EP4662476A1

EP4662476A1 - Method and system for analyte-ligand interaction analysis

Info

Publication number: EP4662476A1
Application number: EP24704709.5A
Authority: EP
Inventors: Robert Karlsson; Olof Karlsson
Original assignee: Cytiva Sweden AB
Current assignee: Cytiva Sweden AB
Priority date: 2023-02-07
Filing date: 2024-02-07
Publication date: 2025-12-17
Also published as: JP2026504487A; WO2024165605A1; KR20250142867A; CN120641734A

Abstract

In various aspects, the present invention relates to a method 700, 800 and system 900 for determining one or more interaction parameters associated with an interaction between an analyte and a ligand. The method comprises contacting 704, 804 a sensor surface having a ligand immobilized thereto with one or more samples containing an analyte; registering 706, 806 a sensor response indicative of binding of the analyte to binding sites of the ligand; and fitting 716, 808 the registered sensor response to an interaction model in order to determine one or more interaction parameters associated with the interaction between the analyte and the ligand, wherein the fitting is constrained by a pre-determined upper and lower limit applied to an analyte saturation parameter associated with the interaction model.

Description

Method and system for analyte-ligand interaction analysis Technical Field The present disclosure relates to analysis of interactions between an analyte and a ligand at a sensor surface, and more particularly to systems and methods for enabling improved determination of interaction parameters associated with such interactions. Background Analytical sensor systems that can monitor interactions between molecules, such as biomolecules, in real time are gaining increasing interest. Such systems typically enable one or more of binding, kinetics, affinity, specificity and concentration of molecules (‘analytes’) contained in sample solutions to be determined. Optical biosensors are particularly useful for this purpose and are usually referred to as interaction analysis sensors or biospecific interaction analysis sensors. A representative such biosensor system is the BIACORE® instrumentation sold by Cytiva, which uses surface plasmon resonance (SPR) for detecting interactions between molecules at a sensing surface without any need for labels. As a respective sample is passed over the sensor surface, the progress of binding can be measured and provides a direct reflection of the rate at which an interaction between molecules is occurring. A typical output from systems such as the BIACORE® system is a graph or curve describing the progress of a molecular interaction with time, including an association phase part and a dissociation phase part. This binding curve, which is usually displayed on a computer screen, is often referred to as a "sensorgram". With the BIACORE® system (and analogous sensor systems) it is thus possible to determine in real time without the use of labelling, and often without purification of the substances involved, not only the presence and concentration of a particular analyte in a sample, but also additional interaction parameters, including kinetic rate constants for binding (association) and dissociation in the molecular interaction as well as the affinity for the interaction being assessed. The association rate constant ( ^^_^) and the dissociation rate constant ( ^^_ௗ) can be obtained by fitting the resulting kinetic data for one or preferably several different sample analyte concentrations to mathematical descriptions of interaction models in the form of differential equations. The affinity (expressed as the association equilibrium constant ^^_^ or the dissociation equilibrium constant ^^_^) can be calculated from the association and dissociation rate constants. Often, however, it may be difficult to obtain definitive kinetic data due to weak binding, and it is therefore usually more reliable to measure the affinity of an analyte by equilibrium binding analysis, which involves determining, for a series of analyte concentrations, the level of binding at equilibrium, or steady state, which is presumed to have been reached at or near the end of the association phase of the binding interaction. A problem arises, however, in that determining affinity through equilibrium binding analysis in this manner has traditionally been reliant on being able to obtain sensor response data across a wide range of concentrations for the analyte. Specifically, traditional analysis techniques require that a sensor response value for the analyte at a concentration approaching the dissociation equilibrium constant, ^^_^, is available. In practice, however, it can be difficult to obtain such data due to practical limitations such as the fact that above a given concentration an analyte may begin to precipitate or aggregate, making accurate readings of the sensor response impossible. As a result, it may not always be possible to obtain an undisturbed sensor response value for analyte concentrations nearing ^^_^. Instead, response values for only a limited range of analyte concentrations may be available. Such a situation may frequently occur during drug candidate screening, to give one example. In such cases, traditional methods for calculating interaction parameters (e.g. ^^_^, ^^_^) fall short and produce unrealistic and inaccurate estimates for these values. While some progress has been made to provide alternative solutions, these still fall short of providing totally accurate data as will be described in further detail below. As can be seen, therefore, existing processes for determining interaction parameters of an analyte-ligand interaction suffer from significant drawbacks. It would be advantageous to provide systems and methods which address one or more of these problems, in isolation or in combination. Overview This overview introduces concepts that are described in more detail in the detailed description. It should not be used to identify essential features of the claimed subject matter, nor to limit the scope of the claimed subject matter. According to one aspect of the present disclosure, there is provided a method for determining one or more interaction parameters associated with an interaction between an analyte and a ligand. The method comprises contacting a sensor surface having a ligand immobilized thereto with one or more samples containing an analyte, and registering a sensor response indicative of binding of the analyte to binding sites of the ligand. Preferably, the sensor surface is contacted with three or more samples containing different concentrations of the analyte. Injection of a series of samples of differing analyte concentrations in this manner may be referred to as a concentration series and provides more reliable results than using a single analyte concentration. Preferably, in order to improve the accuracy of the results, the registered response is the response level of each analyte sample recorded at equilibrium (or as close as possible to equilibrium), which in practice is typically assumed to be at the end of the association phase. The method further comprises fitting the registered sensor response to an interaction model in order to determine one or more interaction parameters associated with the interaction between the analyte and the ligand. Advantageously, the fitting is constrained by a pre-determined upper and lower limit applied to an analyte saturation parameter associated with the interaction model. Fitting a registered sensor response to an interaction model is a known method for determining interaction parameters. What is surprising, however, is that the present inventors have identified that the accuracy of this approach can likely be significantly improved by constraining the fitting in the manner described above and explained in further detail herein. In particular, by applying an upper and lower limit to an analyte saturation parameter associated with the interaction model, the fitting procedure is constrained to producing values within certain boundaries. The present inventors believe that this constraint produces more accurate estimates of the interaction parameters than any existing method. In particular, the present inventors have identified that the disclosed approach effectively provides a middle ground between previous approaches which are either too reliant on the registered response data or, at the other extreme, use a fixed estimated value for the analyte saturation parameter and thereby give too little weighting to the actual registered response data. The presently disclosed approach represents a balance between these competing approaches and, surprisingly, is considered by the inventors to provide more accurate affinity determinations. The one or more interaction parameters which are determined using the disclosed methods may comprise one or more of: the association equilibrium constant, ^^_^, of the interaction; and the dissociation equilibrium constant, ^^_^, of the interaction. These interaction parameters provide valuable insight into the binding behaviour of an analyte in the presence of a ligand, in particular in relation to the affinity of the analyte for the ligand in question. This data can be used to inform a variety of important assays and analyses, for example in candidate drug screening, antibody analysis and quality control. As noted above, fitting of the sensor response data to the interaction model is constrained by a pre-determined upper and lower limit applied to an analyte saturation parameter associated with the interaction model. In one example, the analyte saturation parameter to which the upper and lower limit are applied may be an analyte saturation response value, ^^_^^௫, associated with the interaction model used in the fitting procedure. ^^_^^௫ indicates the maximum possible sensor response for an analyte at a given concentration, i.e. the response which would be expected if the analyte has bound to all available binding sites of the ligand on the sensor surface. As will be described in further detail below, the present inventors have identified that, surprisingly, constraining the fitting with an upper and lower limit applied to ^^_^^௫ is believed to provide increased accuracy in the determination of interaction parameters such as ^^_^ and ^^_^. Fitting the sensor response data to an interaction model based on ^^_^^௫ is not the only option. An alternative is to use an interaction model based on target occupancy, ^^ ^^. In that case, the analyte saturation parameter to which the upper and lower limit are applied is a target occupancy value at saturation, ^^ ^^_^^௧. Target occupancy may be considered to represent an analyte response in percentage (or fractional) terms relative to the response that would be expected at saturation. Accordingly at saturation, where the sensor response is ^^_^^௫, the target occupancy ^^ ^^_^^௧ is 100% (or 1 in fractional terms) because the response will be maximal when there is maximum analyte-ligand binding (i.e. at saturation). When fitting the sensor response data to an interaction model based on target occupancy, the present inventors have once again identified that use of an upper and lower limit applied to the target occupancy at saturation, ^^ ^^_^^௧, is believed to result in better predictions of interaction parameters such as ^^_^ and ^^_^. In one example, the upper and lower limit which are applied to the analyte saturation parameter may be set by a user based on their knowledge of the particular assay. Alternatively, however, the disclosed method may comprise determining an estimated value of the analyte saturation parameter and setting at least one of the upper and lower limit based on this estimated value for the analyte saturation parameter. In other words, an initial estimate of the analyte saturation parameter can be determined and this estimate can then be used as a starting point around which the upper and lower limits are set. This approach means that the fitting procedure is anchored to a best- guess estimate for the analyte saturation parameter which has been previously estimated either from theory or experimental data. This approach improves the likelihood of making accurate determinations of the interaction parameters, compared to simply relying on a user to provide an estimate based on their knowledge of the analyte and its likely interaction with the ligand. In one example, at least one of the upper and lower limit is set as a percentage of the estimated value for the analyte saturation parameter. In other words, if the estimated value represents 100%, then the fitting may be constrained between upper and lower limits that are defined as a percentage of that initial estimate. The present inventors have identified that a particularly suitable lower limit is 75% of the estimated analyte saturation parameter. This constraint has been found to provide highly accurate estimates for the interaction parameters. Similarly, the present inventors have identified that a particularly suitable upper limit is 150% of the estimated analyte saturation parameter. This constraint has also been found to provide highly accurate estimates for the interaction parameters. Hence, in one particularly advantageous arrangement, the fitting procedure is constrained between using values of 75% to 150% of a previously determined estimated value of the analyte saturation parameter. This constraint prevents the fitting procedure from considering values outside of this interval for the analyte saturation parameter, thereby constraining the fitting procedure within predefined boundaries. As noted above, this approach has been found to improve the accuracy of the interaction parameter determination. While limits of 75% and 150% respectively have been found to be particular advantageous, benefits in accuracy are still provided when the lower limit is between 75% and 99% of the estimated value and even when the lower limit is between 25% and 99% of the estimated value. Similarly, benefits in accuracy are provided when the upper limit is between 101% and 150% of the estimated value and even when the upper limit is between 101% and 250% of the estimated value. Hence, the lower limit may be set as between 75% and 99% of the estimated value or alternatively between 25% and 99% of the estimated value. The upper limit may be set as between 101% and 150% of the estimated value or alternatively between 101% and 250% of the estimated value. All of these percentage ranges are believed to provide a benefit in terms of determining accurate interaction parameters. As already mentioned, if the upper and lower limit used to constrain the fitting process are based on a predetermined estimated value of the analyte saturation parameter, then that predetermined estimated value can be determined in a number of ways. In one example, the estimated value of the analyte saturation parameter is determined theoretically based on known models and equations concerning the relationship between analytes and ligands. In that case, determining the estimated value of the analyte saturation parameter may comprise calculating a theoretical estimate of the value based on: the molecular weight, ^^ ^^_^^^, of the ligand; the molecular weight, ^^ ^^_^^^, of the analyte; and the ligand response, ^^_^^^. The ligand response, ^^_^^^, may also be referred to as the immobilisation level of the ligand. An advantage of this theoretical approach is that an initial estimate of the analyte saturation parameter can be determined theoretically without need for a control analyte or running any experiments, which saves time and cost. In one example, if the interaction model being used in the fitting procedure is based on ^^_^^௫, then the predetermined estimated value of the analyte saturation parameter can be an estimated theoretical value of ^^_^^௫, i.e. . This theoretically estimated value of ^^_^^௫ can be determined using the following equation: Alternatively, if the interaction model being used in the fitting procedure is based on target occupancy (To), then the predetermined estimated value of the analyte saturation parameter ( ^^ ^^_^^௧) can be defined to 1. Sample responses ( ^^_^) for an analyte ^^ can be expressed in terms of target occupancy (To_A) using the following relationship: While determining the estimated value of the analyte saturation parameter theoretically is one option, another option is to determine the value experimentally, using a control analyte which is assumed to interact with the ligand in a similar manner to how the analyte of interest interacts. In that case, determining the estimated value of the analyte saturation parameter may comprise contacting the sensor surface with a control analyte, registering a sensor response indicative of binding of the control analyte to binding sites of the ligand, and determining a control analyte saturation parameter for the control analyte. For example, ^^_^^௫^ can be determined for a control analyte. Once the control analyte saturation parameter has been determined, this can be converted into a corresponding saturation parameter for the analyte of interest. For example, ^^_^^௫^ (for the control analyte) can be converted into ^^_^^௫^ (for the analyte of interest). Methods for performing this conversion will be described in more detail in the following description. As already noted, the method may comprise receiving a user input setting the upper and lower limit. In other words, the upper and lower limit around the analyte saturation parameter, by which the fitting procedure is constrained, can be set by a user. As mentioned above, in one example the user may simply set the limits based on existing knowledge of the interaction being analyse. Alternatively, the system may store a predetermined estimate of the analyte saturation parameter (for example one that has been determined in one of the theoretical or experimental manners described above). In that case, the predetermined estimate may act as a default value and the user input can be used to set an upper and lower limit relative to this predetermined estimate value. In one example, the user may enter a numerical value of the upper and lower limits, for example in units of response (RU) or target occupancy. For example, if the predetermined estimated value is a value of ^^_^^௫ of 14 RU, then the user input may set the upper limit as +2 RU relative to the estimated value and the lower limit as -2 RU relative to the estimated value. In that case, the fitting procedure will be constrained to fittings that result in values between ^^_^^௫ of 12 and 16 RU. In another example the user may enter a percentage value which determines the upper and lower limit relative to the predetermined estimated value of the analyte saturation parameter. For example, the user may set the upper limit at 150% of the estimated value of the analyte saturation parameter and may set the lower limit at 75% of the estimated value of the analyte saturation parameter. In the aforementioned example where the ‘default’ value of ^^_^^௫ is 14 RU, these percentage limits would thus constrain the fitting process to fittings that result in values between 10.5 and 22.5 RU. Another practical approach is to set the lower limit to the response value from the sample with the highest concentration of analyte. Once the upper and lower limits for the fitting process have been set, it will be appreciated that a variety of fitting algorithms may be used to fit the sensor response data to the interaction model. The fitting procedure typically involves use of an algorithm to iteratively “guess” values of ^^_^^௫ and ^^_^ and plotting a response curve using those guessed values and an interaction model, the details of which are outlined below. It can then be determined how well each set of guessed values fits to the actual recorded response data. The values of ^^_^^௫ which may be “guessed” are constrained by the aforementioned upper and lower limits. In one example, the fitting comprises applying a minimum chi-square estimation to the registered sensor response to determine the quality or closeness of fit to the response data, i.e. to determine how well each iteration of guessed values fits the response data. In one example, the predetermined interaction model used in the fitting procedure comprises the expression: where ^^_^^ is the registered sensor response at equilibrium, ^^ is the analyte concentration, ^^_^^௫ is the analyte saturation parameter, and ^^_^ is the dissociation equilibrium constant of the interaction. In this example, therefore, fitting the sensor response data to the interaction model involves algorithmically fitting the sensor response data (which provides values of ^^_^^ for corresponding values of ^^) to determine corresponding values of ^^_^^௫ and ^^_^. This involves the algorithm altering both ^^_^^௫ and ^^_^ iteratively, as noted above, to find the combination that gives the best fit as measured by a fitting parameter such as chi- square. As mentioned above, the fitting is constrained in that fitting does not involve values of ^^_^^௫ that are outside the defined upper and lower limits. Once the fitting is concluded, i.e. once a best fit within the constraints of the interaction model and upper and lower limits has been found, a best estimate of the interaction parameter ^^_^ will have been determined. From this ^^_^can also be calculated. The sensor system used to perform the disclosed methods may be a surface plasmon resonance (SPR) system. In that case, registering a sensor response indicative of binding of the analyte to binding sites of the ligand may be based on surface plasmon resonance. The sensor system used to perform the disclosed methods may be an evanescent wave sensing system. In that case, registering a sensor response indicative of binding of the analyte to binding sites of the ligand may be based on evanescent wave sensing. According to another aspect of the present disclosure, a sample analysis system for determining interaction parameters is disclosed. The system comprises a sensing surface configured to detect binding interactions between an analyte and a ligand at the sensing surface and a computing device configured to perform any of the methods disclosed herein. According to a further aspect of the present disclosure, a computer is disclosed, wherein the computer is configured to cause a sample analysis system to perform any of the methods disclosed herein. According to a yet further aspect of the present disclosure, a computer-readable storage medium is disclosed, wherein the computer-readable storage medium comprises instructions which, when executed by a computer, cause the computer to cause a sample analysis system to perform any of the methods disclosed herein. Brief Description of the Figures Illustrative implementations of the present disclosure will now be described, by way of example only, with reference to the drawings. In the drawings: Figure 1 shows a schematic illustration of a biosensor system based on SPR; Figure 2 shows a representative sensorgram showing detector response versus time for an interaction between molecules taking place at the sensor surface; Figure 3 shows values of equilibrium binding response against concentration for an analyte across a wide range of concentrations; Figure 4 shows a curve generated by fitting the data points of Figure 3 to an interaction model; Figure 5 shows values of equilibrium binding response against concentration for an analyte across a narrow range of concentrations; Figure 6 shows a curve generated by fitting the data points of Figure 5 to an interaction model; Figure 7 shows a method for determining a saturation response for an analyte, ^^_^^௫^, based on prior determination of a saturation response for a control analyte, ^^_^^௫^; Figure 8 shows a method for determining one or more interaction parameters associated with an interaction between an analyte and a ligand according to the present disclosure; Figure 9 shows a schematic illustration of a Biacore T200 from Cytiva, which is an example of a sample analysis system that can be used to implement the disclosed methods; and Figure 10 shows the components of an example computer apparatus that can be used to implement the methods described herein. Throughout the description and the drawings, like reference numerals refer to like features. Detailed description This detailed description describes, with reference to Figures 1 and 2, the fundamental principles of biosensors (also referred to as sample analysis systems) and their methods of operation. Drawbacks with existing methodologies for determining interaction parameters using such systems are illustrated with reference to Figures 3 to 7. An improved method for interaction parameter determination is described with reference to Figure 8. Finally, with reference to Figures 9 and 10, the components of an example sample analysis system and example computer apparatus that can be used to implement the methods described herein are described. The methods disclosed herein relate generally to determining one or more interaction parameters, such as the association ( ^^_^) or dissociation ( ^^_^) equilibrium constant, associated with an interaction between an analyte and a ligand. As noted above, a problem with traditional approaches for determining such parameters arises because traditional methods are only reliable when data is available for a wide range of analyte concentrations. More specifically, such methods rely on having response data for an analyte concentration range which covers (and preferably exceeds) the analyte dissociation equilibrium constant ^^_^. Where only a reduced range of data is available (as may happen in a variety of cases where high concentrations of analyte cannot be obtained or reliably studied), then these existing methods fall short because the fitting procedure results in unrealistic and inaccurate estimates for the interaction parameters. One proposed solution to this shortcoming has been to make use of a control analyte. Such an approach is described in European Patent No. 2507618 in the name of GE Healthcare Bio-Sciences AB, the contents of which is hereby incorporated by reference in its entirety. In this approach, steady state binding analysis is first performed for a control analyte to obtain the saturation response for a control analyte, denoted ^^_^^௫^. This control parameter can then be used to estimate the corresponding parameter for the analyte of interest (denoted ^^_^^௫^). Once ^^_^^௫^ has been estimated, this value is then used as a fixed value in the interaction model to enable the interaction parameters of interest (e.g. ^^_^, ^^_^) for the analyte in question to be determined. This approach provides an improvement over previous methodologies which simply relied on free-fitting of the response data to the interaction model with no further constraints or limitations on the analyte saturation parameter. However, the improved method of EP2507618 is itself not without problems. Firstly, this approach requires a control analyte to be found which is not always straightforward. The control analyte needs to be similar to the analyte of interest in terms of its binding characteristics for the extrapolation of ^^_^^௫^ from ^^_^^௫^ to be valid. Finding such a suitable control analyte may take a great deal of experimental work because suitable control analyte candidates must be identified and tested. Often, control analyte candidates exhibit poor performance and are not as effective as anticipated from theory, meaning that frequently a large number of candidates must be tested. In practice, finding a suitable control analyte can take several weeks or months even in sophisticated laboratory settings. This places a significant barrier on performing high volumes of assays because many assays must be preceded by an investigation to find a suitable control analyte. In some cases, no suitable control analyte is available. Even where a suitable control analyte can be found, the present inventors have identified that the conversion of ^^_^^௫^ to ^^_^^௫^ is not always particularly successful because it relies on many assumptions regarding the similarity of the control analyte to the analyte of interest. In practice, these assumptions may not hold as firmly as in theory, meaning that the accuracy of subsequently determined interaction parameters (e.g. ^^_^, ^^_^) is not always particularly high when using this method. The presently disclosed invention seeks to address the above-described shortcomings. In particular, the present inventors have identified that another possibility exists for determining interaction parameters for interactions. The present inventors consider that, surprisingly, more accurate estimates of the interaction parameters can be obtained if the fitting of response data to the interaction model is constrained by an interval (i.e. an upper and lower limit) applied to an analyte saturation parameter (e.g. ^^_^^௫) associated with the interaction model. The present inventors have identified that this method effectively acts as an intermediate position between the traditional approach (free-fitting of data to the interaction model without constraints on the analyte saturation parameter) and the approach of EP2507618 which constrains the fitting with a fixed analyte saturation parameter determined using a control analyte. Advantageously, the disclosed methodology is believed to retain the benefit of the method of EP2507618, namely that it is capable of providing accurate estimates of interaction parameters even when response data is only available for a limited range of analyte concentrations. Importantly, however, the disclosed methodology is not reliant on use of a control parameter, in contrast to the EP2507618 method. Most importantly, by striking a balance between the prior approaches and performing a fitting procedure that is constrained by an interval (i.e. upper and lower limit) rather than a fixed value, the present inventors believe that more accurate estimates of interaction parameters can be obtained than is possible using either of the previously described methodologies. In order to aid understanding, each of the above-described approaches will each now be described in more detail. Firstly, the principles of the underlying sensor technology for interaction analysis will be described. Following this, the traditional free-fitting approach of fitting response data to an interaction model without constraints on the analyte saturation parameter will be outlined. Then, the alternative approach of EP2507618, which uses a fixed value for the saturation response ^^_^^௫, will be explained. Finally, the novel approach of the present disclosure, which improves on both of the previous methods, will be outlined and contrasted to the prior approaches. Background – underlying sensor technology As mentioned above, the present disclosure relates to the evaluation of binding response data obtained for an analyte at a plurality of concentrations, typically at equilibrium (steady state). From this, one or more interaction parameters for the interaction may be determined. Typically, the experimental binding data is obtained by sensor-based technology, which studies the molecular interaction and presents the results in real time as the interactions progress. To aid understanding, some brief background concerning such sensor-based technology will now be provided. Chemical sensors or biosensors (also referred to as “sample analysis systems” herein) are typically based on label-free techniques, detecting a change in a property of a sensor surface, such as e.g. mass, refractive index, or thickness for the immobilised layer, but there are also sensors relying on some kind of labelling. Typical sensor detection techniques include, but are not limited to, mass detection methods, such as optical, thermo-optical and piezoelectric or acoustic wave methods (including e.g. surface acoustic wave (SAW) and quartz crystal microbalance (QCM) methods), and electrochemical methods, such as potentiometric, conductometric, amperometric and capacitance/impedance methods. With regard to optical detection methods, representative methods include those that detect mass surface concentration, such as reflection-optical methods, including both external and internal reflection methods, which are angle, wavelength, polarization, or phase resolved, for example evanescent wave ellipsometry and evanescent wave spectroscopy (EWS, or Internal Reflection Spectroscopy), both of which may include evanescent field enhancement via surface plasmon resonance (SPR), Brewster angle refractometry, critical angle refractometry, frustrated total reflection (FTR), scattered total internal reflection (STIR) (which may include scatter enhancing labels), optical wave guide sensors; external reflection imaging, evanescent wave-based imaging such as critical angle resolved imaging, Brewster angle resolved imaging, SPR-angle resolved imaging, and the like. Further, photometric and imaging/microscopy methods, “per se” or combined with reflection methods, based on for example surface enhanced Raman spectroscopy (SERS), surface enhanced resonance Raman spectroscopy (SERRS), evanescent wave fluorescence (TIRF) and phosphorescence may be mentioned, as well as waveguide interferometers, waveguide leaky mode spectroscopy, reflective interference spectroscopy (RIfS), transmission interferometry, holographic spectroscopy, and atomic force microscopy (AFR). Commercially available biosensors include the afore-mentioned BIACORE® system instruments, manufactured and marketed by Cytiva, Uppsala, Sweden, which are based on surface plasmon resonance (SPR) and permit monitoring of surface binding interactions in real time between a bound ligand and an analyte of interest. In this context, a “ligand” is a molecule that has a known or unknown affinity for a given analyte and includes any capturing or catching agent immobilized on the sensor surface, whereas “analyte” includes any specific binding partner thereto that is typically injected and flows over or past the ligand on the sensor surface. While in the detailed description that follows the present invention is illustrated in the context of SPR spectroscopy, and more particularly the BIACORE® system, it is to be understood that the present invention is not limited to this detection method. Rather, any affinity-based detection method where an analyte binds to a ligand immobilised on a sensing surface may be employed, provided that a change at the sensing surface can be measured which is quantitatively indicative of binding of the analyte to the immobilised ligand thereon. The phenomenon of SPR is well known, suffice it to say that SPR arises when light is reflected under certain conditions at the interface between two media of different refractive indices, and the interface is coated by a metal film, typically silver or gold. In the BIACORE® instruments, the media are the sample and the glass of a sensor chip, which is contacted with the sample by a microfluidic flow system. The metal film is a thin layer of gold on the chip surface. SPR causes a reduction in the intensity of the reflected light at a specific angle of reflection. This angle of minimum reflected light intensity varies with the refractive index close to the surface on the side opposite from the reflected light, in the BIACORE® system the sample side. A schematic illustration of the BIACORE® system is shown in Fig.1. Sensor chip 101 has a gold film 102 supporting capturing molecules (ligands) 103, e.g. antibodies, exposed to a sample flow with analytes 104, e.g. an antigen, through a flow channel 105. Monochromatic p-polarised light 106 from a light source 107 (e.g. LED) is coupled by a prism 108 to the glass/metal interface 109 where the light is totally reflected. The intensity of the reflected light beam 110 is detected by an optical detection unit 111 (e.g. photodetector array). A detailed discussion of the technical aspects of the BIACORE® instruments and the phenomenon of SPR may be found in U.S. Patent No. 5,313,264. More detailed information on matrix coatings for biosensor sensing surfaces is given in, for example, U.S. Patent Nos. 5,242,828 and 5,436,161. In addition, a detailed discussion of the technical aspects of the biosensor chips used in connection with the BIACORE® instruments may be found in U.S. Patent No. 5,492,840. The above publications as well as any other publications, patent applications, patents, or other references mentioned in this disclosure are incorporated by reference in their entirety. When molecules (analyte) in the sample bind to the capturing molecules (ligand) on the sensor chip surface, the concentration, and therefore the refractive index, at the surface changes and an SPR response is detected. Plotting the response against time during the course of an interaction will provide a quantitative measure of the progress of the interaction. Such a plot, or kinetic or binding curve (binding isotherm), is usually called a sensorgram, also sometimes referred to in the art as an “affinity trace” or “affinogram”. In the BIACORE® system, the SPR response values are expressed in resonance units (RU). One RU represents a change of 0.0001 ^ in the angle of minimum reflected light intensity, which for most proteins and other biomolecules corresponds to a change in concentration of about 1 pg/mm² on the sensor surface. As sample containing an analyte contacts the sensor surface, the capturing molecule (ligand) bound to the sensor surface interacts with the analyte in a step referred to as “association”. This step is indicated on the sensorgram by an increase in response (RU) as the sample is initially brought into contact with the sensor surface. Conversely, “dissociation” normally occurs when the sample flow is replaced by, for example, a buffer flow. This step is typically indicated on the sensorgram by a drop in response (RU) over time as analyte dissociates from the surface bound ligand. A representative sensorgram (binding curve) for a reversible interaction at the sensor chip surface is presented in Fig.2. The sensorgram is representative of an interaction involving an immobilised capturing molecule (ligand), for example an antibody, interacting with a binding partner (analyte) in a sample. The binding curves produced by biosensor systems based on other detection principles mentioned above will have a similar appearance. The vertical axis (y-axis) indicates the response (here in resonance units, RU) and the horizontal axis (x-axis) indicates the time (here in seconds). Initially, buffer is passed over the sensing surface giving the baseline response K in the sensorgram. During sample injection, an increase in signal is observed due to binding of the analyte to the ligand. This part L of the binding curve is usually referred to as the “association phase”. Eventually, a steady state condition is reached at or near the end of the association phase where the resonance signal plateaus at M (this state may, however, not always be achieved). It is to be noted that herein the term “steady state” is used synonymously with the term “equilibrium” (in other contexts the term “equilibrium” may be reserved to describe the ideal interaction model, since in practice binding could be constant over time even if a system is not in equilibrium). At the end of sample injection, the sample is replaced with a continuous flow of buffer and a decrease in signal reflects the dissociation, or release, of analyte from the surface. This part N of the binding curve is usually referred to as the “dissociation phase”. The analysis is optionally ended by a regeneration step where a solution capable of removing bound analyte from the surface, while (ideally) maintaining the activity of the ligand, is injected over the sensor surface if the time- length to complete dissociation in buffer becomes unpractical. This is indicated in part O of the sensorgram. Injection of buffer restores the baseline K and the surface is now ready for a new analysis. From the profiles of the association and dissociation phases L and N, respectively, information regarding the binding and dissociation kinetics is obtained. The height of the resonance signal at M represents affinity (the response resulting from an interaction being related to the change in mass concentration on the surface). This will now be explained in more detail below in the context of the various afore-mentioned approaches for determining interaction parameters of an analyte-ligand interaction at the sensor surface. Interaction parameter determination – background In order to aid understanding, some background derivation of the interaction models which underpin the methods of the present disclosure will first be set out. First, we assume a reversible reaction between an analyte A and a surface-bound (immobilised) capturing molecule, or ligand, B which is not diffusion or mass transfer limited and obeys pseudo first order kinetics: A + B ^ AB This interaction model (usually referred to as the Langmuir model) assumes that the analyte (A) is both monovalent and homogenous, that the ligand (B) is homogenous, and that all binding events are independent. It has been established that these assumptions are in fact applicable in the vast majority of cases such that this is a valid assumption in both the free-fitting methodology and the approach of the present disclosure. The rate of change in surface concentration of analyte A (which equals the rate of change in concentration of formed complex AB) during analyte injection is the sum of the rates of the analyte A associating and dissociating: where ^ ^^^ is the concentration of analyte A, ^ ^^^ is the concentration of the ligand B, ^ ^^ ^^^ is the concentration of the reaction complex AB, ^^_^ is the association rate constant, and ^^_ௗ is the dissociation rate constant. After a time ^^, the concentration of unbound ligand B at the surface is ^ ^^ ^^^-^ ^^ ^^^, where ^ ^^ ^^^ is the total, or maximum, concentration of ligand B. Insertion into Equation (1) gives: In terms of detector response units ( ^^ ^^ is detected), this can be expressed as: dR ^k_aC(R _max ^R ) ^k R dt _d where ^^ is the response at time ^^ in resonance units (RU), ^^ is the initial, or bulk, concentration of free analyte (A) in solution, and ^^_^^௫ is the response (in RU) obtained if analyte (A) had bound to all ligand (B) on the surface, also referred to as the saturation response. Rearrangement of Equation (3) gives: where ^^ is the response in resonance units (RU). In integrated form, the equation is: Now, according to equation (4), if ^^ ^^/ ^^ ^^ is plotted against the bound analyte concentration ^^, the slope is – ^ ^^_^ ^^ ^ and the vertical intercept is ^^_^ ^^ ^^_^^௫. If the bulk concentration ^^ is known and the saturation response ^^_^^௫ has been determined (e.g. by saturating the surface with a large excess of analyte), the association rate constant ^^_^ and the dissociation rate constant ^^_ௗ can be calculated. A more convenient method is, however, fitting of the integrated function (5), or numerical calculation and fitting of the differential Equation (4), preferably by means of a computer program. This provides an alternative way to determine ^^_^^௫ if saturating the surface with a large excess of analyte is not feasible. ^^_ௗ may also be determined in the following way. The rate of dissociation can be expressed as: and in integrated form: R^{^ R ^k t} 0 ^{^e} ₍₇₎ where ^^_^ is the response at the beginning of the dissociation phase (when the buffer wash of the surface starts). Equation (6) may be linearized: and a plot of ^^ ^^^ ^^/ ^^_^^ versus ^^ will produce a straight line with the slope = െ ^^_ௗ. More conveniently, however, the dissociation rate constant ^^_ௗ is determined by fitting the exponential rate equation (7). To obtain reliable kinetic constants, the above-described analysis is usually repeated for a number of different analyte concentrations and, suitably, also at least one other ligand density at the sensor surface. Affinity is expressed by the association equilibrium constant ^^_^ ൌ ^^_^/ ^^_ௗ, or the dissociation equilibrium constant (also referred to as simply the equilibrium constant) ^^_^ ൌ ^^_ௗ/ ^^_^. The association constant ^^_^ may alternatively be determined from Equation (3), where ^^ ^^/ ^^ ^^ ൌ 0 at equilibrium, giving: where ^^_^^ is the detector response at equilibrium. Since ^^_^/ ^^_ௗ ൌ ^^_^, insertion in Equation (9) and rearrangement gives: If binding reactions are performed at multiple concentrations, ^^_^ (and by extension ^^_^) may be obtained by non-linear curve-fitting of the data. Alternatively, e.g. when the kinetic data is unreliable or association and dissociation are too rapid to measure accurately, ^^_^^/ ^^ may be plotted versus ^^_^^, which gives the slope ൌ െ ^^_^ (Scatchard plot). Rearrangement of Equation (10) gives: (11) Insertion of ^^_^ ൌ 1/ ^^_^ into Equation (11) gives: Usually, Equation (12) is modified to: Offset (13) where “Offset” is a compensation factor for parallel baseline displacement due to systemic refractive index errors. The offset parameter means that the response signal ^^_^^ need not necessarily equal zero when the concentration, ^^, is zero. This enables the shape of the response curve to be better preserved in cases where the curve of best fit would not naturally pass through zero due to baseline displacement factors. If such factors are minimal and do not need to be accounted for, then the offset term can be zero. Equations (11) and (12) may be modified by introducing a steric interference factor ^^ specifying how many binding sites are on average blocked by one analyte molecule: The response data may be normalised prior to further analysis in order to enhance visualization of low response data. Free-fitting using software-assisted analysis As mentioned above, one traditional approach for determining interaction parameters relies on recording a sensor response for a variety of analyte concentrations and then fitting this response data to a predetermined interaction model, such as one of the models just described, without any further constraints on the parameters. Within the context of this disclosure, this approach is known as a “free-fitting” approach in that no constraints are applied to the analyte saturation parameter ( ^^_^^௫ or ^^ ^^_^^௧) during the fitting. Rather, the goal is simply to find the best fit between the sensor response data and the interaction model and to directly read off the yielded value of the analyte saturation parameter generated by that fit. Accordingly, from this fitting, various parameters such as the saturation response ^^_^^௫ and interaction parameters ^^_^ and ^^_^, can be determined. Because the improved methodology of the present disclosure builds on this prior free-fitting method, the free-fitting method will now be described in more detail. Software for the analysis of kinetic and affinity data is commercially available. Thus, for example, evaluation of kinetic and affinity data produced by the BIACORE ^ instruments is usually performed with the dedicated BIACORE Insight Evaluation® software (supplied by Cytiva, Uppsala, Sweden) using numerical integration to calculate the differential rate equations and non-linear regression to fit the kinetic and affinity parameters by finding values for the parameters that give the closest fit, reducing the sum of squared residuals to a minimum. The free-fitting approach in one example therefore involves determining affinity constants from measured steady state binding levels with the BIACORE Insight Evaluation® software, via the following steps: (i) obtain steady state binding levels ( ^^_^^) from report points on the sensorgrams in the steady state region of the curve (typically region M in Fig. 2, when the sensorgram response is substantially parallel to the x-axis) for a variety of analyte concentrations; (ii) create a plot of ^^_^^ against ^^; and (iii) fit this plot to an interaction model, such as a general “Steady state affinity” fitting model (e.g. Equation 13 or 14) to obtain ^^_^/ ^^_^ and ^^_^^௫. Step (iii) in particular represents the “free-fitting” approach in that the sensor response data is fitted to an interaction model (in this case Equation 13 or 14) without any constraints on the analyte saturation parameter. An example of this free-fitting procedure is shown in relation to Figures 3 and 4. Figure 3 shows an example sensor response, with data points plotted for the response at equilibrium for an analyte at a variety of concentrations ( ^^^. In this example, the binding behaviour of the analyte is stable over a wide range of concentrations, and so data is available for concentrations spanning from around 10 ^^ ^^ to 10 ^^ ^^. Figure 4 shows a curve resulting from fitting the data points of Figure 3 to an interaction model, in this example Equation 13 above. The inflection point of the curve provides a value of ^^_^, which in this example equals around 0.5 ^^ ^^ as indicated by the vertical dashed line. The asymptote of the of the fitted curve provides ^^_^^௫, i.e. the maximal response value obtainable for this analyte. In the example shown, ^^_^^௫ can be seen to be approximately 55 RU as indicated by the horizontal dashed line. Because data is available for a wide range of analyte concentrations in this example, the fitting shown in Figure 4 is reliable and the values of ^^_^ and ^^_^^௫ determined from the fitting are accurate and reproducible. However, it is not always possible to obtain data for such a wide range of analyte concentrations. In particular, the binding behaviour of many analytes becomes unstable at higher concentrations due to solubility issues. For example, some analytes will aggregate or precipitate at concentrations approaching ^^_^. In such cases, only limited response data, at low analyte concentrations, can be obtained. An example of response data for such an analyte is shown in Figure 5. To aid comparison, Figure 5 simply shows the first five data points of the plot of Figure 3. Such a set of data points is representative however of an analyte which exhibits solubility issues at higher concentrations. Figure 6 shows a curve resulting from fitting the data points of Figure 5 to the same interaction model as was used above for Figure 4, i.e. the model exemplified by Equation 13. As can be seen, the values of ^^_^ and ^^_^^௫ which are determined from this fitting are very different to those obtained from Figure 4, where more data points were available. Now, ^^_^ is determined to be only around 0.1 ^^ ^^ (c.f. 0.5 ^^ ^^ from Figure 4) and ^^_^^௫ can be seen to be around 22.5 RU (c.f.55 RU from Figure 4). In other words, the traditional approach of fitting the response data to the interaction model with no additional limitations or constrains on the analyte saturation parameter ( ^^_^^௫ in this case) significantly underestimates ^^_^ and ^^_^^௫ in this example. In many cases the reverse is true and the fitting overestimates ^^_^ and/or ^^_^^௫ when fitting from limited data. In either case, the resulting values of ^^_^, ^^_^^௫ and any additionally derived interaction parameters such as ^^_^ are inaccurate and difficult to replicate. As can be seen, therefore, this traditional free-fitting approach is unreliable when only limited data is available, in particular when the affinity of an analyte is low and data is only available for concentrations below ^^_^. This is problematic because many useful applications and assays, such as fragment-based drug design and fragment affinity analysis, involve analytes with low affinities where high analyte concentrations are unlikely to be stable. Additionally, even if it is theoretically possible to obtain data at sufficiently high concentrations, this may result in very costly assays due to the amount of analyte required at higher concentrations. This high cost may mean that the experiment is not practically feasible at large volumes and throughput. Use of a fixed analyte saturation parameter value As noted above, one approach which has been suggested to address this problem with the free-fitting approach is to reduce the number of variables in the fitting procedure by estimating a fixed value for the analyte saturation response, ^^_^^௫, and using that fixed value during the fitting procedure. In other words, rather than a free-fitting procedure, the fitting is constrained by setting one of the key parameters to a fixed value. This approach, which is exemplified in EP2507618, relies on use of a control analyte to first determine a control analyte saturation parameter, ^^_୫ୟ^^. This control parameter, ^^_୫ୟ^^, can then be converted to a corresponding value of ^^_^^௫^ for the analyte of interest, and ^^_^^௫^ can be used as the fixed value during the fitting. This approach will now be briefly described. An approach 700 for determining a fixed value for the saturation control parameter is set out schematically in Figure 7. At block 702, a sensor surface having a ligand immobilized thereto is provided. This may be considered a setup or configuration step which may be performed manually or automatically. The following steps (i.e. blocks 704-716) then characterise a self-contained method which may be computer- implemented and may be performed in an automated manner by a sample analysis system. At block 704, the sensor surface is contacted with a control analyte. At block 706, the sensor response from binding of the control analyte to binding sites of the ligand is registered. At block 708, the control saturation response ^ ^^_^^௫^^ for the interaction between the control analyte and the ligand is determined. At block 710, the control saturation response ( ^^_^^௫^) is transformed into an analyte saturation response ( ^^_^^௫^) for the analyte, using the relative molar response contribution of the analyte and the control analyte. At block 712, the sensor surface is contacted with one or more samples containing different concentrations of the analyte of interest. At block 714, the sensor response from binding of the analyte to the binding sites is registered. Finally, at block 716 the registered sensor response is fitted to a predetermined interaction model (e.g. Equation 13 above) using the fixed value of the analyte saturation response ( ^^_^^௫^) to determine the interaction parameters. Block 702 of providing a sensor surface having the ligand immobilized thereto involves any suitable ways of immobilizing the ligand to a sensor surface in the particular biosensor used. The immobilized ligand provides binding sites for the control analyte and the analytes to be investigated. In block 704, a suitable control analyte is put in contact with the sensor surface. The control analyte should preferably be selected so that the control saturation response ( ^^_^^௫^) for the interaction between the control analyte and the ligand can be readily determined, at block 708. For example, the control analyte should have a higher solubility, with respect to the affinity ^^_^, compared to the analyte(s) of interest which are being investigated. In one suitable example, the control analyte is provided at a concentration such that it is capable of occupying all binding sites of the ligand on the sensor surface to provide a direct determination of the control saturation response ( ^^_^^௫^) from one interaction event. Alternatively, the control analyte is provided at a concentration range such that it is possible to determine the control saturation response ( ^^_^^௫^) from a non-steady-state interaction between the control analyte and the ligand. In block 710 of transforming the control saturation response ( ^^_^^௫^) to an analyte saturation response ( ^^_^^௫^), the fact that the saturation response ( ^^_^^௫) for each analyte represents the response when all binding sites are occupied is used for the transformation. By using the same sensor surface for determining the saturation response ( ^^_^^௫) for two different analytes, e.g. analytes S and T respectively, ideally the saturation responses ( ^^_^^௫ௌ) and ( ^^_^^௫்) respectively represents the response resulting from the same number of molecules bound to the sensor surface. Hence, the saturation responses ( ^^_^^௫ௌ) and ( ^^_^^௫்) registered using the same sensor surface gives the relative molar response contribution for the two analytes. Therefore, taken that the relative molar response contribution for two analytes is known or can be estimated, then the saturation response ( ^^_^^௫) for one analyte may be calculated (estimated) from the saturation response ( ^^_^^௫) of the other analyte. This relationship is used to transform the control saturation response ( ^^_^^௫^) to an analyte saturation response ( ^^_^^௫^). As mentioned above, there are a number of biosensors available based on a number of different detection techniques, therefore the relative molar response of two different analytes depends on the biosensor used, but the principle is still valid. In one example, the relative molar response contribution of the analyte and the control analyte in block 710 is approximated by the molar weight ratio between the analyte and the control analyte. This approach is valid, or at least a good approximation, for any biosensor technique that directly or indirectly registers the mass of the molecules bond to the sensor surface. In mathematical terms, this approach is characterised by Equation 16: where ^^ ^^_^ is the molar weight of the control analyte and ^^ ^^_^ is the molar weight of the analyte of interest. In one example, the dissociation rate of the control analyte is sufficiently high to reach complete dissociation within a reasonable timeframe after replacing the control analyte with a sample free from analyte capable of binding to the sensor surface, e.g. buffer. Alternatively, a step of regeneration may be necessary to free all binding sites in between the analytes. In some examples, block 710 to block 716 are repeated for a plurality of analytes in order to determine one or more interaction parameters for each of the plurality of analytes based on a saturation response ( ^^_^^௫^) calculated for each analyte, indicated by ref 718 in Figure 7. In order to detect and/or correct for possible degeneration of the sensor surface over time, steps 704-708 may be repeated after steps 710-716 have been performed for a predetermined number of analytes, indicated by ref 720 in Figure 7. The approach 700 of Figure 7 provides an improvement over the traditional free-fitting method. Nevertheless, as noted above, the present inventors have identified that this approach is still far from perfect. One drawback of this approach is that it is entirely reliant on a control analyte being found which can act as a good stand-in for the analyte of interest. Finding a good control analyte is often not possible or at least takes a lot of experimental work. Further, even when a good control analyte can be found, the present inventors have identified that the estimated interaction parameters (e.g. ^^_^, ^^_^) determined through this method are in fact not always entirely reliable. The present inventors have recognised that this inaccuracy results from the method of Figure 7 being too heavily reliant on the determined fixed parameter, i.e. the fixed value of ^^_^^௫^ used in the fitting procedure of block 716. ^^_^^௫^ is directly obtained based on ^^_^^௫^ and so this approach is very reliant on the correspondence between the analyte and the control analyte holding, as well as the accuracy and precision of the experiment conducted to determine ^^_^^௫^ (i.e. blocks 702-708 of Figure 7). If there is inaccuracy in either of these aspects, i.e. in relation to the correspondence (or lack thereof) between the analyte and control analyte and/or in the accuracy and reliability of the experiment to determine ^^_^^௫^, then this will feed directly into the determination of ^^_^^௫^ and make the subsequent determination of interaction parameters like ^^_^ and ^^_^ inaccurate. In view of these problems, neither the free-fitting method nor the more tightly controlled method of Figure 7 achieves satisfactorily accurate measurements in all cases. A new approach, which is believed to improve the reliability of the interaction parameter estimation and which is not reliant on a control analyte, has been identified by the present inventors. The details of this approach will now be described. New approach: fitting with upper and lower limits The present inventors have identified that the interaction parameters can likely be more accurately determined if the fitting process is constrained by an interval, i.e. an upper and lower limit or boundary applied to an analyte saturation parameter being used in the fitting. This approach effectively represents an intermediate approach between the free-fitting approach (which has no constraints on the analyte saturation parameter) and the method of Figure 7 (which is tightly constrained by a fixed value for the analyte saturation parameter, ^^_^^௫^). The present inventors believe that, surprisingly, having a “looser” constraint on the fitting procedure compared to the approach of Figure 7 provides more accurate estimations of the interaction parameters. This is because, as the present inventors have identified, the fitting algorithm is able to more effectively strike a balance between fitting to the actual response data and taking account of a known or estimated approximate value of the analyte saturation parameter. The present approach is able to balance these competing requirements in a manner which is not possible using either the free fitting approach or the approach of Figure 7. The present inventors have also identified that, advantageously, the disclosed approach is generalisable and can be used both where the analyte saturation parameter is the analyte saturation response ( ^^_^^௫) and also where the analyte saturation parameter is expressed in terms of the target occupancy at saturation ( ^^ ^^_^^௧). This increases the versatility of the method and enables it to be applied regardless of whether the results of an experimental assay and associated interaction model are expressed in terms of saturation response or target occupancy. Further, the disclosed approach is not reliant on use of a control analyte (c.f. Figure 7), because a theoretical value for the analyte saturation parameter can be used instead when a control analyte is not readily available. The disclosed novel methodology is set out schematically in Figure 8, which describes a method 800 for determining one or more interaction parameters associated with an interaction between an analyte and a ligand. At block 802, a sensor surface having a ligand immobilized thereto is provided. This may be considered a setup or configuration step which may be performed manually or automatically. The following steps (i.e. blocks 804-808) then characterise a self-contained method which may be computer-implemented and may be performed in an automated manner by a sample analysis system. At block 804, the sensor surface is contacted with one or more samples containing an analyte. If only a single sample is used, it is preferable that the concentration of the sample is equal to at least twice ^^_^ of the analyte, so as to make an effective fitting procedure possible. This is possible for most interactions with high affinity (low ^^_^) because in that case twice ^^_^ is still a manageably low concentration from a solubility perspective. That said, preferably block 804 involves contacting the sensor surface with three or more samples of analyte, each sample having a different analyte concentration. This is beneficial in terms of improving reliability and because it is possible to more effectively study interactions with low affinity (high ^^_^) where it is difficult or impossible to achieve analyte concentrations approaching (let alone twice as much as) ^^_^. In the example where three or more samples of analyte are provided, block 804 involves at least three concentrations of the analyte (provided in three or more samples) being brought into contact with the sensor surface to generate concentration series data. The present inventors have identified that using between 5 and 11 concentrations (provided in between 5 and 11 samples) is advantageous in terms of balancing the need to generate useful data with practical considerations and cost. At block 806, a sensor response indicative of binding of the analyte to binding sites of the ligand is registered. In other words, a sensor response is recorded for each analyte concentration. Typically, the recorded response is the maximal response, i.e. the equilibrium (steady state) response, for each sample that has contacted the sensor, which can be obtained (read off) when the sensorgram response for that concentration is substantially parallel to the x-axis. The considerations and implementation details discussed above in the general discussion of sensors and analyte-ligand interactions, as well as the related comments pertaining to blocks 702 to 706 of the method 800 of Figure 7, apply equally to blocks 802 to 806 of Figure 8. At block 808, the registered sensor response is fitted to an interaction model (e.g. Equation 13 above) in order to determine one or more interaction parameters associated with the interaction between the analyte and the ligand. According to the presently disclosed invention, the fitting is constrained by a pre-determined upper and lower limit applied to an analyte saturation parameter associated with the interaction model. As noted above, this is believed to provide improved accuracy when determining interaction parameters such as ^^_^ and ^^_^. The fitting procedure of block 808 is similar to that of block 716, and the same considerations apply, except in that the fitting of block 808 is constrained by an upper and lower limit on an analyte saturation parameter, such as ^^_^^௫ or ^^ ^^_^^௧ and does not use a fixed value. It will be appreciated that the method may comprise an additional step of receiving said upper and lower limit, for example as a user input. This step may occur at any point in the process of Figure 8. In one implementation, the fitting procedure of block 808 involves applying a best fit estimation, for example a minimum chi-square estimation, to the registered sensor response within the constraints set by the interaction model and the upper and lower limit. For example, in the case where the interaction model is represented by equation 12 or 13 above, then the response data represents the equilibrium responses at each analyte concentration, and the fitting procedure seeks a curve of best fit to the response data. In other words, response data showing response at equilibrium (on the y-axis) versus concentration (on the x-axis) can be plotted and fitted to equation 12 or 13 above. In further detail, values of ^^_^^௫ and ^^_^ can be iteratively “guessed”, and each set of guessed values can be fitted to the interaction model expressed in the aforementioned equations. In view of the upper and lower limits that have been set on the analyte saturation parameter (in this case ^^_^^௫), the fitting procedure is only permitted to consider fittings which test values of ^^_^^௫ that are within the upper and lower limits that have been set. The quality (or “closeness”) of the fit of each set of guessed values can then be determined, for example using a chi-square estimation as noted. The best fitting values can then be determined to be the best estimate of the interaction parameters in question. As noted above, the methods of the present disclosure are not limited to interaction models based on ^^_^^௫. In some cases, the analyte saturation response can instead be expressed as a target occupancy at saturation, ^^ ^^_^^௧. As noted previously, ^^ ^^_^^௧ is the target occupancy when ^^_^ ൌ ^^_^^௫, and ^^_^^௫ and ^^ ^^_^ are related by: ^^ ^^ ^ோಲ ^ ൌ _{ோ^^౮ _^^^^} (17) Similarly, the interaction model to which the data can be fitted can also be expressed in terms of target occupancy as: When this interaction model is used, response data showing target occupancy (on the y-axis) versus concentration (on the x-axis) can be plotted and fitted in accordance with the method of the present disclosure based on equation 18 and an upper and lower limit applied to ^^ ^^_^^௧. As explained briefly above, the upper and lower limit which constrain the fitting may be set in a variety of ways. In one example, the system receives a user input indicative of the upper and lower limit. The user input may take a variety of forms. In one implementation, the interaction model used for the fittings may be based on ^^_^^௫ and the biosensor system may be configured to record response values in RU for different concentrations of analyte. The user may then set the upper and lower limit as point (e.g. integer) values in units of RU. For example, the user may know from past experience that ^^_^^௫ of the analyte of interest is likely to be around 20 RU. The user may thus set the upper limit to a point value of 25 RU and the lower limit to a point value of 15 RU, for example. The same applies if the system is configured in terms of target occupancy, in that the user may enter an upper and lower limit in terms of target occupancy, for example 110% (or 1.1 in decimal terms) for the upper limit and 90% (or 0.9 in decimal terms) for the lower limit. Alternatively, the system may assist the user in setting the upper and lower limits by providing an initial default value of the analyte saturation parameter. In this case, the user input determines how far from the default parameter value the fitting process is allowed to diverge. In other words, the user specifies a value that is lower than the default parameter (i.e. the lower limit) and a value that is higher than the default parameter (i.e. the upper limit) and these values then constrain the fitting in the manner described above. The upper and lower limits may be defined in terms of a unit value (e.g. +/- a certain number of RU units) or in percentage terms. For example, consider the case where the system is configured to operate in terms of ^^_^^௫ and the pre-set default value for ^^_^^௫ is 20 RU. The user input can then indicate the upper and lower limit relative to this default value. For example, the user may set the upper limit as +2 RU and the lower limit as -2 RU. In this example, the fitting process is then constrained to fittings where ^^_^^௫ is between 22 and 18 RU. Alternatively, the input may be provided in percentage terms. For example, the user may set the upper limit as 120% and the lower limit as 80%. In this example, the fitting process is then constrained to ^^_^^௫ values between 24 and 16 RU, these values respectively representing 120% and 80% of the default value of 20RU. A similar approach can be applied when the system operates in terms of target occupancy. In implementations where a default analyte saturation parameter is used as the starting point around which the upper and lower limits are set, a variety of mechanisms for determining said default value can be utilised. Two primary means for determining the default parameter value are available: theoretical estimation and experimental estimation. Either approach can be used to determine the default starting point for the analyte saturation parameter and both approaches are suited to different situations, as will now be explained. A first mechanism for determining the default value of the analyte saturation parameter is to determine a theoretical estimated value. This can be done based on the molecular weights of the analyte and ligand as well as the immobilisation level of the ligand. In particular, in one example a theoretical estimate of ^^_^^௫ can be calculated based on: ^^ ^{ோ^^^ ெ௪ೌ^ೌ} ୫_{ୟ^_௧^^^} ൌ _ெ௪^^^ (19) where ^^ ^^_^^^ is the molecular weight of the ligand, ^^ ^^_^^^ is the molecular weight of the analyte and ^^_^^^ is the immobilisation level, also referred to as the ligand response. The theoretically estimated analyte saturation parameter, i.e. ^^_{୫ୟ^ _௧^^^} is then used as the default value around which the upper and lower limit are set, in the manner described above. A benefit of determining the default or starting value of the analyte saturation parameter theoretically in this way is that there is no requirement for a control analyte to be used. Only the molecular weight of the ligand and analyte as well as the immobilisation level need to be determined. ^^_{୫ୟ^ _௧^^^} can also be expressed in terms of target occupancy as described above. A second mechanism for determining the default value of the analyte saturation parameter is to determine an estimated value experimentally, using a control analyte. In this case, ^^_^^௫ is determined first for a control analyte. The control analyte value is then transformed into a corresponding value for the analyte of interest. The details of how this procedure can be performed are explained above in relation to Figure 7. The determined ^^_୫ୟ^^ value can also be expressed in terms of target occupancy as described above (e.g. as ^^ ^^_^^௧^). Once ^^_^^௫^ or ^^ ^^_^^௧^ has been determined, this value is then used as the default analyte saturation parameter value around which the upper and lower limit are set. In various implementations, embodiments of the present invention may provide a technique that enables use of a model using constrained limits (e.g. with a constrained R_max) instead of one or more models that use free fitted and/or constant parameters (e.g. R_max). However, other alternatives may provide for a possible workflow in which if model control is of low quality or theoretical parameters (e.g. R_max) have to be used, then a wide range for such parameters may be set (e.g. for R_max). For samples that do not provide good results, this would then help to avoid mis-determination of K_D in a systematic way, whereas those samples that do provide good results could have results approaching those of a free fitted model. Additionally, if the model control is of high enough quality, then the parameter range could be set narrower than that of the previous wide range. In this manner, various such embodiments provide the benefit that a user does not have to assess which fitting procedure to use for each series of samples that are analysed but may merely just set a range for the whole evaluation. Various of such ranges may be predetermined, automatically generated (e.g. dynamically) or user defined as appropriate. Automated software switching between various models (e.g. using free fitted, constrained or constant parameters) may thus be provided, in dependence upon the samples being analysed so as to provide optimal analysis without a used having to manually determine which model is optimal in specific given circumstances. For example, whilst a constant model would generally show better performance when an expected R_max is correctly determined, especially for low responses, the question remains of how accurately the expected R_max can be determined, as expected R_max is determined from R_max controls/inputs or a ligand level. It may, for example, be recommended for a user to use R_max controls/inputs. With a normal variation in R_max controls/inputs (e.g. less than 20% when determining K_D for R_max) analysis has shown that use of a constant R_max is equal or better than use of a constrained model where there are low responses. However, if there are any outliers in the R_max /inputs then there may be >> 20% of a correct value, but then use of the constrained model is preferred. Switching between different models used may thus be triggered in dependence upon the responses and/or R_max values, etc. The above-described methods of the present disclosure can be advantageously implemented by a sample analysis system, for example a biosensor. An example sample analysis system which can be used to implement the disclosed methods is the BIACORE® T200 instrument, produced by Cytiva. This instrument is shown in Figure 9. It will be appreciated that this is a non-limiting example of a biosensor system and that the components described below can be generalised to other forms of biosensor systems. More generally, the disclosed methods can be incorporated in and applied to a wide array of other biosensor systems that operate under similar principles and are not limited to implementation in a BIACORE® system. The analysis system 900 comprises a sample compartment 902, which is shown in the closed position in Figure 9. The sample compartment 902 can be opened, and sample solution(s) (generally held within one or more sample reservoirs such as vials) can be inserted into the compartment 902. Once sealed, viewing window 906 allows the sample solutions within compartment 902 to be viewed from outside. During analysis, a sample delivery system (also referred to as a fluid handling system) delivers sample solution from the sample reservoirs held within sample compartment 902 to a sensor surface. At its simplest, the sample delivery system comprises a network of at least one pump and flow channel for routing sample and running buffer through the analysis system 900 and to the sensor. The sensor can be inserted and removed before/after analysis via a sensor chip port 904. Continuous running buffer can be provided from buffer reservoir 908, via a buffer pump (not show) housed in buffer pump compartment 910. Waste material can be collected in waste reservoir 912. The methods disclosed herein can be implemented by a computer system (not shown) housed within or connected to the analysis system 900. Turning finally to Figure 10, Figure 10 shows a schematic and simplified representation of a computer apparatus 1001 which can be used to perform the methods described herein, either alone, in combination with other computer apparatuses or as part of a ‘cloud’ computing arrangement. For example, computer apparatus 1001 may form part of, or be connected (wirelessly or via a wired connection) to, analysis system 900 and may be configured to cause analysis system 900 to perform the various methods disclosed herein. Computer apparatus 1001 may also perform analysis on the readings or information produced by the sensor of analysis system 900. The computer apparatus 1001 in the example shown comprises various data processing resources such as a processor 1002 (in particular, a hardware processor) coupled to a central bus structure. Also connected to the bus structure are further data processing resources such as memory 1004. A display adapter 1006 connects a display device 1008 to the bus structure. One or more user-input device adapters 1010 connect a user-input device 1012, such as a keyboard and/or a mouse to the bus structure. One or more communications adapters 1014 are also connected to the bus structure to provide connections to other computer systems 1001 and other networks. Computer apparatus 1001 may be a local computer or a server. It may be a standalone element or may be part of existing computer hardware for use in a sample analysis laboratory. In operation, the processor 1002 of computer system 1001 executes a computer program comprising computer-executable instructions that may be stored in memory 1004. When executed, the computer-executable instructions may cause the computer system 1001 to cause a sample analysis system 900 to perform one or more of the methods described herein. The results of the processing (for example a sensorgram as shown in Figure 2) may be displayed to a user via the display adapter 1006 and display device 1008. User inputs for controlling the operation of the computer system 1001 may be received via the user-input device adapters 1010 from the user-input devices 1012. It will be apparent that some features of computer system 1001 shown in Figure 10 may be absent in certain cases. For example, one or more of the plurality of computer apparatuses 1001 may have no need for display adapter 1006 or display device 1008. This may be the case, for example, for particular computer apparatuses 1001 which are used only for their processing capabilities and do not need to display information directly to users. Similarly, user input device adapter 1010 and user input device 1012 may not be required. In its simplest form, computer apparatus 1001 comprises processor 1002 and memory 1004. As noted above, the described methods may be implemented using computer executable instructions. A computer program product or computer readable medium may comprise or store the computer executable instructions. The computer program product or computer readable medium may comprise a hard disk drive, a flash memory, a read-only memory (ROM), a CD, a DVD, a cache, a random-access memory (RAM) and/or any other storage media in which information is stored for any duration (e.g., for extended time periods, permanently, brief instances, for temporarily buffering, and/or for caching of the information). A computer program may comprise the computer executable instructions. The computer readable medium may be a tangible or non-transitory computer readable medium. The term “computer readable” encompasses “machine readable”. While various specific combinations of components and method steps have been described, these are merely examples. Components and method steps may be combined in any suitable arrangement or combination. Components and method steps may also be omitted to leave any suitable combination of components or method steps. The singular terms “a” and “an” should not be taken to mean “one and only one”. Rather, they should be taken to mean “at least one” or “one or more” unless stated otherwise. The word “comprising” and its derivatives including “comprises” and “comprise” include each of the stated features, but does not exclude the inclusion of one or more further features. The above implementations have been described by way of example only, and the described implementations are to be considered in all respects only as illustrative and not restrictive. It will be appreciated that variations of the described implementations may be made without departing from the scope of the disclosure. It will also be apparent that there are many variations that have not been described, but that fall within the scope of the appended claims.

Claims

Claims: 1. A method (700) for determining one or more interaction parameters associated with an interaction between an analyte and a ligand, the method comprising: contacting (702) a sensor surface having a ligand immobilized thereto with one or more samples containing an analyte; registering (706) a sensor response indicative of binding of the analyte to binding sites of the ligand; and fitting (716) the registered sensor response to an interaction model in order to determine one or more interaction parameters associated with the interaction between the analyte and the ligand, wherein the fitting is constrained by a pre-determined upper and lower limit applied to an analyte saturation parameter associated with the interaction model.

2. The method (700) of claim 1, wherein the sensor surface is contacted with three or more samples containing different concentrations of the analyte.

3. The method (700) of claim 1 or 2, wherein the one or more interaction parameters comprise one or more of: the association equilibrium constant, ^^_^, of the interaction; and the dissociation equilibrium constant, ^^_^, of the interaction.

4. The method (700) of any preceding claim, wherein the analyte saturation parameter is an analyte saturation response value, ^^_^^௫.

5. The method (700) of any of claims 1-3, wherein the analyte saturation parameter is a target occupancy value at saturation, ^^ ^^_^^௧.

6. The method (700) of any preceding claim, further comprising: determining (708) an estimated value of the analyte saturation parameter; and setting at least one of the upper and lower limit based on the estimated value for the analyte saturation parameter.

7. The method (700) of claim 6, wherein at least one of the upper and lower limit is set as a percentage of the estimated value for the analyte saturation parameter.

8. The method (700) of claim 7, wherein the lower limit is set at between 75% and 99% of the estimated analyte saturation parameter.

9. The method (700) of claim 7, wherein the lower limit is set at between 25% and 99% of the estimated analyte saturation parameter.

10. The method (700) of claim 7, 8 or 9, wherein the upper limit is set at between 101% and 150% of the estimated analyte saturation parameter.

11. The method (700) of claim 7, 8 or 9, wherein the upper limit is set at between 101% and 250% of the estimated analyte saturation parameter.

12. The method (700) of any of claims 6-11, wherein determining an estimated value of the analyte saturation parameter comprises calculating a theoretical estimate of the value based on: the molecular weight, ^^ ^^_^^^, of the ligand; the molecular weight, ^^ ^^_^^^, of the analyte; and the ligand response, ^^_^^^.

13. The method (700) of any of claims 6-11, wherein determining an estimated value of the analyte saturation parameter comprises: contacting (704) the sensor surface with a control analyte; registering (706) a sensor response indicative of binding of the control analyte to binding sites of the ligand; determining (708) a control analyte saturation parameter for the control analyte; and calculating the estimated value for the analyte saturation parameter based on the determined control analyte saturation parameter and the molar weight ratio between the analyte and the control analyte.

14. The method (700) of any preceding claim, further comprising receiving a user input setting the upper and lower limit.

15. The method (700) of any preceding claim, wherein the fitting comprises applying a minimum chi-square estimation to determine the closeness of fit to the registered sensor response.

16. The method (700) of any preceding claim, wherein the predetermined interaction model comprises the expression: where ^^_^^ is the registered sensor response at equilibrium, ^^ is the analyte concentration, ^^_^^௫ is the analyte saturation parameter, and ^^_^ is the dissociation constant of the interaction.

17. The method (700) of claim 16, wherein the predetermined interaction model further comprises an offset term to compensate for parallel baseline displacement due to systemic refractive index errors.

18. The method (700) of any preceding claim, wherein registering a sensor response indicative of binding of the analyte to binding sites of the ligand is based on surface plasmon resonance (SPR).

19. The method (700) of any of claims 1-17, wherein registering a sensor response indicative of binding of the analyte to binding sites of the ligand is based on evanescent wave sensing.

20. A sample analysis system (900) for determining interaction parameters, comprising: a sensing surface configured to detect binding interactions between an analyte and a ligand at the sensing surface; and a computing device configured to cause the sample analysis system to perform the method of any of claims 1-19.

21. A computer configured to cause a sample analysis system to perform the method of any of claims 1-19.

22. A computer-readable storage medium comprising instructions which, when executed by a computer, cause the computer to cause a sample analysis system to perform the method (700) of any of claims 1-19.

23. A computer program comprising instructions which, when the program is executed by a computer, cause the computer to cause a sample analysis system to perform the method (700) of any of claims 1-19.