Characterising Aromatic Side Chains in Proteins through the Synergistic Development of NMR Experiments and Deep Neural Networks

Nuclear magnetic resonance (NMR) spectroscopy has become an important technique in structural biology for characterising the structure, dynamics and interactions of macromolecules. While a plethora of NMR methods are now available to inform on backbone and methyl-bearing side-chains of proteins, a characterisation of aromatic side chains is more challenging and often require s specific labelling or 13C-detection. Here we present a deep neural network (DNN) named FID-Net-2, which transforms NMR spectra recorded on simple uniformly 13C labelled samples to yield high-quality 1H-13C correlation spectra of the aromatic side chains. Key to the success of the DNN is the design of a complementary set of NMR experiments that produce spectra with unique features to aid the DNN produce high-resolution aromatic 1H-13C correlation spectra with accurate intensities. The reconstructed spectra can be used for quantitative purposes as FID-Net-2 predicts uncertainties in the resulting spectra. We have validated the new methodology experimentally on protein samples ranging from 7 to 40 kDa in size. We demonstrate that the method can accurately reconstruct high resolution two- dimensional aromatic 1H-13C correlation maps, high resolution three-dimensional aromatic- methyl NOESY spectra to facilitate aromatic 1H-13C assignments, and that the intensities of peaks from the reconstructed aromatic 1H-13C correlation maps can be used to quantitatively characterise the kinetics of protein folding. More generally, w e believe that this strategy of devising new NMR experiments specifically for analysis using customised DNNs represents a substantial advance that will have a major impact on the study of molecules using NMR in the years to come. .CC-BY-NC-ND 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted April 2, 2024. ; https://doi.org/10.1101/2024.04.01.587635doi: bioRxiv preprint 3

Nuclear Magnetic Resonance (NMR) spectroscopy is a ubiquitous technique in material science, chemistry, structural biology and clinical diagnosis. In bioscience, NMR provides unprecedented insight into functional motions (1–7) and non-covalent interactions (8–10) with atomic resolution . The technique therefore excellently complements AI -generated protein structures, e.g. from AlphaFold2, as well as structures obtained by cryo -electron microscopy (CryoEM) (11–13). Over many decades, a series of developments that include advances in hardware, sample preparation, and novel NMR pulse sequences have steadily raised the ‘size-limits’ of proteins that can be studied using solution-state NMR. Specific advances include the

of per-deuteration (14), 15N-1H TROSY (15), and methyl-TROSY methods (16). Using these techniques , it is now possible to record amide 15N-1H and methyl 13C-1H correlation maps in megadalton sized proteins. However, studying functional side chains, such as charged or aromatic side chains, which are often present in enzymatic active sites and within interaction hotspots, are much more challenging. We showed recently that employing 13C-detection allows for a characterisation of charged side chains, such as arginine and lysine, in proteins up to ~40 kDa (17, 18). For small proteins 1H-detected NMR methods are available to probe lysine and negatively charged side chains, which have provided insight into molecular recognition, salt -bridge, and hydrogen - bond formations (19, 20). These experiments are often performed on uniformly 13C labelled proteins samples using constant-time (CT) experiments that eliminate the peak splitting arising due to homonuclear 1JCC couplings in the indirect 13C dimension (21, 22) to record high resolution [13C-1H] correlation maps at different backbone and side-chain sites. Characterisation of aromatic side chains, on the other hand, has generally required specific labelling (23–26) because of non-uniform 1JCC couplings and attenuation of signal due .CC-BY-NC-ND 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted April 2, 2024. ; https://doi.org/10.1101/2024.04.01.587635doi: bioRxiv preprint 4 to substantial transverse relaxation during the constant-time period. There is therefore a clear need for improved methods to facilitate more detailed analysis of aromatic residues and their dynamics within proteins over a range of sizes of proteins to promote a greater understanding of how proteins function and interact. Deep learning methods have had a substantial impact on all areas of science in recent years (27), solving key problems in biophysics and computational biology (13, 28). Previous work from us and others have demonstrated applications of deep neural networks (DNNs) for transforming and analysing magnetic resonance data including analysing EPR DEER data (29), reconstructing non -uniformly sampled spectra, peak picking , and virtual homonuclear decoupling (30–34). Key to the success of these networks has been the ability to simulate an arbitrary amount of realistic training data (29, 34), overcoming problems of overfitting and data bottlenecks that often beset these models. A shortcoming that exists in many existing DNNs in the field , however, is their inability to report reliable and quantitative uncertainties associated with the transformations. In this work, we present a new DNN architecture, FID -Net-2, which uses data from a specially designed set of NMR experiments to not only reconstruct high resolution 1H-13C correlation maps of the aromatic side -chains in proteins , but also provide the uncertainty associated with the resulting spectra. The correlation maps generated by the DNN are free of the multiplet splittings and line broadenings that traditionally have degraded the quality of such spectra. We have validated the new DNN based methodology experimentally by accurately reconstructing high -resolution arom atic 1H-13C correlation spectra of the ~20 kDa L99A mutant of T4 lysozyme (L99A -T4L) as well as the 40 kDa Maltose Binding Protein (MBP) . Further, the utility of the new methodology is demonstrated by i) reconstructing high-resolution three-dimensional aromatic-methyl NOESY spectra to obtain aromatic 1H-13C assignments and .CC-BY-NC-ND 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted April 2, 2024. ; https://doi.org/10.1101/2024.04.01.587635doi: bioRxiv preprint 5 ii) quantitating the peak intensities in the reconstructed high-resolution aromatic 1H-13C correlation maps recorded with varying exchange times to obtain the forward and reverse rate constants for the folding of the A39 FF domain from human HYPA/FBP11.

Due to variable 1JCC couplings (~55 to ~72 Hz) and fast 13C transverse relaxation, constant- time experiments are not routinely used to record high resolution 13C-1H correlation maps at various aromatic sites in proteins. Hence, we decided to develop a DNN to transform regular HSQC-like spectra, which contain multiplet splittings in the indirect ( 13C) dimension, into a high-resolution 13C-1H correlation map with sharp singlet peaks in the 13C dimension. Designing a pulse-sequence to aid recognition of the aromatic multiplet structure in proteins by the DNN We have previously successful ly trained the FID-Net (31) architecture to virtually decouple and enhance the resolution of 13C-1H correlation spectra reporting on the methyl -groups of large proteins (35). An initial attempt to use the same strategy for the aromatic region of 13C- 1H correlation spectra of medium -to-large proteins was not satisfactory in our hands . We believe the reason for this is that the aromatic region of 13C-1H correlation spectra contains cross-peaks with different multiplet structures in the 13C dimension, whereas the methyl region essentially only contains doublets with a near uniform splitting of about ~35 Hz. In the aromatic region, singlets are observed for histidine 13Cε1, doublets for tryptophan 13Cδ1, and triplets for tyrosine and phenylalanine 13Cδ and 13Cε, respectively. Hence the DNN (or a human) cannot differentiate between two singlets with the same 1H chemical shifts separated by ~55 to ~72 Hz from a doublet , making it nearly impossible to train the DNN to perform a robust transformation between coupled and uncoupled spectra. Similarly, two doublets with the same .CC-BY-NC-ND 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted April 2, 2024. ; https://doi.org/10.1101/2024.04.01.587635doi: bioRxiv preprint 6 1H chemical shifts, 1JCC couplings and chemical shifts differing by 1JCC can be mistaken for a triplet. To facilitate a robust transformation by the DNN for resolution enhancement , we decided to take several steps. The first step was to design an NMR experiment that provides unique information about the multiplet structure of the cross-peaks so that the trained DNN can uniquely distinguish the multiplet structure of the cross -peak that it is transforming into a singlet. The DNN should then be able to avoid converting a doublet into two singlets or a triplet into two singlets. Figure 1 . Encoding of unique features in 13C NMR spectra. (a) The core element of the pulse sequence that allows for evolution of the scalar couplings and thus encod es unique features of the multiplet structure. The chemical shift evolution time in the 13C dimension is denoted t1. Simulated 1D spectra showing the expected signals for a singlet ( b), doublet (c) and a triplet ( d) when the scalar couplings have been evolved for 0 ms (red) or 2.3 ms (green). 1JCC was set to 70 Hz while the transverse relaxation rate was set 5 s-1. (e) One-dimensional 13C slices of a 13C,1H correlation spectrum on L99A- T4L recorded at a temperature of 298K and at a static magnetic field of 16.4 T. The slices are shown for the cross-peak arising from H31 13Cδ2-1Hδ2 for τcoup of 0.0 ms (red) and 2.3 ms (green). The multiplet structure of the cross-peaks can be discerned by comparing two spectra: one corresponding to a normal 13C-1H HSQC spectrum and a second one in which the 13C-13C .CC-BY-NC-ND 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted April 2, 2024. ; https://doi.org/10.1101/2024.04.01.587635doi: bioRxiv preprint 7 couplings have evolved for a small amount of time , τcoup = 2.3 ms (~1/6 1JCC) (Figure 1a), in the indirect (13C) dimension. During the τcoup delay, magnetisation arising from a singlet will not evolve while the two lines of the doublet will evolve with frequencies corresponding to ±JCC/2 and the time evolution of the two lines can be succinctly represented as {exp(− i π JCC τcoup), exp(i π JCC τcoup)}. Along similar lines, the two outer lines of a triplet will evolve with frequencies corresponding to ±JCC while the inner line, that is of twice the hight, will not evolve its phase, and represented as {exp(− 2i π JCC τcoup), 2, exp(2i π JCC τcoup)}. Ignoring the effects of relaxation, spectra recorded with τcoup = 0 and 2.3 ms will be indistinguishable from one another for a singlet. On the other hand spectra recorded with τcoup = 2.3 ms from doublet and triplet sites will contain a combination of absorptive and dispersive lineshapes, while the τcoup = 0 ms spectra only contains absorptive lineshapes. Ideal spectra calculated for the pair of experiments (red τcoup = 0 ms (red); τcoup = 2.3 ms (green)) are shown in Figure 1b for a singlet, in Figure 1c for a doublet and in Figure 1d for a triplet. Figure 1e shows a one-dimensional 13C slice extracted from 1H-13C datasets recorded on L99A-T4L using the complementary pair of experiments described. The slice originate s from the 13Cδ2 site of H31 , where the spectrum recorded with τcoup = 0.0 ms is in red and the one recorded with τcoup = 2.3 ms is shown in green. The multiplet pattern arising from the regular spectra (red) in Figure 1e can arise either from two singlets or a doublet, but the spectrum recorded with τcoup = 2.3 ms (green) that contains a combination of absorptive and dispersive lineshapes shows that it does not originate from two singlets (Figure 1b vs. 1e) but from a doublet (Figure 1c vs 1e). Along similar lines overlapping doublets can be distinguished from a triplet because the two components of the doublet evolve with frequencies of ±JCC/2 during the τcoup = 2.3 ms delay while the components of the triplet evolve with a different set frequencies namely 0, ± 1JCC once again leading to different lineshapes in the spectra recorded with τcoup = 2.3 ms . To summarise, the unique .CC-BY-NC-ND 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted April 2, 2024. ; https://doi.org/10.1101/2024.04.01.587635doi: bioRxiv preprint 8 features, or pattern, generated by recording the second spectrum that incorporates evolution due to the 13C-13C coupling allows the DNN to identify the correct spin-system. Training and assessing the performance of the FID-Net-2 DNN To improve the spectral reconstruction from the two complementary datasets described above we made several key changes to the FID-Net architecture that we have devised previously. We name this new general architecture FID-Net-2. The main difference between the original FID- Net and the new FID-Net-2 architecture is that two complete 2D planes are processed within the architecture, as opposed to a sliding window of 1D spectra (Figure S1). Furthermore, FID- Net-2 outputs two set s of tensors (spectra), one output corresponding to the desired virtually decoupled and resolution-enhanced 1H,13C correlation spectrum, I(vH,vC), and a second tensor describing the uncertainty of the intensity for each point in the enhanced spectrum, s(vH,vC). The architecture is described in detail in Figure S1. Training a DNN such as FID-Net-2 requires a large amount of training data. For FID-Net-2 the training data consists of the complementary HSQC datasets with (2.3 ms) and without evolution due to 1JCC couplings and a target high - resolution HSQC spectrum free of splittings in the 13C dimension. FID-Net-2 is then trained so that it learns to virtually decouple the desired high-resolution 13C-1H correlation map from the complementary HSQC datasets. The desired target high resolution HSQC spectrum free of splittings in the 13C dimension cannot be experimentally obtained from a uniformly 13C enriched sample and moreover would be infeasible to obtain for all the proteins required for training even if experime ntally accessible. However, as we have now shown in multiple publications, it is now established that DNNs for transforming experimental NMR spectra can be trained on synthetic data. The FID-Net-2 model was trained on approximately 30×10 6 sets of synthetically generated spectra. .CC-BY-NC-ND 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted April 2, 2024. ; https://doi.org/10.1101/2024.04.01.587635doi: bioRxiv preprint 9 The lo ss function ( Losstotal) developed for training FID-Net-2 includes three parts, Losstotal = Loss1 + Loss2 + Loss3. Loss1 corresponds to the traditional mean-square-error (MSE) between the target and predicted intensities. Loss2 was designed to ensure a gaussian distribution of the predicted uncertainties and Loss3 was designed to ensure that the uncertainties predicted agree with the RMSD between the target and predicted spectra . See

for a detailed description of the training procedure. Finally, it should be noted that FID-Net-2 can reconstruct high -resolution 1H-13C correlation maps from complementary HMQC or HSQC datasets because the same 13C chemical shift and the 1JCC terms of the Hamiltonian are active during the t1 evolution period (13C dimension) in both of these experiments. We initially assessed the performance of the trained FID -Net-2 model on set s of synthetic data , where the advantage is that the ground -truth is known . A summary of this assessment is shown in Figure 2. Figure 2a shows a representative example where FID-Net-2 is applied to a spectrum expected from an approximately 20 kDa protein at 298K. For such a case we expect about 50 cross-peaks and transverse relaxation rates of about 45 ± 20 s-1 in both the 13C and 1H dimensions. In contrast to other DNN transformations of NMR data, FID -Net- 2 transforms the input and produces two outputs, that is, the desired correlation spectrum (middle) and the uncertainty associated with the transformation (right). Note that the input consists of two 2D planes, whereas only one is shown in Figure 2a. .CC-BY-NC-ND 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted April 2, 2024. ; https://doi.org/10.1101/2024.04.01.587635doi: bioRxiv preprint 10 Figure 2. (a) Transformation with FID-Net-2 of randomly generated synthetic data corresponding to a 20 kDa protein (298K; 700 MHz). The transverse relaxation rates in the 13C and 1H dimensions were chosen from a random distribution with mean of 45 s-1 and standard deviation of 20 s-1. Other parameters match those in Table S1. ( b) Transformation with FID -Net-2 of randomly generated synthetic data corresponding to a 40 kDa protein (310K; 700 MHz). The transverse relaxation rates in the 13C and 1H dimensions were chosen from a random distribution with mean of 95 s-1 and standard deviation of 20 s- 1. Other parameters match those in Table S1. (c,d) Assessment of the predicted error, where to the left is the χi v.s. RSMD and to the right is a histogram of t he calculated χi = (predi - targeti)/σi, showed a normal distribution with mean of nearly 0 and standard deviation of nearly 1. The plots in ( c) and (d) are calculated over 10 random spectra, each with a Loss1 between 6.0×10-3 and 7.0×10-3, meaning these data are representing data amongst the worst 40%. .CC-BY-NC-ND 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted April 2, 2024. ; https://doi.org/10.1101/2024.04.01.587635doi: bioRxiv preprint 11 Firstly, it is seen that FID-Net-2 is able to eliminate the strong solvent signal to produce well-resolved spectra consisting of singlet cross -peaks. Of note is that the trained FID -Net-2 indeed produces point-by-point uncertainties, σi, that match what is expected, as judged from a gaussian distribution of 𝜒! = (𝑡𝑎𝑟𝑔𝑒𝑡! − 𝑝𝑟𝑒𝑑𝑖𝑐𝑡𝑒𝑑!)/σ! , and predicted σi that match the RMSD obtained from differences between predicted and target spectra ( Figure 2c). Figure 2b shows an application of FID-Net-2 to a simulated spectrum of a larger protein with a molecular mass of about 40 kDa. For such a protein one expects about 110 cross -peaks in the aromatic region and transverse relaxation rates of about 95 ± 20 s -1. Again, the transformation of the input produces a clean well -resolved spectrum with predicted uncertainties that follow the desired criteria (Figure 2d). Effectively, Figures 2c,d shows that the implementation of Loss2 and Loss3 was successful. One could argue that real experimental spectra potentially contain features, or artefacts, that have not been included in the training data, or that there is the potential that a future user will obtain data that contains artefacts that have not been included in the simulation data. Thus, we have not aimed to include every possible artefact that a future user might encounter in the training data, but instead show that the trained FID-Net-2 model is robust when transforming data that contains artefact not included in the training set. To test the robustness of FID-Net-2, and in particular its ability to produce reliable error estimates, we produced synthetic data where the common artefact of t1-noise encountered in NMR spectroscopy was included (Figure S2). Although t1-noise was not included in the training data in anyway FID-Net-2 reconstructed the desired spectrum from the input data and more importantly predicted uncertainties that are only slightly underestimated from the expected ones ( Figure S2). Thus, although this is not a comprehensive analysis of all possible artefacts, one can expect that, when situations that have not been included during training are encountered , FID-Net-2 will report larger errors that agree with the uncertainty of the predicted spectrum. .CC-BY-NC-ND 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted April 2, 2024. ; https://doi.org/10.1101/2024.04.01.587635doi: bioRxiv preprint 12 Figure 3. Transformation of experimental spectra of L99A -T4L. (a) 13C-1H HSQC spectrum reporting on the aromatic region of the 18 kDa L99A-T4L (298K; 700 MHz). Correlations with different coupling multiplicity are clearly visible which leads to severe overlap in this medium size protein. (b) The high resolution 1H-13C map reconstructed by FID-Net-2 from two 13C-1H HSQC spectra, recorded with τcoup = 0.0 and 2.3 ms does not contain the multiplets seen in ( a) leading to significantly l ower overlap. (c) The uncertainty in the intensities of the reconstructed spectrum (b) predicted by FID-Net- 2. (d, e, f) one-dimensional representative slices of the spectra in a, b, and c, respectively. FID-Net-2 reconstructs high -resolution aromatic 13C-1H correlation maps from experimental data Evaluations and assessments on synthetic data as shown above are important to judge the

of the trained FID -Net-2 model. However, it is by applying FID -Net-2 to real experimental data that we will truly understand its capabilities. Initially we recorded aromatic two-dimensional 13C-1H HSQC correlation spectra of the 18 kDa, L99A mutant of lysozyme from the phage T4 (36) (L99A-T4L) at 16.4 T (700 MHz) , Figure S3 . Apart from being relatively large compared to other proteins whose aromatic residues have been examined using .CC-BY-NC-ND 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted April 2, 2024. ; https://doi.org/10.1101/2024.04.01.587635doi: bioRxiv preprint 13 NMR, L99A-T4L also exhibits conformational exchange that results in differential line - broadening further testing the ability of FID-Net-2 to reconstruct high-resolution spectra from coupled spectra. As expected, using a traditional Fourier transform to process the 13C-1H HSQC data results in 13C-1H correlation maps with multiplets in the 13C dimension that show substantial overlap ( Figure 3a). In contra st, when the complementary pair (with and without the coupling delays) of 13C-1H HSQC data sets are processed using the FID-Net-2 model, a well-resolved spectrum of high quality is obtained. Furthermore, the produced uncertainties are clearly not uniformly distributed over the spectrum as is the case for thermal noise processed with a linear Fourier transformation. It is well-known that DNNs produce mappings that are highly non-linear and one cannot therefore simply assess the performance, or accuracy, from the RMSD of a transformed spectrum in an area without cross -peaks, which is custom for standard processed spectra. The produced uncertainties in Figure 3c clearly show that the uncertainties are centred around strong cross -peaks and near highly overlapped peaks. The aromatic 13C-1H correlation maps reconstructed by FID -Net-2 from datasets with differing coupling delays are both better resolved and contain more signal compared to constant -time HSQC spectra (Figure S4). Having evaluated the trained FID -Net-2 model on synthetic data, including synthetic data with t1-noise, as well as on good -quality experimental data, we sought to further assess how the trained model behaves when the data contains artefacts that are not included in the training data. We did so experimentally by deliberately mis -setting the Z1 and Z2 shims of the NMR spectrometer to create an inhomogeneous field and thus create lineshapes that deviate dramatically from the Lorentzian lineshapes used for trai ning (Figure S5). For L99A-T4L we recorded 13C-1H HSQC correlation spectra with optimal shimming and with non -optimal shimming and subsequently compared peak -intensities and peak -positions, in line with the .CC-BY-NC-ND 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted April 2, 2024. ; https://doi.org/10.1101/2024.04.01.587635doi: bioRxiv preprint 14 NUScon criteria (37). Excellent correlations are obtained both for peak positions and intensities (Figure S5) showing that FID-Net-2 can robustly reconstruct spectra from experimental data recorded under suboptimal conditions. Applications to larger proteins: FID-Net-2 reconstructs the high-resolution aromatic 13C- 1H correlation map of 40 kDa E. coli Maltose Binding Protein Recording high resolution aromatic 13C-1H correlation maps for large proteins remains a challenge due to the short 13C transverse relaxation times that make constant-time HSQC spectra very insensitive. The HMQC spectrum recorded on 40 kDa E. coli Maltose Binding Protein in complex with β -Cyclodextrin (MBP) at 310K contains few resolved correlations (Figure 4a) and a large number of correlations are severely overlapped due to 1JCC splittings in the indirect dimension. The 1H-13C correlation map reconstructed by FID -Net-2 however is much better resolved , once again demonstrating the efficacy of FID -Net-2 at reconstructing high-resolution aromatic 1H-13C correlation maps. We have chosen to use HMQC rather than HSQC type datasets as they are about 10% more sensitive (see Figure S6). The NOESY based strategy described below can in principle be used for the assignment of the correlations in Figure 4b but this is beyond the scope of this work. .CC-BY-NC-ND 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted April 2, 2024. ; https://doi.org/10.1101/2024.04.01.587635doi: bioRxiv preprint 15 Figure 4. Transformation of experimental spectra of the 40 kDa MBP. (a) 13C-1H HMQC spectrum reporting on the aromatic region of the 40 kDa MBP, recorded at 310K and at 700 MHz. Substantial overlap is observed with few resolved cross -peaks. (b) Processing with the FID -Net-2 model of two 13C-1H HMQC spectra, recorded with τ coup = 0 .0 and 2.3 ms. Many w ell-defined cross -peaks are observed, and the overlap is substantially less than in a. (c) A one-dimensional slice of the input 13C-1H HMQC spectrum is compared with th e corresponding one-dimensional slice of the output from FID - Net-2. The uncertainties predicted by the DNN model are shown as a blue filled area. .CC-BY-NC-ND 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted April 2, 2024. ; https://doi.org/10.1101/2024.04.01.587635doi: bioRxiv preprint 16 Using the 40 kDa MBP protein, with substantial peak overlap, we further assessed the FID-Net-2 mapping and the estimation of uncertainties. In summary, we recorded two sets of spectra, one with low signal-to-noise (8 scans) and one set with high signal-to-noise ratio (128 scans). Since these spectra were recorded on the same sample using the same NMR spectrometer (700 MHz; 310K), one expects that the signal intensities are proportional and that any deviations are captured by the uncertainties predicted by t he trained FID -Net-2 model. Figure S7 shows an excellent correlation between the two transformed datasets, and it also shows that the deviations are well captured by the predicted uncertainties, thus providing further evidence that the trained FID -Net-2 model transforms the data accurately, e ven noisy data, and also produces quantitative uncertainties. Exploiting FID-Net-2 to obtain aromatic 1H-13C assignments from NOESY experiments Obtaining aromatic 1H and 13C assignments in medium size proteins is challenging because HSQC-NOESY type spectra have poor resolution in the aromatic 13C dimension due to 1JCC couplings, while the CT -HSQC-NOESY spectra suffer from poor signal-to-noise due to the short transverse relaxation times of aromatic 13C nuclei. FID-Net-2 provides a ready solution to the problem. In order to assign the chemical shifts of the aromatic 13C-1H spectrum of L99A- T4L, we recorded 13CMethyl-13CAromatic-1HAromatic and 1H-13CAromatic-1HAromatic three-dimensional NOESY spectra ( Figure S8) and processed these with FID -Net-2 in the 13CAromatic-1HAromatic dimensions. A summary of these spectra and the chemical shift assignment procedure that utilises 13C,1H methyl assignments are shown in Figure 5. Figure 5a highlights how the uncertainties in intensity provided by FID -Net-2 aid in analysing the NOESY spectra. Cross - peaks with uncertainties that are as large as the signal intensities should be very carefully assessed, whereas cross-peaks (even weak ones), with small uncertainties can be confi dently interpreted. Based on a previous 13C,1H methyl assignment (38), these two spectra were .CC-BY-NC-ND 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted April 2, 2024. ; https://doi.org/10.1101/2024.04.01.587635doi: bioRxiv preprint 17 sufficient to assign the correlations seen in the high-resolution aromatic 13C,1H correlation map (Figure S9). Figure 5. Aromatic 1H-13C assignments from NOESY spectra reconstructed using FID-Net-2. (a) Strips from the 1H-1H planes of the 3D 1H-13CAromatic-1HAromatic NOESY spectrum of L99A-T4 Lysozyme (25 oC; 700 MHz) used for the assignment of Trp 138. (b) The residue Trp 138 is highlighted as magenta sticks on a cartoon representation of the T4 Lysozyme structure [PDB ID: 3dmv] (39). The residues in close proximity to Trp 138 are shown in cyan sticks and their distances from the aromatic side-chain of Trp 138 are also shown in the figure . (c) Strips from the 1H-13C planes of the 3D 13CMethyl-13CAromatic- 1HAromatic NOESY s pectrum of L99A-T4 Lysozyme (25 oC; 700 MHz) focussing on Trp 138 . The structure of the protein was used to identify aromatic and methyl protons that are close to one another, following which the complementary pair of 3D NOESY spectra that contain cross peaks between aromatic and methyl protons that are proximal to one another was used to assign the aromatic 1H and 13C resonances. FID-Net-2 was used to process the 13CAromatic-1HAromatic dimensions. Quantitative characterisation of protein dynamics using FID-Net-2 Previous DNNs devised to transform NMR spectra were not quantitative with respect to the intensities of cross -peaks (35) and were not useful to study chemical exchange, characterise .CC-BY-NC-ND 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted April 2, 2024. ; https://doi.org/10.1101/2024.04.01.587635doi: bioRxiv preprint 18 binding or other studies where accurate peak intensities are necessary. FID-Net-2 was however trained to be quantitative in this regard . To exploit this aspect of FID -Net-2, we recorded longitudinal exchange (40) spectra (EXSY /ZZ exchange ) on the A39G mutants of the FF domain (A39G-FF), Figure 6. The aromatic 13C,1H chemical shift assignment of A39G-FF was obtained using the 3D NOESY spectra described above, Figure S10 . A39G-FF exchanges slowly between the folded state and the unfolded state (41) and the addition of a small amount of urea (1 M) increases the unfolded state population giving rise to two sets of peaks in NMR spectra. As seen in Figure 6b, the FID-Net-2 transformed 13C,1H correlation map clearly shows the two sets of cross-peaks reporting on the exchange between the folded and unfolded states of A39G -FF. A least -squares analysis of the data provided the exchange rate (kex) and the population of the unfolded species (pU). To assess the quality of the data, we also recorded 15N,1H ZZ exchange spectra and obtained an exchange rate and a population (kex = 4.1 ± 0.2 s-1 and pU = 38.7 ± 0.8%.) in agreement with those obtained from the FID -Net-2 transformed spectra (kex = 3.4 ± 0.3 s-1 and pU = 36.3 ± 1.7%) thus experimentally demonstrating that spectra transformed with FID-Net-2 can be used for quantitative analyses. .CC-BY-NC-ND 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted April 2, 2024. ; https://doi.org/10.1101/2024.04.01.587635doi: bioRxiv preprint 19 Figure 6. Transformations with FID-Net-2 are quantitative . Regular 13C-1H correlation map (a) and the FID-Net-2 reconstructed 13C-1H correlation map from a ZZ exchange (TEX = 150 ms) experiment reporting on the aromatic region of the 7 kDa the A39G mutant FF domain in the presence of 1M Urea (275K; 600 MHz). Both spectra contain peaks arising from the folded (F) as well as the unfolded (U) state of the protein. The regular (FFT) spectrum ( a) is severely overlapped while the FID -Net-2 reconstructed spectrum (b) is much better resolved allowing one to identify both diagonal (F ➝ F and U ➝ U) as well as exchange cross-peaks (F ➝ U and U ➝ F) arising from the 13C𝜁2-1H𝜁2 site in W11. (c) Intensities extracted from ( b) for various TEX delays were analysed using the standard Bloch - McConnnell formalism (42) to obtain the exchange parameters. The dashed lines are drawn using the best fit parameters ( kex = 3.39 ± 0.32 s-1 and pU = 36.3 ± 1.7 %). (d) Intensities extracted a 15N ZZ exchange experiment on the same sample, for diagonal (F ➝ F and U ➝ U) and well as exchange peaks (F ➝ U and U ➝ F). The dashed lines are drawn using the best fit exchange parameters (kex = 4.08 ± 0.17 s-1 and pU = 38.7 ± 0.8 %).

Being able to characterise the regulation, interactions, and dynamics of medium and large proteins in solution is paramount to understand ing molecular functions. To that end, it is imperative to have tools to characterise aromatic side chains in proteins that are critical .CC-BY-NC-ND 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted April 2, 2024. ; https://doi.org/10.1101/2024.04.01.587635doi: bioRxiv preprint 20 reporters of function because these sites are often located in interaction hot spots, involved with substrate binding, regulation and catalysis. Specific isotopic labelling (23–25, 43, 44), has been one of the only means to characterise aromatic residues in medium -sized proteins. However, these labelling schemes limit the number of probes available and require the use of specific precursors that often lead to reduced protein yield of the samp les. Here we presented an attractive alternat e method to characterise functional aromatic residues in medium -sized proteins, wh erein a pair of complementary 1H-13C datasets recorded using a uniformly 13C-isotopically enriched protein sample are processed with the FID-Net-2 model to obtain the desired high-resolution aromatic 13C-1H correlation map. It is important to note that this methodology, based on processing with a deep neural network, offers simultaneous access to all the 13C-1H spin-pairs in all the aromatic side chains in the protein and does not require specific ally labelled samples. The FID-Net-2 network architecture is itself providing a new way to transforming NMR spectra using DNNs, because it not only produces resolution enhanced spectra, but also provides a good estimate of the uncertainty in the intensities of these spectra. We have exploited these abilities of FID-Net- 2 by obtaining chemical shift assignments (L99A-T4L) and characterising chemical exchange (A39G-FF). We believe that our new methodology will allow for a general and easy characterisation of functional aromatic side chains in medium-sized proteins. Two major developments contribute to the success of FID-Net-2: i) the design of new NMR experiments with the sole goal of aiding the DNN and ii) training t he DNN to estimate uncertainties of the transformed spectra. Datasets with τcoup set to 2.3 ms are recorded solely to provide unique features for the DNN to analyse. Due to 1JCC evolutions during τcoup, spectra obtained from such datasets will contain dispersive components in the 13C dimension making them unappealing to a human NMR spectroscopist , but nonetheless useful to the DNN that utilises the information present in such datasets to reconstruct high resolution 1H-13C .CC-BY-NC-ND 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted April 2, 2024. ; https://doi.org/10.1101/2024.04.01.587635doi: bioRxiv preprint 21 correlation maps. T he uncertainties estimated by F ID-Net-2 are crucial to both applications presented here. Knowledge of the uncertainties was critical for both identifying ‘valid’ cross- peaks in the NOESY spectra for the purposes of assignment and for obtaining kinetic parameters from the variation of cross -peak intensities as a function of mixing time. As with other convolutional neural networks, it is likely that the trained FID-Net-2 model presented in this study can be re-trained to transform other types of spectra. It is now clear that processing and transforming NMR spectra with DNNs is a powerful tool. However, we believe that to truly exploit the potential of DNNs in NMR, it is not enough to just devise new DNNs that transform existing experimental data , but to devise new experiments specifically for the DNN s to exploit as we have done here. Concomitantly developing DNNs and experimental methods will in the future to come allow for new insights, in AI-assisted NMR spectroscopy and likely also in other related scientific fields. .CC-BY-NC-ND 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted April 2, 2024. ; https://doi.org/10.1101/2024.04.01.587635doi: bioRxiv preprint 22

The FID-Net-2 architecture Our aim was to develop a DNN to map 13C-1H correlation NMR spectra reporting on the aromatic region of uniformly 13C-labelled proteins into spectra of high resolution. Standard 13C-1H spectra of uniformly labelled proteins are affected by one-bond 13C-13C homonuclear scalar couplings , line broadenings, and residua l solvent signals . The developed DNN will therefore need to (i) virtually decouple the multiplet structures arising from the homonuclear couplings, (ii) generally enhance the resolution, and ( iii) remove solvent signals. Finally, (iv) we also require that the DNN is able to predict the accuracy with which it does the mapping, which means that the DNN provides point-by-point uncertainties s (v1H,v13C), of the predicted output I(v1H,v13C). As noted in the main text and Figure 1, two input spectra are required in order for this transformation to be robust. It should be noted that the mapping performed by the developed DNN will not increase the information in the provided data , but will combine the information in the two input spectra and generate a spectrum that is of high resolution and easily interpretable by the end-user spectroscopist. To achieve the above requirements for the DNN, the previous FID-Net architecture (31) was substantially altered in several ways, including, ( i) full 2D planes are transformed as opposed to using a sliding window, ( ii) both the 13C and 1H dimensions are processed within the same architecture, (iii) a refinement step in the frequency domain was included in the end, and (iv) uncertainties are also predicted. Of note is that the last layer of FID-Net-2 produces a tensor of size (512,400,2), where the first (512,400) plane is the 1H-13C resolution enhanced spectrum and the second (512,400) plane is the confidences. A sig moidal activation, 1/(exp(- x)+1), is used to ensure that the confidences take values between 0 and 1. Standard deviations are calculated from the confidence, conf, by: 𝜎 = 1 0.998 × sigmoid(𝑐𝑜𝑛𝑓) + 0.001 − 1 .CC-BY-NC-ND 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted April 2, 2024. ; https://doi.org/10.1101/2024.04.01.587635doi: bioRxiv preprint 23 Finally, the predicted spectrum and the predicted uncertainties, σ, are convolved with a sine - bell window function, with offset of 0.4π , before calculating the losses. The architecture is detailed in Figure S1. Synthetic spectra for training FID-Net-2 The FID-Net-2 DNN was trained exclusively on synthetic data , summarised in Figure 2, and subsequently evaluated on synthetic data and experimentally acquired from protein samples. The resolution in the 13C dimension was enhanced both with virtual decoupling and by decreasing the effective transverse relaxation rate. When decreasing the effective transverse relaxation rate, care must be taken, so that the DNN does not generate artefacts from very broad features in the spectrum. We found that halving the effective relaxation rate worked well in the 13C-dimension, that is, R2,tar = 0.5 R2,inp, where the input rates, R2,inp, were randomly generated from a normal distribution with mean of 50 s-1 and standard deviation of 20 s-1 and R2,tar is the target transverse relaxation rate. The multiplet structures of the 13C-13C couplings in the input spectrum were simulated by generating two sets of coupling constants, J1,C and J2,C, that were each drawn from a normal distribution with mean of 63 Hz and standard deviation of 10 Hz. Subsequently 20% of J1,C and 20% of J2,C were set to zero, which result s in 64% triplet structures, 4% singlet structures, and 32% doublet structures. To simulate non-weak couplings, roofing effects were added by multiplying the FID in the 13C dimension by Ccos(𝜋𝐽",$𝑡") + 𝜚" 𝑖 sin(𝜋𝐽",$𝑡")I × Ccos(𝜋𝐽%,$𝑡") + 𝜚% 𝑖 sin(𝜋𝐽%,$𝑡")I. Here ρ1 and ρ2 are factors to include roofing effects and these are both drawn from a normal distribution with mean of 0 and standard deviation of 0.08. Each spectrum contained between 40 and 200 cross -peaks, with chemical shifts uniformly distributed along the 13C-dimension. The 1H chemical shift were generated to increase the overlap of cross -peaks. Firstly, initial 1H chemical shifts 𝛿& ' were drawn from a normal distribution with mean of 0 ppm and standard deviation of SW/4. Subsequently, to .CC-BY-NC-ND 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted April 2, 2024. ; https://doi.org/10.1101/2024.04.01.587635doi: bioRxiv preprint 24 increase the overlap, the final 1H chemical shifts were calculated using the following empirical equation, which also ensures that cross -peaks are not on the edge of the spectrum in the 1H dimension: δ& = 0.2 × SW × tanhRS2𝛿& ' SW T ( U + 0.3 × SW × tanhW2𝛿& ' SW X In the 1H dimension, the input simulated data included 1H-1H homonuclear couplings. Similar to the 13C dimension, two sets of coupling constants were generated J1,H with an average of 8 Hz and a standard deviation of 2 Hz and J2,H with an average of 4 Hz and a standard deviation of 2 Hz; 10% of J1,H were set to zero and 50% of J2,H were set to zero. Roofing effects, that is non-week couplings, were simulated in the same way as for the 13C-dimension. Solvent signals were simulated in the 1H frequency domain as 𝑠𝑜𝑙𝑣𝑒𝑛𝑡(𝑖) = 10 × 𝑖𝑛𝑡 × \𝑠𝑙𝑝 ] 1 𝑥! + 0.1 − 0.9_ − (1 − 𝑠𝑙𝑝)𝑥! ` where int is a random number drawn from the same normal distribution used to assign peak intensities, slp is a random number between 0 and 1 (uniform) . When the 1D 1H frequency- domain spectrum contains N points, then xi is 0/N, …, (N-1)/N. Half of the solvent residuals were inverted in the 1H dimension, such that the DNN learned to deal with solvent signals from both the left and the right side of the spectrum. Finally, the residual solvent signal generated in frequency domain was Fourier transformed to generate the solvent signal in the time domain, which was added to the synthetically generated random spectrum. The FID-Net-2 model was trained on a diverse range of NMR parameters ( Table S1) and so can be used without need for further retraining and the approach can be used with standard 1H-13C HSQC or HMQC pulse sequences. .CC-BY-NC-ND 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted April 2, 2024. ; https://doi.org/10.1101/2024.04.01.587635doi: bioRxiv preprint 25 Training the FID-Net-2 architecture with synthetic spectra The FID -Net-2 model was trained on approximately 30×10 6 sets of spectra, where one set consisted of a target 2D spectrum ( target) and two input spectra, without coupling evolution, inputno-coup, and with 2.3 ms coupling evolution in the 13C dimension, inputcoup. Briefly, chemical shifts were randomly distributed in the 13C dimension, while more condensed in the 1H dimension to mimic increased overlap. For the input spectra, we also added random gaussian noise and a solvent signal akin to a residual water signal. A maximum of 200 cross- peaks were generated. All training parameters are provided in Table S1. The DNN model, Figure S1, was developed and trained using the TENSORFLOW 2.11 library (45) with the KERAS (46). As mentioned in the text specialised loss functions were used to train the network with the total Loss ( Losstotal = Loss1 + Loss2 + Loss3). Loss1 corresponds to the traditional idea of minimising the difference between the predicted output spectrum and the target spectrum, whereas Loss2 is restraining a Gaussian distribution of the predicted errors, and Loss3 is restraining the calculated uncertainties to match the RMSD between the predicted and target spectrum, over 200 linear bins. Specifically, the fun ction for Loss1, also referred to as mean - square-error (MSE) is simply defined as: 𝐿𝑜𝑠𝑠" = 1 𝑁 c(𝑡𝑎𝑟𝑔𝑒𝑡! − 𝑝𝑟𝑒𝑑𝑖𝑐𝑡!)% ! [1] Where the sum is over all points in the spectrum and N is the total number of points in the 2D plane (400 × 512). The losses Loss2 and Loss3 were designed specifically for Fid -Net-2. For Loss2, a value 𝜒! was first calculated as 𝜒! = 𝑡𝑎𝑟𝑔𝑒𝑡! − 𝑝𝑟𝑒𝑑𝑖𝑐𝑡! 𝜎! , [2] .CC-BY-NC-ND 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted April 2, 2024. ; https://doi.org/10.1101/2024.04.01.587635doi: bioRxiv preprint 26 where 𝜎! is the predicted error (output from FID -Net-2). Our goal was to have 𝜒! follow a standard gaussian distribution with zero mean and standard deviation of 1. To achieve this, the 1/2th, 1st, 2nd, 3rd, and 7/2th momenta of 𝜒! were restrained as follows, 𝐿𝑜𝑠𝑠% = c gR 1 𝑁 c 𝜒! ) ! U − 𝑀)i ) ∈ ," %; "; %; (; . %/ % [3] where M1/2 = j− " %k " # Γ j ( 0k /√𝜋, M1 = 0, M2 = 1, M3 = 0, M7/2 = 2(/0 (1 − 𝑖) Γ j 2 0k /√𝜋, and Γ() is the gamma function. For the calculation of Loss3, the predicted errors, σi, were binned into 200 bins (linear), with the bins equally spaced between 0 and max(σi). Within each of these 200 bins, the average of the σi was calculated and restrained to be equal to the RMSD between the predicted points and the target points, for points corresponding to this bin. Specifically, 𝐿𝑜𝑠𝑠( = c g 1 𝑁3 c 𝜎! ! ∈ 3 − n 1 𝑁3 c(𝑡𝑎𝑟𝑔𝑒𝑡! − 𝑝𝑟𝑒𝑑𝑖𝑐𝑡! )% ! ∈ 3 i 3 ∈ 4567 % [4] The model was trained to a total loss of 8.7×10 -3 and Loss1 of ca. 5×10-3. Below, the trained model is first assessed on synthetic data and subsequently we evaluate the model on a series of experimental data. The ADAM (47) optimiser was used for training with a learning rate that changed throughout the training, β1=0.9, β2=0.98, and ε=10 -9. Mini -batching was used with 4 set of spectra in each mini-batch and the weights saved for every 2000 batches. The learning rate, lr, was calculated as 𝑙𝑟(𝑠𝑡𝑒𝑝) = 1 2884 min(𝑎", 𝑎%) , where 𝑎" = 1 s𝑠𝑡𝑒𝑝 and 𝑎% = 3.5 × 108.𝑠𝑡𝑒𝑝 .CC-BY-NC-ND 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted April 2, 2024. ; https://doi.org/10.1101/2024.04.01.587635doi: bioRxiv preprint 27 The parameter, step, is a counter for batches used in training. Thus, after an initial warm -up period, the largest learning rate used is about 2.45×10 -6, whereafter the learning rate decays. The FID-Net-2 architecture was trained on the NMRBox facility (48) using two Nvidia A100 GPUs. Assessment using synthetic data Once trained, the performance of the trained FID -Net-2 model was initially evaluated on synthetically generated data, as shown in Figure 2. Two independent assessments were made, one to represent a protein of about 20 kDa and one to represent a protein of about 40 kDa. Parameters used to generate the synthetic spectra were the same as those used for training, Table S1, except that for the 20 kDa protein only between 45 and 55 cross-peaks were generated with R2(1H) and R2(13C) both drawn from a normal distribution with mean of 45 s-1 and standard deviation of 20 s-1. For the 40 kDa protein 110 -120 cross-peaks were generated with R2(1H) and R2(13C) both drawn from a normal distribution with mean of 95 s-1 and standard deviation of 20 s-1. NMR Samples: All three [U -15N13C] protein samples were prepared by over expressing the proteins in E. coli BL21(DE3) cells transformed with the appropriate plasmids and grown in M9 medium supplemented with 1 g/L of 15NH4Cl and 3 g/L of 13C-glucose as nitrogen and carbon sources respectively. L99A-T4L (38), A39G -FF (41) and MBP (49) were all purified as described previously. The L99A-T4L sample consisted of ~1 mM [U -15N13C] protein dissolved in 50 mM sodium phosphate, 25 mM NaCl, 2 mM EDTA , 2 mM NaN3, ~99% D2O, pH 5.5 buffer. The A39G-FF samples consisted of ~1 mM [U -15N13C] protein dissolved in 50 mM sodium acetate .CC-BY-NC-ND 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted April 2, 2024. ; https://doi.org/10.1101/2024.04.01.587635doi: bioRxiv preprint 28 , 100 mM NaCl, 2 mM EDTA , 2% D2O pH 5.7 buffer. The MBP samples consisted of ~0.5 mM [U -15N13C] protein dissolved in 2 0mM sodium phosphate , 1mM EDTA, 2mM β - cyclodextrin, 99% D2O, pH 6.5 buffer. NMR Experiments: Two-dimensional 13C-1H correlation spectra: The 2D HSQC and HMQC datasets of L99A- T4L (Figure 3) and MBP ( Figure 4) used as input for FID -Net-2 were recorded on a 1 mM (L99A-T4L) or 0.5 mM (MBP) uniformly [13C,15N]-labelled samples using the pulse sequences described in Figure S3a,b, with τcoup = 0.0 ms and 2.3 ms, on a Bruker 700 MHz Avance III spectrometer equipped with Z-gradient triple-resonance TCI cryoprobe. The data was acquired with 768 and 200 (L99A-T4L) or 128 (MBP) complex points in the 1H and 13C dimensions, respectively, with spectral widths of 10000 Hz and 5000 Hz. The datasets were recorded as pseudo-3D spectra. An interscan delay of 1 s was used. The constant -time experiments ( Figure S4 ) were recorded on a 1 mM L99A -T4L uniformly [13C,15N]-labelled sample using a standard Bruker pulse sequences (hsqcctetgpsp) with coherence-selection gradients. The data was acquired with 768 and 128 (30.4 ms constant time) or 60 (15.2 constant -time) complex points in the 1H and 13C dimensions, respectively, with spectral widths of 10000 Hz and 5000 Hz. An interscan delay of 1 s was used and the data was recorded at 278K. HMQC-type Spectra of L99A-T4L used to assess out-of-scope behaivour of FID-Net- 2 and with poor shimming (Figure S5) were recorded on a 1 mM uniformly [13C,15N]-labelled samples using the pulse sequences described in Figure S3a, with τcoup = 0.0 ms and 2.3 ms, on a Bruker 600 MHz Avance HD spectrometer equipped with Z -gradient triple-resonance TCI cryoprobe. The data was acquired with 768 and 200 complex points in the 1H and 13C .CC-BY-NC-ND 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted April 2, 2024. ; https://doi.org/10.1101/2024.04.01.587635doi: bioRxiv preprint 29 dimensions, respectively, with spectral widths of 9009 Hz and 5000 Hz. The datasets were recorded as pseudo-3D spectra. An interscan delay of 1 s was used. Three-dimensional NOESY spectra: The 3D 1H-13C-1H NOESY dataset of L99A-T4L (Figure 5a) used as input for FID-Net-2 were recorded on a uniformly [13C,15N]-labelled sample using the pulse sequences described in Figure S3a,d, with τcoup = 0.0 ms and 2.3 ms, on a Bruker 700 MHz Avance III spectrometer equipped with Z -gradient triple-resonance TCI cryoprobe. The data was acquired with 1024, 128, and 96 complex points in 1H, 1HNOESY, and 13CAro dimensions, respectively, with spectral widths of 14280 Hz (1H), 5000 Hz (13C), and 8000 Hz (1HNOESY). Four scans were collected per increment with a recycle delay of 1 s . The mixing time was 100 ms. The 3D 1H-13CAro-13CMethyl datasets of L99A -T4L (Figure 5c) and A39G -FF used as input for FID -Net-2 were recorded on uniformly [ 13C,15N]-labelled samples using the pulse sequences described in Figure S8, with τcoup = 0.0 ms and 2.3 ms, on a Bruker 700 MHz Avance III spectrometer equipped with Z -gradient triple-resonance TCI cryoprobe. The data was acquired with 1024, 128, and 80 complex points in 1H, 13CNOESY, and 13CAro dimensions, respectively, with spectral widths of 14280 Hz (1H), 5000 Hz (13CAro), and 5000 Hz (1CMethyl). Four scans were collected per increment with a recycle delay of 1 s. The mixing time was 120 ms for the L99A-T4L sample and 200 ms for the A39F-FF sample. Longitudinal exchange (EXSY ; ZZ exchange ) spectra : The longitudinal aromatic 13C,1H exchange dataset of A39G -FF ( Figure 6 ) was recorded on a 0.5 mM uniformly [ 13C,15N]- labelled samples using the pulse sequences described in Figure S3c, with τcoup = 0.0 ms and 2.3 ms, on a Bruker 600 MHz Avance HD spectrometer equipped with Z-gradient triple-resonance .CC-BY-NC-ND 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted April 2, 2024. ; https://doi.org/10.1101/2024.04.01.587635doi: bioRxiv preprint 30 TCI cryoprobe. The sample was dissolved in H 2O buffer. An interscan delay of 1 s was used and the data was recorded at 274K. The data was acquired with 768 and 128 complex points in 1H and 13CAro dimensions, respectively, with spectral widths of 9009 Hz (1H), 5000 Hz (13C). Sixteen scans were collected per increment with a recycle delay of 1 s . The exchange delays were 25 ms, 50 ms, 100 ms, 150 ms, 200 ms, 250 ms and 300 ms. The longitudinal aromatic 15N,1H exchange dataset of A39G -FF ( Figure 6 ) was recorded on a 0.5 mM uniformly [13C,15N]-labelled samples using a standard pulse sequence. An interscan delay of 1 s was used and the data was recorded at 274K. The data was acquired with 1536 and 128 complex points in 1H and 15N dimensions, respectively, with spectral widths of 10000 Hz (1H), 2136 Hz (13C). Eight scans were collected per increment with a recycle delay of 1 s. The exchange delays were 25 ms (duplicate), 50 ms, 100 ms, 150 ms, 200 ms (duplicate), 250 ms, 300 ms, 400 ms, 600 ms, and 800 ms. Data processing: All experimental NMR spectra were processed with NMRPIPE (50) or using the python libraries NMRGLUE (51) and NUMPY. .CC-BY-NC-ND 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted April 2, 2024. ; https://doi.org/10.1101/2024.04.01.587635doi: bioRxiv preprint 31 Data availability: The experimental data is available from the corresponding author upon request. Code availability: The code for processing 13C-1H HSQC/HMQC spectra with FID -Net-2 is available from the corresponding author upon request.

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Dr Luke Nightingale is acknowledged for helpful discussions. The BBSRC (BB/R000255/1), Wellcome Trust (ref. 101569/z/13/z), and the EPSRC are acknowledged for supporting the NMR facility at University College London. Access to ultra -high field NMR spectrometers was supported by the Francis Crick Institute through provision of access to the MRC Biomedical NMR Centre. The Francis Crick Institute receives its core funding from Cancer Research UK (FC001029), the UK Medical Research Council (FC001029), and the Wellcome Trust (FC001029). This study made use of NMRbox: National Center for Biomolecular NMR Data Processing and Analysis (48), a Biomedical Technology Research Resource (BTRR), which is supported by NIH grant P41GM111135 (NIGMS). Some computational aspects of this work were supported by the Francis Crick Institute (DFH) through provision of access to the Scientific Computing STP and the Crick data Analysis and Management Platform (CAMP). The Francis Crick Institute (CAMP) receives its core funding from Cancer Research UK .CC-BY-NC-ND 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted April 2, 2024. ; https://doi.org/10.1101/2024.04.01.587635doi: bioRxiv preprint 35 (FC010233), the UK Medical Research Council (FC010233), and the Wellcome Trust (FC010233). PV acknowledges intramural funding from TIFR Hyderabad (DAE, Government of India, Project No. RTI 4007). For the purpose of open access, the author has applied a Creative Commons Attribution (CC BY) licence to any Author Accepted Manuscript version arising. This research is supported by the UKRI and EPSRC (EP/X036782/1). Author information: V.K.S., G.K., P.V. and D.F.H designed the research; D.F.H. designed and trained all the DNNs; V.K.S. produced all isotope labelled samples; V.K.S., P.V. and D.F.H. performed and analysed NMR experiments; V.K.S assigned the chemical shifts . All of the authors analysed the data, discussed the results and wrote the paper. .CC-BY-NC-ND 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted April 2, 2024. ; https://doi.org/10.1101/2024.04.01.587635doi: bioRxiv preprint