Classifications

• • G—PHYSICS
  • G01—MEASURING; TESTING
  • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
  • G01N21/00—Investigating or analysing materials by the use of optical means, i.e. using sub-millimetre waves, infrared, visible or ultraviolet light
  • G01N21/17—Systems in which incident light is modified in accordance with the properties of the material investigated
  • G01N21/55—Specular reflectivity
  • G01N21/552—Attenuated total reflection
  • G01N21/553—Attenuated total reflection and using surface plasmons

Definitions

• the present invention relates to a method of analysing molecular binding interactions at a sensing surface, and more particularly to a method of determining the affinity for the interactions based on steady state binding data and which permits an at least partially automated procedure.
• the invention also relates to an analytical system including means for such automated affinity evaluations as well as to a computer program for performing the method, a computer program product comprising program code means for performing the method, and a computer system containing the program.
• Analytical sensor systems that can monitor interactions between molecules, such as biomolecules, in real time are gaining increasing interest. These systems are often based on optical biosensors and usually referred to as interaction analysis sensors or biospecific interaction analysis sensors.
• a representative such biosensor system is the BIACORE® instrumentation sold by Biacore AB (Uppsala, Sweden) which uses surface plasmon resonance (SPR) for detecting interactions between molecules in a sample and molecular structures immobilized on a sensing surface.
• SPR surface plasmon resonance
• a typical output from the BIACORE® system is a graph or curve describing the progress of the 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”.
• the affinity (expressed as the affinity constant K ⁇ or the dissociation constant Kj)) can be calculated from the association and dissociation rate constants. Many times, however, it may be difficult to obtain definitive kinetic data, and it is therefore usually more reliable to measure the affinity 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. To ensure that the association phase of the binding curve is indeed likely to have reached steady state, one usually determines in advance the necessary time length of sample injection (i.e. sample contact time with the sensor chip surface) for the bound analyte to reach equilibrium under the conditions intended to be used for the affinity measurements. Since both the time taken to reach equilibrium and the time it takes for the anlyte to dissociate are governed primarily by the dissociation rate constant, approximate injection times may also be estimated from the dissociation constant.
• sample injection i.e. sample contact time with the sensor chip surface
• a quality control is usually performed by the operator to discard sensorgrams which are of unacceptable quality due to instrument-related faults, such as e.g. air spikes caused by air bubbles in the fluid flow.
• the object of the present invention is to improve the determination of the affinity of a molecular binding interaction.
• This object is achieved by a method based on the finding that other interaction data than steady state binding level data from a data set (usually a binding curve) may be used to estimate or determine if the steady state binding data of the data set is reliable.
• data from one domain of a binding curve e.g. the dissociation phase
• the method can be at least partially automated and may automatically exclude unreliable steady state binding level data.
• the present invention therefore provides a method of determining affinity for a molecular binding interaction from measured steady state binding data, which method comprises the steps of: a) providing a plurality of experimental binding data sets for the binding interaction between two chemical (incl. biochemical) species, wherein each data set contains binding data measured at multiple time points during an association phase and a dissociation phase of the interaction, b) selecting from the plurality of experimental binding data sets a plurality of binding data measured at a defined time point at or near the end of the association phase as representing steady state binding data, c) subjecting each data set to a quality control which comprises estimating the reliability of the steady state binding data by evaluating other binding data of the same data set, d) excluding each data set which is estimated in step c) to contain unreliable steady state binding data, and e) determining the affinity from the steady state binding data of remaining data sets.
• steps c) to e) comprise the following steps: selecting pluralities of other binding data from the plurality of experimental binding data sets; determining which ones of the pluralities of other binding data fall within a predetermined range, the pre-determined range representing the quality of the ones of the experimental binding data sets; excluding from the final plurality of experimental binding data sets poor-quality experimental binding data sets, whereby the poor-quality experimental binding data sets have pluralities of other binding data falling outside of the predetermined range; and determining the affinity from the steady state binding data from the final plurality of experimental binding data sets.
• the present invention provides an analytical system for studying molecular interactions, which comprises data processing means for performing the above method.
• the present invention provides a computer program comprising program code means for performing the method.
• the present invention provides a computer program product comprising program code means stored on a computer readable medium or carried on an electrical or optical signal for performing the method.
• the present invention provides a computer system containing a computer program comprising program code means for performing the method.
• Figure 1 is a schematic side view of a biosensor system based on SPR.
• Figure 2 is a representative sensorgram where the binding curve has visible association and dissociation phases.
• Figure 3 shows twelve different diagrams where the curve fitting error for affinity is plotted in a log(dissociation rate constant) versus log(association rate constant) map at different sample injection time lengths.
• FIG. 4 is a flow chart of an embodiment of affinity determination according to the present invention.
• the present invention relates to the evaluation of steady state binding data for a molecular binding interaction from a plurality of data sets for the interaction to determine the affinity for the interaction, wherein other interaction data from a data set than steady state binding data is used to estimate the reliability of the steady state binding data of the data set.
• the experimental binding data is obtained by sensor based technology which studies the molecular interactions and present the results in real time as the interactions progress.
• Chemical sensors or biosensors 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.
• 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.
• 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
• 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).
• SERS surface enhanced Raman spectroscopy
• SERRS surface enhanced resonance Raman spectroscopy
• TIRF evanescent wave fluorescence
• phosphorescence phosphorescence
• waveguide interferometers waveguide leaky mode spectroscopy
• RfS reflective interference spectroscopy
• transmission interferometry holographic spectroscopy
• AFR atomic force microscopy
• biosensors include the afore-mentioned BIACORE® system instruments, manufactured and marketed by Biacore AB, 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.
• 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 surface
• analyte includes any specific binding partner thereto.
• 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.
• SPR 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.
• 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.
• FIG. 1 A schematic illustration of the BIACORE® system is shown in Fig. 1.
• Sensor chip 1 has a gold film 2 supporting capturing molecules (ligands) 3, e.g. antibodies, exposed to a sample flow with analytes 4, e.g. an antigen, through a flow channel 5.
• Monochromatic p-polarised light 6 from a light source 7 (LED) is coupled by a prism 8 to the glass/metal interface 9 where the light is totally reflected.
• the intensity of the reflected light beam 10 is detected by an optical detection unit 11 (photodetector array).
• An optical detection unit 11 photodetector array
• 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 "affinity trace” or "affmogram”.
• affinity trace or "affmogram”.
• 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 correspond to a change in concentration of about 1 pg/mm ⁇ on the sensor surface.
• association 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 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 indicated on the sensorgram by a drop in 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 sensing surface having an immobilised capturing molecule, or ligand, for example an antibody, interacting with a binding partner therefor, or 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).
• buffer is passed over the sensing surface giving the baseline response A in the sensorgram.
• an increase in signal is observed due to binding of the analyte.
• association phase This part B of the binding curve is usually referred to as the "association phase".
• association phase Eventually, a steady state condition is reached at or near the end of the association phase where the resonance signal plateaus at C (this state may, however, not always be achieved).
• 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).
• 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 D of the binding curve is usually referred to as the "dissociation phase".
• the analysis is 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. This is indicated in part E of the sensorgram. Injection of buffer restores the baseline A and the surface is now ready for a new analysis.
• This interaction model (usually referred to as the Langmuir model), which assumes that the analyte (A) is both monovalent and homogenous, that the ligand (B) is homogenous, and that all binding events are independent, is in fact applicable in the vast majority of cases.
• [A] is the concentration of analyte A
• [B] is the concentration of the ligand B
• [AB] is the concentration of the reaction complex AB
• k a is the association rate constant
• k ⁇ is the dissociation rate constant
• Equation (1) K[ ⁇ ] ⁇ [B ⁇ ]- UB ⁇ -kAAB] (2) at
• Equation (3) KC(R ⁇ -R) - KR (3) at where R is the response at time t in resonance units (RU), C is the initial, or bulk, concentration of free analyte (A) in solution, and R max is the response (in RU) obtained if analyte (A) had bound to all ligand (B) on the surface. Rearrangement of Equation (3) gives:
• TM k a CR ⁇ - (k.C + k, )R (4)
• R is the response in resonance units (RU).
• RU resonance units
• Equation (6) may be linearized:
• the above described analysis is usually repeated for a number of different analyte concentrations and, suitably, also at at least one other ligand density at the sensor surface.
• K/ ⁇ may be obtained by non-linear curve-fitting of the data.
• Equation (12) is modified to:
• Equations (11) and (12) may be modified by introducing a steric interference factor n specifying how many binding sites are on average blocked by one analyte molecule:
• the binding model is fitted simultaneously to multiple binding curves obtained with different analyte concentrations C (and/or with different levels of surface derivatization Rmax)- This is referred to as "global fitting", and based on the sensorgram data such global fitting establishes whether a single global k a or k ⁇ will provide a good fit to all the data.
• the results of the completed fit is presented to the operator graphically, displaying the fitted curves overlaid on the original sensorgram curves.
• the closeness of the fit is also presented by the chi-squared ( ⁇ 2) value, below referred to as "chi2", a standard statistical measure. For a good fitting, the chi2 value is in the same magnitude as the noise in RU ⁇ .
• the present invention relates to a method for determining the affinity (KA or KD) for a molecular binding interaction from multiple steady state binding data measured for the interaction, which method is amenable to automation, thereby permitting sets of experimental binding data for a plurality of different interactions to be collected and the respective affinities for the different analytes to be determined with minimum labour to the operator.
• data set refers to the data representing a binding curve, such as a sensorgram.
• a "batch" of data sets, as the term is used herein, comprises two or more data sets.
• a prerequisite for such an automated affinity evaluation procedure is the automatic exclusion of steady state data which is unreliable, meaning, for instance, either that the binding interaction has not essentially reached equilibrium when the binding level data is read, or that the steady state part of the binding curve is defective in some other respect.
• the steady state binding data is usually read at a report point at or near the end of the association phase.
• a report point is in fact a short time window, typically about five seconds, over which the detected response values are averaged.
• the slope of this binding curve region which should be planar at equilibrium.
• detection noise will usually cause even equilibrated binding curves to have sloping report points. Increasing the report point window will not remedy the situation to any appreciable extent.
• the reliability of the steady state data of a binding curve is estimated based on binding data taken from other parts, or domains, of the binding curve. From such binding data different "reliability indicators" may be estimated.
• a first such reliability indicator is the dissociation rate, which may be used to determine if it is likely that the interaction has approached equilibrium or not in the association phase at the experimental conditions used. (For equilibrium to be considered to have substantially been reached, the slope of the curve in the steady state detection window is typically less than about 1% per second, preferably less than about l%o per second (about 0.03 RU/s for R ma ⁇ of about 30 RU).) Thus, if the dissociation rate is too slow, the time that the sample contacts the sensing surface may not be sufficient time for equilibrium to be reached. More specifically, for the BIACORE® and similar systems where the sample passes the sensing surface in a fluid flow, it has been found that for each sample injection time length (i.e.
• dissociation rate limit (which is substantially independent on the association rate) below which it is not possible to reliably calculate the affinity (K ⁇ . or KTJ) in steady state analysis.
• This dissociation rate limit may advantageously be determined empirically, such as by actual tests or by computer simulation as described below.
• a mathematical expression may calculate minimum dissociation rates for different KD's. Binding data to determine the dissociation rate is usually taken from the dissociation phase but may also be taken from the association phase, or from both domains of the binding curve. To provide for automatic exclusion (by software) of sensorgrams which are likely not to have reached equilibrium, an injection length-dependent dissociation rate limit is set, and the sensorgram(s) in which the estimated dissociation rate is below the set value for the injection length used may automatically be excluded from the data sets to be used for calculating the affinity.
• a second reliability indicator that basically may be determined from a domain on the binding curve that is different from the report point window is the last part of the sensorgram, such as e.g. the last 30 seconds of the association phase. If this curve part (which includes the report point window) has a downward (negative) slope, this is an indicator that something is wrong and that such a sensorgram should be excluded from the sensorgrams used for the affinity determination.
• other reliability indicators may be used in combination with the two indicators described above.
• Such additional reliability indicators may relate to single curves (e.g. like the first reliability factor mentioned above) or to multiple curves (e.g. sensorgrams forming a concentration series) and may, for instance, include one or more of those listed below. - Too few curves having a signal (report point) above the noise level.
• the graph signal (report point) versus concentration is not monotonous. The difference between the highest and the lowest signal is insufficient. The concentration series is too narrow. Too few curves are available for analysis. After exclusion of non-reliable batches of data sets, the "affinity model" is fitted to all accepted batches as is per se known in the art.
• the quality of the fit, the reliability of the calculated affinity and optionally other quality measures are calculated before the results of the affinity evaluation are presented to the operator.
• An exemplary flow chart for a software-assisted affinity evaluation is shown in
• BIACORE® e.g. BIACORE® TlOO system or BIACORE® AlOO system
• the user is assumed to have produced a fairly a large number of sensorgrams (e.g. about 300 to 2000 per 24 hours) for a plurality (e.g. about 30 to 200) of analyte-ligand interactions (as mentioned above, "ligand” here means an analyte-specific interactant immobilized to a sensor surface). For each analyte-ligand pair, a series of different analyte concentrations have been run.
• the sensorgrams obtained for such a concentration series is referred to below as a "batch" of sensorgrams.
• Optimum performance of an affinity assay has been found to be obtained for a concentration series of at least six, e.g. ten, different analyte concentrations where all concentrations reach equilibrium, the highest concentration equilibrating at R max and the lowest concentration having Req ⁇ 0-2*R max .
• a number of surface areas with different densities (surface concentrations) of immobilized ligand and a single analyte concentration may be used instead of a single ligand density and several different analyte concentrations.
• a first step 401 the software presents to the user the analytes and immobilized ligands ("spots") which have been run, and the user selects the batches of data sets, i.e. sensorgrams, to be analysed.
• the software then prepares the data for analysis by, for each analyte/ligand combination, cutting out the data for the affinity analysis, the base line association phase and dissociation phase being defined by the flow rate and the event "injection stop".
• the report point "binding_late” is used for the affinity determination, and sensorgram data are used for quality control.
• a third step 403 the software performs for each batch a first quality control of the prepared data for individual sensorgrams as well as for the complete batch by applying a first set of predefined "rules" based on different reliability indicators.
• the following two rules are particularly useful for evaluating the reliability of the steady state binding data:
• the dissociation rate is usually determined by (i) cutting out the dissociation phase, (ii) fitting the dissociation rate, and, if the fit is acceptable, (iii) determining if the dissociation rate obtained is within the preset approved range. If not, a penalty is attached to the batch containing the curve.
• the first set of rules may further include:
• the following four batch penalty levels may be used: 3 - forces exclusion of batch 2 - forces user to inspect 1 - suspicious 0 - no problem detected.
• Batches without penalties or with a single penalty are accepted for analysis without further action. If a batch has any penalty 3, or if the sum of all penalties for a batch is 5 or greater, the batch is automatically excluded. Batches with a sum of penalties equaling 2, 3 or 4 are marked for user inspection.
• a cross-validation preferably a "leave-one out cross- validation” (see e.g. Wold S., Technometrics, 20 (1978) 397-406), is performed to (i) find out if there are any outliers, and (ii) to obtain an estimate of the variability of the calculated parameters (chi2 5 standard variations).
• chi2 is significantly improved (at an approximately 99% confidence level) due to removal of one curve in a batch, it is removed in a step 405a. Only one curve may be removed from each batch. In case of more than one outlier, a penalty is attached to the batch.
• the first set of rules from the third step 403 are re-evaluated in a step 405b, the affinity model is refitted to the data in a step 405 c, and the cross-validation is re-calculated in a step 405 d, without any resulting curve removal, however.
• a second set of rules are applied to the data resulting from step 405 or 405c, which rules may include: (2a) If the standard deviation of the Kj)' s calculated in the cross-validation procedure in steps 405 or 405c is too large, a penalty is attached to the batch.
• a third set of rules may be applied to test if the parameters obtained have reasonable values, which rules may include:
• a seventh step 407 all penalties for each batch are collected and based on the same penalty criteria as described above, a batch is graded to be excluded, inspected or accepted. All batches graded to be excluded are then excluded, and the batches graded to be inspected are clearly labeled. Accepted batches are handled as accepted.
• the curve batches are presented to the user.
• the user may, if desired, in a step 408a modify the batches by including one or more batches that were previously excluded.
• the user may also include and exclude curves from a batch and change initial values for the fitting procedures.
• a refit of the affinity model to the modified batches is made in a step 408b.
• a ninth step 409 the final results are presented, and the user is allowed to "finish and lock" the affinity evaluation.
• the invention also extends to computer programs, particularly computer programs on or in a carrier, adapted for putting the method of the invention into practice.
• the carrier may be any entity or device capable of carrying the program.
• the carrier may comprise a storage medium, such as a ROM, a CD ROM, a DVD or a semiconductor ROM, or a magnetic recording medium, for example a floppy disc or a hard disk.
• the carrier may also be a transmissible carrier, such as an electrical or optical signal which may be conveyed via electrical or optical cable or by radio or other means.
• the carrier may be an integrated circuit in which the program is embedded. Any medium known or developed that can store information suitable for use with a computer system may be used. It is to be understood that the invention is not limited to the particular embodiments of the invention described above, but the scope of the invention will be established by the appended claims.

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• 2006
  • 2006-06-12 WO PCT/SE2006/000679 patent/WO2006135309A2/en active Application Filing
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