Time- and site-resolved kinetic NMR for real-time monitoring of off-equilibrium reactions by 2D spectrotemporal correlations

Nuclear magnetic resonance (NMR) spectroscopy provides detailed information about dynamic processes through line-shape changes, which are traditionally limited to equilibrium conditions. However, a wealth of information is available by studying chemical reactions under off-equilibrium conditions—e.g., in states that arise upon mixing reactants that subsequently undergo chemical changes—and in monitoring the reactants and products in real time. Herein, we propose and demonstrate a time-resolved kinetic NMR experiment that combines rapid mixing techniques, continuous flow, and single-scan spectroscopic imaging methods, leading in unison to a 2D spectrotemporal NMR correlation that provides high-quality kinetic information of off-equilibrium chemical reactions. These kinetic 2D NMR spectra possess a high-resolution spectral dimension revealing the individual chemical sites, correlated with a time-independent, steady-state spatial axis that delivers information concerning temporal changes along the reaction coordinate. A comprehensive description of the kinetic, spectroscopic, and experimental features associated with these spectrotemporal NMR analyses is presented. Experimental demonstrations are carried out using an enzymatically catalyzed reaction leading to site- and time-resolved kinetic NMR data, that are in excellent agreement with control experiments and literature values.

Supplementary Note 2. On experimental accuracy: The effects of flow rate, imaging spatial resolution, and temporal resolution, on the signal-to-noise ratio.
The effects of spatial resolution on the signal-to-noise ratio (SNR) of spectrotemporal 2D NMR correlations can be inferred from the usual relationships between SNR and resolution in MRI. 1 Assuming that the SNR of a conventional NMR experiment on the sample is given by The integral ratio of ethanol over BAEE, α, is larger than 1. b) Integration regions, indicated by the circles, for the reactant (black) and product (red). c) Spectral cross sections taken from two distinct regions along the field-of-view: from the edge of the coil (left) and in the middle of the coil (right). d) The integrals of BAEE (IR) and ethanol (IP) are plotted against position, which were further corrected to match the relative intensities measured in (a). Prior to the kinetic analysis the integrals IR and IP for each position were normalized according to ! " ! = ! ! /(! ! + ! " ) and ! " " = ! " /(! ! + ! " ). Only the signals contained with ± 0.7 cm of the center of the coil were used in the kinetic analysis, due inefficient excitation outside this region.
where M0 and nrms denote the targeted site's magnetization and the root-mean-square of the noise, then, for a given spatial resolution Dz of the EPSI experiment, SNR will decrease as: 2 !"# )*+, = !"# !"#$ ∆' (  (S2.2) where L is the overall sample length along z, and it is assumed that no diffusion-induced losses occur. This SNR dependence on spatial resolution is illustrated experimentally in Supplementary Simulations assumed an off-equilibrium binary chemical reaction between BAEE and trypsin (monitoring the methyl regions as a function of time/position) undergoing plug flow. All the parameters, except for the concentrations assumed, are indicated in each figure. The parameters used in these simulations mirror their experimental counterparts as closely as possible. The horizontal red bars indicate the positions from which the 1D time-resolved NMR spectra are extracted, which are displayed to the right of their corresponding 2D contour. Besides the indicated parameters, the initial concentration of the enzyme trypsin was increased from 7.5 μM to 25 μM for the faster flow rate (v = 852 μm/s, smaller dead time) in order to accurately capture the zero-order rate kinetics in the sensitive region of the NMR coil (matching the conditions of the experiment). White normally-distributed Gaussian noise was added to each dataset. show that, contrast to the simulations above, flow does reduce SNR. Modelling this is challenging as one must be able to accurately account for the effects of turbulent flow -something our singleaxis gradient system is ill-equipped for measuring. In the absence of this, experimental tests were conducted at different flow rates to examine the sensitivity losses. The SNR was seen decreasing in a manner that was commensurate with increasing flow rates (Supplementary Simulations assuming random turbulences (not shown) also led to the introduction of noise in the spectral-containing regions.
It is enlightening to consider how the kinetic time resolution ΔtR will affect the available SNR. Assuming that the off-equilibrium reaction mixture is flowing with a uniform velocity v, the corresponding temporal resolution will be ΔtR = Dz/v. Hence, following Eq. (S2.2), the experiment's sensitivity will be related to the latter as Since in general ( • ∆* ) << L, the SNR of these experiments will therefore be reduced vs that of a conventional counterpart; this is expected for an imaging-based acquisition. Further, for a fixed flow velocity, an improvement in the kinetic time resolution -i.e., a decrease in ΔtR-will be associated with a concomitant reduction in SNR. Under ideal conditions one might also increase the kinetic time resolution without SNR penalties by increasing n, as a faster flow will reveal more details about the kinetics without changing the spatial resolution. As shown in Supplementary   Figure 6, however, SNR decreases in our system with increasing n as a result of flow non-idealities.

Gradients.
This paragraph provides a description for the NMR response of a reacting off-equilibrium chemical reaction characterized by a zero-order rate law (i.e., +  Mathematically, the B signal can thus be represented in terms of these two distinct time-dependent contributions as: and, where G ,→. (* 5 ) = > is the probability for the reaction to occur at *′ and < . = Cω . − # 3. , which has the same units as the < , defined above. These integrals readily evaluate to the following expressions to give the signal of B for all post-excitation times *: and, This is Equation (4) in the main text. Contributions to the B-spin NMR signal arising from excited equilibrium magnetization present at t = 0 are straight-forward to account for, and are described by a complex exponential akin to that in Equation (S3.1), evolving at < . and possessing a preexponential magnetization value that is time independent (i.e., independent of the chemical kinetics).  Therefore, Equation (S4.3) demonstrates that at the end of the second gradient pulse, the contribution of stationary spins (i.e., v independent spins) to the transverse phase is refocused whilst the contributions emanating from moving spins remain. This type of bipolar gradient readout is therefore selective for spins that are moving after a duration of 2`/.

(ii) A symmetric pair of bipolar gradients is flow-compensated
Supplementary Figure 8b shows a pair of symmetrically-placed bipolar gradients, that are again applied along the 4 direction collinear with the uniform flow. \ 2 and \ 3 are the same in this case as derived above, so \ 8 and \ 9 are then:

(iii) A pair of bipolar gradients is not flow-compensated
Supplementary Figure 8c shows a pair of bipolar readout gradients, of the kind that would concatenate in an EPSI sequence. The phase accumulated at \ 8 and \ 9 in this case is: The total phase at the end of the sequence is therefore

(v) A pre-phased bipolar gradient is flow compensated
Supplementary Figure 8e shows a bipolar gradient readout preceded by a pre-phasing period lasting half the length of a single readout gradient (i.e., Ta). In this case, only \ 8 needs to be explicitly calculated, since the phase evolution for the first read gradient and pre-phaser is identical to that of a conventional gradient echo (Equation (S4.13)). Therefore,  The right-most column shows with dotted lines the relative intensity changes of reactants and products under the different flow conditions, as quantified from the EPSI spectra in the left-most column. Also indicated in these graphs by straight lines are linear fits of each intensity data set, after invoking the plug-flow assumption. Not surprisingly there is an excellent agreement of the apparent kcat and t0 for the top-most row, and a very good agreement of the apparent k in the bottom double-parabolic flow profile, as well.