Towards in vivo applications of111 Ag perturbed angular correlation of -rays (PAC) spectroscopy

111 Ag-perturbed angular correlation of γ -rays (PAC) spectroscopy provides information on the nuclear quadrupole interactions

In PAC spectroscopy the correlation, in time and space, between two γ-rays emitted in succession from a radionuclide is measured (Frauenfelder and Steffen, 1965;Hemmingsen et al., 2004).The angular correlation between the two γ-rays depends on the properties of the nuclear decay while the perturbation -leading to the PAC acronym -is controlled by the interaction of the nucleus in the intermediate state (i.e.prior to the emission of the second γ-ray) with extra-nuclear magnetic fields or electric field gradients.Thus, in the absence of magnetic fields, measuring the perturbed angular correlation of the two γ-rays allows for the determination of the nuclear quadrupole interaction (NQI) of the PAC probe in the intermediate nuclear state.
The radioactive emission of metallic radionuclides can be exploited to image and treat cancer if they are firmly coordinated via a chelating agent to a biologically-active vector (e.g.peptide, antibody) capable to direct the location of the radionuclide mainly towards tumors, thus minimizing the damage of surrounding healthy sites (Price and Orvig, 2014;Ramogida and Orvig, 2013;Tosato et al., 2020aTosato et al., , 2021Tosato et al., , 2022)).A solid understanding of the stability of the radionuclide complexes in vivo is pivotal to obtain safe and effective radiopharmaceuticals.However, the conventional methods to attain information on the integrity of these radioactive complexes often rely on non-radioactive surrogates under conditions that do not always properly simulate the biological media.Since PAC is sensitive to the changes in the local environment of the nucleus, and because most biological material is relatively transparent to γ-rays, PAC spectroscopy can be a useful tool to non-invasively investigate the fate of a radionuclide attached to a carrier molecule under very low concentrations (10 − 12 M) and truly biologically relevant conditions.
Applications of PAC in the field of radiopharmaceuticals are rather limited and have mainly been conducted with compounds labeled with 111 In (t 1/2 = 2.83 days), a radioisotope also suitable for single photon emission computed tomography (SPECT) imaging (Kurakina et al., 2020;Marsden et al., 1991;Ramogida and Orvig, 2013;Smith et al., 1987).Unfortunately, 111 In often gives PAC spectra with low information content due to the so-called "after effects" derived from the 111 In to 111 Cd nuclear decay, that give rise to relaxation phenomena obscuring the PAC spectra (Hemmingsen et al., 2004 and references therein;Haas and Shirley, 1973) or can even trigger the degradation of the original molecular structure (Kurakina et al., 2020;Shpinkova et al., 2002).111 Ag (t 1/2 = 7.45 days) is an unconventional radiometal that could be employed for cancer therapy and associated SPECT imaging (Aweda et al., 2013;Chattopadhyay et al., 2008;Tosato et al., 2020a).It may also be used in PAC spectroscopy, although only a limited number of 111 Ag-PAC publications exist to date (Balogh et al., 2020(Balogh et al., , 2022;;Haas and Shirley, 1973;Hemmingsen et al., 2004 and references therein;Liu et al., 2008;Sas et al., 2006).This may be partially due to the fact that only a very small fraction of the 111 Ag-decays is "PAC active", i.e. pass through the γ-γ-cascade which is measured in the PAC experiment (vide infra), and thus a 111 Ag-PAC measurement typically requires at least several hours to achieve a decent signal-to-noise ratio.Moreover, from a radiopharmaceutical perspective, the lack of suitable Ag(I) chelators has reduced the interest toward this radionuclide so far, limiting its application in drug design and pre-clinical research.On the other hand, 111 Ag-PAC spectra are in general significantly less affected by deleterious "after effects" than 111 In-PAC spectra, and the 111 Ag half-life is long enough to carry out the potentially time-consuming radiochemical processes and to allow its delivery to more distant PAC-measurement facilities.As a result, 111 Ag may in some cases become an attractive alternative to 111 In.
This work aims to illustrate the potential of 111 Ag-PAC to provide insight on the structure and stability of 111 Ag-labeled compounds in biological environments.To accomplish this, we have simulated the 111 Ag-PAC signals for 111 Ag(I) bound to molecules having different molecular weights, and therefore displaying tumbling rates (rotational diffusion) on different time scales.The simulated spectra show how different scenarios may be elucidated, for example: 111 Ag(I) is stably coordinated by a low-molecular-weight probe represented by a single chelator moiety, or the 111 Ag-chelator complex is not stable in vivo and 111 Ag is transchelated by a high-molecular-weight protein.Next, these spectra were compared to the PAC experimental data obtained from a pilot study in which solutions of 111 Ag(I) bound DO4S and 111 Ag(I) in human serum, representative of each scenario, were analyzed.We hope this may serve as inspiration for future application of in vivo 111 Ag-PAC studies, including the design of chelators, and the evaluation of the stability of 111 Ag-labeled radiotracers.

General
All solvents and reagents were purchased from commercial suppliers (Sigma-Aldrich, Fluka, VWR Chemicals) and were used without further purification.1,4,7,ethyl]-1,4,7,10-tetraazacyclododecane (DO4S) was synthesized in our laboratories according to previously reported procedures (Tosato et al., 2020b).Human serum was obtained after centrifugation from the blood of a healthy volunteer and stabilized by the addition of heparin.The human serum sample was kept in the refrigerator when not used.
The purification procedure was performed using an anion exchange column (Dowex 1x8) after the dissolution of the irradiated powder in aqua regia as reported in the literature (Bauer et al., 1997). 111Ag(I) was selectively eluted by using 6 M HCl acid in several fractions containing different amounts of radioactivity.Fractions were concentrated by evaporation, and then added with a proper amount of water. 111Ag(I) was provided as 1 M HCl samples.

PAC instruments and data analysis
A digital PAC setup, DIGIPAC (Nagl et al., 2010), using five 1.5"⨯1.5"LaBr 3 (Ce) detectors, was used for the spectroscopic measurements.The time resolution was 0.9 ns for the combined γ-γ coincidences, and the time-per-channel was 0.7910 ns.The initial data processing was conducted with the software PacMan and PacMaster (Nagl et al., 2010(Nagl et al., , 2011)).All measurements were conducted with the samples at room temperature but otherwise kept in a refrigerator.
The data analysis and the simulation of PAC spectra were carried out with the Winfit program (provided by prof.T. Butz) using 550 data points (the first 10 points were always excluded due to systematic errors).A Lorentzian line shape was used with the parameter δ accounting for line broadening due to a static distribution of electric field gradients (EFGs).
All spectra were initially analyzed with two nuclear quadrupole interactions (NQIs), one with slow (or no) molecular reorientation and one with rapid molecular reorientation.Only NQIs with amplitude above the noise level (i.e.amplitude larger than the standard deviation) were kept in the final fit.
The experimental equivalent of G 22 (t) (vide infra) to which the NQI parameters are fitted is (1): where W(180 • ,t) and W(90 • ,t) are the geometrical mean of coincidence spectra recorded with 180 • and 90 • between detectors, after adjustment to the same (t = 0) start channel and correction for random coincidences.

111 Ag-PAC theory
The decay scheme of 111 Ag is shown in Fig. 2. For the vast majority, 111 Ag directly decays to the 111 Cd ground state (I = 1/2 + ) by β − -emission.However, 7% of the decays populate the 111 Cd excited state (I = 3/2 + , E = 342 keV) which subsequently has a 1.4% relative probability of decaying to the ground state by the emission of two consecutive γ-rays used in 111 Ag-PAC spectroscopy.Note that it is the nuclear quadrupole interaction (NQI) in the 111 Cd intermediate state (I = 5/2 + , E = 245 keV) which is probed in 111 Ag-PAC spectroscopy.
The β-decay of 111 Ag is accompanied by recoil energy of the 111 Cd daughter nucleus of up to around 500 kJ/mol, i.e. comparable to chemical bond energies.Moreover, the change of element and oxidation state from Ag(I) to Cd(II) in itself leaves the system out of equilibrium.Therefore, a significant amount of energy is deposited locally at the PAC probe site, and one cannot a priori exclude that the metal ion dissociates from the complex.However, 111 Ag PAC data on metal sites in proteins (Balogh et al., 2020;Hemmingsen et al., 2004) indicate that the 111 Cd (II) usually remains at the metal ion binding site, although the coordination geometry may change within a few hundreds of nanoseconds after the decay.Similarly, quantum chemical molecular dynamics simulations indicate that the kinetic energy is dissipated within picoseconds (Fromsejer et al., 2022), but that the local metal site structure may change to accommodate Cd(II).For static and randomly oriented molecules, the NQI is essentially characterized by two parameters, typically presented as the interaction strength (ω 0 ) and the asymmetry parameter (η).
For each species, the parameter δ accounts for minor static structural variations from one molecule to the next, giving rise to the so-called static line broadening, and A eff describes the effective amplitude of the signal, which is constant for a given radionuclide and given sampledetector geometry.Finally, λ reflects the characteristic rate of stochastic dynamics, such as molecular rotational diffusion.For a more thorough description of PAC parameters, we refer the reader to the literature (Hemmingsen et al., 2004).
The perturbation function for randomly oriented molecules and in the slow dynamics time regime (ω 0 ≫ λ) for a PAC isotope with spin I = 5/2 of the intermediate state is given by (2): where a i and ω i depend on the quadrupole frequency (ω 0 ) and the asymmetry parameter (η) of the NQI.Thus, in this time regime, the perturbation function exhibits damped oscillations given by the three cosine functions and the exponential damping factor.
In the fast dynamics time regime (ω 0 ≪ λ) the perturbation function becomes a purely exponentially decaying function given by (3): Note that the decay rate is determined by ω 0 , η, and λ, but that these parameters cannot be determined independently in a single experiment.In the intermediate time regime (ω 0 ≈ λ) there is no analytical expression for the perturbation function, but it can be modelled numerically (Danielsen et al., 2002;Zacate and Hemmingsen, 2021).

Molecular rotational diffusion
In a simple model, the molecular dynamics may be described as exclusively originating from rotational diffusion with a characteristic rotational correlation time (τ c ) defined as (4): i.e. neglecting the intramolecular motion.
The rotational correlation time may be determined for spherical molecules using the Stokes-Einstein-Debye (SED) relation ( 5) (Perrin, 1934;Lavalette et al., 1999): where V is the effective molecular volume of the molecule with radius r m , typically including a hydration layer of radius r h (which was set to r h = 3 Å), ξ is the viscosity, k is Boltzmann's constant, and T is the absolute temperature.The molecular radius may be determined as ( 6): where M is the molecular mass, ρ is the density of the molecule, and N A is the Avogadro's number.The density depends on the investigated molecules and, in this study, it was set equal to the density of water at room temperature (1 g/cm 3 ).The choice of ρ = 1 g/cm 3 and r h = 3 Å has no significant impact on the conclusions in this work.
For small molecules, the SED assumption of a homogenous distribution of mass throughout the rotating spherical molecule breaks down, and the mass displaying rotational diffusion may be smaller than the molecular mass.This situation includes for example a complex formed by a central heavy metal ion in water surrounded by 6 coordinating water molecules.

Simulated 111 Ag-PAC spectra
The simulated 111 Ag-PAC data are presented in Fig. 3 for two sets of typical NQI parameters (ω 0 = 100 Mrad/s and η = 0, panel A; ω 0 = 500 Mrad/s and η = 0, panel B) for 111 Ag bound to molecules with molecular masses spanning from 100 g/mol to 1000000 g/mol in aqueous solution and at room temperature.As previously indicated, the perturbation function is exponentially decaying in the rapid rotational diffusion time regime (small molecules) and exhibits damped oscillations in the slow rotational diffusion time regime (large molecules).Consequently, the change of the PAC signal with the molecular mass demonstrates that PAC spectroscopy is sensitive to changes in rotational diffusion over 4 orders of magnitude of molecular mass of the molecule that binds 111 Ag.
For the low frequency series (ω 0 = 100 Mrad/s, η = 0, Fig. 3 -panel A), the slow reorientation time regime is observed for molecular masses >100000 g/mol, while the signal is heavily damped in the range 10000-40000 g/mol.Finally, the rapid reorientation time regime is found for molecular masses <4000 g/mol.In vitro, these ranges can be shifted in a controlled manner by changing the temperature or viscosity of the solution.However, in vivo -for example in blood -the span of possible temperatures and viscosities are more limited, typically changing the rotational correlations time by no more than a factor of 10 from those indicated in Fig. 3.For instance, an increase of viscosity by a factor of 4 would roughly shift the ranges indicated above towards lower molecular masses by the same factor, i.e. slow rotational diffusion for molecular masses >25000 g/mol, intermediate for molecular masses = 1000-2500 g/mol, and fast rotational diffusion for molecular masses <1000 g/mol.The low frequency PAC signal is desirable in the sense, that changes in molecular mass as small as a factor of 2 (i.e. the labeled molecule binds to another molecule of the same molecular mass) give rise to significant changes in the PAC signal across almost the entire range of molecular masses.On the other hand, the high frequency PAC signal (ω 0 = 500 Mrad/s, η = 0, Fig. 3 -panel B), remains in the information-rich, slow reorientation time regime for smaller molecular masses.However, once the molecular mass is < 10000 g/mol, the signal is strongly damped, and essentially remains damped for all the smaller molecular masses.This is an effect of the frequency, ω 0 , entering the exponent quadratically (equation ( 3)), i.e. high frequency signals fall into a loss-of-signal "darkness" for molecular masses <10000 g/mol.This effect can in some cases be advantageous, for instance when a 111 Ag-labeled small molecule (giving practically no signal) binds to a large molecule such as a protein, thereby giving rise to the emergence of a signal, in analogy to a fluorescent probe lighting up upon binding.
In most bio-applications of PAC spectroscopy in the literature, sucrose is added to the solution to increase the viscosity, aiming to slow down the rotational diffusion and thereby ensuring that the system is in the slow dynamics time regime (Hemmingsen et al., 2004 and references therein).This is desirable because the damped oscillatory PAC signal (in the slow dynamics time regime) is more information-rich than the heavily damped signal (in the intermediate time regime) and the exponentially decaying signal (in the rapid dynamics time regime).Indeed, in the slow dynamics time regime, all three PAC parameters reflecting structure and dynamics (i.e.ω 0 , η, and λ) can be determined independently.On the other hand, the significant change in the PAC signal with the change of molecular mass may be exploited to monitor the dynamics experienced by the PAC probe.As an example, this was reported for the binding of plastocyanin to photosystem 1, which is part of the electron transport in photosynthesis (Danielsen et al., 1999).In  S2) using r h = 3 Å, ρ = 1 g/cm 3 , ξ = 1.0 mPa s, T = 298.15K, and the molecules are assumed to be rigid (i.e.no intramolecular dynamics).Perturbation functions above the red lines are calculated within the fast molecular reorientation approximation (low molecular masses) and exhibit pure exponential decay.Perturbation functions below the red lines are calculated within the slow molecular reorientation approximation (high molecular masses) and exhibit damped oscillations.Perturbation functions indicated in red are in the intermediate time regime, where neither of the two approximations are valid.Notice that the dynamic range in which the PAC signal is sensitive to molecular mass spans several orders of magnitude.(For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)aqueous solution 111 Ag(I) bound to plastocyanin (molecular mass ~ 10000 g/mol) gives a strongly damped PAC signal (intermediate time regime), as expected from Fig. 3.However, upon the addition of the large photosystem 1 to the sample, the rotational diffusion was significantly slowed down, and a damped oscillatory signal was observed, thereby demonstrating the formation of the plastocyanin-photosystem 1 complex.
At the other extreme, it is possible to change from the rapid dynamics time regime to the intermediate time regime.In the limit of very rapid rotational diffusion or very low frequency NQIs, the exponent (− 2.8ω 0 2 (1+η 2 /3)/(λt)) of equation ( 3) converges to 0, thereby leaving the angular correlation unperturbed (i.e.G 22 (t) = 1), in contrast to the rapid loss of signal occurring in the intermediate dynamics time regime where G 22 (t) approaches to 0 within the first short time span, i.e. within about the first 10 ns of G 22 (t).This situation was exploited to study the binding of Cd(II) to the enzyme superoxide dismutase (SOD) (Bauer et al., 1991).The Cd(II)-SOD complex displayed dynamics in the intermediate time regime (i.e. a strongly damped perturbation function) while free Cd(II) in solution essentially gave G 22 (t) = 1 presumably reflecting both a low frequency NQI (assuming that the aqua ion of Cd (II) coordinates six water molecules in an octahedral coordination geometry) and rapid rotational diffusion, thereby allowing for discrimination of free Cd(II) in solution and Cd(II) bound to SOD.In that study, the authors used the so-called time integrated PAC spectroscopy (TI-PAC) recording the integral of the PAC signal over the first 150 ns of the perturbation function.The main advantage of TI-PAC is that a decent S/N may be achieved considerably faster than when recording the full-time dependence of the perturbation function.In many cases, TI-PAC may also be the method of choice for 111 Ag-PAC spectroscopy, in particular, because of the long time necessary (hours to days) to record a time-dependent PAC spectrum for this isotope.

Experimental 111 Ag-PAC spectra
In this section we present a pilot 111 Ag-PAC study with examples of spectra, which as it turned out, fall into the three-time regimes of rotational reorientation presented above (i.e.slow, intermediate, and fast), thus illustrating the span of spectroscopic features that may be encountered in vivo.  1 are determined.Although, the S/N obtained in this pilot study is not impressive, it is adequate for the conclusions presented in the following sections.The S/N may be improved by increasing the 111 Ag activity in the samples.In this work the 111 Ag activity of each sample was on the order of 1 MBq by the start of the PAC measurement, which typically lasted a 1-5 days.The activity can be increased by at least an order of magnitude without saturating the detectors and introducing excessive dead-time.The amount of 111 Ag produced by neutron irradiation of isotopically enriched 110 Pd is not a limitation, as typical batch activities by the end of production are on the order of 1 GBq and can be further increased if required.Thus, it is feasible to achieve better S/N than obtained for in the samples in the present work.
The 111 Ag-PAC signal of [ 111 Ag]Ag(I) added to the phosphate buffered solution with no chelator present (Fig. 4 -red line and Table 1 sample a) exhibits damped oscillatory behavior and can be analyzed with one static NQI.The data, therefore, indicate that Ag(I) is precipitated or embedded in very large complexes.The low frequency and high asymmetry of the NQI (ω 0 = 142(5) Mrad/s, η = 0.73( 7)) indicate that Ag(I) occupies a site with coordination number >2, akin to low frequency signals observed for non-linear coordination, e.g.observed in AgNO 3 (s) and Ag 2 SO 4 (s) (Lerf and Butz, 1987).The damping of the PAC signal can either be due to a number of different inequivalent Ag(I) sites

Table 1
Parameters fitted to 111 Ag-PAC data (see main text and Fig. 4).Sample conditions are described in detail in the methods section.
in the precipitate, rotational diffusion (for nanosized particles), or to the recoil experienced by the 111 Cd daughter nucleus after the β − decay, causing Cd(II) to occupy various binding sites with different local structure.
The main component of the PAC signal of [ 111 Ag]Ag(I) in presence of DO4S in a 1:1 M ratio (Fig. 4 -green line and Table 1 -sample b), is an exponentially decaying signal, accounting for ~ 80% of the total signal.This signal falls in the fast dynamics time regime illustrated in the upper part of Fig. 3 -panel A (i.e. in the opposite extreme as compared to Ag(I) in human serum -vide infra).This signal is in accordance with Ag(I) bound to the rapidly tumbling chelator, and indicates that the majority of Ag(I) is in the form of [Ag(DO4S)] + (and not precipitated) under these conditions, as expected (Tosato et al., 2020a).The exponentially decaying signal which presumably originates from Ag(I)-DO4S is significantly different from the signal recorded for Ag(I) with no chelator present, hence, at the phenomenological level, precipitated Ag(I) in buffered solution can be discriminated from Ag(I) bound to a chelator in solution.Only the decay constant, c = 2.8(ω 0 ) 2 /(λ)(1+ η 2 /3) can be extracted from the data in this case of fast dynamics, giving c = 9 (2) μs − 1 .If the effective rotating molecular mass of the Ag(I)-chelator complex and the hydration layer are assumed to be 600 g/mol and 3 Å, respectively, the calculated rotational correlation time (τ c ) is 0.8 ns.This result gives an estimated ω 0 = 60 Mrad/s (assuming that η = 0) which is in qualitative agreement with ω 0 expected for the previously reported structure of [Ag(DO4S)] + , i.e. a complex in which Ag(I) is six coordinated with four ammines and two exchanging thioethers (Gyr et al., 1997;Tosato et al., 2020a).There is another low amplitude component accounting for the remaining ~ 20% of the signal, which is very similar to the one recorded for sample (a), indicating that a minor fraction of Ag(I) is not bound to DO4S and remains in the structure observed for Ag(I) in sample (a).
The main component of the PAC signal of the [ 111 Ag]Ag(I) solution in presence of DO4S in a 1:0.5 M ratio (Fig. 4 -yellow line and Table 1 sample c), gives a signal with the same characteristic exponential decay as sample (b), presumably again reflecting the presence of the [Ag(DO4S)] + complex (vide supra).However, the amplitude of this signal, A = − 0.041(5), is significantly lower than the amplitude of the same signal in sample (b), where the total amplitude is − 0.11(2) (= − 0,02− 0,09, Table 1).In PAC spectroscopy the total amplitude of the signal for a given radionuclide and at a fixed sample-detector geometry is constant.Thus, there is a missing fraction of the signal for sample (c), i.e. about half of the signal which is not accounted for.This strongly indicates that the remaining part of the signal decays to zero within the first 5-10 ns, i.e. a situation illustrated with the red lines in Fig. 3, representing dynamics on the intermediate time scale.This finding is in agreement with the experimental conditions of 1:0.5 metal:chelator molar ratio, i.e. that half of the Ag(I) is bound to the chelator, while the rest is free in solution.Note that the pH for this sample was around 5.0, and this lower pH presumably shifts the equilibrium of the precipitate observed in sample (a) (pH = 6.7) towards species in solution, which then display rotational diffusion on the intermediate time scale, giving rise to the missing fraction of the PAC signal.This demonstrates that PAC spectroscopy may provide quantitative results on the radiochemical incorporation efficiency, complementing the more commonly used radio-thin layer chromatography (TLC) or radio-high performance liquid chromatography (HPLC) analyses.
The 111 Ag-PAC signal for [ 111 Ag]Ag(I) in human serum (Fig. 4 -blue line and Table 1 -sample d), displays a high frequency NQI and slow rotational diffusion, indicating that Ag(I) is either bound to large biomolecules or precipitated, but not bound to low molecular mass species.Thus, this signal falls in the range illustrated in the lower part of Fig. 3panel B.
The high frequency (ω 0 = 435(7) Mrad/s) and low asymmetry parameter (η = 0.2(1)), is similar to the 111 Ag-PAC signal reported for a single crystal of [Ag(imidazole) 2 ]NO 3 (s) (ω 0 = 425.5(1)Mrad/s, η = 0.240(1) (Hansen et al., 1999)), where Ag(I) occupies an almost linear coordination geometry with two coordinating imidazoles.This finding is in a good agreement with a bis-histidine linear coordination proposed for Cu(I) when binding to human serum albumin (HSA) (Sendzik et al., 2017).Thus, in analogy to Cu(I), it is conceivable that Ag(I) is bound to the same albumin binding site.Moreover, HSA constitutes the main carrier protein of human serum at a concentration of ⁓ 0.6 mM (the concentration of Ag(I) in our experiment was 47 μM) and it is plausible that it transports Ag(I) ions as it does with other metals.On the other hand, the fitted inverse rotational correlation time, λ slow (= 1/τ c ) = 2(6) μs − 1 , is rather low, assuming that Ag(I) is bound to HSA (molecular mass of 66500 g/mol) and would correspond to an Ag(I) binding species with an estimated molecular mass of ⁓ 610000 g/mol (using a viscosity of 1.8 mPa s at RT for human serum).The S/N of the current data and the large error bar on λ slow do not allow for reliable conclusions on this matter although it is possible that Ag(I) induces aggregation of HSA (Alhazmi et al., 2021) or that the long time needed for the PAC measurement caused clustering of the plasmatic proteins.An alternative interpretation could be, that Ag(I) is precipitated in the form of Ag 2 O and, although no 111 Ag-PAC data have been reported for this compound, the linear Ag(I) two-coordination in Ag 2 O is likely to give a high frequency PAC signal similar to the observed NQI.

Conclusion
With this work we present simulated PAC spectra, illustrating the information that may be derived from 111 Ag-PAC experiments.We particularly focus on the effect of rotational diffusion on PAC spectra, and how changes in rotational correlation time (caused by changes in molecular mass of the 111 Ag binding species) may be observed.The qualitative appearance of the PAC spectra differs depending on the NQI and the characteristic rate of dynamics, λ, and is typically divided into the slow (ω 0 ≫ λ), intermediate (ω 0 ≈ λ), and fast (ω 0 ≪ λ) dynamics time regimes.A pilot series of 111 Ag PAC experiments were compared to the simulated spectra, and as it turns out, the experimental data include examples of both slow, intermediate, and fast dynamics.As such, the data illustrate that the PAC signal for 111 Ag(I) in human serum is significantly different from that for 111 Ag(I) bound to a small molecule like an Ag(I)-chelator.Therefore, 111 Ag-PAC spectroscopy may be applied to monitor the in vivo fate of a 111 Ag-labeled compound.
In a broader perspective one may envisage: 1) stability studies of 111 Ag-radiopharmaceuticals, where the characteristic PAC signal, reflecting rapid molecular rotational diffusion, would indicate that 111 Ag(I) remains bound to the chelator, 2) dissociation studies of 111 Ag from the original compound followed by binding to another (bio) molecule of different molecular mass such as serum proteins, 3) binding studies of 111 Ag-based radiopharmaceuticals, where binding of a 111 Ag-labeled (small) molecule to another (large) molecule gives rise to a significant change in molecular mass and thereby in the rotational correlation time, 4) monitoring the in vivo lifetime of a molecular vehicle transporting 111 Ag-labeled radiotracer, such as lipid nanoparticles used to deliver drugs (Derksen et al., 1988;Forssen, 1997;Hwang and Mauk, 1977;Kamkaew et al., 2019;Mauk et al., 1980;Meares and Westmoreland, 1971;Roerdink et al., 1989), because 111 Ag will bind to (bio) molecules once the drug delivery agent degrades.A secondary point is that PAC spectroscopy may give insights into the metal coordination environment of the protein binding site, thus facilitating the identification of the carrier protein in vivo.Finally, PAC spectroscopy may be applied to analyze the binding of a radionuclide to a chelator, providing an alternative approach to the more common chromatographic methods.

Fig. 2 .
Fig. 2. Decay scheme for 111 Ag.Absolute β and γ-ray intensities are given in % per 111 Ag decay, additional intensity proceeds via emission of conversion electrons that are not detected in this work.In this work the 97-245 keV γ-γ cascade from the 111 Cd 342 keV excited state, which occurs in 0.1% of the 111 Ag decays, is used for PAC spectroscopy (Collins et al., 2014; 2016).

Fig. 3 .
Fig. 3. Simulated 111 Ag-PAC perturbation functions for different molecular masses (indicated to the right) of the molecule to which 111 Ag is bound, and two different representative sets of 111 Ag-PAC parameters.Panel A: ω 0 = 100 Mrad/s, η = 0. Panel B: ω 0 = 500 Mrad/s, η = 0 (A eff = − 0.1 in both panels, and the plots of the individual perturbation functions are shifted vertically by 0.03 units each to facilitate visual inspection).τ c is calculated according to the Stokes-Einstein-Debye approximation (see TableS2) using r h = 3 Å, ρ = 1 g/cm 3 , ξ = 1.0 mPa s, T = 298.15K, and the molecules are assumed to be rigid (i.e.no intramolecular dy- 111 Ag-PAC spectra were recorded for solutions containing: (a) [ 111 Ag]Ag(I) in buffered solution, (b, c) [ 111 Ag]Ag(I) in presence of DO4S in two different metal-to-ligand molar ratios, and (d) [ 111 Ag]Ag(I) in human serum.The resulting spectra are shown in Fig. 4 from which the parameters in Table

Fig. 4 .
Fig. 4. 111 Ag-PAC data and fit (bold faced line).(A) Time scale from 0 to 300 ns; (B): Zoom-in on the first 100 ns (included for a better visual evaluation of the initial oscillatory signals).Red: [ 111 Ag]Ag(I) in buffered solution (sample a); green: [ 111 Ag]Ag(I) in presence of DO4S in a 1:1 metal-to-ligand ratio (sample b); yellow: [ 111 Ag]Ag(I) in presence of DO4S in 1:0.5 metal-to-ligand ratio (sample c); blue: [ 111 Ag]Ag(I) in human serum (sample d).(For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.) the decay rate of the exponentially decaying signal appearing in the fast dynamics time regime, see eq. (3), c = 2.8