Overview of METRICWe aim to infer the true nutrient profile based on the assessed one and the measured gut microbial composition. A naive way to do this is to train a machine-learning model with the assessed nutrient profiles and microbial compositions as the input and the true nutrient profiles as the output. However, this is not feasible because such training requires the true nutrient profiles that are not easily available. To address this issue, we developed METRIC that does not rely on the true nutrient profile during its training but still can remove random errors in the assessed nutrient profile during testing (Fig. 2). During the training, we generated the corrupted nutrient profiles by adding random noise to the assessed nutrient profiles, and then trained METRIC to remove the added noise by taking the corrupted nutrient profiles and the measured microbial compositions as its input and generating the assessed nutrient profiles as its output (Fig. 2a). We introduced the corrupted nutrient profiles to avoid METRIC copying the assessed nutrient profiles directly to the output, thus forcing METRIC to remove the added noise. Note that the training of METRIC did not use true nutrient profiles.Fig. 2: The architecture and workflow of METRIC (microbiome-based nutrient profile corrector) to infer true nutrient profiles.For simplicity, we used a hypothetical example with n = 3 training samples and 2 samples in the test set. For each sample, there are \({N}_{s}\) microbial species and \({N}_{n}\) nutrients. Across panels, microbial species and their relative abundances are colored blue. Nutrients and their amounts are colored red. The corrupted nutrient profiles are created by adding different types of random noise (i.e., Gaussian, Uniform, etc.) to the assessed nutrient profiles. Icons associated with assessed/corrupted nutrient profiles are bounded by solid black/dashed lines. Icons associated with true nutrient profiles are bounded by solid green lines. a During the training of METRIC, the method takes corrupted nutrient profiles and microbial compositions as the input and learns to infer assessed nutrient profiles. b Similar to multilayer perceptrons, METRIC has several hidden layers in the middle. The skip connection provides the corrupted nutrient profile directly to one layer before the final output, enabling it to skip the propagation through the hidden layers. The skipped corrupted nutrient profile multiplied by the weight parameter \(\alpha\) and the final hidden layer (the bottom gray nodes) multiplied by (\(1-\alpha\)) add up as the final output (the bottom red nodes). c The well-trained METRIC is applied to the test set to generate predictions for nutrient profiles whose values are compared to true nutrient profiles.The architecture of METRIC is a neural network that consists of three hidden layers, in addition to its input and output layers (Fig. 2b). Each hidden layer has a fixed dimension of 256. The link weights in the neural network are initialized using the Xavier Initialization. The training loss is the mean squared error. The predictive performance is assessed by the mean Pearson correlation coefficient between true and predicted nutrient concentrations averaged across all nutrients \(\bar{\rho }\). One unique feature is the skip connection that adds the corrupted nutrient profiles directly to the final output of neural networks, which previously has been shown to enhance the training and predictive performance for deep neural networks29. Similar to the existence of the skip connection in Noise2Noise22, the introduction of the skip connection enables the neural networks to adjust the prediction based on the corrupted nutrient profile, ensuring that output variables would not deviate too much from the corrupted nutrient profile. More details about the architecture can be found in the Methods section. Overall, METRIC is a generic “denoiser” that learns to remove any random noise added to the nutrient profile. With this generic ability to remove random noise, the well-trained METRIC should be able to remove random measurement errors by generating predictions closer to the true nutrient profiles when it takes the assessed nutrient profiles and microbial compositions as its input (Fig. 2c).We split each dataset into two non-overlapping parts: a training and a test set. METRIC was trained on the training set and then used to generate predictions for the test set. The correction performance is measured by comparing the predicted nutrient profiles with the “true” nutrient profiles in the test set (how we obtain the “true” nutrient profiles for each scenario will be explained in separate sections below). To measure the predictive performance of each nutrient, we adopted the Pearson Correlation Coefficient \(\rho\) between its predicted and true corrected values.METRIC can reduce measurement errors in nutrient profiles of synthetic dataWe first validated METRIC using synthetic data for which we know the ground truth. We used the Microbial Consumer-Resource Model (MiCRM)30 to generate three types of data: (1) true nutrient profiles (i.e., the ground-truth nutrient consumption), (2) assessed nutrient profiles (i.e., the true nutrient profiles with random noise added to mimic measurement errors), and (3) corrupted nutrient profiles (i.e., the assessed nutrient profiles with artificially added random noise). MiCRM simulates the process of nutrient consumption by microbes and the following microbial growth30. Note that the random noise added to assessed and corrupted nutrient profiles are different. For simplicity, we only considered the nutrient consumption in MiCRM and did not model the nutrient production because most dietary nutrients cannot be produced by microbes. We created different samples by randomly sampling nutrient fluxes and then running the community assembly until we achieved a steady state. We consider sampled ground-truth nutrient fluxes as true nutrient profiles and the steady-state microbial abundances as microbial compositions. Gaussian noise \({{{\rm N}}}(0,\,{\sigma }^{2})\) with the mean of zero and standard deviation \(\sigma\) is added to true nutrient profiles to create assessed nutrient profiles. More details about MiCRM, the generation of synthetic data, and added noise can be found in the Methods section.We generated 250 samples by simulating the assembly process for 250 independent communities with 20 nutrients and 20 bacterial species. We trained METRIC on 200 samples and tested it on the remaining 50 samples. We measured how assessed values and corrected values (i.e., predicted values on the test set) respectively correlate with true values. For each nutrient, we measured \({{\rm{\rho }}}\) between its corrected values from predictions and its true concentration (denoted as \({{{\rm{\rho }}}}_{{{\rm{c}}}}\)). Similarly, we calculated \({{\rm{\rho }}}\) between its assessed concentrations and its true concentration (denoted as \({{{\rm{\rho }}}}_{{{\rm{a}}}}\)). As the standard deviation \(\sigma\) of the Gaussian noise increases, METRIC starts to correct the introduced noise, represented by the switch from negative values of (\({{{\rm{\rho }}}}_{{{\rm{c}}}}-{{{\rm{\rho }}}}_{{{\rm{a}}}}\)) to positive values in Fig. 3a. It is natural to expect that the correction of nutrient profiles with weaker noises does not work (\({{{\rm{\rho }}}}_{{{\rm{c}}}} \, < \, {{{\rm{\rho }}}}_{{{\rm{a}}}}\) for small \(\sigma\) in Fig. 3a), because the correction is not necessary when the measurement error is small (e.g., when \({{{\rm{\rho }}}}_{{{\rm{a}}}} \, > \, 0.8\)). We focus on the case of \(\sigma=1.5\) from now on. The difference between the two metrics (i.e., \({{{\rm{\rho }}}}_{{{\rm{c}}}}-{{{\rm{\rho }}}}_{{{\rm{a}}}}\)) reflects the correction performance. The nutrient in Fig. 3d, e is slightly corrected (\({{{\rm{\rho }}}}_{{{\rm{c}}}}-{{{\rm{\rho }}}}_{{{\rm{a}}}}=0.01\)), while the nutrient in Fig. 3f, g is strongly corrected (\({{{\rm{\rho }}}}_{{{\rm{c}}}}-{{{\rm{\rho }}}}_{{{\rm{a}}}}=0.09\)). Most nutrients have a better alignment between their corrected values and true values (Fig. 3h).Fig. 3: METRIC can correct the measurement error in assessed nutrient profiles on synthetic data from MiCRM (microbial consumer-resource model)30.The Pearson’s Rank Correlation Coefficient \(\rho\) is adopted to evaluate the correlation across various types of nutrient profiles. All corrected/true values shown are the log of nutrient concentrations. a \({\rho }_{c}\) (i.e., \(\rho\) between corrected and true values) and \({\rho }_{a}\) (i.e., \(\rho\) between assessed and true values) decrease as the standard deviation of added Gaussian noise \(\sigma\) increases. Data are presented as mean values +/− standard error of the mean (SEM), derived from five training repeats (n = 5) for each case. All following panels focus on the case of \(\sigma\) = 1.5. b The correlation between assessed values and true values of log concentrations of one nutrient among different samples. c The correlation between corrected values (predictions of METRIC) and true values of log concentrations of the same nutrient among different samples. Similar comparisons for the other two nutrients are shown in (d, e) and (f, g). h The correction performance of all nutrients is measured by (\({\rho }_{c}-{\rho }_{a}\)). Source data are provided as a source data file.METRIC mitigates measurement errors added to nutrient profiles in real dataNext, we tested METRIC on three real-world datasets. The first dataset, MCTS (MiCrobiome dieT Study), comes from a unique study that investigated the influence of diets on gut microbial composition31. It is unique because a large number of samples (n = 210) of paired nutrient profiles and microbial compositions were collected. The nutrient profiles were calculated from ASA24 (see Methods). Different from the availability of true nutrient profiles in synthetic data, the true nutrient profiles are not available for real data. To deal with this issue, we treated the nutrient profiles derived from ASA24 as the “true” nutrient profiles and added random noise (Gaussian noise with the mean of zero and standard deviations \(\sigma\)) to them as “assessed” nutrient profiles. As \(\sigma\) increases, METRIC starts to better correct the introduced noise (Fig. 4a). We focus on the case of \(\sigma=1.0\) from now on. We found that carotene has a large \({\rho }_{{{\rm{a}}}}\) and is not improved by METRIC (\({\rho }_{{{\rm{a}}}}=0.99\) versus \({\rho }_{{{\rm{c}}}}=0.97\) in Fig. 4b, c). By contrast, fiber has a small \({{{\rm{\rho }}}}_{{{\rm{a}}}}\) and is strongly improved (\({{{\rm{\rho }}}}_{{{\rm{a}}}}=0.35\) versus \({{{\rm{\rho }}}}_{{{\rm{c}}}}=0.58\) for Fig. 4f, g). We believe that the large correction in the total fiber intake was due to most fibers being digested by gut microbes24,25. Overall, nutrients with smaller \({{{\rm{\rho }}}}_{{{\rm{a}}}}\) have better correction performance, and nutrients with large \({{{\rm{\rho }}}}_{{{\rm{a}}}}\) rarely improved (Fig. 4h). The mean correction performance averaged over all nutrients is \((\bar{{\rho }_{c}}-\bar{{\rho }_{a}})=0.079\).Fig. 4: METRIC can correct the measurement error in assessed nutrient profiles on real data from MCTS (microbiome diet study)31.The Pearson’s Rank Correlation Coefficient \(\rho\) is adopted to evaluate the correlation across various types of nutrient profiles. All nutrient concentrations are in the unit of grams. All corrected/true values shown are the log of nutrient concentrations. a \({\rho }_{c}\) (i.e., \(\rho\) between corrected and true values) and \({\rho }_{a}\) (i.e., \(\rho\) between assessed and true values) decrease as the standard deviation of added Gaussian noise \(\sigma\) increases. Data are presented as mean values +/− standard error of the mean (SEM), derived from five training repeats (n = 5) for each case. All following panels focus on the case of \(\sigma\) = 1.0. b The correlation between assessed values and true values of log concentrations of carotene among different samples. c The correlation between corrected values (predictions of METRIC) and true values of log concentrations of carotene among different samples. d, e The similar comparison for octadecanoic acid shows a modest correction. f, g The similar comparison for fiber shows a strong correction. h The correction performance for all nutrients is measured by (\({\rho }_{c}-{\rho }_{a}\)). Source data are provided as a source data file.We also tried to run METRIC without using the microbial composition, finding that the correction performance (\(\bar{{\rho }_{c}}-\bar{{\rho }_{a}}=0.067\)) is worse than that with included microbial composition (Supplementary Fig. 1). We also computed the sensitivity which is defined as the ratio between the reduction in \(\rho\) of nutrient \(\alpha\) and the perturbation amount of species \({i}\) (Supplementary Fig. 2), which could detect some possible interactions between nutrients and species. For example, the sensitivity of monounsaturated fatty acids towards Bacteroides uniformis is large (~0.025, larger than 99.98% of the inferred sensitivity values), and is supported by the previously observed reduction of monounsaturated fatty acids by Bacteroides uniformis32. In addition, our sensitivity analysis revealed that the top three microbial taxa linked to fiber content correction, which exhibit the highest sensitivity values, are well-documented as fiber degraders in the literature: Bacteroides plebeius33, Parabacteroides sp34, and Bacteroides sp35.Then, we applied METRIC to the second dataset MLVS (Men’s Lifestyle Validation Study)36,37. Specifically, we utilized the composition of gut microbiomes and the one-day dietary assessment of the 7-day dietary records (7DDRs). The 7DDRs are widely recognized to be the most reliable estimation of dietary intake because participants are required to measure and report gram weights for foods both before they start eating and after they finish, thereby enabling the calculation of the actual food consumption based on the difference in weight38. To guarantee the usefulness of gut microbial composition in correcting dietary assessment, we required the identification of paired microbial compositions and dietary assessments with matching dates. In MLVS, a total of 599 paired samples with matching dates were found. Similarly, as we did for the MCTS dataset, we regarded the nutrient profile derived from the 7DDRs as the “true” nutrient profile and added varying levels of Gaussian noise to it as the “assessed” nutrient profile. Then we trained METRIC on 80% of the data and tested it on the remaining 20%. Consistent with our previous findings, the trained METRIC exhibits an ability to correct the nutrient profile (Fig. 5a), especially for large \(\sigma\). For the case of \(\sigma=1.0\), the mean correction performance \((\,\bar{{\rho }_{c}}-\bar{{\rho }_{a}})\) is \(0.072\) (Fig. 5h). Across all nutrients, dietary fiber was the strongest corrected nutrient (Fig. 5f, g).Fig. 5: METRIC can correct the measurement error in assessed nutrient profiles from MLVS (men’s lifestyle validation study)36,37.The Pearson’s Rank Correlation Coefficient \(\rho\) is adopted to evaluate the correlation across various types of nutrient profiles. All nutrient concentrations are in the unit of grams. All corrected/true values shown are the log of nutrient concentrations. a \({\rho }_{c}\) (i.e., \(\rho\) between corrected and true values) and \({\rho }_{a}\) (i.e., \(\rho\) between assessed and true values) decrease as the standard deviation of added Gaussian noise \(\sigma\) increases. Data are presented as mean values +/- standard error of the mean (SEM), derived from five training repeats (n = 5) for each case. All following panels focus on the case of \(\sigma\)=1.0. b The correlation between assessed values and true values of log concentrations of fructose among different samples. c The correlation between corrected values (predictions of METRIC) and true values of log concentrations of fructose among different samples. d, e The similar comparison for monounsaturated fatty acids shows a modest correction. f, g The similar comparison for dietary fiber shows a strong correction. h The correction performance for all nutrients is measured by (\({\rho }_{c}-{\rho }_{a}\)). Nutrient names are not added due to lack of space. Source data are provided as a source data file.Finally, we applied METRIC to the third dataset WE-MACNUTR (Westlake N-of-1 Trials for Macronutrient Intake)39. WE-MACNUTR is a dietary intervention study that implemented a ‘complete feeding’ strategy, providing three isocaloric meals per day to 28 participants over a span of 72 days. Each participant completed high-fat, low-carbohydrate and low-fat, high-carbohydrate diets in a randomized sequence, with a 6-day wash-out period between them. Since the diets were completely controlled and well-documented, the nutrient profile derived from this dataset closely reflects the true nutrient profile. In WE-MACNUTR, we found 317 paired samples with both microbial compositions and nutrient profiles. Considering the nutrient profile from the complete feeding as the true nutrient profile, we introduced varying levels of noise (Gaussian noise \({{{\rm N}}}(0,\,{\sigma }^{2})\) with different standard deviations \(\sigma\)) to create the assessed nutrient profile. Like our earlier results, METRIC can correct the nutrient profile when \(\sigma\) is large (Fig. 6a). When \(\sigma=1.0\), the mean correction performance \((\bar{{\rho }_{c}}-\bar{{\rho }_{a}})\) is \(0.118\) (Fig. 6h) and dietary fiber again exhibits a substantial correction (Fig. 6f, g).Fig. 6: METRIC can correct the measurement error in assessed nutrient profiles from WE-MACNUTR (Westlake n-of-1 trials for macronutrient intake)39.The Pearson’s Rank Correlation Coefficient \(\rho\) is adopted to evaluate the correlation across various types of nutrient profiles. a \({\rho }_{c}\) (i.e., \(\rho\) between corrected and true values) and \({\rho }_{a}\) (i.e., \(\rho\) between assessed and true values) decrease as the standard deviation of added Gaussian noise \(\sigma\) increases. All nutrient concentrations are in the unit of grams. All corrected/true values shown are the log of nutrient concentrations. Data are presented as mean values +/− standard error of the mean (SEM), derived from five training repeats (n = 5) for each case. All following panels focus on the case of \(\sigma\) = 1.0. b, The correlation between assessed values and true values of log concentrations of magnesium among different samples. c The correlation between corrected values (predictions of METRIC) and true values of log concentrations of magnesium among different samples. d, e The similar comparison for threonine shows a modest correction. f, g The similar comparison for dietary fiber shows a strong correction. h The correction performance for all nutrients is measured by (\({\rho }_{c}-{\rho }_{a}\)). Nutrient names are not added due to lack of space. Source data are provided as a source data file.To provide a more representative picture of METRIC’s robustness and effectiveness across different noise levels, we also investigated situations where the correction is less effective for all three datasets (standard deviation of the noise \(\sigma=0.5\); Supplementary Figs. 3–5). Although the overall correction performance (\({\bar{\rho }}_{c}-{\bar{\rho }}_{a}\)) is weak when \(\sigma=0.5\), the correction still works well for nutrients with smaller \({\rho }_{a}\) (e.g., dietary fibers). We also evaluated the predictive performance using a more quantitative metric, the mean absolute error. We found that the overall pattern in correction performance measured by mean absolute error aligns with that measured by Pearson correlation across datasets (Supplementary Figs. 6–8). For the MLVS and WE-MACNUTR datasets, we also tried to evaluate METRIC’s correction performance without using the microbial composition, finding that the correction performance is comparable to that achieved when the microbial composition is included (Supplementary Figs. 9, 10). This implies that METRIC can still be leveraged to correct nutrient profiles even in the absence of gut microbial compositions.We capitalized on the longitudinal nature of the MCTS dataset to explore whether increasing temporal offsets between microbiome and diet data impacts the correction efficiency of our method. Specifically, we increased the offset by aligning the diet of day \(t\) with the microbiome of day \(t+\Delta t\) and subsequently correcting nutrient profiles. Our analysis reveals that the correction performance progressively decreases as the offset \(\Delta t\) deviates from 1 day (Supplementary Fig. 11). This serves as a validation of METRIC, as it indicates that microbiome-diet relationships are causal.Given the absence of ground-truth nutrient profiles for direct validation, we instead conducted an indirect validation of our method by checking if the noise level of real-life nutrient profiles is within the regime where we can remove the random measurement errors well. We found that the correction performance of METRIC is great when the mean Pearson correlation coefficient \({\bar{\rho }}_{a}\) is below 0.8 (Figs. 4–6). Due to the lack of ground-truth nutrient profiles to directly quantify the noise level, we can only approximate this indirectly by reflecting the nutrient variability using the multiple-day 7DDRs in MLVS. Specifically, we calculated the Pearson correlation coefficient \(\rho\) between concentrations of a nutrient derived from one 7DDR and its average values obtained from multiple 7DDRs for seven consecutive days (Supplementary Fig. 12a). We found that the mean Pearson correlation coefficient \(\bar{\rho }\) is \(0.77\), which is below 0.8. Additionally, 62.0% of 329 nutrients have \(\rho \, < \, 0.8\). A similar analysis on the dataset MCTS revealed that \(\bar{\rho }=0.63\) and 95.0% of nutrients have \(\rho \, < \, 0.8\) (Supplementary Fig. 12b). The WE-MACNUTR dataset was not analyzed due to the absence of dietary assessments. These findings across both datasets confirm that the approximated noise levels are within a range where METRIC is effective at correcting random measurement errors.We also examined the impact of noise with a non-zero mean by introducing the Gaussian noise \({{{\rm N}}}(\mu,\,{\sigma }^{2})\). For the three datasets we used, we set \(\sigma=1\) as this is the regime where our method, METRIC, consistently shows strong correction performance. We then gradually increased the mean of the noise \(\mu\) from 0.0 to 2.0 to create the assessed nutrient profile. When applying METRIC to remove the noise, we observed that its correction performance diminishes to zero as \(\mu\) increases (Supplementary Figs. 13–15), indicating that METRIC can remove the random error but not the systematic drift or shift.
