METHOD FOR QUANTITATIVE DETERMINATION OF HOST MOLECULE CONCENTRATION (CTOT) IN HOST MOLECULES AND CONCENTRATION MEASURING DEVICE

Description

[0001] The invention relates to a method for quantitatively determining a host molecule concentration of host molecules according to the preamble of claim 1.

[0002] According to a second aspect, the invention relates to a concentration measuring device according to the preamble of claim 13.

[0003] A method for quantitative analysis using 129< Xe is known from the article "Quantitative biosensor detection by chemically exchanging hyperpolarized 129Xe" by S. Korchak et al., Phys. Chem. Chem. Phys, 2018, 20, 1800 and from EP 3 330 729 A1. It is based on the interaction of xenon atoms with molecular host molecules and can provide insights from the perspective of fundamental chemistry as well as biomedical analytics and imaging technology through nuclear magnetic resonance. Xenon forms reversible host molecule-xenon complexes that can be detected by nuclear magnetic resonance (NMR).

[0004] If the host molecule—as provided in a preferred embodiment—comprises a receptor molecule segment for binding a target molecule and an intercalation molecule segment that particularly easily intercalates xenon, a large number of target molecules can also be quantitatively determined. Enzymes, antibodies, or fragments thereof, which bind the respective ligands (substrate, antigen) as the target molecule highly specifically and effectively, are particularly suitable for the receptor molecule segment. Conversely, ligands can also be used as the receptor molecule segment for a xenon host molecule in order to bind a suitable enzyme or antibody as the target molecule. Organic guest molecules such as cucurbit[6]urils, cryptophanes, or pillararenes have proven suitable for the intercalation molecule segment, but xenon-binding proteins or peptides can also be used here.

[0005] Xenon is inert and non-toxic, and gaseous under laboratory conditions. It dissolves readily in aqueous and physiological fluids and exhibits a distinct resonance frequency shift for each specific binding site. Preferably, an isotopic mixture containing the isotope 129< Xe can be present in natural abundance (approximately 26%) or enriched (up to over 90%). If the hyperpolarized 129< Xe (hpXe) is prepared by spin exchange optical pumping (SEOP), as provided in a preferred embodiment, the detection sensitivity is increased by orders of magnitude.

[0006] A further increase in sensitivity is achieved by the use of NMR saturation transfer techniques—provided according to a preferred embodiment—in which the presence of the host molecule is indirectly observed (hyperpolarized xenon chemical exchange saturation transfer, HyperCEST). The depolarization of host-bound hpXe by selective irradiation with depolarizing radiation, which is a radiofrequency (RF) irradiation, forces the simultaneous continuous decrease of the dissolved hpXe signal due to the spatial exchange of xenon atoms from the solution into the host molecule-xenon complex and vice versa.

[0007] While HyperCEST is well established for qualitative studies, it is currently not possible to determine the host molecule concentration with acceptable uncertainty and without extensive, specific prior knowledge. The highly asymmetric exchange rates due to the significantly different concentrations of dissolved xenon and xenon bound in the host molecule-xenon complex, the predominance of multiple reaction mechanisms, and the limitation to the single dissolved xenon signal have proven difficult to measure.

[0008] The invention is based on the object of improving the determination of the host molecule concentration using hyperpolarized xenon, in particular with regard to correctness, accuracy and required prior knowledge.

[0009] The invention solves the problem by a method having the features of claim 1.

[0010] According to a preferred embodiment, the xenon concentration ( ρ) by the xenon partial pressure (p) in a gas in exchange equilibrium with the solution. Specifically, it is determined as the product of the xenon solubility (s) of xenon in the solution and the xenon partial pressure (p) in a gas in exchange equilibrium with the solution, according to Henry's law.

[0011] According to a second aspect, the invention solves the problem by a concentration measuring device having the features of claim 12.

[0012] The advantage of the invention is that the host molecule concentration can be calculated solely from the measurement data measured by the magnetic resonance measurement unit. This generally simplifies the measurement of the host molecule concentration. Established methods require calibrations using reference material as similar as possible to the sample, but with a precisely known host and / or target molecule concentration, which – especially with biological material – is often not achievable or only with unsatisfactory quality.

[0013] Another advantage is that in many cases, a quantitative determination of the host molecule concentration is possible with such low measurement uncertainty that quantitative research on such host molecules becomes possible. This is especially true if the host molecule contains a receptor molecule segment, allowing the biomolecule of interest to be bound as a target molecule.

[0014] In the context of the present description, a host molecule is understood to be a molecule that forms a host molecule-xenon complex with xenon.

[0015] The feature that the signal intensity of the high-frequency signal is measured in the frequency interval around the resonance frequency of the dissolved xenon is understood in particular to mean that the area of ​​the peak is determined in the magnetic resonance spectrum.

[0016] The host complex frequency is the Larmor frequency for xenon in complex with the host molecule.

[0017] The feature that the xenon is selectively depolarized in the host molecule-xenon complex means that the frequency of the depolarizing radiation is chosen to be equal to the host complex frequency, so that dissolved xenon is depolarized as little as possible or not at all.

[0018] Preferably, the host molecule concentration is determined solely from the signal intensities, the xenon concentrations, the irradiation amplitudes, and, if applicable, the irradiation times. This specifically means that no other physical quantities measured using a different method are used to determine the host molecule concentration.

[0019] According to a preferred embodiment, the xenon concentration ( ρ)by the xenon partial pressure (p) in a gas that is in exchange equilibrium with the solution. In particular, it is determined as the product of a xenon solubility (s) of xenon in the solution and the xenon partial pressure (p) in a gas that is in exchange equilibrium with the solution, according to Henry's law. The xenon solubility s of xenon in a solution is known from the literature with low measurement uncertainty for a wide variety of solutions, in particular physiological solutions such as blood, urine or cerebrospinal fluid and in particular for all practically relevant solvents. It is possible and, according to a preferred embodiment, provided that this xenon solubility is stored, for example, in a digital memory of the computing unit.

[0020] Preferably, the method comprises the steps of (a) measuring signal intensities S( ρ ,ν,t) at different xenon concentrations ( ρ) and different irradiation amplitudes (ν) each at at least two different times (t) during the irradiation, (b) calculating an effective temporal decay rate δ( ρ ,ν) from the signal intensities S( ρ ,ν,t) for a given xenon concentration and irradiation amplitude and (c) calculating a xenon leakage rate k off ( ρ ) and a xenon entry rate k on ( ρ ) depending on the xenon concentration ( ρ) This is preferably done by adjusting the effective decay rates δ( ρ ,ν) by means of square error minimization to the formula . Thereafter, the host molecule concentration C tot< of host molecules is preferably determined by fitting, in particular by means of square error minimization of the xenon leakage rates k off ( ρ ) and the xenon entry rates k on ( ρ ) to the formula k off ρ k on ρ = 1 KC tot + 1 C tot ρ calculated.

[0021] By adjusting the given parameters, namely xenon leakage rates k off ( ρ ) and the xenon entry rates k on ( ρ ), to the given formula, it is understood that the parameters are varied in a known manner, for example, using the Levenberg-Marquardt algorithm, so that the deviation between the measured data and the best-fit curve specified by the formula is minimized. The deviation is preferably determined by summing the squared deviation between the respective measured value and the function value.

[0022] The feature that the host molecule concentration is determined by fitting to the given formula is understood in particular to mean that a mathematical operation is performed that corresponds to this fitting. It is always possible to use other formulas for fitting, for example, by substituting one variable for another. However, such a calculation is equivalent to fitting to the above formula.

[0023] Furthermore, it is unnecessary to calculate the xenon exit rates and the xenon entry rates explicitly. Rather, it is sufficient to calculate numerical values ​​from which the xenon exit rates and the xenon entry rates can be calculated without further performing a square error minimization, for example, by multiplying a factor or adding a summand.

[0024] Preferably, the method further comprises the step of determining a binding constant K, which describes a binding strength of xenon to the host molecule, by fitting by means of square error minimization to the formula k off ρ k on ρ = 1 KC tot + 1 C tot ρ . Preferably, a dissociation rate coefficient c_ and / or a rate coefficient k for the degenerate exchange are also determined by fitting by means of square error minimization to the formula k off ( ρ ) = c_ + kρ certainly.

[0025] Alternatively, it is also possible to adjust the host molecule concentration C tot< and, if appropriate, the host molecule concentration C tot< , the dissociation rate coefficient c_, the rate coefficient k for the degenerate exchange and the binding constant K by adjusting the effective decay rates δ( ρ ,ν) by means of square error minimization to the formula δ ρ ν = c _ + k ρ K C tot 1 + K ρ 2 πν 2 2 πν 2 + c _ + k ρ 2 to calculate.

[0026] Even without the irradiation of depolarizing radiation, the hyperpolarization decreases over time through natural decay. The resulting exponential decay of the polarization can be described by a reference decay rate R( ρ,ν ). To determine this reference decay rate R( ρ ,ν), the method preferably comprises the steps of (a) measuring a reference signal intensity SR ( ρ ,ν,t) at different xenon concentrations ρ of the dissolved xenon and different irradiation amplitudes v and times t at a mirror symmetry frequency fs , which is the sum of (i) a resonance frequency of the dissolved xenon and (ii) the difference between the resonance frequency and the host complex frequency, and (b) calculating a temporal reference decay rate R( ρ , n ) from the reference signal intensities SR ( ρ,ν,t). The same xenon concentration and irradiation amplitudes are used as for determining the signal intensities S( ρ ,v,t). The rate R( ρ ,ν) also includes the possibly slight depolarization of the dissolved xenon during irradiation with the host complex frequency to depolarize xenon in the complex with the host molecule.

[0027] To reduce the systematic measurement uncertainty, it is advantageous if the reference decay rate differs from the effective temporal decay rate δ( ρ ,ν). In most cases, the reference decay rate R( ρ ,ν) is small compared to the effective temporal decay rate δ( ρ ,ν). However, this correction can become significant when the host molecule concentration is very small. With the thus corrected decay rate (δ( ρ ,ν) - R( ρ,ν)) the host molecule concentration C tot< and, if necessary, the other coefficients can then be calculated as described above.

[0028] Instead of calculating the host molecule concentration C tot< and other parameters from the effective decay times according to the two alternatives described above, it is possible, as a further alternative or in addition, to calculate these parameters directly from the signal intensities. To do this, the signal intensity S(p,v,t) is first measured at different xenon concentrations (p), different irradiation amplitudes (v), and different time points (t), so that time-dependent signal intensity measurement data are obtained. The signal intensity measurement data thus obtained are then fitted to the formula using square error minimization S ρ ν t ∝ A ρ 1 + a ρ exp − c _ + k ρ K C tot 1 + K ρ 2 πν 2 2 πν 2 + c _ + k ρ 2 + R ρ ν t adjusted, whereby preferably the dissociation rate coefficient c_, the rate coefficient k for the degenerate exchange, the binding constant K, a device-specific signal amplitude A and a parameter α describing the generation of hyperpolarization are also determined. Optionally, depending on the required accuracy, the reference decay rate R( ρ ,ν) can be neglected, or determined and taken into account as described above. The time t specified in the formula begins with the irradiation of the depolarizing radiation.

[0029] According to a preferred embodiment, the xenon concentration (p) of the dissolved xenon is the product of the partial pressure of xenon (p) in a gas atmosphere in exchange equilibrium with the solution and the solubility (s) of xenon in the liquid at the partial pressure p. Typically, the solubility s is independent of the partial pressure, so that the substitution p=sp applies to the aforementioned formulas of the alternative approaches (its derivation follows below).

[0030] If the concentration of a substance is to be determined that does not form a host-xenon complex with xenon, it is advantageous if the host molecule has a receptor molecule segment for binding a target molecule, an intercalation molecule segment, and the target molecule. The intercalation molecule segment has a structure such that xenon can be intercalated. For example, the intercalation molecule segment is a cucurbituril, a cryptophane, or a pillararene. The target molecule is usually not covalently bonded to the receptor molecule segment. Since the bond, which is usually hydrogen bonding and / or van der Waals bonding, is comparatively strong, the target molecule is considered part of the host molecule.

[0031] The use of enzymes or antibody molecules (or fragments thereof) as receptor molecules is particularly advantageous due to their high specificity and binding strength to ligands (substrate, antigen) as target molecules. Conversely, a ligand can also serve as a receptor molecule segment to bind an enzyme or antibody as a target molecule.

[0032] In a concentration measuring device, it is possible for the computing unit to be constructed from two or more sub-computing units. Preferably, the computing unit is designed to carry out a method comprising steps (b) to (e) of claim 1, preferably with the additional steps mentioned in one or more subclaims.

[0033] With the method according to the invention, host molecule concentrations below one micromole per liter, and in some cases even below one nanomole per liter, can be measured. The measurement uncertainty (relative deviation) for the host molecule concentration is – depending on the quantification method (alternative) – less than 5% to less than 20%. This measurement uncertainty appears comparatively high, but for the quantification of many biomarkers (target molecules) it is smaller than with known measurement methods.

[0034] It is also important that the inventive method only requires experimental specifications for the concentration of dissolved xenon, as well as the irradiation amplitude and irradiation time, and does not require, as in the known methods, recourse to reference measurements on biological reference material, which is often unavailable or only available in unsatisfactory quality. According to a preferred embodiment, it is advantageous if the xenon concentration is determined by the xenon partial pressure (p) in a gas atmosphere in exchange equilibrium with the solution, and in particular as the product (Henry's law: p=sp) of the xenon solubility (s) and the xenon partial pressure (p). The variation of the xenon concentration underlying the inventive method can then be achieved simply by controlling the xenon partial pressure in the gas atmosphere.The solution is a common laboratory solution (organic and aqueous solutions, buffers) or, in particular, a possibly prepared body fluid, such as blood, urine, or cerebrospinal fluid, for which precise information on xenon solubility can be found in relevant tables. Irrespective of this, established metrological methods are available for the precise determination of xenon solubility in a given solution.

[0035] According to a preferred embodiment, the host molecule concentration is at most 500 nanomoles per liter, preferably at most 100 nanomoles per liter, more preferably at most 10 nanomoles per liter, and especially preferably at most 1 nanomole per liter. The host molecule concentration is particularly preferably at most 500 picomoles per liter, in particular at most 200 picomoles per liter. At such low host molecule concentrations, a signal originating from the xenon that is part of the host molecule-xenon complex can no longer be detected by measurement. However, the method according to the invention also makes it possible to determine the host molecule concentration in these cases.

[0036] Preferably, the xenon-containing solutions are prepared by varying the xenon concentration. For example, the partial pressure of xenon at which xenon or a xenon-containing gas mixture is passed through the solution is changed. In particular, the xenon-containing solutions differ only in their xenon concentrations. Preferably, neither the host molecule is removed nor added, nor is the amount of solvent in the solution changed.

[0037] According to a preferred embodiment, no measurement signal originating from the xenon in the host molecule-xenon complex is used when determining the host molecule concentration.

[0038] For example, the host molecule is an amyloid. In particular, the method according to the invention is a method for determining an amyloid concentration, for example, in a body fluid.

[0039] The invention is explained in more detail below with reference to the accompanying drawings. Figure 1: Part 1a shows a schematic view of the processes during xenon exchange. Part 1b shows the NMR spectrum at a high host molecule concentration in physiological solution in exchange equilibrium with a gas atmosphere of hyperpolarized xenon. Part 1c shows the NMR spectrum at a low host molecule concentration in physiological solution in exchange equilibrium with a gas atmosphere of hyperpolarized xenon. Part 1d shows an excerpt of the experimental data set of signal intensities of the dissolved xenon for a low host molecule concentration in physiological solution at various xenon concentrations (p) of dissolved xenon (expressed by the xenon partial pressure (p) in a gas atmosphere in exchange equilibrium with the solution according to p=sp with a xenon solubility (s)) as well as various irradiation amplitudes (v) and times (t). Figure 2: a schematic view of a concentration measuring device according to the invention.and Figure 3a shows the quantitative evaluation of standard xenon NMR spectra at a high concentration of 4.12 mM CB6 (CB6 = cucurbit[6]uril) in physiological solution (90% phosphate-buffered saline, 10% D2O at 25 °C) in exchange equilibrium with a gas atmosphere of hyperpolarized xenon using a tabulated xenon solubility (s=0.00394 Mbar -1< ) ​​and the applied xenon partial pressure p to determine the concentration p=sp of dissolved xenon. Figure 3b shows the quantitative evaluation according to the inventive method for 16.5 µM CB6 in physiological solution in exchange equilibrium with a gas atmosphere of hyperpolarized xenon by fitting the model function according to equation [3] to the effective decay rates to determine the entry and exit rates and subsequent determination of the exchange parameters c-, k,K and C tot< by fitting the entry and exit rates to the model equations [5] and [9] using a tabulated xenon solubility (s=0.00394 Mbar -1< ) ​​and the applied xenon partial pressure p to determine the concentration p=sp of dissolved xenon, and Figure 4 the quantitative evaluation according to the inventive method for 16.5 µM CB6 in physiological solution in exchange equilibrium with a gas atmosphere of hyperpolarized xenon by fitting the model function according to equation [ 4 ] to the effective decay rates for the direct calculation of the parameters c-, k, K and C tot< using a tabulated xenon solubility (s=0.00394 Mbar -1< ) ​​and the applied xenon partial pressure p to determine the concentration p=sp of dissolved xenon. ,

[0040] The considered host-guest exchange situation is in Figure 1aA host molecule 10, for example, cucurbit[6]uril, and a xenon guest atom 12.1 can form a host molecule-xenon complex 14. Additional xenon guest atoms 12.j (j = 2, 3, ...) are dissolved in a solution 16.

[0041] The dissolved xenon guest atoms 12.j have a resonance frequency f R , which corresponds to their Larmor frequency, the xenon guest atoms bound in the host molecule 10 resonate at the host complex frequency fw, which corresponds to the Larmor frequency of the host molecule-xenon complex 14.

[0042] With a xenon entry rate k on , xenon gas atoms 12.j enter a host molecule-xenon complex 14 from solution 16. With a xenon exit rate k off , xenon gas atoms 12.j exit the host molecule-xenon complex 14 and enter solution. These processes are governed by both dissociative and degenerate exchange.

[0043] Solution 16 is irradiated with depolarizing radiation 18 at the host complex frequency fw. This effectively depolarizes the xenon (here, xenon atom 12.2) bound in the host molecule-xenon complex.

[0044] The dissolved xenon emits a high-frequency signal 20 which has a signal intensity S.

[0045] Figure 1b shows the spectrum of the high-frequency signal 20 for the case of a high host molecule concentration C tot< . It can be seen that the spectrum has two maxima P1, P2. The first maximum P1 originates from xenon bound in the host molecule-xenon complex 14. The second maximum P2 originates from dissolved xenon not trapped in the host molecule-xenon complex 14.

[0046] As is usual in NMR measurement technology, the maxima are normalized to a reference frequency in ppm (parts per million), here the signal of dissolved xenon to 196 ppm.

[0047] Figure 1cshows the spectrum of the high-frequency signal 20 for the case of a very low host molecule concentration C tot< . It can be seen that the first maximum P1 is no longer detectable. Instead, the method according to the invention enables a measurement of the host molecule concentration C tot< based on the signal intensity S of the dissolved xenon (P2) (for example, as the area under the peak).

[0048] This signal intensity S can be described by S ρ ν t ∝ M Xe ρ exp − k on eff ρ ν + R ρ ν t , wherein M Xe p = A ρ 1 + aρ applies.

[0049] The amplitude factor M Xe in equation [ 2 ] is proportional to the xenon concentration (p) of dissolved xenon by an instrumentation-dependent factor A and scaled by 1 / (1+αρ), where the parameter α (Greek "alpha") indicates the degree of hyperpolarization induced by spin-exchange opticel pumping (SEOP).

[0050] The effective decay rate here is the sum ( k on eff ρ ν + R ρ ν ) from a saturation transfer rate induced by exchange with irradiated host molecule-xenon complexes k on eff ρ ν and a reference decay rate R(p,v), which describes the natural decay or a direct depolarization by irradiation.

[0051] In many cases, R(p,v) is practically independent of the dissolved xenon concentration and often also of the irradiation amplitude (R is then the constant natural decay rate) or can be completely neglected in relation to the saturation transfer rate due to the difference in size.

[0052] The saturation transfer rate induced by exchange with irradiated host molecule-xenon complexes ( k on eff ρ ν ) can be described as k on eff ρ ν = k on ρ f ρ ν = k on ρ 2 πν 2 2 πν 2 + k off ρ 2 ,

[0053] With the entry rate k on (ρ) and the exit rate k off (ρ) for the formation and dissolution of the host molecule-xenon complex. The term f(p,v) refers to the only partial saturation of xenon bound in the host molecule-xenon complex 14, when the residence time of the xenon in the complex 1 / k off is too short for a given irradiation amplitude v of the depolarizing radiation to achieve complete magnetization quenching.

[0054] From an analytical approximate solution of the Bloch-McConnell equation for the saturation of the spin of xenon atoms in a host molecule-xenon complex by resonant irradiation, it follows explicitly that, for a negligible spin-spin relaxation rate, k on eff ρ ν = c _ + k ρ K C tot 1 + K ρ 2 πν 2 2 πν 2 + c _ + k ρ 2 .

[0055] So it applies k off ρ = c _ + k ρ , which describes the xenon leakage rate by components of dissociative exchange (c_) and degenerate exchange (kp).

[0056] The kinetic equilibrium for the exchange of magnetization between the pools of dissolved ( M Xe ) and xenon bound in the host molecule-xenon complex 14 ( M CXe ) is quickly established. Therefore, k on = k off M CXe / M Xe .

[0057] Since all xenon atoms are hyperpolarized in the same way by a common source, their polarization is the same in both pools, so that the ratio of the magnetizations of host-bound xenon and dissolved xenon is equal to that of the concentrations of host-bound xenon and dissolved xenon M CX e / M Xe = Kρ / 1 + Kρ C tot / ρ .

[0058] Where K is the binding constant and C tot< is the total concentration of host molecules. The factor Kρ / (1+ Kρ ) is the fraction of host molecules occupied by xenon atoms. Thus, the xenon entry rate is explicitly k on ρ ν = c _ + k ρ K C tot 1 + K ρ .

[0059] Figure 2schematically shows a concentration measuring device 22 having a sample receptacle 24 for receiving the solution 16, for example, in a sample vessel 26. The concentration measuring device also includes a magnet 42 for generating a magnetic field with a strength of preferably at least 1 Tesla in the solution 16.

[0060] To adjust the xenon concentration ρ, xenon is introduced into the solution by means of an introduction device 28. For example, by bubbling, an exchange equilibrium is achieved between a xenon gas atmosphere and the solution, so that the xenon concentration (p) of dissolved xenon is determined by the xenon gas pressure, in particular, it is equal to the product of the xenon solubility (s) and the partial pressure of xenon in the bubbling gas (p) (Henry's law: p=sp).

[0061] The saturation transfer rate k on eff ρ ν (Equation [ 4 ]) is determined by seven parameters. The xenon concentration (p) of dissolved xenon is adjusted by the introduction device 28, in a preferred embodiment by gas bubbling and according to Henry's law as p=sp with the xenon solubility s and the xenon partial pressure p. The irradiation amplitude v is adjusted by controlling a magnetic resonance measuring unit 32 of the concentration measuring device 22 by means of a computing unit 34.

[0062] The magnetic resonance measuring unit 32 is designed to automatically irradiate the xenon-containing solution 16 with the depolarization radiation 18 and to measure the signal intensity S of the radio-frequency signal 20. The computing unit 34 is designed to automatically (a) control the magnetic resonance measuring unit so that it emits the depolarization radiation 18 with a host complex frequency fw and the irradiation amplitude v.

[0063] In addition, the computing unit controls the introduction device 28 so that the xenon concentration p in the solution 16 has a predetermined value. A measurement plan is stored in the computing unit 34, which specifies which combinations of xenon concentrations p and irradiation amplitudes v are to be set.

[0064] The computing unit 34 then detects a decrease in the signal intensity S(p,v,t) for the different, but fixed (p,v) settings by measuring the dissolved xenon signal at at least two different times of irradiation (t) and determining the signal intensity. In other words, the signal decrease described in equation [1] is tracked by the dissolved xenon signal intensity for incremented saturation time t; subsequently, the respective effective temporal decay rate can be derived, for example, by a monoexponential data fit.

[0065] The computing unit 34 then automatically calculates the host molecule concentration C tot< from the signal intensities S, the xenon concentrations p, and the irradiation amplitudes v and, if applicable, the irradiation times (t). This evaluation is described below.

[0066] According to a first alternative, the effective decay rate over time is determined from the experimentally measured signal intensities for different, respectively fixed xenon concentrations (p) of dissolved xenon and irradiation amplitudes v. The determination of the xenon exchange rates k off (ρ) and k on (ρ) is determined by fitting to the model function [ 3 ]. k off (ρ) and k on (ρ), obtained in this way for different settings of p, obey equations [ 5 ] and [8] respectively, and also the equation k off ρ k on ρ = 1 KC tot + 1 C tot ρ .

[0067] The parameters c_, k, K and C tot< are then determined from the intercept and the slope of the respective data fit.

[0068] According to a second alternative, the effective decay rates under (p,v) variation are determined by fitting the model function k on eff ρ ν = c _ + k ρ K C tot 1 + K ρ 2 πν 2 2 πν 2 + c _ + k ρ 2 according to equation [ 4 ] and thus the parameters c_, k, K and C tot< are directly determined.

[0069] According to a third alternative, the parameters, in particular the host molecule concentration C tot< , are chosen such that the values ​​calculated from them using equation [ 1 ] reflect the measured data of the signal intensities, i.e. the measured signal intensities dependent on time t, which are sampled at the different (p,v) settings, with a minimum quadratic deviation.

[0070] The xenon concentration p of dissolved xenon appears only in the product with unknown, sought-after exchange parameters (with k and 1 / C tot< in the first alternative; with k and K in the second alternative; with k, K, A and α in the third alternative). In a preferred embodiment, the xenon concentration is determined by the xenon partial pressure (p) in a gas atmosphere in exchange equilibrium with the solution, in particular calculated as the product p=sp (Henry's law) of the xenon solubility (s) with the xenon partial pressure (p). Values ​​with low measurement uncertainty exist in the literature for the solubility s, which are used to solve the determination equations for the first (equations [3], [5], [8] and [9]), second (equation [4]) and third alternative (equation [1]) under the substitution p=sp. Alternatively, the solubility s for the given solution can be determined using established metrological measurements.

[0071] Depending on the required accuracy for quantifying the parameters c_, k, K, and C tot<, the three described alternatives can be supplemented by a reference decay rate R(p,v), which is subtracted from the aforementioned effective decay rate (alternatives 1 and 2) or explicitly considered (alternative 3). It results from signal intensities at different xenon concentrations (ρ) and different irradiation amplitudes (v) at different irradiation times (t) at a mirror symmetry frequency, which is the sum of (i) a resonance frequency (f R ) of the dissolved xenon and (ii) the difference between the resonance frequency (f R ) and the host complex frequency (fw).

[0072] The parameters c_, k, K determined in this way and in particular the host molecule concentration C tot< are then output, for example on a schematically drawn display 36.

[0073] Figure 2also shows that the concentration measuring device 22 can have a xenon hyperpolarization device 38, which can be part of the introduction device 28. Xenon is hyperpolarized by means of the xenon hyperpolarization device 38. The mechanism for this is well known and will therefore not be described further. The xenon concentration of dissolved xenon is measured by means of a xenon concentration meter 40. In a preferred embodiment, the xenon partial pressure of a gas mixture in exchange equilibrium with the solution is measured and used to determine the xenon concentration (p) of dissolved xenon, in particular as the product of the xenon solubility (s) and the xenon partial pressure (p) according to Henry's law (p=sp). The xenon concentration meter 40 is connected to the computing unit 34.

[0074] Figure 3ashows the quantitative evaluation of standard xenon NMR spectra at a high concentration of 4.12 mM CB6 (CB6 = cucurbit[6]uril) in physiological solution, which serves to validate the inventive method. The xenon concentration (p) of dissolved xenon is adjusted by means of exchange equilibrium with one atmosphere of a certain xenon partial pressure (p=0.02 to 1.2 bar) according to p=sp (Henry's law) at a xenon solubility (s). Since at these concentrations, signals from both dissolved and complex-bound xenon are present ( Fig. 1b), the ratio k off / k on , which leads to the determination of K and C tot< (equation [9]), can be calculated directly from the signal intensities according to equation [7], replacing p=sp and using the solubility s=0.00394 Mbar -1< from the literature. As recently described, at high guest molecule concentrations, k off (and thus c - and k) can also be determined from the signal intensities analogous to equation [5], replacing p=sp and using the solubility s=0.00394 Mbar -1< from the literature. The high concentration of 4.12 mM CB6 was prepared by weighing out starting material of the specified purity.

[0075] Figure 3a In sub-figure (a), the xenon escape rate k off for the CB6-xenon complex is shown as a function of the xenon partial pressure p. The xenon escape rates from signals of CB6-bound xenon are shown as squares, and those from signals of dissolved xenon are shown as circles.

[0076] Figure 3ashows in part (b) the ratio M Xe / M CXe of the signal intensity of freely dissolved and CB6-bound xenon, as a function of the partial pressure p.

[0077] Error bars in (a) and (b) are uncertainties from signal integration. The lines represent linear least-squares fits of the data for numerical estimates of the kinetic parameters according to Equations [5] and [9], respectively, with the substitution p=sp.

[0078] Figure 3b shows the quantitative evaluation according to the inventive method for 16.5 µM CB6 in physiological solution. The xenon concentration (p) of dissolved xenon is adjusted by exchange equilibrium with one atmosphere of a certain xenon partial pressure (p=0.02 to 0.8 bar) according to p=sp (Henry's law) at a xenon solubility (s). Due to the low host concentration, the complex with hyperpolarized xenon is not detectable as a separate signal ( Fig. 1c). The weakly concentrated solution of only 16.5 µM CB6 was obtained from the highly concentrated solution of 4.12 mM by dilution.

[0079] Sub-figure (a) shows the effective decay rates as a function of the irradiation amplitude v for different settings of the partial pressure p. The lines are nonlinear least squares fits of the function according to equation [ 3 ] replacing p=sp to obtain the xenon entry rate k on and the xenon exit rate k off (alternative 1). Sub-figure (b) shows this xenon exit rate k off for the complex dissociation as a function of the applied partial pressure p. Sub-figure (c) shows the ratio k off / k on as a function of the partial pressure p. The lines are best-fit lines for the calculation of the parameters according to equations [ 5 ] and [9] replacing p=sp and using the solubility s=0.00394 Mbar -1< from the literature. Figure 4shows the adaptation of the model function according to equation [ 4 ] replacing p=sp and using the solubility s=0.00394 Mbar -1< from the literature to the effective decay rates for the direct calculation of the parameters c-, k, K and C tot< (Alternative 2).

[0080] In Table 1, the numerical results of the evaluation according to alternatives 1 and 2 as well as by adapting the model function according to equation [ 1 ] to the signal intensities (alternative 3) under the replacement ρ=sp and using the solubility s=0.00394 Mbar -1< from the literature are compared with the reference values ​​from the highly concentrated CB6 solution and the sample weight. Tab. 1 Method \ Parameter C _ / ms -1< k / M -1< ms -1< K / M -1< C dead< / mM C dead< / mM after weighing Standard NMR 1,12 ± 0,01 116 ± 5 280 ± 13 4,18 ± 0,15 4,12 Alternative 1 1,10 ± 0,01 120 ± 4 274 ± 15 0,0160 ± 0,0007 0,0165 Alternative 2 1,10 ± 0,01 134 ± 10 258 ± 9 0,0169 ± 0,0005 Alternative 3 1,18 ± 0,03 122 ± 15 193 ± 17 0,0193 ± 0,0013 List of reference symbols 10 Host molecule A instrumentation-dependent 12 Xenon guest atom factor 14 Host molecule-xenon complex c_ Dissociation rate coefficient 16 Solution C dead< Host molecule concentration 18 Depolarizing radiation f R Resonance frequency f W Host complex frequency 20 High-frequency signal j Running index xenon atoms 22 Concentration meter k Rate coefficient 24 Sample collection K k on eff Binding constant 26 Sample vessel Saturation transfer rate 28 insertion device k off ( ρ ) Xenon leakage rate k on ( ρ ) Xenon entry rate 30 bubbling gas M Xe Amplitude factor 32 Magnetic resonance measurement unit p Partial pressure 34 Computing unit R(p,v) Reference decay rate 36 Advertisement s Solubility of xenon in the solvent of the solution 38 Xenon hyperpolarization device ρ, s p Xenon concentration in the solution 40 Xenon concentration meter S( ρ ,n,t) Signal intensity 42 magnet SR ( ρ ,n,t) Reference signal intensities α Polarizer parameters t Time d( ρ ,n) effective temporal decay rate v Irradiation amplitude

Claims

1. A method to quantitatively determine a host molecule concentration (Ctot) of host molecules (10) comprising the steps: (a) introducing hyperpolarised xenon into a solution (16) of host molecules (10), resulting in a solution containing xenon (16), which contains dissolved xenon and xenon in a host molecule-xenon complex (14) with a host molecule (10), (b) irradiating the solution containing xenon (16) with electromagnetic depolarisation radiation (18) with a host complex frequency (fw) for the at least partially selective depolarisation of xenon and host molecule-xenon complex (14), and (c) subsequently measuring a signal intensity (S) of a high-frequency signal (20) at least in a frequency interval around a resonance frequency (fR) of the dissolved xenon, at at least two different points in time during irradiation (t), characterised by the steps: (d) irradiating solutions containing xenon (16) of various xenon concentrations of dissolved xenon with depolarisation radiation (18) of various irradiation amplitudes (v) and detecting the respective signal intensities (S) and (e) determining the host molecule concentration (Ctot) from the signal intensities (S), the xenon concentrations and the irradiation amplitudes (v).

2. The method according to claim 1, characterised in that (a) the host molecule concentration (Ctot) is only determined from the signal intensities (S), the xenon concentrations (s·p) and the irradiation amplitudes (v) or (b) the solutions containing xenon (16) of various xenon concentrations (s·p) of dissolved xenon are irradiated with depolarisation radiation (18) of various irradiation amplitudes (v) and various irradiation times (t) and the host molecule concentration (Ctot) is determined from the signal intensities (S), the xenon concentrations (sp), the irradiation amplitudes (v) and the irradiation times (t) wherein s is the xenon solubility and p the xenon partial pressure.

3. The method according to claim 1 or 2, characterised by the steps: (a) measuring the signal intensity at various xenon concentrations (s·p) and various irradiation amplitudes (v) at various points in time during irradiation (t), thereby obtaining signal intensity measurement data (S) as a function of concentration, irradiation amplitude and time, (b) calculating effective temporal decay rates (δ(p,ν)) from the signal intensities (S) for a given xenon concentration (s·p) and irradiation amplitude v and (c) calculating a xenon leakage rate koff(p) and a xenon entry rate kon(p) as a function of the xenon concentration (s·p) by adjusting the effective decay rate (δ(p,v)) to the following formula by minimising the square error δ p υ = k on p 2 πν 2 2 πν 2 + k off p 2 , (d) as well as determining at least the host molecule concentration Ctot of host molecules (10) by adjusting the xenon leakage rates (koff(p)) and the xenon entry rates (kon(p)) to the formula k off p k on p = 1 KC tot + s C tot p , wherein s is the xenon solubility and K a binding constant.

4. The method according to claim 3, characterised in that in addition (a) a binding constant K, which describes a binding strength of xenon to the host molecule (10), is determined by adjusting it to the following formula by minimising the square error: k off p k on p = 1 KC tot + s C tot p , (b) a dissociation rate coefficient c_ and (c) a rate coefficient (k) k for degenerate exchange are determined by adjusting them to the following formula by minimising the square error: koff(p) = c_ + ksp.

5. The method according to one of the preceding claims, characterised by the steps: (a) measuring the signal intensity at various xenon concentrations (s·p) and various irradiation amplitudes (v) at various points in time during irradiation (t), thereby obtaining signal intensity measurement data (S) as a function of concentration, irradiation amplitude and time, (b) calculating the effective temporal decay rates (δ(p,ν)) from the signal intensities (S) for a given xenon concentration and irradiation amplitude, (c) calculating the host molecule concentration Ctot, of the dissociation rate coefficient c_, of the rate coefficient k for degenerate exchange and of the binding constant K by adjusting the effective temporal decay rates (δ(p,ν)) to the formula δ p ν = c _ + ksp K C tot 1 + Ksp 2 πν 2 2 πν 2 + c _ + ksp 2 .

6. The method according to one of the preceding claims, characterised by (a) measuring a reference signal intensity at various xenon concentrations (sp) and various irradiation amplitudes (v) at various points in time during irradiation (t) at a mirror symmetric frequency, which is the sum of (i) a resonance frequency (fR) of the dissolved xenon and (ii) the difference from the resonance frequency (fR) and the host complex frequency (fw), thereby obtaining reference signal intensity measurement data as a function of concentration, irradiation and time (SR), (b) calculating an effective temporal reference decay rate ((p,v)) from the reference signal intensities (S) for a given xenon concentration and irradiation amplitude, and (c) deducting the reference decay rate (R(p,v)) from the effective decay rate (δ(p,ν)) for a given xenon concentration (s·p) and irradiation amplitude (v).

7. The method according to one of the preceding claims, characterised by the steps: (a) measuring the signal intensity at various xenon concentrations (s.p) and various irradiation amplitudes (v) at various points in time during irradiation (t), thereby obtaining signal intensity measurement data (S) as a function of concentration, irradiation amplitude and time, (b) calculating at least the host molecule concentration Ctot, the dissociation rate coefficient c_, a rate coefficient k for degenerate exchange, the binding constant K and the signal amplitude A, a parameter α that describes the generation of hyperpolarisation, by adjusting the measured signal intensities to the following formula by minimising the square error: S p ν t ∝ Asp 1 + ap exp − c _ + ksp K C tot 1 + Ksp 2 πν 2 2 πν 2 + c _ + ksp 2 t 8. The method according to claim 7, characterised by (a) measuring time-dependent reference signal intensities (SR) at various xenon concentrations (s·p) and various irradiation amplitudes (v) at various points in time during irradiation (t) at the mirror symmetrical frequency, (b) calculating the reference decay rate in the time (R(p,v)) from the reference signal intensities (SR) for a given xenon concentration and irradiation amplitude, and (c) fitting the signal intensities (S) to the following formula using the reference decay rate (R(p,v)) by minimising the square error S p ν t ∝ Asp 1 + ap exp − c _ + ksp K C tot 1 + Ksp 2 πν 2 2 πν 2 + c _ + ksp 2 + R p ν t .

9. The method according to one of the preceding claims, characterised in that (a) the host molecule (10) comprises a receptor molecule section for binding a target molecule, a deposit molecule section and a target molecule that is attached to the receptor molecule section, (b) the receptor molecule section is a protein or peptide, especially an enzyme, an antibody, a fragment or a ligand thereof, or a nucleic acid, especially a DNA or RNA fragment, and / or (c) the deposit section has a molecular structure that binds xenon, especially a protein, a peptide, a nucleic acid, a fragment or complexes thereof, or another organic or synthetic compound, especially cucurbiturils, cryptophanes or pillararenes.

10. The method according to one of the preceding claims, characterised in that the host molecule concentration (Ctot) is at most 500 nanomol per litre, in particular at most 10 nanomol per litre oder 1 nanomol per litre, or even lies in the picomol per litre range.

11. The method according to one of the preceding claims, characterised in that the solution containing xenon (16) is produced by changing the xenon concentration (sp) without changing the host molecule concentration (Ctot).

12. A concentration measurement device (22) for quantitatively determining a host molecule concentration (Ctot) of host molecules (10) in a solution (16), with (i) a magnet resonance measurement unit (32) designed to automatically irradiate the solution containing xenon (16) with electromagnetic depolarisation radiation (18) and measure a signal intensity of a high-frequency signal (20) at a resonance frequency (fR) of the dissolved xenon, and (ii) a computing unit (34), (iii) characterised in that the concentration measurement device (22) comprises an insertion device (28) designed to automatically adjust a xenon concentration by introducing xenon into the solution, (iv) the computing unit (34) is configured to automatically carry out a method comprising the steps: (a) controlling the insertion device (28) such that the xenon concentration (s·p) has a predetermined value, (b) controlling the magnet resonance measurement unit (32) such that it emits depolarisation radiation (18) with a host complex frequency (fw) and irradiation amplitude (v) and duration (t), (c) detecting a xenon concentration (sp) of the xenon dissolved in the solution (16), (d) detecting the signal intensities (S) of the high-frequency signal (20) at at least two different points in time during irradiation, and (e) calculating the host molecule concentration (Ctot) from the signal intensities, the xenon concentrations (sp), the irradiation amplitudes (v) and, where possible, irradiation times (t).

13. A concentration measurement device (22) according to claim 12, characterised by (a) the insertion device (28) for automatically introducing hyperpolarised xenon into the solution (16) and (b) a concentration gauge (40) for detecting the xenon concentration (s·p) in the solution (16), (c) wherein the computing unit (34) is designed to automatically change the xenon concentration (p) and / or the irradiation amplitude (v) and irradiation time (t) according to a predetermined measurement plan.

14. A concentration measurement device (22) according to claim 13, characterised by (a) a xenon hyperpolarisation device (38) for generating hyperpolarised xenon that is connected to the insertion device (28) for supplying the hyperpolarised xenon. (b) wherein the computing unit (34) is configured to automatically carry out a method according to one of the claims 1 to 11.