ = ω_fιeld (J₁ - .₂ ) + (ω_fιeldt₂ - θ_max ) + (θ_max - θ) = ω_fιeld (t_ι - t₂) + π/2 + (θ_max - θ)

Since ω_fιejd,t_λ , t₂, (θ_miEi - θ) is measured easily, (jJ_fιejdt_λ - θ is then calculated. This angular reference ω_fιeldt - θ_max can therefore be used as a reference for the determination of any physical parameters of the particle which are function of (ϋ_βeldt -G and not of θ (e.g. magnetic moment and torsional torque, as explained in next sections).

This reference may be easier and quicker to find than the zero-torque orientation. Determining the magnetic moment of bonded beads The principle of the determination of the torque τ is explained in the following:

It is assumed that the particle is a particle with a permanent magnetic moment (μ) bonded to a surface by a biological moiety (e.g. a molecule with a biological binding), which is assumed to behave like a spring with a spring constant (k).

Due to the spring, the magnetic moment of the particle has an equilibrium orientation (i.e. the zero-torque orientation), which can possibly be determined as aforementioned. For simplicity reason, this zero-torque orientation is defined hereafter to be zero (i.e. the angles "(9" will correspond in the next description to a relative angular value of the beads with respect to their own θo).

According to the invention, two methods are provided to calibrate the magnetic torque in a way that is essentially independent of the strength of the molecular spring. The methods are suitable when the viscous drag is known with a sufficiently high precision. According to a first method to assess the magnetic torque, a non-rotating magnetic field (B) is aplied at an angle +(X₁ , leading to a rotation of the magnetic moment over an angle θi with respect to the zero-torque orientation, according to the following equation: μB ήn(a_x -Q₁ ) = -IcQ₁ (4)

In a second step of the first embodiment, the magnetic field is flipped (in a preferred embodiment: not rotated, see, for example, Fig. 4) to an angle -(X₁, with respect to the equilibrium orientation (zero-torque orientation). The particle now rotates towards the magnetic field newly oriented due to the magnetic torque. At each moment in time the torque balance is given by:

μB Sw(CL₁ +Θ₂) + £Θ₂ = 8πηR^~ (5)

In a practical device, the angular velocity of the particle can be measured for different orientations of the particle (02< θi). From this measurement the spring constant (k) and the magnetic moment (μ) can be derived. One way to calibrate/determine the permanent magnetic moment of the particle is by measuring the angular velocity at an angle Θ2 and at an angle -Θ2. In these situations the torques (kθ) due to the spring are equal in magnitude but opposite in direction. The torque balance at an angle -θ₂ is given by: dθ μB Sm(O₁ - θ₂) - kθ₂ = 877/7R³ — (6)

The summation of Equations (5) and (6) gives:

So by measuring the angular velocity of the particle at two equal angles on both sides of the equilibrium orientation (zero-torque orientation), the permanent magnetic moment of the particle can be determined.

According to a second method to assess the magnetic moment of a bead, two rotating magnetic fields Bi and B_2, having the same angular velocity ω, but different field strengths are successively applied, and the angular velocity of the particles are measured for the same θ value (with respect to the zero-torque orientation.

Thus the two following equations with two unknowns are found:

After subtraction of these equations, the magnetic moment (μ) is given by:

dθ dθ dt dt μ = SπηR^':

B₁ Sm(Wt₁ - Θ) - B₂ sin(ωt₂ - θ)

(10) This calculation may be implemented in reference of either the zero-torque orientation or ωt - θ_max .

Determining the stiffness of bonded beads

Once the magnetic moment is known, the torsional torque or the torsional spring constant (so-called binding stiffness) can be calculated.

A first method of determining the binding stiffness of the bonded bead uses the measured angular position of the beads over time when a rotating magnetic field is applied in the plane of the bonding surface.

As aforementioned explained (Fig. 6), the angular displacement of bonded beads in such a rotating field oscillates as a function of time with a clear asymmetry in the peaks between a forward movement 1 of the bead (when the beads follow the magnetic field) and a backward movement 2 of the bead (when the beads rotate back to their equilibrium position). Fig. 7A and 7B show the results of actual measurement for beads bonded to a surface via IgG-G bonds. The data were taken on particles that showed a rotation response to a magnetic field. Fig. 7A and 7B show that the angular displacement oscillates as a function of time for both samples. The amplitude of the oscillation is lower for the surface that was coated using a higher concentration of IgG. This can be explained by the presence of multiple protein G-IgG bonds between the bead and the surface due to a higher IgG coverage of the substrate. Consequently, the torsional constant k(θ) should be higher for the bonded beads that were prepared using 1000 nM IgG than for those prepared using 50 nM IgG. Using the data of the forward movement 1 presented in Fig. 7A and 7B, the torque produced by the torded bond, k(θ)θ, can be computed as a function of the angular orientation θ directly from the said equation of motion.

Fig. 8 shows the measured torque (torsional constant k(θ) times the angular orientation θ+ θo) computed for the results shown in Fig. 7A and 7B. This result shows a linear dependence of the torque on the angular orientation which indicates that k is independent of θ. Moreover, the measured torque on the bead bound to the surface that was functionalized with 1000 nM IgG has a steeper gradient than compared to the sample prepared by using 50 nM IgG. This corresponds to a torsional constant k = 1 x 10^~18 Nm and k = 3 x 10^~18 Nm for the sample prepared using 50 nM respectively 1000 nM IgG.

It is to be noticed that, in this particular case, since k{θ)θ depends linearly on the rotation angle θ, k can be found simply by determining the slope of the forward rotational period in Fig. 8.

To implement this first method of determining the binding stiffness, only a single measurement of the rotation angle as a function of time is required to extract directly k(θ) from the equation of motion of bound beads. Nevertheless, the magnetic moment (μ) and the zero-torque position (θo) needs to be previously known:. In particular, the zero-torque (or equilibrium) position of the bead θo needs to be calculated from previous measurements as aforedetailed. To avoid this preliminary zero -torque determination, one can determine the reference ωt - θ_max : it is indeed possible to compute the torsional torque due to the twisted biological complex for every rotation angle θ +θ₀ throughout the clockwise rotation of the bead: k(ββ = μBsin(ω_fιeldt -Q ) - 8κR³dQ / dt ₍₁₁₎

The rotation angle is now written as θ +θ₀ to illustrate that the obtained torque kφ β is actually shifted along the x-axis by an angle equal to the equilibrium position of the bead θo which is unknown. Note that the angular velocity dd I dt of the bead can be computed for every rotation angle θ +θ₀ by determining the slope of the graphs shown in figures 7 A and 7B. A second method of determining the binding stiffness of the bonded bead uses, like the first method, the measured angular position of the beads over time when a rotating magnetic field is applied in the plane of the bonding surface.

But this method needs further to assume that the torsional spring constant k does not depend on the angle. This assumption is true for rotation in the linear regime, i.e. far from saturation and before irreversible deformation occurs of the biological moiety that is present between the particle and the surface. Then the following other method can be used to compute k: this method is based on the approximation that the angular velocity of the bead dθ/dt is also constant throughout the forward motion 1 of the bead.

Consequently, the second derivative of the equation of motion d²θ/dt is equal to zero so that the derivative of the equation of motion is given by:

Solving for k then gives

This equation can be solved by using two different magnitudes of the applied magnetic field. By determining the derivative dθ/dt at a certain phase lag ωt -θ between field and magnetic moment it is possible to compute k. As aforementioned, it is not mandatory here to know the zero-torque position, only the phase lag at 90° is necessary to know (as previously explained). The results of computation are given in figure 9 for the two beads discussed from Fig. 7 and 8.

Figure 9 shows the measured torsional constant k of the beads after computation. This indicates that the torsional constant k is higher for the sample prepared using 1000 nM IgG. This again provides evidence that this bead is bound to the substrate with more bonds compared to the bead corresponding to the sample prepared using 50 nM beads. It should be noted that the computed values for k are slightly lower than the torsional constant k determined from figure 8. This is due to, when the torsional spring constant is determined from figure 8, more datapoints are taken into account for the linear fit and as a result the outcome is more accurate. It should be noted that this alternative method can only be used when k is constant with respect to the rotation angle θ. When k does have a dependence on θ, the second derivative of the equation of motion has an extra term involving dk/dθ. Consequently, the equation cannot be easily solved for k.

From the determination of the torsional constant k for each bead bonded to a surface, it is possible to determine which beads are specifically bonded to the surface and which beads are unspecifϊcally bonded to the surface, by applying an appropriate calibration method. This calibration may be based on the knowledge of typical values of non-specific and specific bonds. For example, some kinds of non-specific interactions (e.g. weak van der Waals bindings) are easier to rotate than specific molecular interactions, and some other kinds of non-specific interactions (e.g. strong covalent-like interactions, or multiple parallel interactions between particle and surface) are more difficult to rotate than specific molecular interactions: by a method of double screening, it is therefore possible to retain from the results only the specific bindings, increasing significantly the accuracy in the measurements.

In several cases, examples were given with a micrometer-sized particle having a permanent magnetic moment. Clearly, the proposed methods also apply for particles with other sizes, and with other mechanisms of magnetic torque generation, e.g. via a field-dependent magnetic moment, a shape anisotropy, or a crystalline anisotropy.

Particles can be single particles, but also particle combinations or composites, e.g. to induce special magnetic properties (e.g. a shape anisotropy) or to generate orientational contrast that facilitates the detection of particle orientation.

Most generally, the magnetic moment μ of a particle is a function of the applied magnetic field B_^ giving a magnetic torque ¹^ _m that is the cross-product of moment and field. The dependence of magnetic moment of a particle on the magnitude and direction of the field is given by the mechanisms of moment generation, which are determined by the shape and the composition of the magnetic material inside the particle. One example is a moment that is permanent, i.e. a locked moment that has a fixed orientation in the particle and is independent of the applied field (for the field magnitudes used). Another example is a moment that is oriented along a preferred axis in the particle, and that can be switched along the axis by an applied field with a minimum size (coercive field). Another example is a superparamagnetic moment, i.e. a moment that aligns with the direction of the applied field with a certain relaxation time. Another example is a moment that depends on the applied field and has different magnetizabilities along different axes, e.g. due to shape anisotropy or crystalline anisotropy. Generally, the moment of a particle is a sum of different components, the components having different properties of moment generation. The total torque on the particle is the sum of the torque contributions due to the different moments.

Earlier examples mostly focused on a particle with a permanent moment. As an additional example, we give equations for a superparamagnetic particle with a uniaxial shape anisotropy, i.e. a particle with different linear susceptibilities in different directions. The super-paramagnetic low-frequency torque (i.e. at frequencies where the imaginary part of the susceptibility can be neglected) on an object with a shape anisotropy is given by:

parallel ^~ X perpendicular /^Sml/" J

With V the volume of the object, χ_paraiiei and χ_per_Pendicuiar the susceptibility parallel with and perpendicular to the easy-axis of the object. Due to the different susceptibilities, the magnetic moment is not parallel to the magnetic field, which causes a net magnetic torque on the particle. Note that the torque on the particle is maximum when the angle θ between the applied magnetic field and the easy axis of the object is 45 degrees. Above 45 degrees, the torque decreases with increasing angle and when the angle exceeds 90 degrees, the magnetization of the object is flipped and the torque changes direction.

In one limit, namely the limit of a very long and narrow rod, χ_perpendicuiar can be neglected compared to χ_paraiiei and the torque is given by:

τ = ₀H²Vx _parallel sm(2Q )

In another limit, namely the limit wherein the particle has no shape anisotropy i.e. Xperpendicuiar = Xparaiiei, no torque can be applied to the object at low field frequencies. At high field frequencies a torque can still be applied, even without the presence of permanent moment and/or a shape anisotropy, due to the finite relaxation time of the induced magnetization (see Janssen, X.J.A., Schellekens, A.J., Van Ommering, K., Van IJzendoorn, L.J., Prins, M.W.J., Biosens. Bioelectron. 24 (2009), 1937-1941).

The abovedescribed mechanisms of moment and torque generation are suited for the invention, i.e. the same techniques can be used to determine a surface binding characteristic of the bonded particle and/or a magnetic property of the particle, with adaptations according to the applicable moment equations. To give just one example, for a purely permanent moment, the condition of maximum-torque generation is when the moment and field make an angle of 90 degrees. For a superparamagnetic particle with only an uniaxial shape anisotropy, the condition of maximum-torque generation occurs when the moment and field make an angle of 45 degrees.

While the invention has been illustrated and described in detail in the drawings and foregoing description, such illustration and description are to be considered illustrative or exemplary and non-restrictive; the invention is thus not limited to the disclosed embodiments. Variations to the disclosed embodiments can be understood and effected by those skilled in the art and practicing the claimed invention, from a study of the drawings, the disclosure, and the appended claims. In the claims, the word "comprising" does not exclude other elements or steps, and the indefinite article "a" or "an" does not exclude a plurality. A single processor or other unit may fulfill the functions of several items recited in the claims. The mere fact that certain measures are recited in mutually different dependent claims does not indicate that a combination of these measures can not be used to advantage. Any reference signs in the claims should not be considered as limiting the scope.

Claims

1. Method for determining properties of a particle bound to a surface reacting to a magnetic field, comprising the steps of: (a) determining an angular reference referring to a particular orientation of the bonded particle,

(b) sequentially applying at least two different magnetic fields to the bonded particle or applying one rotating field to the bonded particle;

(c) measuring an angular velocity of the bonded particle and an angular value relating to the orientation of the bonded particle; and

(d) determining a magnetic characteristic or a binding characteristic of the bonded particle from said angular velocity, angular value and angular reference.

2. The method of claim 1, wherein the angular reference is the zero-torque orientation of the bonded particle.

3. The method of claim 2, wherein the zero-torque orientation is determined in step (a) by applying a first rotating field for identifying the first maximum-torque orientation of the bonded particle, by applying subsequently a second rotating field having an opposite orientation for identifying another first maximum-torque orientation of the bonded particle, and by calculating the mean value between the said measured first maximum-torque orientations.

4. The method of claim 1, wherein the angular reference is the phase lag between the orientation of the bonded particle and the orientation of an applied magnetic field when the torque is maximum, and the angular value of step (c) is a phase lag between the orientation of the bonded particle and the orientation of the applied magnetic field.

5. The method of claim 4, wherein the said phase lag of step (a) is determined by applying a rotating field and identifying the first maximum torque.

6. The method of claim 1, wherein the first of the two magnetic fields of step (b) is applied so as to attract the orientation of the bonded particle into a first angular direction, and the second of the two magnetic fields of step (b) is applied so as to attract the orientation of the bonded particle into a second angular direction opposite the first angular direction with respect to the angular reference.

7. The method of claim 6, wherein the measurement of step (c) is performed after applying the first magnetic field according to step (b), and/or after applying the second magnetic field according to step (b).

8. The method of claim 2, wherein step (c) is performed at a first angular orientation of the bonded particle when the first magnetic field is applied and at a second angular orientation of the bonded particle when the second magnetic field is applied, wherein the first and second angular orientations of the bonded particle have opposite signs with respect to the angular reference, and/or have the same absolute value.

9. The method of claim 1, wherein the two magnetic fields in step (b) are a first and second rotating magnetic field rotating according to opposite angular directions.

10. The method of claim 9, wherein the second rotating field is applied by reversing the first rotating field.

11. The method of claim 1 , wherein the two magnetic fields are static magnetic fields , and wherein the first of the two magnetic fields is oriented on a first side of the angular reference, and the second of the two magnetic fields is oriented on a second side of the angular reference.

12. The method of claim 11 , wherein the absolute value of the angle between the orientation of the first magnetic field and the angular reference and the absolute value of the angle between the orientation of the second magnetic field and the angular reference are similar, and the magnetic moment of the bonded particle is calculated thereafter in step (d) based on the angular velocities of the bonded particle measured at these two angles in step (c).

13. The method of claim 1, further comprising the following step (aθ) prior to step (a):

(aθ) providing a fluid sample including a magnetizable or magnetic particle onto the surface, wherein the particle binds to the surface.

14. The method of claim 1, wherein the magnetic moment of the bonded particle is calculated in step (d) by applying in step (b) two rotating magnetic fields having different magnitudes and by performing step (c) for the two fields at a same angular orientation of the bonded particle.

15. The method of claim 1, wherein the torsional torque is calculated in step (d) after having calculated the magnetic moment of the bonded particle.

16. The method of claim 1, wherein the torsional constant is calculated in step (d) after having calculated the magnetic moment of the bonded particle.

17. The method of claim 1, wherein the bond between the bonded particle and the surface is a biochemical bond, and wherein the method further comprises a step of determining whether the biochemical bond is specific or non-specific.

18. The method of claim 1, wherein the method further comprises the implementation of similar and simultaneous steps (a) through (d) for other particles bound to the surface.

19. Biosensor system for carrying out the method of claim 1 , comprising: a sensor surface adapted to bind thereon at least one particle via a biochemical bond, field-generating means adapted to generate a sequence of at least two different magnetic fields or a rotating field to the at least one bonded particle; controlling means adapted to operate the field-generating means so as to generate the sequence of the magnetic fields or the rotating field; and measuring means adapted to detect the angular velocity and an angular value relating to the orientation of the particle bound to the sensor surface. processing means for determining the angular reference, and a magnetic characteristic or a binding characteristic of the bonded particle from said angular velocity and angular value and from the angular reference.

20. Computer program product comprising one or more computer readable media having computer executable instructions for performing the steps of the method of claim 1.