Glucose exchange parameters in a subset of physiological conditions

The chemical exchange of labile protons of the hydroxyl groups can be exploited in a variety of magnetic resonance experiments to gain information about the groups and their physicochemical environment. The exchangeable –OH protons provide important contributions to the T2 of water signals thus contributing to the T2-weighted contrast of MRI images. This exchange can be exploited more specifically and sensitively in chemical exchange saturation transfer (CEST) or longitudinal rotating frame relaxation (T1,ρ) experiments. Since glucose is omnipresent in living organisms, it may be seen as a rather universal probe. Even though the potential was first recognized many years ago, practical use has remained scarce due to numerous challenges. The major limitation is the rather low glucose concentration in most tissues. The other obstacles are related to multiple dependencies of the exchange parameters, such as temperature, pH, and concentration of various ions that are not known in sufficient detail for glucose. Thus, we embarked on evaluating the exchange parameters of a model that included every relevant chemical site for all –OH protons in both dominant enantiomers of glucose. We have (1) obtained conventional one-dimensional proton NMR spectra of glucose solutions in suitable temperature ranges, (2) we have iterated through several exchange models with various degrees of freedom determined by the number of distinguishable –OH proton sites and compared their performance, (3) we extrapolated the parameters of the best model of physiological temperature and (4) we demonstrated the use of the parameters in virtual experiments. As the main results, (1) we have obtained the temperature dependence of exchange parameters with reliable confidence intervals in three different pH values, with two of them reaching physiological temperature, and (2) we show how the parameters can be used in virtual experiments, helping to develop new applications for glucose as an NMR/MRI probe.

Exchange rate (Hz) Figure 7: Fits of the temperature series for sample of pH=7.00.Exchange rate obtained by MCMC fit for each site are shown at calibrated temperatures, zoomed around the data points.Note that the lowest-temperature points are systematically out of trend.Removing these points may be considered after rigorous justification.Table 3: Exchange rates extrapolated to 310 K, 1M glucose at pH=7.00, using restricted model, with partial assignment.The water is used as a reference, therefore the chemical shift is zero.Exchange rate of water is calculated from the other exchange rates on the fly, so there is no need to specify it in the model.The fractional concentration of water is here set as 110 mol/l (of water hydrogen atoms).For confidence intervals of these paremeters, see Tables 1, 6 and 7, from which this table is assembled.Note however, that the chemical shifts correspond to the temperature of ∼295 K since no extrapolation of those was attempted.a Suitably narrow range is used where the assignment is obvious.The chemical shift can be estimated from the spectrum.b With the sign we indicate, that in this (restricted) model, the exchange rate of β is set equal to the α on the left in the table.This way, the chemical shifts of corresponding α and β (of the same carbon) are obtained during the fitting.

Figure 5 :
Figure 5: Hypothetical simulated spectra in -OH region of separate α and β anomers of 1M glucose in 1xPBS, at pH=6.21, temperature = 270 K at magnetic field of 11.7 T

Figure 6 :
Figure 6: Fits of the temperature series for sample of pH=6.21.Exchange rate obtained by MCMC fit for each site are shown at calibrated temperatures, zoomed around the data points.

Figure 8 :
Figure 8: Examples of histograms of exchange rates obtained in MCMC simulations, for sample of pH=6.21, at 270 K and 290 K.The distributions are approximately symmetric.

Figure 9 :
Figure9: Examples correlation functions of saved steps obtained in MCMC simulations, for sample of pH=6.21, at 270 K.One can see that the correlation time is short on the scale of MCMC simulation, therefore the space is probably sampled well.

Figure 10 :
Figure10: Spectra at low concentration of glucose, pH = 6.21, clearly the fitting for spectrum of 0.04 M glucose at 290 K has to be discarted.

Table 1 :
Exchange rates extrapolated to 310 K, 1M glucose at pH=6.21, using restricted model, with partial assignment.

Table 2 :
CONT: Exchange rates extrapolated to 310 K, 1M glucose at pH=6.21, using restricted model, with partial assignment.

Table 4 :
CONT: Exchange rates extrapolated to 310 K, 1M glucose at pH=7.00, using restricted model, with partial assignment.

Table 5 :
Exchange rates extrapolated to 310 K, 1M glucose at pH=7.38, using restricted model, with partial assignment.

Table 6 :
CONT: Exchange rates extrapolated to 310 K, 1M glucose at pH=7.38, using restricted model, with partial assignment.

Table 11 :
Example defining the restricted exchange model of ∼ 1M glucose at temperature of 269.5 K

Table 12 :
Example defining the restricted exchange model for fitting at low temperature (270 K) and pH=6.21

Table 13 :
Example defining the restricted exchange model for fitting at higher temperature (295 K), at pH=6.21.The chemical shift ranges are narrowed arround the values obtained at low temperature to prevent swapping.

Table 14 :
Parameters of the Eyring equation for exchange rates obtained by linear fit of the linearized Eying equation.Note that parameters for pH=7.38 should be used only in low temperatures for estimates of exchange rates.