BINDING ASSAY ANALYSIS

Abstract

Methods for determining a sample concentration of target entities in a sample, for example, determining a concentration of target antigens or antibodies in a blood sample or other biological sample.

Claims

1. A method for determining a sample concentration of target entities in a sample, the method comprising: obtaining assay data comprising data points of respective local measurements indicative of a local concentration of the target entities at each of a plurality of assay areas of an assay assembly, wherein the assay areas are connected in series such that a sample flowing through the assay assembly flows past each assay area in sequence, and wherein each assay area comprises a plurality of probe entities immobilized at a surface of the assay area, the probe entities being, arranged to bind to the target entities in the sample, such that the concentration of the target entities is depleted as the sample flows from one of the assay areas to the next; modeling, the assay data with a parameterized function of the local measurements against a quantity indicative of the position of the respective assay areas in the sequence, wherein one or more of the parameters are dependent on the sample concentration; and determining a value indicative of the sample concentration based on at least one of the one or more parameters.

2. A method according to claim 1, wherein the parameterized function is derived from assay data sets obtained for a range of sample concentrations.

3. A method according to claim 1, wherein one of the one or more parameters is indicative of an offset amount which offsets the quantity indicative of the position of the assay area in the sequence such that the parameterized function is a function of the local measurements against the quantity indicative of the position of the assay area in the sequence, offset by the offset amount.

4. A method according to claim 3, wherein the offset amount is determined by minimizing a difference between the respective local measurement and a corresponding value of the parameterized function for each assay area of the assay assembly.

5. A method according to claim 1, wherein the parameterized function is characteristic of the assay assembly.

6. A method according to claim 5, wherein the parameterized function is at least in part defined by one or more fixed parameters characteristic of the assay assembly.

7. A method according to claim 6, wherein the one or more fixed parameters are determined from data sets of local measurements against the quantity obtained for respective sample target concentrations spanning a range of sample target concentrations.

8. A method according to claim 1, wherein the parameterized function is a logistic function.

9. A method according claim 8, wherein the parameterized function is proportional to $\frac{{\mathrm{DP}}_{\mathrm{ma}.Math..Math.x}}{1+\exp \left[\mathrm{Shape}\times \left({\mathrm{DZ}}_i+\mathrm{Offset}\right)\right]}$ wherein DP.sub.max and Shape are fixed parameters characteristic of the assay assembly, Offset is a parameter dependent on a sample target concentration, and DZ.sub.i is indicative of the position of the respective assay area, i, in the sequence.

10. A method according to claim 9, including fitting the parameterized function to the assay data by adjusting the value of Offset, and determining the value indicative of the concentration of target entity in the sample based on Offset.

11. A method according to claim 1, comprising determining the value based on at least one of the one or more parameters using a calibration function, wherein the calibration function comprises a first function for use at sample concentrations of target entities above a given value, and a second function for use at sample concentrations of target entities below the given value.

12. A method according to claim 9, wherein the value indicative of the sample concentration is determined using a calibration function and wherein the calibration function comprises a first function for use at sample concentrations of target entities above a given value, and a second function for use at sample concentrations of target entities below the given value, wherein the first function is a function of Offset, and the second function is a function of: $\frac{{\mathrm{DP}}_{\mathrm{ma}.Math..Math.x}}{1+\exp \left[\mathrm{Shape}\times \mathrm{Offset}\right]}$

13. A method according to claim 1, wherein each local measurement is indicative of a variation in a refractive index at the surface of the respective assay area.

14. A method according to claim 13, wherein the refractive index at the surface of the respective assay area is determined based on the detection of a change in Surface Plasmon Resonance.

15. A method according to claim 13, wherein the variation in the refractive index at the surface of the respective assay area is amplified by an amplifier solution flowing past the respective assay area, wherein the amplifier solution is arranged to interact with target entities bound to the surface of the assay area such that the variation in the refractive index at the respective assay area is amplified when the amplifier has interacted with the hound target entities.

16. A method according to claim 15, wherein each local measurement comprises a difference between a pre-amplification signal and post-amplification signal, wherein the pre-amplification signal has been detected after interaction of the sample with the respective assay area and before interaction of the amplifier solution with target entities bound to the respective assay area, and the post-amplification signal has been detected after interaction of the amplifier solution with target entities bound to the respective assay area.

17. A method according to claim 16, wherein modeling the assay data comprises using an adjustment term to account for a bulk refractive index of the sample.

18. A method according to claim 17, wherein the adjustment term is determined based on a difference between a baseline signal detected prior to interaction of the sample with the assay area and the pre-amplification signal.

19. A method according to claim 15, wherein each local measurement is indicative of a rate at which the amplifier solution interacts with the respective assay area.

20. A method according to claim 15, wherein each local measurement comprises a measurement indicative of the time taken from introduction of the amplifier solution into the respective assay area to detection of a signal feature, for example a maximum or threshold signal amplitude.

21. A method according to claim 1, wherein an amount of probe entities with target entities between each pair of the plurality of assay areas is substantially constant.

22. A method according to claim 1, where the quantity indicative of the position of the assay area in the sequence is indicative of an amount of probe entities upstream of the position of the assay area.

23. A method according to claim 1, wherein each assay area is connected to the next, assay area in the sequence via a conduit.

24. A method according to claim 1, wherein obtaining assay data comprises: introducing a sample into the assay assembly; causing the sample to flow through the assay assembly; and carrying out local measurements at each assay area.

25. A system for determining a sample concentration, of target entities in a sample, the system comprising, a processor arranged to: obtain assay data comprising data points of respective local measurements indicative of a local concentration of the target entity at each of a plurality of assay areas of an assay assembly, wherein the assay areas are connected in series such that a sample flowing through the assay assembly flows past each assay area in sequence, and wherein each assay area comprises a plurality of probe entities immobilized, at a surface of the assay area, the probe entities being arranged to bind to the target entities, such that the concentration of the target entities is depleted as the sample flows from one of the assay areas to the next; model the assay data with a parameterized function of the local measurements against a quantity indicative of the position of the respective assay areas in the sequence, wherein one or more of the parameters are dependent on the sample concentration; and determine a value indicative of the sample concentration based on at least one of the one or more parameters.

26. A system according to claim 26 arranged to carry Out the method of claim 1.

27. A system according to claim 25, the system further comprising: an assay assembly comprising a plurality of assay areas connected in series such that a sample flowing through the assay assembly flows past each assay area in sequence, and wherein each assay area comprises a plurality of probe entities immobilized at a surface of the assay area, the probe entities being, arranged to bind to the target entities, such that the concentration of the target entities is depleted as the sample flows from one of the assay areas to the next; and at least one detector arranged to carry out local measurements at each assay area to obtain assay data comprising data points of respective local measurements indicative of a local concentration of the target entities at each of the plurality of assay areas; wherein the processor is arranged to obtain assay data from the at least one detector.

28. A method for determining a sample concentration of target entities in a sample, the method comprising: obtaining assay data comprising a local measurement indicative of a local concentration of the target entity at an assay area of an, assay assembly, wherein the assay area comprises a plurality of probe entities immobilized at a surface of the assay area, the probe entities being arranged to bind to target entities, wherein the local measurement is based on signals indicative of a variation in a refractive index at the surface of the assay area, such variation being amplified following interaction of an amplifier solution with target entities bound to the surface of the assay area, and wherein the local measurement comprises a difference between a pre-amplification signal and post-amplification signal, wherein the pre-amplification signal is detected after interaction of the sample with the assay area and before interaction of the amplifier solution with target entities bound to the assay area, and the post-amplification signal is detected after interaction of the amplifier solution with target entities bound to the assay area; adjusting the local measurement using an adjustment term such that a bulk refractive index, of the sample is taken into account; using, the adjusted local measurement to determine a value indicative of the sample concentration.

29. A method according to claim 28, wherein the adjustment term is determined based on a difference between a baseline signal detected prior to interaction of the sample with the assay area and the pre-amplification signal.

30. An assay assembly for determining a sample concentration of target entities in a sample, the assay assembly comprising a plurality of assay areas serially connected such that a sample flowing through the assay assembly flows past each assay area in sequence, wherein: each assay assembly comprises an inlet and an outlet; for each pair of assay areas in the plurality of assay areas, the outlet of a first assay area is coupled to the inlet of a second assay area by a coupling portion, such that a sample flowing through the assay assembly flows from the first assay area to the second assay area via the coupling portion for each pair of assay areas in the plurality of assay areas; and each assay area comprises a plurality of probe entities immobilized at a surface of the assay area, the probe entities being arranged to bind to the target entities, such that the concentration of the target entities is detectably depleted as the sample flows from one of the assay areas to the next.

31. A microfluidic device comprising an assay assembly according to claim 30.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0059] Specific embodiments are described below by way of example only and with reference to the accompanying drawings in which:

[0060] FIG. 1—is a schematic illustration of a device comprising an assay assembly;

[0061] FIG. a—is a schematic illustration of a cross-sectional view of target-probe binding in an assay area of the assay assembly of FIG. 1;

[0062] FIG. 2b—is schematic illustration of a cross-sectional view of amplifier-target binding an assay area of the assay assembly of FIG. 1;

[0063] FIG. 3—is a schematic illustration of a system for determining the concentration of a target entity in a sample;

[0064] FIG. 4—is a graphical representation of a depletion master curve;

[0065] FIG. 5—is a graphical representation of the depletion curve of FIG. 4 is using experimental data;

[0066] FIG. 6—is a flow chart showing a method for determining the concentration of a target entity in a sample;

[0067] FIG. 7—is a sensorgram illustrating the variation in a response amplitude with time and illustrating local measurements Δ.sub.31, Δ.sub.32 and Δ.sub.21;

[0068] FIG. 8—is a sensorgram illustrating the variation in a response amplitude with time and illustrating a local measurement G.sub.amp; and

[0069] FIG. 9—is a sensorgram illustrating the variation in a response amplitude with time and illustrating a local measurement Δ.sub.t.

DETAILED DESCRIPTION OF THE INVENTION

[0070] With reference to FIG. 1, a centrifugal or “lab on a disc” microfluidic device 2 is arranged for rotation about an axis 4. Typically, the microfluidic device 2 is a microfluidic polycarbonate disc having an outer diameter of 120 mm, a thickness of ˜1.2 mm, and a hole in the centre of the disc measuring 15 mm in diameter. The disc comprises two 0.6 mm discs bound together by a thin-film polymer. The microfluidic features shown in FIG. 1 and described below are defined in one of the discs and the thin film. The other of the two discs comprises SPR areas provided with a gold coated diffraction grating as described below. The disc 2 comprises an assay assembly 6 which has a plurality chambers 8 arranged in series such that each pair of chambers in the plurality is linked by a conduit 10. The chambers are aligned with SPR areas. A sample, for example blood or other liquid, is introduced into the assay assembly 6 via an inlet conduit 14, which forms an inlet for the first chamber 8 in the series, and the sample leaves the assay assembly via an outlet conduit 12, which forms an outlet for the final chamber 8 in the series. Each chamber 8 measures 0.02 mm in depth and is placed at a distance of 50 mm from the centre of the disc. Each chamber is typically approximately 50 nl in volume and the assay assembly and device are arranged such that approximately 100 μl of liquid can flow through the assay assembly in approximately 5-6 minutes.

[0071] With reference to FIG. 2a, a single chamber 8 will now be described. The chamber 8 comprises an inlet 16 through which a sample may enter the chamber 8 from a connecting conduit 10 (or the inlet conduit 14 in the case of the first chamber in the series) and an outlet 18 through which the sample may leave the chamber 8 via a connecting conduit 10 (or the outlet conduit 12 in the case of the final chamber in the series). When a sample is passed through the chamber, the sample flows through the chamber from the inlet 16 to the outlet 18 in the direction shown by the arrow ‘F’ in FIG. 2a.

[0072] The chamber 8 has a surface 20 comprising a grating of sinusoidal shape (not shown) measuring 100 nm in height and having a period of 1600 nm. The surface 20 is gold coated and has a monolayer of probe entities 22 immobilized on top of the gold surface. Each probe entity 22 has the ability to specifically bind to a specific corresponding target entity 24 which may be present in a sample passed through the chamber 8, such that when a sample containing target entities 24 flows through the chamber 8, specific target entities 24 in the sample bind to the probe entities 22 at the chamber surface 20.

[0073] As a sample is passed through the assay assembly, the flow of the sample is a laminar flow at sufficient rate such that diffusion or other mixing effects are substantially negligible throughout the assay assembly. Accordingly, only target entities 24 in a portion of the sample adjacent the chamber surface 20 will be available for binding with the probe entities 22. As the sample passes from one chamber 8 to the next, due to the laminar flow of the sample, the same portion of sample will be adjacent the surface 20 of each chamber 8, hence only target entities 24 present in that same portion of the sample are available for binding. In this way, the concentration of target entities 24 in the portion of the sample adjacent each surface 20 is depleted as the sample flows from one chamber 8 to the next.

[0074] Due to probe entities in only a thin layer being available for binding, a concentration change in target entities bound to the probe entities from one chamber to the next is detectable using SPR technology. For example, a detectable change in concentration in the liquid layer adjacent the surface 20 may be 0.5 nM from one point in a chamber 8 to a corresponding point in the next chamber 8.

[0075] With reference to FIG. 3, a system 26 for determining the concentration of a target entity 24 in a sample is now described. The system 26 comprises a microfluidic device 2 comprising an assay assembly 6 as described above. A light source 28 is provided and aligned such that emitted light is incident on a detection zone 30 of the surface 20 a chamber 8. Typically the light source 28 is a polarized monochromatic light source, for example a diode laser. When in use, an amount of light incident on the detection zone 30 is reflected from the surface 20 and the reflected light is detected by a detector 32. The detector 32 is arranged to measure the light intensity of the reflected light beam as a function of angle over time.

[0076] The system further comprises a drive for rotating the device 2 to drive liquid flow in the device 2, under the control of a controller, such that various liquids including a sample are introduced into the device 2 and flow through the assay assembly 6 in a defined sequence. The drive is not illustrated in FIG. 3 for the sake of clarity but further details of how liquid flows may be controlled can be found in WO 2011/122972 and WO2012/131556, incorporated herein by reference.

[0077] When in use, changes in the refractive index at the surface 20 of the detection region 30 due to the presence of bound target entities or a bound target-amplifier complex (see below) cause changes in the resonant behavior of the surface 20, specifically changes in surface plasmon resonance behaviour. This can be detected by detecting a change in the angle at which a light intensity minimum occurs in the reflected light as a function of time. The binding of target entities 24 to probe entities 22 at the surface 20 of the chamber 8 causes a change in the refractive index at the surface 20. Accordingly, the amount of target-probe binding at the surface 20 of the chamber 8 can be quantitatively determined by detection of changes in the refractive index at the chamber surface 20, for example by detecting change in the angle at which surface plasmon resonance occurs. In some embodiments, alternative approaches for determining surface plasmon effects may be used. Examples of SPR measurement techniques are given in:

Jiri Homola, “Surface Plasmon Resonance Sensors for Detection of Chemical and Biological Species”, Chem. Rev. 108, pages 462-493 (2008), incorporated herein by reference.

[0078] The depletion of the local concentration of target entity 24 as the sample flows from one chamber 8 to the next can be thought of as establishing a portion of a master depletion curve 35, which is illustrated in FIG. 4, with the starting concentration of the sample defining the portion. The master depletion curve 35 characterizes the variation in a local measurement indicative of the concentration of target entity 24 at the surface 20 of each of a respective chamber 8 against a quantity indicative of the amount of probe entities upstream of the position of the chamber 8 in the sequence.

[0079] The master depletion curve 35 may be understood conceptually by considering a hypothetical system having an unlimited number of notional chambers (and hence detection zones) into which a sample having a very high concentration of target entities is introduced. As the sample is introduced into the assay assembly, the initial chambers in the sequence are saturated with target entities, hence a measurement signal saturates at a maximum amplitude of the local measurement, DP.sub.max. As the sample flows through the sample chambers in sequence the amount of target entities becomes successively depleted and the amplitude of the local measurements at each chamber decreases. As the sample flows through further chambers the amount of target entities is further depleted, the amplitude of the local measurements reaches a minimum amplitude, DP.sub.min. The local measurements for the remaining notional chambers are then approximately constant at this minimum amplitude.

[0080] The master depletion curve 35 may be understood by considering experimental or hypothetical data from a plurality of experiments carried out at different starting target entity concentrations of the sample using assay assemblies having fixed depletion characteristics. Depletion characteristics are determined by factors including fluidic characteristics, for example the flow rate of sample through the assay assembly 6, the height and width of the chambers 8, and the length of the detection circuit; characteristics of the recognition layer, for example, the density of probe entities 22, the avidity and affinity of the probe entities 22 for the target entities 24; and characteristics of the target entity 24, for example the diffusion coefficient; amongst others. An assay assembly used to carry out the experiments typically has 5-10 chambers, accordingly the depletion data obtained will be representative of only a section of the master depletion curve, as explained above.

[0081] With reference to FIG. 5, the master depletion curve may further be understood as a curve combining data from real or notional experiments carried out at a range of known starting concentrations. The data obtained may be thought of as being ‘stitched’ together to form the master depletion curve. If the experimental data sets ‘overlap’ where certain chambers in separate experiments have the same or similar local target concentrations, the data sets may be notionally ‘shifted’ along the x axis until a smooth line is obtained.

[0082] In the example illustrated in FIG. 5, the master depletion curve may be thought of as a combined depletion curve from four experiments, (i)-(iv). Each experiment is carried out using an assay assembly comprising five chambers and so a data set comprising five data points is obtained from each experiment. The starting concentration of target entity used in experiment (i) is higher than that used in (ii), which is in turn higher than that used in (iii), which is higher than that used in (iv). Using knowledge of the starting concentration of each experiment, the data sets can be ‘stitched’ together to form the master depletion curve.

[0083] The master depletion curve is represented by a parameterized function. In a specific embodiment, the function is a logistic function.

[0084] The parameterized function models the amplitude of local measurements, DP, made at a respective chamber against a quantity, DZ.sub.i indicative of the position in the sequence of the chamber 8 and hence detection zone or area, more specifically, the amount of probe entities upstream of the position of the chamber 8, i, in the sequence. In some embodiments the position and amount quantities are essentially the same, save for some scaling. In other embodiments where the amount for each chamber is not constant, the relationship may be more complicated as illustrated below.

[0085] Example values of DZ.sub.i are shown in Tables 1, 2, 3 and 4 below where ‘#DZ’ is the position of the chamber (hence detection zone) in the sequence, ‘DZ capacity’ is the relative capacity of the chamber to bind to target entities, and ‘DZ.sub.i’ is the value indicative of the amount of probe entities upstream of the position of the chamber, i, in the sequence (which is of course also indication of the position in the sequence). DZ.sub.i is used in the parameterised function. In each of the examples shown in Tables 1-4, detection is made in the centre of the each chamber. Table 1 shows the case where the chambers each have the same relative capacity for binding target entities (for example the same amount of probe entities above to bind target entities). In this example, the values of DZ.sub.i used are 0.5, 1.5, 2.5, 3.5 and 4.5 (the 0.5 offset being representative of binding occurring in each chamber upstream of the detection area).

TABLE-US-00001 TABLE 1 #DZ 1 2 3 4 5 DZ Capacity 1 1 1 1 1 DZi for fit 0.5 1.5 2.5 3.5 4.5

[0086] Table 2 shows the case where the relative capacity of the chamber doubles from one chamber to the next. This difference in the relative capacity of the chambers is accounted for in the value of DZ.sub.i used.

TABLE-US-00002 TABLE 2 #DZ 1 2 3 4 5 DZ Capacity 1 2 4 8 16 DZi for fit 0.5 2 5 11 23

[0087] Table 3 shows the case where the 1.sup.st, 4.sup.th and 5.sup.th chambers have a relative capacity of 1 and the 2.sup.nd and 3.sup.rd chambers have a relative capacity of 2. Again, this difference in relative capacity is accounted for by adjustment of DZ.sub.i.

TABLE-US-00003 TABLE 3 #DZ 1 2 3 4 5 DZ Capacity 1 2 2 1 1 DZi for fit 0.5 2 4 5.5 6.5

[0088] The chambers may be connected by microfluidic circuitry. In some embodiments, chambers are connected by microfluidic circuitry, the circuitry between the chambers having a binding capacity for target entities. Table 4 above shows the case where the assay areas have a relative binding capacity of 1 and the circuitry between the chambers have a relative capacity of 0.5. Detection is not carried out in the circuitry. In this case, DZ.sub.i is adjusted according to Table 4 to account for the relative capacity of the system.

TABLE-US-00004 TABLE 4 #DZ 1 2 3 4 5 DZ Capacity 1 2 2 1 1 DZi for fit 0.5 2.5 5 7 8.5

[0089] The parameterized function comprises constants which relate to the assay assembly and its depletion characteristics, DP.sub.max and Shape, and which are fixed for a given assay assembly and assay. The function also comprises a parameter dependent on the concentration of target entities 24 in the sample, Offset, which is indicative of the starting concentration of a sample. The parameter, Offset, is determined by fitting the parameterised function to the data points for each experiment carried out.

[0090] In the above notional and illustrative explanation, Offset determines the location of the data points for the actual chambers/detection areas on the master depletion curve.

[0091] With reference to FIG. 4, Offset can be understood as a value indicative of the extent to which the master depletion curve is shifted along the x axis. For example, for a sample having a low target concentration, the local measurement obtained at the first chamber in the sequence is a correspondingly low measurement, DP.sub.1. For the master depletion curve to fit this experimental data it must be shifted such that the local measurement, DP.sub.1, corresponds to the value of DZ.sub.i which is indicative of the first chamber, 1=1. This is shown by DZ.sub.1=0.5 in FIG. 4. The amount by which the master depletion curve must be shifted, and in which direction, in order to fit the assay data obtained will depend on the target concentration of the sample. Accordingly, the value of Offset is determined by fitting the parameterised function, and hence the master depletion curve, to the respective local measurements obtained at each chamber in the assay assembly.

[0092] The parameterised function is given by the expression shown in equation (5) below.

[00007]$\begin{array}{cc}\mathrm{DP}=\frac{2\times {\mathrm{DP}}_{\mathrm{ma}.Math..Math.x}}{1+\exp \left[\mathrm{Shape}\times \left({\mathrm{DZ}}_i+\mathrm{Offset}\right)\right]}& \left(5\right)\end{array}$

[0093] As described above with respect to FIG. 4, DP.sub.max is the maximum amplitude of the local measurement which can be obtained at a first chamber 8 of an assay assembly and remains constant throughout an experiment. The parameter Shape is indicative of the rate at which the concentration of target entities at the chamber surface is depleted as the sample flows from one chamber to the next. This value depends on the depletion characteristics of the assay assembly and remains constant throughout an experiment for a given assay assembly and assay. exp is typically euler's number, e, however any other suitable base may be used with a corresponding adjustment in the other parameters.

[0094] As explained above, DZ.sub.i corresponds to a value indicative of the amount of probe entities upstream of the position of the respective chamber, i, in the sequence. With reference to FIG. 2a, the detection zone 30 for each chamber 8 is a portion at the centre of the chamber surface 20. Accordingly in this arrangement, for each chamber, DZ.sub.i may take a positive half integer value i.e. 0.5, 1.5, 2.5, 3.5 etc. Alternatively, DZ.sub.i may take an integer value, or any other suitable value indicative of the amount of probe entities upstream of the position of the chamber in the assay assembly.

[0095] The constants Shape and DP.sub.max are determined by characterizing a batch of assay assemblies prior to carrying out an experiment to determine a sample concentration. Each assay assembly is only used once and hence experiments to characterise a batch of assemblies are carried out using respective assay assemblies from the same manufacturing batch to characterise the batch of microfluidic devices 2. The determined values of Shape and DP.sub.max are verified as being representative of the batch by validation experiments using other assemblies of the batch with samples of known sample concentration or target entities. The determined values are then associated with the microfluidic devices 2, for example, by shipping with the device 2, for example as an indication on packaging, or marking the device itself 2 to indicate the values, for example using a bar code or other suitable means for carrying this information. The packaging and/or disc may carry this information directly or may carry a link to a remote location where this information is held for access over a network for example the internet.

[0096] These values are constant for the assay assembly across all the respective local measurements. DP.sub.max and Shape, which are collectively denoted by λ, are determined using known experimental data obtained from a plurality of experiments, j, each having a known starting concentration of target entities (the concentrations spanning a range of concentrations of interest) and each carried out using an assay assembly having a plurality of assay areas, i. DP.sub.max and Shape are determined by minimizing the following sum:

[00008]$\begin{array}{cc}\underset{j=1}{\overset{m}{.Math.}}.Math.\underset{i=1}{\overset{n}{.Math.}}.Math.{\left[\mathrm{DP}\left({\mathrm{DZ}}_i\right)-f_{\lambda }\left({\mathrm{DZ}}_i+\mathrm{Offset}\right)\right]}^2& \left(6\right)\end{array}$

where DMZ) is the local measurement at the assay area, i, and f is the corresponding value of the parameterized function having constants λ. Data from m experiments is used, each experiment having been carried out using an assay assembly having n assay areas. In some embodiments, the parameters of Shape and DP.sub.max are determined using any suitable optimization technique, e.g. least square, gradient descent, regression or Chi-squared minimization techniques. From the sum, (6), above, ‘Offset’ is also determined for each of the plurality of experiments, j, hence a relationship between ‘Offset’ and the starting concentration of target entities is determined. This relationship between Offset.sub.j and concentration, Concentration.sub.j, for each of the plurality of experiment, j, defines data points {Concentration.sub.j, Offset.sub.j} that can be used to fit a calibration function. As will be described further below, this calibration function is used to determine the sample concentration based on the value of Offset.

[0097] Using an assembly from a batch that has been characterized (values for λ, determined) assay experiments to find unknown concentrations of target entities in a sample are carried out. The value of Offset is fit to the assay data from a given experiment in order to provide an indication of the starting concentration of the sample. For the avoidance of doubt, reference herein to the ‘starting concentration’ should be understood as referring to the concentration of target entities in a sample to be tested. The parameterized function may be fit to the assay data and the value of Offset determined by minimizing the following sum:

[00009]$\begin{array}{cc}\underset{i=1}{\overset{n}{.Math.}}.Math.{\left[\mathrm{DP}\left({\mathrm{DZ}}_i\right)-f\left({\mathrm{DZ}}_i+\mathrm{Offset}\right)\right]}^2& \left(7\right)\end{array}$

where DP(DZ.sub.i) is the local measurement at the assay area, i, and f is the corresponding value of the parameterized function. Minimization of this or any suitable cost function can be carried to obtain the best fit of the parameterized function to the assay data. In some embodiments, least-square regression minimization techniques are used and validated using a chi-squared test.

[0098] Once the value of Offset has been determined by fitting the parameterized function to the experimental data obtained, a value indicative of the starting target concentration of the sample can be determined using a calibration function.

[0099] The calibration function comprises a first function and a second function. The first function, f.sub.1, is used to determine the target concentration for samples where the target concentration is known to be high and is a function of ‘Offset’, for example f.sub.1 may be found by fitting a suitable function to the data points, {Concentration.sub.j,Offset.sub.j}, described above. The second function, f.sub.2, is used to determine the target concentration for samples where the target concentration is known to be low and is a function of the undepleted measurement that would be obtained by the system, in other words, a function of the hypothetical local measurement when DZ.sub.i=0. Accordingly, the second function is a function of the expression (8) below:

[00010]$\begin{array}{cc}\frac{2\times {\mathrm{DP}}_{\mathrm{ma}.Math..Math.x}}{1+\exp \left[\mathrm{Shape}\times \mathrm{Offset}\right]}& \left(8\right)\end{array}$

[0100] In some embodiments, the first and second functions are represented in the form of an exponential function as shown by equations (9a) and (9b) below.

f.sub.1=X.sub.1+Y.sub.1exp[−Z.sub.1×Offset]  (9a)

f.sub.2=X.sub.2+Y.sub.2exp[+Z.sub.2×DP(DZ.sub.i=0)]  (9b)

DP(DZ.sub.i=0) is the amplitude of the local measurement when DZ.sub.i=0. The parameters X.sub.1,2, Y.sub.1,2 and Z.sub.1,2 are be obtained by fitting to experimental data in a similar manner as described above.

[0101] In some embodiments, determining the sample concentration is an iterative process. For example, a first step may be applied initially followed by a second step that provides a more refined result. Specifically, in some embodiments, the first function is used in the first step to determine a value indicative of concentration. If the value is below a threshold, the second step re-calculates the value using the second calibration function. In some embodiments, the order is reversed and the first function is used in the second step if the value from the first step (from the second function) is above a threshold.

[0102] Alternatively, in some embodiments the calibration function is a single function relating Offset to the target concentration of the sample.

[0103] In some embodiments, the calibration curve of sample concentration against Offset is a logistic function e.g. a 4PL nonlinear regression model. In the case of a 4PL model, the sample concentration is a function of (Offset, a, b, c, d), where a, b, c and d are parameters of the model which may be obtained using minimization techniques, for example Chi-squared minimization techniques, and experimental data as described above.

[0104] A method for determining the concentration of target entities in a sample will now be described in overview with reference to FIG. 6. In a first step 36 assay data is obtained. The assay data obtained comprises a plurality of data points, each data point corresponding to a local measurement carried out at a respective chamber 8. The local measurements relate to the detection of changes in a refractive index at the surface of each of the respective chambers and are indicative of the concentration of target entity 24 at the surface 20 of the respective chamber 8. The assay data is modeled with the parameterized function at a second step 38, as described above, the parameterized function comprising the parameter, Offset, dependent on the concentration of the target entity in the sample. A value indicative of the concentration of the target entity in the sample is then determined at a third step 40 based on ‘Offset’ using the first and second calibration functions described above. It will be understood that at some point prior to step 38, for example when loading the device 2 into the system 26, the parameters λ, are loaded into the system, for example by manual entry or by reading a tag, such as a barcode, carrying this information, as described above.

[0105] The system 26 described above and shown in FIG. 3 is used to obtain assay data. Firstly a buffer solution is made to flow through into the assay assembly 6 as a baseline, followed by a sample to be tested, an amplifier solution, and finally a wash with a second buffer solution. With reference to FIG. 7, for each respective chamber 8, changes in the refractive index at the chamber surface 20 can be detected by the detector 32 such that the amplitude of the detected signal, for example change in the angle at which surface plasmon resonance occurs, increases in direct proportion to the magnitude of the change in refractive index at the chamber surface 20.

[0106] For each respective chamber 8, once the buffer solution has flowed through the chamber 8, a baseline measurement 42 is measured for the detection region 30. The sample comprising an amount of target entities 24 is then introduced into the chamber 8. As the target entities 24 bind to probe entities 22 at the surface 20 of the chamber, the refractive index at the surface 20 changes and consequently the amplitude of the measured signal for the detection region 30 increases 44a. In some cases, a proportion of the target-probe binding is reversible hence a reduction 44b in the amplitude of the measured signal for the detection region 30 may occur until a steady state is reached. Such reduction may not be observed in cases where the concentration of target entity 24 in the sample is very high.

[0107] With reference to FIG. 2b and FIG. 7, the amplifier solution is then made to flow through the chamber 8. Active components 25 in the amplifier solution bind to the target entities 24 which are in turn bound to the probe entities 22. A sufficiently high concentration of amplifier is made to flow through the chamber 8 such that the bound target entities are saturated with amplifier.

[0108] This results in a further change to the refractive index at the surface 20 of the chamber 8 and consequently the amplitude of the measured signal for the detection region 30 increases 46a. As with the target-probe binding, in some cases a proportion of the amplifier-target binding is reversible hence a reduction 46b in the amplitude of the measured signal for the detection region 30 may occur until a steady state is reached. Such reduction may not be observed in cases where the concentration of active component in the amplifier is very high.

[0109] Finally the second buffer solution is made to flow through the chamber 8 to wash away any remaining unbound sample or amplifier. Consequently, the amplitude of the measured signal for the detection region 30 remains constant 48. The local measurements may be any of a number of suitable measurements, some of which are described in more detail in the embodiments below.

[0110] Alternatively, assay data may be obtained via any other suitable means, or may be obtained from a previously run assay, possibly run by a third party.

[0111] Once the assay data has been obtained it is modeled with the parameterized function and a value of ‘Offset’ is determined as described above. The constants DP.sub.max and Shape characteristic of the assay assembly having been previously determined using the method described above and having been marked on the microfluidic device itself, for example using a bar code. The parameterized function models the local measurements carried out at each respective chamber 8 against the quantity, DZ. The quality of fit of the measured data to the parameterized function is evaluated, for example by calculation of Pearson's coefficient for the fit, using Chi-squared minimization techniques or using any other suitable means. The quality of the fit is compared to a predetermined threshold such that, if the quality of fit is not sufficiently good to meet the threshold, the data is discarded.

[0112] Once the value of Offset has been determined by fitting the parameterized function to the assay data obtained, a value indicative of the target concentration of the sample can be determined using the calibration function as outlined above.

Embodiment 1

[0113] In a first embodiment, local measurements are carried out at each of the respective chambers 8 in the assay assembly by detecting the amplitude of the baseline response obtained prior to a sample being made to flow through the chamber 8, B.sub.1, shown as detection point 1 on FIG. 7, detecting the amplitude of the response following flow of the second buffer through the chamber 8, B.sub.3, shown at detection point 3 on FIG. 7, and determining a difference between the two responses, Δ.sub.31=B.sub.3−B.sub.1.

[0114] The parameterized function for each respective local measurement is therefore given by equation (10) below.

[00011]$\begin{array}{cc}{\Delta }_{31}\cong \frac{2\times {\mathrm{DP}}_{\mathrm{ma}.Math..Math.x.Math..Math.\_.Math..Math.\mathrm{amp}}}{1+\exp \left[\mathrm{Shape}\times \left({\mathrm{DZ}}_i+\mathrm{Offset}\right)\right]}& \left(10\right)\end{array}$

[0115] Where DP.sub.max.sub._.sub.amp is the maximum amplitude of the local measurement at a chamber 8 following interaction of the amplifier with the chamber 8. In this case, since measurements B.sub.1 and B.sub.3 are each made when the bulk solution in the chamber is buffer solution (i.e. the bulk solution at each measurement has the same refractive index), as DZ.sub.i becomes larger, DP will tend towards zero hence the amplitude DP.sub.min of the master curve/parameterised function is zero.

Embodiment 2

[0116] A potential drawback with the approach outlined in Embodiment 1 is that there can be drift in the signals being compared, for example, due to fluctuations in temperature, vibrations in the system etc. In the example of Surface Plasmon Resonance, the signal is dependent on the local refractive index near the detection surface. Such a signal therefore comprises contributions from (i) the probe/target layer having a certain density of target entities bound thereto; (ii) the surrounding liquid; (iii) the metal present at the surface of the chamber e.g. gold. The refractive index of these three contributions is dependent on the temperature and so drifts in temperature will cause drift in the signal detected. Similar drift effects result from mechanical vibrations in the system.

[0117] This is shown on FIG. 7. As a result of this drift, the noise level in the system is higher and the detection capability decreases as a result. To overcome this, a local measurement Δ.sub.32 can be used instead of Δ.sub.31, as will now be described.

[0118] Local measurements, Δ.sub.32, are carried out at each of the respective chambers 8 in the assay assembly. Δ.sub.32 is measured by detecting the amplitude of a response, B.sub.2, following interaction of the sample with the chamber surface 20 and prior to interaction of the amplifier with target entities bound to the surface, shown as detection point 2 in FIG. 7. The amplitude of the response following introduction of the second buffer into the chamber 8, B.sub.3, is then detected shown as detection point 3 on FIG. 7, and a difference between the two responses, Δ.sub.32=B.sub.3−B.sub.2 is determined.

[0119] Measuring Δ.sub.32 this has the advantage that the measurement is made over a shorter time period (because the time between B.sub.2 and B.sub.3 is shorter than the time between B.sub.1 and B.sub.3) and so the effect of drift is reduced.

[0120] When B.sub.2 is detected the bulk material in the chamber 8 is the sample, whereas when B.sub.3 is detected the bulk material in the chamber 8 is buffer solution. The sample and the buffer solution each have a different refractive index, therefore the local measurement, Δ.sub.32, comprises a contribution caused by the change in the bulk material from sample to buffer solution between B.sub.2 and B.sub.3. Accordingly, Δ.sub.32 can be represented by equation (11) shown below.

Δ.sub.32=f(Offset)+Δ.sub.bulk  (11)

[0121] Where f(Offset) is the parameterized function/master curve and Δ.sub.bulk is the contribution due to the refractive index of the sample.

[0122] Where the sample is blood, for example, the change in the refractive index due to the difference in bulk solution between B.sub.2 and B.sub.3, Δ.sub.bulk, will vary from person to person and is accordingly is unknown quantity.

[0123] Δ.sub.bulk can be obtained as a further variable parameter by fitting the function (11) to the experimental data, that is adjusting Offset and Δ.sub.bulk at the same time. Alternatively, with reference to FIG. 7, Δ.sub.21 can be measured, as will be described below, and used as an approximation to Δ.sub.bulk (ignoring the effect of unamplified target-probe binding). Δ.sub.21 is measured by detecting the amplitude of the baseline response, B.sub.1, once buffer solution has flowed through the assay assembly, detecting the amplitude of a response, B.sub.2, following interaction of the sample with the chamber surface 20 and prior to interaction of the amplifier with target entities bound to the surface, and determining a difference between B.sub.1 and B.sub.2, i.e. Δ.sub.21=B.sub.2−B.sub.1. The measurement Δ.sub.21 can be thought of according to equations (12) below.

Δ=Δ.sub.unamplified.sub._.sub.binding+Δ.sub.bulk  (12)

[0124] Where Δ.sub.unamphfied.sub._.sub.binding is the contribution due to the unamplified binding of target entities to the surface of the chamber. Since the contribution to the signal from the bulk is much greater than the contribution from the unamplified binding of target entities to the surface of the chamber, measurement Δ.sub.21 can be considered as approximately equal to Δ.sub.bulk. Accordingly, in some embodiments, Δ.sub.32−Δ.sub.21 can be used as the local measurements, i.e. the local measurements are modeled as Δ.sub.32−Δ.sub.21=f(Offset). Of course, it is equivalent to model Δ.sub.32=Δ.sub.21+f(Offset) and this is done instead in some embodiments.

Embodiment 3

[0125] In another embodiment, a change of the amplitude of the response signal detected by the detector 32 as the amplifier flows across the surface 20 of the chamber 8, G.sub.amp, is used as the local measurement. This measurement reflects the rate at which the active components in the amplifier bind with target entities 24 bound to the respective chamber 8.

[0126] The master depletion curve shown in FIG. 4 and described above also applies in this case where the local measurement is G.sub.amp, and the corresponding model is G.sub.amp=f(Offset), with f defined as discussed above, albeit with its parameters adapted accordingly, for example, DP.sub.max being the notional maximum rate of change for a saturated chamber 8. In the example shown in FIG. 8, G.sub.amp equates to the gradient of the curve at time t.sub.1, indicated by point 4 on the sensorgram. Of course, any other suitable, for example amplification, rate dependent measurement may also be taken.

Embodiment 4

[0127] In yet another embodiment, a time taken from introduction of the amplifier into the respective chamber to detection of a threshold amplitude of the response signal or a feature of the signal (e.g. a maximum) is measured. By using 1/Δ.sub.t as the local measurement, the master depletion curve shown in FIG. 4 and described above also applies and the experimental data can be modeled as 1/Δ.sub.t=f(Offset), with f defined as above, albeit with its parameters adjusted accordingly, e.g. DP.sub.max being the notional maximum value of 1/Δ.sub.t (minimum of Δ.sub.t) for a saturated chamber 8.

[0128] Of course, any other suitable time dependent measurement may also be taken.

[0129] Using the same system and method as described above and taking any suitable local measurement, when the concentration of the active component in the amplifier is not sufficiently high to saturate the assay assembly, the local measurements are also dependent on this active component concentration which will deplete as the amplifier flows from one chamber to the next. The parameterized function is therefore arranged to account for this dependency. For example, the parameterized function may contain an additional parameter to account for the depletion in the active component concentration. Alternatively or in addition, the ‘Shape’ parameter may be a vector varying with both the sample concentration and amplifier concentration. In some embodiments, the effect of the concentration of amplifier can be thought of as being akin to the effect of the density of probe entities present in the assay assembly as a first approximation. Accordingly, for example, the value of DZ.sub.i may be adjusted to account for the amplifier concentration in a similar way to how DZ.sub.i is adjusted to take into account the relative binding capacity of the assay assembly as described in detail above.

[0130] In general, if amplifier concentrations are non-saturating, two depletion effects occur: 1) depletion of target entities; 2) depletion of amplifier. (2) will depend on the concentration of target entities at each detection area. The overall effect will depend on the combination of these two effects. Each effect is, in some embodiments, assessed independently and a higher-order function is used to combine both effects. Alternatively, both effects may simply be captured by using a suitable higher-order function and/or a function with more parameters for fitting the depletion characteristics (e.g. a 4PL or 5PL function).

[0131] It will be understood that whether or not the amplifier is provided in a saturating concentration is independent of the local measurement used and a non-saturating amplifier concentrations may be used with any of local measurements identified in the embodiments described above or indeed any other local measurement.

[0132] It will be understood that the above description is of specific embodiments by way of example only and that many modifications and alterations will be within the skilled person's reach and are intended to be covered by the scope of the appendent claims. For example, whilst the description above has been set out in terms of detection of changes in surface plasmon resonance, it will be appreciated that any other suitable means for quantitatively detecting an amount of target-probe binding at the surface 20 may be used, for example, UV absorption fluorescence of the target entity 24 and/or detection of a label bound to the target entity 24 may be used. In some embodiments, a plurality of detection zones is provided in a single chamber, for example with detection areas from which signals are measured spaced along a strip of functionalized surface.