WO2006037797A1

WO2006037797A1 - A method of evaluating experimental data

Info

Publication number: WO2006037797A1
Application number: PCT/EP2005/055039
Authority: WO
Inventors: Kaupo Palo
Original assignee: Olympus Corporation
Priority date: 2004-10-06
Filing date: 2005-10-06
Publication date: 2006-04-13
Also published as: EP1805677A1

Abstract

The present invention provides a method for evaluating complex experimental data. Such data are e. g. gathered by fluorescence measurements. An initial model is provided which describes such data. Relationships between physical parameters of such initial model are determined and used to determine a derived model. This derived model has a set of derived parameters on which the physical parameters of the initial model depend. Each derived parameter is determined to be either a free fit parameter, an elastically fixed fit parameter or a rigidly fixed parameter. The experimental data are fitted against the derived model. The derived model and the derived parameters are determined in such a way that the number of derived free fit parameters is smaller than the number of physical parameters.

Description

A method of evaluating experimental data

The present invention relates to a method of evaluating experimental data typically gathered from a number of samples of a similar physical content. It can be particularly applied to the evaluation of experimental data gathered from the high throughput screening of chemical libraries to identify potential drug candidates.

In the pharmaceutical pre-clinical research, chemical libraries of thousands of compounds are screened in order to identify those compounds which interact with a target involved in a disease pathway. Due to the high number of compounds to be assessed, measurements are conducted in a high throughput manner with only limited measurement time available to assess each individual compound. Typical measurement times may be in the order of one second per compound. Specifically, fluorescence-based measurements are being applied in such high throughput screening because they offer unprecedented sensitivity and flexibility. Apart from the limitations on measurement time, it is desirable to use compound libraries sparingly by conducting individual measurements on a small amount of compound. To this end, confocal fluorescence techniques have proven to be very useful since they allow observation of individual molecules in small volumes of highly diluted sample. One of the most commonly cited fluorescence techniques with single-molecule sensitivity is fluorescence correlation spectroscopy (FCS) which can resolve different species on the basis of different translational diffusion coefficient (Rigler et al., Eur. Biophys. J. 22: 169-175, 1993). Recently, this fluorescence fluctuation method found its counterpart in fluorescence intensity distribution analysis (FIDA), a technique that discriminates different fluorescent species according to their specific molecular brightness (Kask et al., Proc. Natl. Acad. Sci. USA 96: 13756 - 13761, 1999). Both FCS and FIDA have also been extended to variants with two detectors monitoring different polarization compounds or emission bands of fluorescence; fluorescence cross-correlation (Kask et al., Biophys. J. 55: 213 - 220, 1989), and two-dimensional FIDA (Kask et al., Biophys. J. 78: 1703 - 1713, 2000). 2D-FIDA is worthy of particular mention due to its outstanding statistical accuracy. The superior quality of data associated with 2D-FIDA has made it a method of choice for a number of high throughput drug-screening applications (Ullmann et al., Innovations Pharm. Technol., 30 - 40, 1999). Nevertheless, statistical accuracy is a limiting factor to the quality of screening results as one strives to minimize measurement times.

The output data from each sample in fluorescence-based drug screening is typically a single parameter, e.g. the degree of polarization of fluorescence. However, in FCS, FIDA, 2D-FIDA and other techniques the primary data is a complex data set, e.g. a correlation function or histogram of photon count numbers. In the latter case, the data are usually fitted against a model having a set of physically meaningful parameters. Such techniques, though being beneficial due to the high information content derived from measurements, often suffer from the problem that the data acquisition time which can be spent per sample is very short, and therefore the data are typically too inaccurate in order to estimate all physical parameters meaningfully.

It is an object of the present invention to provide a method which allows for the evaluation of complex experimental data with improved accuracy. This object is solved by the method according to claim 1. Preferred embodiments of the method according to the present invention are the subject of the dependent claims.

The present invention provides a method for assessing samples, in particular fluorescent samples, comprising the steps of:

- providing experimental data on samples, in particular by monitoring fluorescence emitted from these samples;

- providing an initial model for describing said data, which initial model has physical parameters;

- determining relationships between the physical parameters of the initial model;

- utilizing the relationships to determine a derived model, which derived model has a set of derived parameters on which the physical parameters of the initial model depend;

- determining each derived parameter to be either a free fit parameter, an elastically fixed fit parameter or a rigidly fixed parameter;

- fitting the experimental data against said derived model; wherein the derived model and the derived parameters are determined in such a way that the number of derived free fit parameters is smaller than the number of physical parameters.

A basic idea of the invention is to restrict the volume where the solution is searched in the space of model parameters in the most favorable manner. To this end, in a first step experimental data are collected, e.g. by carrying out fluorescence measurements on a multitude of samples. These might contain different chemical compounds screened for their interaction with a pharmacological target. It is known in the art to collect complex data comprising a multitude of data points per sample, which are evaluated by fitting the data to a model describing the expected behavior of the data. For example, data for each sample may comprise a histogram or a correlation function of fluorescence photon count numbers. Initial models describing the expected behavior of such data, as known in the art, depend on physical parameters such as molecular brightness, molecular diffusion rates, and/or molecular concentrations of the constituents of the samples under test. In the prior art, fitting the experimental data to such a model will require determination of all physical parameters from the fits carried out on the individual data sets, which is often impractical due to the limited statistical accuracy of the experimental data. According to the method of the invention, this problem is solved by identifying relationships between the physical parameters of the initial model and, using these relationships, transforming the initial model to a new, derived model which depends on a new set of derived parameters. The derived model and derived parameters are chosen in such a way that, when fitting experimental data against the derived model, the number of free derived parameters in the fit is smaller than the number of physical parameters in the initial model. Because a smaller number of free parameters needs to be determined in the fit against the derived model, these parameters can be determined with higher statistical accuracy.

According to one aspect of the invention, the relationships between physical parameters are determined from the results of measurements carried out on reference samples. These relationships are used to determine a derived model and derived parameters exhibiting the desired reduced degrees of freedom. Alternatively, such relationships may be derived from theoretical observations or a priori knowledge.

In a preferred embodiment, the number of derived parameters is smaller than the number of physical parameters, and/or at least one derived parameter is determined to be an elastically fixed fit parameter or a rigidly fixed parameter. In one aspect, the number of derived parameters is inherently smaller than the number of physical parameters, corresponding to a reduced number of degrees of freedom in the fitting process. An equivalent hereto is the introduction of a rigidly fixed derived parameter which directly reduces by one the number of degrees of freedom of the fitting process. An elastically fixed parameter is typically characterized by a penalty function introduced in the fitting process which favors parameter values close to a predetermined value. Such a parameter, though not directly reducing the degrees of freedom by one, is favorable because it renders the fitting procedure more robust.

The experimental data may preferably include data from one or more test sample(s) and data from one or more reference sample(s), which reference samples preferably differ with respect to at least one physical parameter. As mentioned above, it is favorable to make use of measurements carried out on reference samples in order to determine the relationships between physical parameters of the initial model. In particular, when conducting high throughput screening of chemical compounds in the pharmaceutical area, it is convenient to make measurements on so-called "high controls" and "low controls". Such controls are samples with known properties which are selected to represent different levels of biochemical activity, e. g. a very high/low degree of inhibition of binding between a ligand and a pharmaceutical target under study. Thereby, it is possible to obtain reference points spanning the space of parameter values expected from the multitude of screened chemical compounds (see in particular figures 5 and 6). In a particular preferred embodiment, the reference samples are grouped into one or more kinds, which are expected to have similar or identical physical parameters, and wherein the experimental data from the reference samples are globally fitted yielding estimates of physical parameters of said initial model for each of said kind of reference samples. This embodiment is also very advantageous when conducting high throughput screening experiments with high and low controls as discussed above and is further shown in more detail in figure 7a to c.

The relationships between physical parameters of the initial model may be established as a theoretically or empirically grounded subspace through points in a space of physical parameters representing said kinds of reference samples. Said relationship may be established as a curve. The relationship may in particular be a linear one, graphically represented e.g. by a straight line or a planar surface. If one already knows from theory about the general characteristics of the relationship between physical parameters, results from one or two kinds of reference samples measurements may be sufficient to reliably define the exact relationship. As an alternative, a multitude of reference samples spanning the range of expected parameter values can be evaluated and the relationship between parameters be determined empirically by interpolating between these reference results.

In a further preferred embodiment, the number of dimensions of the subspace is lower than the number of physical parameters of the initial model. In particular, one or more derived parameter(s) spanning the subspace are determined to be free fit parameters, and one or more other derived parameter(s) describing deviations from said subspace are determined to be elastically fixed fit parameters or rigidly fixed parameters. This embodiment is further depicted in figure 8b and discussed in the corresponding description thereto.

It may be advantageous to conduct additional steps of fitting the experimental data against one or more additional model(s), and comparing a quality of the fits of the experimental data against the derived model of claim 1 and against said one or more additional model(s). The rationale of introducing additional models is to verify whether the model used initially provides a valid description of sample properties or whether deviations, which may be due to artifacts, occur between the data and the initial model. There are many possible sources of deviations. It may be that an error has occurred during sample preparation and the initial amount of material A (e.g. the fluorescently labeled ligand) or B (e.g. the pharmaceutical target) is inaccurate. The low fit quality may also be due to the so-called compound artifacts, e.g. in a high throughput screening scenario:

• there is unexpected abnormal auto-fluorescence of the test compound that adds up to the normal (expected) fluorescence signal;

• the test compound that is expected to be optically inactive may unexpectedly turn out to quench fluorescence;

• the test compound may cause aggregation of molecules leading to abnormal properties of the fluorescence signal.

Part of the artifacts can be corrected for by applying an extended model to account for the effects. One may, for instance, apply an additional model accounting for additional or reduced fluorescence arising from impurities and/or test compounds in the sample(s). The quality of fit of the extended model compared to the quality of fit of the initial constrained model indicates which kind of artifact is the most probable one. The quality of fit of two alternative models is adequately compared by applying the F-test as known in the art to the corresponding values of χ² , the mean square deviation between data and respective model. If no known model leads to satisfactory fit quality, then one can conclude that the particular sample is a deviant of unknown type, the results of which will typically be discarded. In general, the introduction of additional models may be conducted in accordance with the flow charts depicted in figures 11 or 12.

Typically, the experimental data are obtained from measurements on test samples, and the physical parameters include concentrations of one or multiple constituents of the test samples. Such experimental data may be obtained from measurements on a multitude of test samples, each such test sample containing preferably a different test compound, the biochemical activity of which is studied (see the discussed high throughput screening scenario). It is particularly preferred to obtain the experimental data by monitoring fluorescence emitted from one or more sample(s). Figures 1 to 4 show data acquisition principles suitable for such fluorescence measurements. In particular, figure 4 shows raw data acquired in a 2D-FIDA measurement. This measurement technique relies on a confocal optical set-up where fluorescence is monitored by two detectors, which either monitor the emitted fluorescence at two wavelength bands or through orthogonally aligned polarization filters. This technique has also been applied in the examples underlying figures 7 and 9.

The following figures illustrate the method according to the present invention in more detail. Figure 1 shows typical raw data gathered from fluorescence measurements. Such raw data have been collected utilizing a state- of-the art confocal microscopic set-up.

Figure 2 shows a photon count number histogram, i.e. a distribution of the frequency of registering certain numbers of photon counts in a predetermined time interval, the so-called dwell- time. The data have been gathered from fluorescence measurements, and are influenced by the concentration and molecular brightness of the sample constituents, the geometry of the confocal measurement volume, the statistics of diffusive molecular motion inside the confocal measurement volume, and detector dead time and afterpulsing. Within the FIDA method, these data are fitted against a model which takes into account the aforementioned physical parameters.

Figure 3 shows a correlation function of a fluctuating fluorescence intensity signal, as known from FCS. The data have been gathered from fluorescence measurements, and are influenced by the concentration and molecular brightness of the sample constituents, the geometry of the confocal measurement volume, and the statistics of diffusive molecular motion inside the confocal measurement volume. Within the FCS method, these data are fitted against a model which takes into account the aforementioned physical parameters.

Figure 4 shows a two-dimensional photon count distribution. The x-axis represents photon counts registered within a predetermined time interval on a detector receiving a first fluorescence wavelength. The y-axis represents photon counts registered within a predetermined time interval on a detector receiving a second fluorescence wavelength. The grey scale of dots represents the frequency of registering a given combination of photon counts during the total measurement duration. The data have been gathered from fluorescence measurements, and are influenced by the concentration and molecular brightness of the sample constituents, the geometry of the confocal measurement volume, the statistics of diffusive molecular motion inside the confocal measurement volume, and detector dead time and afterpulsing. Within the 2D-FIDA method, these data are fitted against a model which takes into account the aforementioned physical parameters.

Figure 5 shows a typical scenario in high-throughput screening in the pharmacological industry. A fluorescently-labeled ligand and its corresponding pharmacological target protein are part of the sample under study. Both ligand and target protein typically form a complex due to specific binding interactions; this interaction plays a role in a disease pathway. The formation of the complex may e. g. be detected applying FCS, due to the different translational diffusion times of the unbound ligand and the ligand-target complex. Chemical libraries can be tested for their power to inhibit the ligand- target binding interaction.

Figure 6 shows concentrations of free fluorescently labeled ligand and ligand bound to its corresponding pharmacological target, as observed in an experiment according to figure 5. The end point of the straight line represent reference samples exhibiting maximum and minimum binding interactions between ligand and target. All points on the straight line represent possible intermediate values corresponding to varying degrees of binding interactions; the varying degrees are due to the presence of more or less potent inhibitors in the chemical library under study. The concentrations (bound) and (free) are not independent from each other but a linear relationship exists between these two physical parameters. This is due to the fact that a constant total concentration of labeled ligand is present in each sample and that free ligand is converted to bound ligand by the binding interaction with the target. The relationship between the physical parameters may be known a priori or may be derived from experiments on reference samples, i. e. through interpolation between the end points shown in the figure.

Figure 7a graphically illustrates the method of globally fitting reference sample data. One typical kind of reference samples in high-throughput screening is the so-called "low control" (LCtrl), i. e. a sample which is known to exhibit a low degree of inhibition. In contrast, the so-called "high control" (HCtrl) represents a high degree of inhibition, achieved by adding a known potent inhibitor to the sample. Relevant physical parameters for 2D-FIDA measurements are indicated: the concentration c of free and bound ligand and the molecular brightness Ql and Q2 observed in two orthogonal axes of polarization of the fluorescence emitted by the free and bound ligand, respectively. As indicated by the arrows, some physical parameters are expected to be constant for both kinds of reference samples. In the present example, this is the case for the molecular brightness in the high and low control. Global fitting of all reference sample data is performed. This means that molecular brightness parameters are not used as independent free parameters in fitting the individual reference sample data to separate model functions. Rather the totality of reference sample data is fitted to the model, adapting individual concentration parameters for each sample and just a single set of molecular brightness parameters applied consistently to all samples.

Figures 7b and c illustrate results of 2D-FIDA measurements on control samples, evaluated by conventional fitting (figure 7b) and global fitting according this embodiment of the present invention (figure 7c). In both figures, the x- and y-axes denote the brightness registered on two fluorescence detectors; the black circles represent brightness values attributed to a complex of fluorescently labeled ligand bound to its target whereas the empty circles represent brightness values attributed to the unbound fluorescently labeled ligand. When fitting the data independently in a conventional manner, the brightness values for the complex show strong statistical scattering (figure 7b). The outcome can be significantly improved by global fitting as can be seen from figure 7c. Comparison of the results in figure 7b and c shows that the results from conventional fitting are also significantly biased towards lower values on the x-axis. Theoretical analysis confirms that the results of the global fit yield a realistic average value for the brightness of the complex.

Global fitting is particularly useful in the above mentioned situation due to the following considerations. Minimal inhibition means that the solution contains only a small amount of free molecules A, but the amount of molecule A may be sufficient to interfere with the signal from complex AB. Maximal inhibition conversely eliminates most of molecules of type AB from the solution. To determine specific parameters of molecule A, it is statistically advantageous to use the measurements of the maximal inhibition, provided one knows the specific parameters of molecule of type AB beforehand. The method of present invention solves the problem of mutual dependencies by global fitting data from minimal and maximal inhibition control samples, assuming the specific parameters of molecules A and AB being the same in both kinds of samples.

Figure 8 illustrates a reduction of degrees of freedom according to the method of the present invention. Figure 8a (left figure) shows the space spanned by two physical parameters, concentration of free ligand (C^f) and concentration of bound ligand (C^b). In a fit of experimental data to a model as conducted according to the prior art, both parameters are treated as free fit parameters. In Figure 8b (right figure), the diagonal arrow indicates the relationship between physical parameters, here concentration of free ligand (C^f) and concentration of bound ligand (C^b). The straight line defines a sub- space within the space of physical parameters. This sub-space has a lower number of dimensions (here: one dimension) than the original space of physical parameters (here: two dimensions). According to a preferred embodiment of the present invention, a derived model is chosen which depends on a first derived parameter describing variations of relative concentrations of sample constituents along the straight line; this parameter is treated as a free fit parameter. To allow for deviations of the total concentration, which could easily arise from imperfections in the preparation of the samples, this preferred embodiment introduces a second derived parameter describing deviations of a sample composition from a straight line. According to the method of the present invention, this second derived parameter may be elastically fixed in the fitting process, i. e. in judging the quality of the fit a penalty is introduced which increases with increasing deviation from the straight line. This is illustrated by the grey shading in the background of figure 8b. As an alternative, one may rigidly fix said second derived parameter, e. g. in cases where one expects deviations to be negligible.

As said above, figure 8b describes a case when the total concentration is elastically fixed in fitting. This means that an a priori probability distribution for the corresponding value has been assigned, or one expects that the true value deviates from the given value. Mathematically this is accomplished e.g. by adding the following penalty term to the function which is minimized in the fitting process: W (l x - x₀ ) ,2

where w is the weight of the penalty for deviation of parameter x from the expected valuex₀. The rationale of elastic fixing is that one cannot fully control the value of the parameter by experimental preparation procedures. Elastic fixing allows the parameter to deviate from the expected value as long as this significantly improves fit quality.

Figure 9 shows the improvement obtained by conducting the fitting according to the preferred embodiment of the present invention, as further explained in the figure description to figure 8b. Figure 9a depicts binding degrees for a variety of samples as determined by conventional fitting according to the prior art. Black circles represent results obtained using an initial model with two free fit parameters; empty circles represent results obtained using an initial model with four free fit parameters, two of which account for experimental artifacts, the so-called background intensity. Since the statistical quality of the raw data is limited, it is not possible to reliably determine the binding degree in the four- para meter model. Figure 9b depicts binding degrees determined from the same raw data by fitting to a derived model according to the present invention, applying one derived free fit parameter and one elastically fixed fit parameter (black circles) or three derived free fit parameters and one elastically fixed fit parameter (empty circles). The improvement in statistical quality is especially apparent in the case of the four- para meter model. Reliable estimates for the binding degree are obtained while properly taking into account the background intensity.

Figures 10a and 10b illustrate possible errors in the evaluation of experimental data, which may be introduced by fitting to an inappropriate model when evaluating data according to the state of the art. The depicted assay scenario refers to binding of multiple fluorescenctly labeled ligand molecules to target entities. Figure 10a (top figure) depicts a histogram of particle fluorescence brightness that may be encountered in such a sample: In addition to free labeled ligand molecules, which exhibit a well-defined molecular brightness, complexes of multiple ligands and the target entity are observed, which exhibit a higher brightness with a broader distribution, due to the binding of a varying number of labeled ligands to each target entity. Besides those sample constituents, which might be modeled by a simple physical model, compound fluorescence may be present in some of the samples, depending on the properties of the individual compounds under observation. Figure 10b (bottom figure) shows the erroneous result obtained when fitting data from a sample exhibiting compound fluorescence to the simple model: The compound fluorescence is largely attributed to the contribution from the free labeled ligand, resulting in a biased determination of free ligand brightness and concentration. This problem is solved by one preferred embodiment of the invention, namely the introduction and comparison of multiple physical models, as further discussed referring to figure 11.

Figure 11 depicts a flow chart for a preferred embodiment of the present invention, which makes use of multiple models in order to account for varying sample properties or experimental artifacts in an optimized way. Three models are depicted on the left-hand side of the figure. The standard model accounts for two fluorescent sample components, as well as background signals due to background fluorescence or scattering. A simplified model neglects the background fluorescence, and may produce more robust results for measurements unaffected by background signal. However, if this model is erroneously applied to measurements influenced by background signal, the result may be biased. A third, enhanced model accounts for an additional, significant fluorescence contribution arising from compound fluorescence. While it is advantageous to apply this model to sample data actually affected by such compound fluorescence, it is undesirable to apply the enhanced model in all cases, since the additional degree of freedom introduced in the fitting step reduces statistical robustness of the method. According to this embodiment of the present invention, experimental data for each sample are fitted to each of the three models. Subsequently, the fit quality achieved by each model is assessed, and the model yielding the best fit is chosen to derive the assay signal, e.g. the binding degree. It should be noted that the best fit is not necessarily characterized by the minimal mean square deviation between experimental data and fit model, since the introduction of additional free parameters will, in general, result in reduced mean square deviations. An appropriate statistical test, which takes into account the number of the degrees of freedom, shall be used to assess fit quality. Such tests are known in the art, e.g. the Student test. It is in general preferred to apply the method according to the present invention, i.e. the use of derived models with a reduced number of degrees of freedom, in the more complex models applied in this embodiment (here: standard model and enhanced model).

Figure 12 shows an alternative implementation of the present invention to use additional models. Instead of fitting the experimental data to multiple models always, it may be preferred to assess data according to the initial model first and thereafter, depending on the results obtained, decide whether fitting to an additional model is desirable. This approach optimizes evaluation time by avoiding redundant fitting processes. This approach is of particular relevance for high throughput screening scenarios where evaluation time may be a critical bottleneck.

Example

As an example, solutions of fluorescently-labeled ligand molecules (A) and target molecules (B) are investigated. The ligand and target molecules may bind to each other, thereby chemically forming a complex (AB). Different test compounds (I) are added to the solution to determine their ability of inhibiting the binding reaction. By known methods of detection of fluorescence and subsequent analysis of data (e.g. FCS, FIDA, 2D-FIDA), it is possible to quantify the amount of complex AB and free molecules A in the solution. A fluorescence detection method is suited for the task, if the initial model describing the collected signal from the solution depends sensitively on the physical parameters, i.e. here concentrations of molecule A (C_A) and complex AB (CAB). In the present example, a confocal microscope setup for monitoring fluorescence from test samples is used. The method of prior art of analyzing two- dimensional photon count number distributions (2D-FIDA) is applied to determine the concentrations. In 2D-FIDA established in the polarization mode, fluorescent molecules are characterized by a pair of specific brightness values that correspond to parallel and perpendicular polarization channels.

A binding degree of binding between ligand and target is defined as a measure of inhibition induced by the test compound:

C_A binding = 'AB

C ^A + ^τ C ^ AB Forming one molecule of complex AB consumes exactly one molecule A. It follows that a linear relationship between the physical parameters holds:

C ^A + ^τ C ^AB - ^~ C ^ total I where C_totai denotes the total concentration of the fluorescently- labeled ligand introduced to the sample, being in part in the complex and in part free. This relation allows the transition to a derived model by replacing the initial two physical parameters C_A and CAB with a new set of derived parameters, e.g. C_A and C_totai- By keeping Ctotai physically fixed through appropriate sample preparation procedures, the two-parameter problem is reduced to a single-parameter problem. The value of Ctotai is determined from a reference measurement.

The control experiments allow for further restriction of the parameter space. Using a known inhibitor, samples with minimal (C_Amin) and maximal (C_Amaχ) chemically possible value for C_A are prepared. From reference measurements on these samples, the values of C_Amj_n, C_Amaχ and Ctotai are determined. These reference measurements are also used to determine specific parameters of fluorescent molecules such as diffusion time, specific brightness, and polarization degree.

It follows that any sample under consideration must have the concentrations C_A and C_AB within a linear subspace described by relations:

C_A = C_Aπάnr + C_Amκ (\ - r)

^AB ⁼ V^ total ^~ ^Armn F + V^ total ^~ ^ Λmax Xl ^{~ r}) where only r is an unknown parameter after evaluation of control samples and takes values between 0 and 1 corresponding to maximal and minimal inhibition, respectively. With the described procedure, the multi-parametric problem has been reduced to a one-dimensional one and the parameter range has been restricted. The advantage of the method is that it yields a better statistical accuracy by using knowledge from control experiments to reduce the number of unknown parameters.

The values C_A and C_AB are evaluated from the data by fitting the restricted model against the data. Typically, the least squares criterion has been applied. Those skilled in the art may, however, also e.g. apply the maximum likelihood criterion.

Claims

1. A method for assessing samples, in particular fluorescent samples, comprising the steps of:

2. A method according to claim 1 wherein the number of derived parameters is smaller than the number of physical parameters, and/or at least one derived parameter is determined to be an elastically fixed fit parameter or a rigidly fixed parameter.

3. A method according to claim 1 or 2 wherein said experimental data include data from one or more test sample(s) and data from one or more reference sample(s), which reference samples preferably differ with respect to at least one physical parameter.

4. A method according to claim 3, wherein experimental data obtained from reference samples are used to determine relationships between physical parameters of the initial model.

5. A method according to claims 3 or 4, wherein the reference samples are grouped into one or more kinds, which are expected to have similar or identical physical parameters, and wherein the experimental data from the reference samples are globally fitted yielding estimates of physical parameters of said initial model for each of said kind of reference samples.

6. A method according to any of claims 3 to 5, wherein said relationships between physical parameters of the initial model are established as a theoretically or empirically grounded subspace through points in a space of physical parameters representing said kinds of reference samples.

7. A method according to claim 6, wherein said relationship is established as a curve.

8. A method according to claim 6 or 7, wherein said relationship is established to be linear.

9. A method according to any of claims 6 to 8, wherein the number of dimensions of the subspace is lower than the number of physical parameters of the initial model, and wherein one or more derived parameter(s) spanning the subspace are determined to be free fit parameters, and one or more other derived parameter(s) describing deviations from said subspace are determined to be elastically fixed fit parameters or rigidly fixed parameters.

10. A method according to any of the preceding claims, comprising the additional steps of

- fitting the experimental data against one or more additional model(s), and

- comparing a quality of the fits of the experimental data against the derived model of claim 1 and against said one or more additional model(s).

11. A method according to any of the preceding claims, wherein the experimental data are obtained from measurements on test samples, and the physical parameters include concentrations of one or multiple constituents of the test samples.

12. A method according to any of the preceding claims, wherein experimental data are obtained from measurements on a multitude of test samples, each such test sample containing preferably a different test compound, the biochemical activity of which is studied.

13. A method according to any of the preceding claims, wherein the experimental data are obtained by monitoring fluorescence emitted from one or more sample(s).

14. A method according to claim 12 or 13, wherein an additional model accounts for additional or reduced fluorescence arising from impurities and/or test compounds in the sample(s).

15. A method according to any of the preceding claims, wherein at least one pair of said kinds of reference samples are selected to represent different levels of biochemical activity of the test compound of the sample.