In this study polarization transfer to a heteronucleus is achieved through a selective rotation of the proton singlet–triplet states driven by a combination of a rotating magnetic field and a weak bias field. Surprisingly we find that efficient polarization transfer driven by a STORM (Singlet–Triplet Oscillations through Rotating Magnetic fields) pulse in the presence of sub-μT bias fields requires rotation frequencies on the order of several kHz. The rotation frequencies therefore greatly exceed any of the internal frequencies of typical zero- to ultralow field experiments. We further show that the rotational direction of the rotating field is not arbitrary and greatly influences the final transfer efficiency. Some of these aspects are demonstrated experimentally by considering hyperpolarized (1-13C)fumarate. In contrast to most of the existing methods, the STORM procedure therefore represents a promising candidate for quadrupolar decoupled polarization transfer in PHIP experiments.An integral part of  Rapidly rotating magnetic field induces hyperpolarization read-out at low- or zero-field. Upon hydrogenation the nuclear singlet order of the hydrogen gas is carried over to the product molecule. However, the resulting nuclear singlet order located on the product molecule is NMR silent. Efficient conversion of nuclear singlet order into observable magnetization is thus an integral part of the method.For the case of hydrogenative-PHIP (considered here) the 10–21 High field methods benefit from the usual advantages, spectral separation between hetero- and homonuclei, strong pulse schemes with error compensation and applicability to a broad class of molecular systems.11,15,21–24 However, these benefits often come at a price. Some technical challenges may arise due to additional relaxation phenomena and coherent leakage, which may lead to significant polarization losses.17,25,26A number of techniques already exist for this purpose, both at high and low magnetic fields.10,13,14,17–19 This has been utilised to produce large quantities of chemically pure and hyperpolarized (1-13C)fumarate, for example.19 The reaction was carried out inside a pressurised metal reactor, which itself was placed inside a magnetic shield. The polarization transfer was performed by sweeping the magnetic field in the sub-microtesla regime. Such a setup would be impossible at high magnetic fields as the reaction vessel is incompatible with pulsed radio-frequency methods.Some of these issues may be circumvented at low magnetic fields.20 A magnetic field geometry with the oscillating field applied along the same direction as the main magnetic field is unusual for NMR, indeed if the oscillating field is applied in the conventional transverse plane the WOLF pulse becomes ineffective.We have recently demonstrated that efficient polarization transfer may also be performed in the presence of a weak static magnetic field superimposed with a weak oscillating low field (WOLF) along the same direction.27,28 However, at low magnetic fields it is technically trivial to generate rotating magnetic fields that are resonant with the nuclear spin transition frequencies. This way perturbations due to the counter-rotating components are simply avoided.Generally speaking, the description of oscillating fields in the low magnetic field regime is complicated. In contrast to high field experiments both the resonant part and the counter-rotating part of the linearly polarised field have to be considered.13C)fumarate, and explore the STORM condition as a function of the bias field, rotation frequency and sense of rotation.In this work we demonstrate that the application of transverse rotating fields may be exploited for the polarization transfer step in PHIP experiments. The application of a suitable STORM (Singlet–Triplet Oscillations through Rotating Magnetic fields) pulse enables polarization transfer from the singlet pair to a heteronucleus leading to substantially enhanced NMR signals. We validate some of these concepts experimentally by generating hyperpolarized  and a positive homonuclear coupling constant J12. The heteronuclear J coupling Hamiltonian may be split in its symmetric and anti-symmetric partFor the remainder of the discussion we assume the coupling constants The nuclear spin ensemble may further be manipulated by the application of external magnetic fields. The magnetic field Hamiltonian is constructed by coupling the spin angular momenta to the external magnetic field taking their respective magnetogyric ratio's into accountThe total spin Hamiltonian is then given by2.1z-axis. The z-bias Hamiltonian is given byConsider now the application of a time-dependent rotating magnetic field in the presence of a weak bias field along the laboratory frame The total spin Hamiltonian may now be expressed as a combination of scalar-coupling terms, the bias term and the rotating field contributionH(t). To this end we consider an interaction frame transformation rotating all three spins equally around the laboratory frame z-axis. The angular frequency is chosen to coincide with ωrotIt turns out to be advantageous to isolate the rotating part of H̃(t) is given byThe corresponding interaction frame Hamiltonian 2.2Beff. The coupling of the effective field to the I and S spins may be characterised by the effective nutation frequencies ωXeffθXeffWithin the interaction frame the spins evolve under a new effective magnetic field z-axis. An alternative representation of H̃ is thus given byHeff represents the effective field Hamiltonian in the absence of the anti-symmetric heteronuclear J-couplingsThe polar angles describe the field direction with respect to the laboratory frame The transformation X is defined as a composite rotation of spins I and SConsider now the set of STZ states aligned along the effective magnetic field directionS0μ′〉. The rotated STZ states thus represent the approximate eigenstates of H̃ and the heteronuclear coupling term HΔIS may be considered a perturbation.These states are exact eigenstates of the effective field part of the interaction frame Hamiltonian2.32S systems at sufficiently low magnetic fields we may approximate the initial state of the spin ensemble by pure singlet populationS represents the unity operator for spin S. Because the initial state of the ensemble is rotationally invariant we may express ρ(0) in a straightforward manner in the rotated STZ basisFor typical PHIP experiments involving IHΔIS no heteronuclear magnetisation may be extracted out of the system, however the presence of HΔIS causes coherent mixing within the manifolds {|S0β′〉,|T0β′〉, |T−1α′〉} and {|S0α′〉,|T0α′〉, |T+1β′〉}.In the absence of ωrot. Taking the first manifold for example, one may show to first order in perturbation theory that the following inequalities are well satisfiedn〉 represents any state outside the manifold.Strictly speaking these two manifolds are not completely isolated from all other states. But as illustrated in S0β′〉 and |T−1α′〉 state is given byThe energy separation between the |ωSTORM such thatAs a result, coherent state mixing is maximised by choosing an optimised rotation frequency S0β′〉 and |T−1α′〉 state, and leads to a level anti-crossing (LAC) if the anti-symmetric heteronuclear J-couplings are included .Application of a rotating magnetic field with τ under the TLS approximation are given by35Consider now starting from the density operator in S0β′〉 and |T−1α′〉 state may be achieved by applying the STORM pulse for a duration τ* = π/ωnutST. Since the STORM pulse is only resonant with the |S0β′〉 ↔ |T−1α′〉 transition all other states experience negligible evolution. The idealised density operator after such a STORM pulse is thus given byS spin magnetisation proportional to cos(θSeff). The state of the S spins may be extracted by tracing over the I spins of the systemA complete population inversion between the |θSeff) approaches unity. Representing the transfer amplitude in a slightly more intuitive form:S spin Larmor frequency and angular rotation frequency exceed the S spin nutation frequency (|ωS0 + ωrot| ≫ |ωS1|).As a result, the heteronuclear spins become fully polarised as cos in D2O, heating to 60 °C, and passing through a Millex 0.22 μm PES filter.The precursor solution for fumarate was prepared by dissolving 100 mM disodium acetylene dicarboxylate, 100 mM sodium sulfite, and 6 mM [RuCp*(MeCN)Para-hydrogen was produced by passing hydrogen gas over an iron oxide catalyst packed in a 1/4 inch stainless steel tube cooled by liquid nitrogen which results in para-enrichment level of 50%.J-coupling parameters for the molecular system are consistent with ref. About 2% of the fumarate molecules contain a naturally-occurring nucleus. The two nuclei and the nucleus form a three-spin-1/2 system of the type discussed above. The 3.2A sketch of the equipment is shown in 3.3para-Enriched hydrogen gas is bubbled through the solution at 6 bar pressure for 30 seconds. The rotating field is generated constantly by the waveform generator, the amplitude is kept constant (BSTORM = 4). The solenoid is switched off by a relay for a period τ to pre-set the bias field (Bbias) and to mimic a STORM pulse. Afterwards the sample was removed manually and inserted into the Oxford 400 MHz magnet equipped with a Bruker Avance Neo spectrometer.k point density at a spectral width of 200 ppm. Additional decoupling was used for all experiments. Thermal equilibrium spectra were recorded at room temperature with a recycle delay of 120 s, averaging the signal over 512 transients.The free-induction decays were initiated by a hard pulse of 14.7 kHz rf amplitude and recorded with 65 4BSTORM = 4 μT. The rotation frequencies, 1150 Hz for (a) and 223 Hz for (b), correspond to the root of the pSz ≃ 6%. These results are comparable with previous methods under similar experimental conditions.14,17,18,20 Significant improvements in the polarization are expected by addressing few aspects of the setup. Fully enriched para-hydrogen would lead to 3-fold enhancement, whereas careful optimization of the reaction conditions would further lead to a better polarization yield.14,18 Some minimal losses could be also avoided by using a fully automated experimental procedure.The solid black line in τ at bias field of 0 T and 2 μT are shown in Integrated signal amplitudes as a function of the rotation frequency and the STORM pulse duration 20 In agreement with the analytic expression given by J-coupling parameters of fumarate given in ref. The frequency profiles obtained at different bias fields display a significant change in their width. At zero-field the full width at half maximum of the profile was estimated to be ∼350 Hz whereas at 2 μT bias field width got reduced to ∼5 Hz. These matching conditions are much broader than the 0.4 Hz width observed in the profiles using the WOLF method.5para-hydrogen induced polarization. The polarization transfer is achieved through a combination of a rotating magnetic field and a small bias field. Despite low values of the static bias field, the rotation frequency needed to drive the transfer is strikingly large. However, the principle of the method described here is rather intuitive and a simple explanation may be given within the framework of level-anti crossings, at least when the Hamiltonian is expressed within the interaction frame of the rotating magnetic field. Based on the LAC picture we were able to establish the resonance conditions for singlet–triplet mixing and determine the corresponding population transfer rate. In particular, we have shown that the rotational direction plays an important role in correctly establishing the resonance condition, and should be chosen carefully in the experimental context.In this work we have studied the polarization transfer from singlet order to heteronuclear magnetization in the context of 10–21 The STORM method introduced here is conceptually simple and provides a few advantages over other existing low field methods. The potential polarization losses caused by additional relaxation effects in high magnetic fields are entirely avoided with use of low magnetic fields.17,25,26 However, at ultra-low fields quadrupolar nuclei such as 2H or 14N often act as polarization sinks, and may lead to a significant drops in the polarization transfer efficiency. The presence of quadrupolar nuclei is expected to be particularly disrupting to adiabatic field sweep methods, some of which are routinely utilised in the generation of hyperpolarized (1-13C)fumarate.17–19 In contrast to field sweep methods, the STORM method allows one to freely select the strength of magnetic fields as well as the rotation frequency. It is thus conceivable that optimal conditions for the magnetic field strength and rotation frequency exist at which the 2H or 14N spins do not interfere with the polarization transfer process. We therefore believe that STORM pulses represent promising candidates for a new class of quadrupolar decoupled polarization transfer methods in the near future. Applications to other hyperpolarization techniques such as PHIP-SABRE  are also conceivable.9,11,12,25There are other methods to convert nuclear singlet order into heteronuclear polarization, including resonant pulse schemes in high field as well as magnetic field-cycling at low magnetic fields.There are no conflicts to declare.


Video animations of regional acinar and vascular strain are acquired in vivo. Maps of strain distribution due to positive-pressure breaths and cardiovascular activity in lung acini and blood vessels are derived based on CT images. Regional strain within the lung peripheral airspaces takes average values of 0.09 ± 0.02. Fitting the expression S = kVn, to the changes in peripheral airspace area (S) and volume (V) during a positive pressure breath yields an exponent n = 0.82 ± 0.03, suggesting predominant alveolar expansion rather than ductal expansion or alveolar recruitment. We conclude that this methodology can be used to assess acinar conformational changes during positive pressure breaths in intact peripheral lung airspaces.The magnitude and distribution of strain imposed on the peripheral airspaces by mechanical ventilation at the microscopic level and the consequent deformations are unknown despite their importance for understanding the mechanisms occurring at the onset of ventilator-induced lung injury. Here a 4-Dimensional (3D + time) image acquisition and processing technique is developed to assess pulmonary acinar biomechanics at microscopic resolution. Synchrotron radiation phase contrast CT with an isotropic voxel size of 6 µm It is generally agreed that excessive mechanical strain due to inflation2, cyclic recruitment-derecruitment3, increased energy dissipation within the parenchyma4 and associated inflammation5 are contributing factors. The magnitude and distribution of strain imposed on the peripheral airspaces by mechanical ventilation at the microscopic level and the resulting deformation of peripheral airspaces are unknown despite their importance for understanding the mechanisms occurring at the onset of ventilator-induced lung injury (VILI). Indeed, a fundamental question that has remained elusive for decades is how the lung acinus expands with lung inflation6. This question is particularly pressing in the context of severe acute respiratory syndrome due to coronavirus-2 pandemic (SARS-CoV-2) where VILI has been recognized as a contributing factor to patient morbidity and mortality7.Mechanical ventilation used during anaesthesia or in acute respiratory failure causes or worsens strain-induced lung tissue injury9, ultrasound (US)10, magnetic resonance tomography11 (MRI) and X-ray computed tomography (CT)12 have been used to quantify regional tissue strain, or the normalized deformation of a tissue that changes shape or volume following mechanical loading over time. Because of the limitations in tissue penetration  and spatial resolution , X-ray imaging is the most suitable modality for imaging the lung tissue morphology. However, in its practical implementation, a compromise is made between the spatial resolution, temporal resolution, size of the imaging field and sensitivity.Imaging methods for high resolution in vivo assessment of peripheral airspace deformation dynamics are lacking. The reason lies in the difficulty of determining effective structural deformation due to the motion blurring at microscopic resolution, which is induced by respiration and cardiovascular activity. Different imaging modalities such as optical coherence tomography (OCT)13. By changing the level of positive pressure at the airway opening, they were able to resolve alveolar structures at different levels of inflation. However, imaging the lung in static conditions is less physiological and does not allow capturing the full scope of local lung mechanics. This is because the lung tissue is viscoelastic, meaning that its apparent elastic properties depend on the rate of volume change14.To minimize motion blurring occurring in vivo, cardiac gating methods have been employed where the electrocardiographic activity is monitored and image acquisition is synchronized with a given phase of the cardiac cycle. Using a prospective cardiac gating technique, Lovric et al. were able to image mouse lungs at 1.1 µm voxel size during static breath hold conditions18. This approach refers to sequential acquisition of 3D images with prospective gating or retrospective sorting of image projections with respect to a periodic motion. Available methods based on X-ray attenuation using commercial x-ray sources have significant limitations arising from low available X-ray flux, which reduces spatial resolution for a given signal-to-noise ratio, and prolongs acquisition time. Clinical 4DCT combined with image registration of images at 16 time points within the respiratory cycle has been used to assess regional lung expansion and strain in humans, at voxel dimensions of ~ 0.5 mm19, which does not allow resolving alveolar structures. Besides motion blurring, another limitation of high-resolution CT imaging is that the lung being an air-filled organ, it weakly attenuates x-rays which reduces sensitivity. Previously, dynamic phase-contrast 4DCT utilizing x-rays produced with a synchrotron source have been used to asses lung tissue motion and regional expansion in in vivo rabbit pups20 and mice21. This technique takes advantage of the high intensity and coherence of synchrotron radiation to acquire 3D images of the lung at resolutions of 15 µm voxel size and 16 time points per respiratory cycle20 and up to 50 time points per respiratory cycle at 20 µm voxel size21.To circumvent this limitation, dynamic four-dimensional (3D + time) x-ray CT (4D-CT) imaging techniques have been developedS = kVn, to the changes in peripheral airspace area (S) and volume (V) during a positive pressure breath, where k is a constant, and n the exponent of volume changes with respect to the change in surface area. With a perfectly isotropic expansion, surface area necessarily increases in proportion to V2/3 (n = 0.67) because surface area varies as the square and volume as the cube of a characteristic linear dimension. Departure from this value would indicate a configurational change of the acinus with inflation22. Assuming an acinar structure with an axial duct from which alveoli open radially, the relative shape and changes in ductal and alveolar volumes result in different overall surface changes relative to volume. Based on this approach in lungs fixed at different volumes, Gil et al.23 described different mechanisms of acinar configurational changes (S ∝ Vn): (1) sequential recruitment-derecruitment (n = 1); (2) isotropic balloonlike inflation (n = 0.67); (3) simultaneous change in alveolar size and shape, e.g.: from dodecahedral to spherical, due to alveolar septal unpleating (n > 0.67); (4) crumpling of the alveolar surface with anisotropic, accordion-like deformations of the entire peripheral airspace units (n = 1). The results of Gil et al. suggested that although all these mechanisms are involved, they tended to occur at different lung volumes. At lower lung volumes, deformation occurred predominantly within the alveolar ducts (S = kV0.33), while at higher lung volumes, alveolar inflation predominated, with simultaneous change in alveolar shape and volume. Because of the limitations of current imaging techniques, to date this issue has not been investigated in deep lung acini in vivo and in dynamic conditions6.One approach to describe how the conformation of terminal airspaces is altered by inflation, is to determine the changes in the surface area of airspaces in proportion to volume, by fitting the expression 324. We applied this methodology to acquire maps of strain distribution due to positive-pressure breaths in the lung acini and in blood vessels. We show that this methodology can be used to assess conformational changes during positive pressure breaths in intact peripheral lung airspaces in vivo.Here we extend 4D-CT of lung tissue biomechanics to smaller length scales and higher temporal resolution than previously achieved, in live anesthetized rats under controlled mechanical ventilation. We use phase-contrast imaging with radiation produced with a synchrotron source, and a combination of technological advances including a fast-imaging camera connected to optics allowing an isotropic voxel size of 6 µm3 voxel size CT imaging in the temporal scale of minutes. Due to the strong cardiac-induced deformations, the alveolar structures often do not return to the same position at end-expiration, which makes dynamic tomography very challenging at micrometric spatial resolutions, using 4DCT17. Here we used a combination of a fast-imaging camera connected to optics allowing an isotropic voxel size of 6 µm3 : 5.9 ± 0.3 cmH2O; driving pressure (Pmax – PEEP): 5.7 ± 0.8 cmH2O; respiratory rate: 72 ± 7.2 bpm; tidal volume: 2.8 ± 0.2 ml/kg. Figure Dynamic strain maps of airspaces and blood vessels are shown in Supporting video 25 imaged whole mouse lungs in vivo, using a liquid metal jet laboratory X-ray source at 30 frames/s at ~ 50 µm resolution, which allowed assessing the regional tidal lung expansion. Although large-scale regional lung expansion inhomogeneity in between regions about the size of lobes is well known, much less data is available on the deformation of the lung tissue at subacinar scales. In this study we imaged a region that represents ~ 10% of the healthy rat lung volume at end-expiration. The size of the field of view, which was determined by the dimensions of the X-ray beam and the characteristics of the detection system, allowed to fully assess deep lung structures in a representative sample of the lung. Assessing other lung regions would require repeating the scan. Imaging the entire lung dynamically by 4DCT at this spatial and temporal resolution using larger beam dimensions and field of view is limited by the amount of data that is generated, that needs to be transferred, stored and processed, which is on the order of several TB for a single scan. Nevertheless, future studies should allow studying how microscopic strain distribution in the lung airspaces and blood vessels determines structural damage and inflammation, under mechanical ventilation.Previously, Yen et al.n calculated by fitting the expression 2O and back. The mean value of this exponent was 0.82 ± 0.03  and internal surface area (S) of the segmented acini within a representative ROI throughout a respiratory cycle is shown in Fig. mentclass2pt{minim28. Post-mortem light microscopic measurements of fixed or frozen lungs have found conflicting results regarding the configurational changes of lung acini with lung inflation. Some have suggested that alveoli expand isotropically29. This means that linear dimensions of alveolar structures vary as the cube root of lung volume (V1/3). Others however, have found some degree of anisotropic expansion with the alveolar duct volume changing proportionately more than alveolar volume30. Previously, Carney et al. investigated the mechanical behavior of subpleural alveoli during lung inflation in vivo, using intravital microscopy through a thoracotomy incision in dogs8. They found that above 20% TLC, alveolar volume remained stable while an increasing number of alveoli were recruited and concluded that lung volume changes predominantly occurred as a result of alveolar recruitment. However, in their study alveolar mechanics was analyzed in initially degassed lungs in open chest animals which may have promoted alveolar collapse. Using intravital microscopy and optical coherence microscopy (OCT), Mertens et al.31 investigated alveolar dynamics through a pleural window in open-chest mice with normal and injured lungs. They found that alveolar distension rather than recruitment was the main mechanism of lung inflation. Besides species and methodological differences that may explain the discrepancy in the data from intravital microscopy in these and other studies34, there has been concern that the mechanical behavior of subpleural alveoli may be different from those deep in the lung.The changes in lung acinar shape as a function of lung inflation have been assessed post-mortem in fixed or frozen tissue samples using light microscopy and electron microscopy35 investigated lung acinar dynamics in post-mortem mice without tissue fixation in static conditions, using synchrotron phase-contrast microtomography. They found that the alveolar duct diameter changed dramatically during inflation at low pressures and remained relatively constant above an airway pressure of ~ 8 cmH2O, where alveolar inflation predominated with S = kV0.8735. Lovric et al.36 studied alveolar expansion in post-mortem mouse lungs also using synchrotron phase-contrast microtomography at static pressures of 10–30 cmH2O. Their results indicated inflation of the existing alveoli, without evidence of recruitment, however, they did not measure the changes in surface area with respect to volume. The findings of the present study (S = kV0.82) while obtained in vivo and in dynamic conditions under realistic mechanical ventilation settings are very similar to those of Sera et al. at airway pressures > 8 cmH2O. This finding is indicative of an anisotropic behavior of the overall lung acinus, where the stress–strain relation in alveolar ducts, mainly determined by high densities of connective tissue situated around the alveolar mouths39, is different from that of alveoli, determined by the connective tissue within the alveolar septa as well the surface tension properties of the air–liquid interface40. A schematic illustration of the how acinar conformation changes result in different exponents in S = kVn is provided in Fig. Sera et al.3 voxel size at 78 time points per breath, which to our knowledge is the highest achieved so far in dynamic imaging. We found that under the applied mechanical ventilation settings, regional lung strain within the lung peripheral airspaces took values of 0.09 ± 0.02 in anesthetized rats. Our data suggest that the conformational changes in lung airspaces are indicative of predominant alveolar expansion rather than ductal expansion or alveolar recruitment. We further analyzed the deformation in pulmonary blood vessels and found a large disparity depending on caliber. We believe this methodology will be instrumental in advancing our understanding of the dynamics of stress and strain within the lung parenchyma under mechanical ventilation and devising ventilation modes to preserve the lung parenchyma from stretch-induced injury.We developed a 4D synchrotron phase-contrast micro-CT technique allowing for the in vivo assessment of the expansion of lung acini with an isotropic 6 µm41, selecting a photon energy of 40 keV. Monochromatic radiation impinged on the sample 146 m from the source and was detected by a fast Complementary metal–oxide–semiconductor (CMOS) PCO Edge 5.5 camera  coupled to a 250 μm thick Cerium-doped Lutetium Aluminum Garnet (LuAG:Ce) scintillator and optics yielding an isotropic pixel size of 6 μm2. The field of view of the camera was reduced to 15.4 × 1.2 mm2 to achieve a frame rate of ~ 500 fps, as a compromise between field of view and temporal resolution. The sample to detector distance was set to 4 m to utilize propagation-based phase contrast imaging42.The experiments were performed at the biomedical beamline (ID-17) of the European Synchrotron Radiation Facility . Briefly, X-rays produced by a multipole wiggler were monochromatized using a double bent Laue Si (111) monochromator43 and were approved by the ESRF Ethical Committee on Animal Experimentation  and the French Ministry of Higher Education and Research under the number: 2017071816174477. The study was performed on 3 female OFA rats . Anesthesia was induced by intra-peritoneal injection of 1.5 to 2 ml kg−1 body weight of a solution containing Ketamine (40 mg ml−1) and Xylazine (20 mg ml−1). The animal was tracheostomized and a 14 G polyethylene catheter  was inserted and secured with a gas-tight seal. A 26 G polyethylene catheter  was inserted in the jugular vein for fluid replacement . After surgery, the animal was immobilized in the vertical position in a custom-made plastic holder and placed on a remote-controlled rotation stage in the experimental hutch for imaging. Anesthesia was maintained during the duration of the experiment with 1% inhaled isoflurane . The animals were mechanically ventilated with a tidal volume of 8 ml kg−1, FiO2 = 0.5; PEEP = 6 cmH2O at baseline. After verifying adequate depth of anesthesia , muscle relaxation was induced by Atracurium injection (4 mg kg−1) to avoid motion and suppress spontaneous breathing. The electrocardiogram (ECG), was recorder by placing subcutaneous needle electrodes on the paws, and the neck, connected to a differential amplifier . ECG, airway pressure and air flow were continuously sampled at 10 kHz and recorded using a Powerlab 16/35 data acquisition device   Figure.44. It was based on the synchronization between the heartbeat and the mechanical ventilation, which ensured a periodic lung parenchymal motion, as required by dynamic CT acquisitions. Briefly, the ECG signal was processed in real-time with a peak detector, which generated a square signal of predefined length and duty cycle when a R wave was detected, at the time instant t. The square signal was transmitted to the mechanical ventilator controller, to trigger an assisted breath. The R wave detection was disabled for the whole duration of the square signal. In the specific experiment discussed here, the square signal duration was −1 was set to include approximately 700 respiratory cycles per scan, over a total duration of 8.8 min.The image acquisition protocol was described in detail in a previous publication44 was used to reconstruct 4D CT images. In this approach each projection: The image processing workflow is shown in Fig. 45 software, after application of Paganin’s single material phase retrieval algorithm46. Cupping artefact which frequently occurs in local tomography where the object is larger than the field of view, was dealt with using the STRAIGTHEN_SINOS option in PyHST2. Since the ECG signal is not perfectly periodic, the projections were not equally spaced. Hence, 78 3D-CTs were finally reconstructed.The projections corresponding to the same time interval were sorted in 3D image stacks discretizing 47, based on the image histogram. To classify the former voxels as proximal, intermediate and terminal, an iterative process was performed. The axial regions of the proximal bronchi were identified by carrying out a stepwise 3D erosion process. Assuming the proximal bronchi are quasi cylindrical, these bronchi were identified by linear regression as regions where volume will decrease linearly with respect to the number of erosion steps, based on the root mean square error. The full volume of primary bronchi was then recovered by morphological dilatation. Intermediate structures were subsequently identified as structures requiring less erosion steps than the primary bronchi. All the selected voxels which were not classified as proximal or intermediate were classified as terminal structures, with a similar approach as the ones described previously in the literature49. Using this method, terminal airways as well as the proximal and intermediate blood vessels were identified. Occasionally, additional manual editing was performed as necessary by adding markers on the image and carrying out a watershed.The same segmentation process was used for blood vessels and air airspaces. Otsu's algorithm allowed for a first partitioning of air and non-air voxels50 and is published within the Python Image Registration Toolkit (PIRT)51. A Sum of Squared Differences (SSD) similarity metric was applied, as well as a Laplacian regularization term. The registration algorithm was applied in a pairwise fashion, between each time step and the immediately previous one, to compute the displacement field x is a point in the 3D space, n the number of images from the start of the breathing cycle. This two-step computation of the displacement field allowed to minimize registration errors. The error value was defined, as:A non-rigid registration algorithm was used in order to deform the segmented airspace or vascular volumes. The registration algorithm applies a B-spline grid to represent the original segmented greyscale volume. It was initially proposed by Klein et al.https://scikit-image.org)52. Skeletons were produced for the segmented airspace volume at each time instant 53. Each pair of skeletons, We investigated whether completely deflated airspaces were inflated upon inspiration, a phenomenon referred to as “recruitment”. To this end, we used skeletonization, a process that reduces binary objects to 1-pixel width representations, in order to extract the airspace topology. This was performed with the Skeletonize_3D toolkit  kernel-based convolution was applied55, which grants linear consistency:The divergence theorem was applied to compute the volume change:56.It should be noted that the convolution above considers only the segmented voxels. The computed maps of local strain at each time point within the respiratory cycle were then rendered using ParaView softwareh the mean Gaussian curvature57, which represents how the surface changes with respect to volume57.For the surface change computation, a similar expression to Eq.  was usedSupplementary Video 1.Supplementary Video 2.Supplementary Video 3.Supplementary Information 1.


The capability to design microbiomes with predictable functions would enable new technologies for applications in health, agriculture, and bioprocessing. Towards this goal, we develop a model-guided approach to design synthetic human gut microbiomes for production of the health-relevant metabolite butyrate. Our data-driven model quantifies microbial interactions impacting growth and butyrate production separately, providing key insights into ecological mechanisms driving butyrate production. We use our model to explore a vast community design space using a design-test-learn cycle to identify high butyrate-producing communities. Our model can accurately predict community assembly and butyrate production across a wide range of species richness. Guided by the model, we identify constraints on butyrate production by high species richness and key molecular factors driving butyrate production, including hydrogen sulfide, environmental pH, and resource competition. In sum, our model-guided approach provides a flexible and generalizable framework for understanding and accurately predicting community assembly and metabolic functions. Microbiomes designed with predictable functions could enable broad applications in health, agriculture and bioprocessing. Here the authors use a model-guided approach to design diverse synthetic human gut communities for production of the health-relevant metabolite butyrate. Many of these processes critically impact human health, agriculture and environmental sustainability, including oceanic CO2-fixation2, production of growth-promoting molecules in the plant rhizosphere3, and degradation of indigestible dietary substrates in humans4. The functions performed by microbiomes are shaped by complex and dynamic interactions between constituent community members and their environment. Developing the capabilities to engineer microbiome properties holds promise to address grand challenges facing human society in agriculture, degradation of the environment, and human health5.Microbial communities carry out pivotal chemical transformations in nearly every environment on EarthClostridioides difficile infection in the human gut6, produce valuable chemicals in anaerobic digestors7, or extract minerals via bioleaching8. Optimization of such desired functions performed by undefined communities is challenging due to unknown components and their interactions and the difficulty in quantifying the contributions of organisms to the function of interest. Further, undefined communities used in fecal microbiota transplantation (FMT) to treat human diseases have resulted in unpredictable patient outcomes attributed to complex and unknown ecological interactions between donor and recipient microbiomes9. In addition, FMT can lead to potential adverse health consequences including the transfer of antibiotic-resistant pathogens12. For these reasons, there is substantial interest in exploiting the properties of defined microbial communities for enhanced controllability, reproducibility, and environmental safety.Undefined communities isolated from natural environments have been exploited to treat 13 and in model host systems15 to decipher potential causal interactions influencing system behaviors. Using in vitro culturing, synthetic communities of bacteria isolated from the human gut16 or soil17 have been used to demonstrate that pairwise interactions are major determinants of multi-species community assembly. Beyond community assembly, synthetic communities have been used to interrogate how community context impacts the production or consumption of molecules relative to individual species20. In real-world environments, defined consortia have been used for environmental cleanup21, protection of plant hosts from pathogen infection23, and treatment of recurrent C. difficile infection25. However, the widespread deployment of synthetic microbiomes has been hindered by our limited capabilities for accurate prediction of community assembly and function.The bottom-up construction of synthetic microbiomes enables the investigation of reduced complexity assemblages with control of initial community composition . Defined microbial communities have been extensively studied both in vitro26. In addition, the community composition–function landscape can be shaped by variation in the activity of metabolic pathways (i.e. metabolic flexibility) driving the function of interest due to the availability of ecological niches27. Therefore, developing the capabilities to systematically explore this complex landscape could enable the discovery of synthetic microbiomes with optimized functions that can be harnessed for diverse applications.Identifying synthetic communities that perform functions with desired specifications is highly challenging due to a large design space that grows exponentially with the number of organisms. The web of interactions between constituent community members and abiotic factors  can potentially generate many local optima representing a rugged community composition–function landscape28 or identify promoter combinations driving enzymes in a metabolic pathway to maximize valuable molecule production30. In the microbiome field, empirical and top-down approaches are frequently used to design microbial communities as opposed to data-driven approaches14. In one example, a model-guided procedure was used to identify gut microbial communities that elicit a target immune response in mouse models31. However, variation in host colonization masked the contributions of specific microbes and the high biological variability between replicates of the same community limited the observability of significant increases in the immune response. Computational modeling frameworks that can predict how interactions between species shape community assembly and functional outputs are needed to advance the rational design of synthetic microbiomes.In metabolic and protein engineering, computational models informed by high-throughput experimental measurements have been used to design optimized protein sequences with high protein stability32, diet-induced obesity35, colitis37, opportunistic pathogen infection38, diabetes39, and colorectal cancer40. Predictable modulation of butyrate production of gut microbiota with defined bacterial therapeutics is challenging as evidenced by the failure to modulate fecal butyrate concentration in individuals with metabolic syndrome via supplementation with a butyrate producing bacterial strain41. The effects of introducing invader therapeutic species depends on the availability of ecological niches and the complex interactions between resident and invader species. A detailed and quantitative understanding of these interactions could guide the design of microbiome interventions for predictable shifts in butyrate concentration.Butyrate production is a major function of the gut microbiome associated with protection from a wide range of human diseases, including arthritis42 and the beneficial role of butyrate produced by gut microbiota on myriad health outcomes41, we sought to develop the capability to predict butyrate production of diverse synthetic human gut communities. To this end, we leveraged interpretable data-driven models to design synthetic communities with desired butyrate concentrations and to decipher significant microbial interactions impacting butyrate production. By quantifying interactions that impact growth and butyrate production separately, we demonstrated that in some contexts, accurate prediction of butyrate producer abundance can predict butyrate production, while in other community contexts, interactions modifying metabolic activities must be captured. We used our models to design communities of up to 25 diverse and prevalent gut bacterial species with a broad range of butyrate production capabilities and uncovered key insights into metabolic interactions impacting butyrate production by analyzing our model as well as the metabolic profiles and environmental modification of the designed communities. Finally, we used our model to investigate how biodiversity–ecosystem function relationships constrain the design of butyrate production in the system. Our generalizable framework provides a foundation for the data-driven design of complex microbial communities for biological objectives and could be extended to other microbiome engineering applications including the production or degradation of health-relevant molecules, production of compounds to enhance plant growth, or sustainable biomanufacturing of valuable molecules.Due to significant interest in the development of defined bacterial therapeutics for human health applications43. To investigate the landscape, we developed a modeling framework to guide the iterative design of informative experiments . To estimate parameters for the regression model, we use Lasso regression to identify the most impactful interactions. Altogether, the composite gLV and regression model predicts the probability distribution of the metabolite concentration given an initial condition of species abundances  at a specific time point to the concentration of an output metabolite at that time. This model was based on a phenomenological model of metabolite production used in bioprocess engineering expanded to microbial communities (see the “Methods” section). In the regression model, the first-order terms capture the monospecies production per unit biomass and the interaction terms represent the impact of inter-species interactions on metabolite production per unit biomass (i.e. deviations from constant metabolite production per unit biomass45 or metabolic pathways46 with properties that satisfy desired performance specifications. We hypothesized that this engineering-inspired approach could be used to explore community design spaces and understand the composition–function mapping for butyrate production. Each cycle consisted of: (1) a design phase wherein we used our model informed by experimental observations to simulate a vast number of potential community compositions to identify sub-communities that satisfied biological objectives (i.e. desired butyrate concentrations), (2) a test phase wherein the selected sub-communities were assembled and species abundance and butyrate concentration were measured, and (3) a learn phase wherein patterns in our experimental data were used to estimate model parameters and to extract information about the key microbial interactions influencing community assembly and butyrate production.In metabolic and protein engineering, a design–test–learn cycle (DTL) has been used to design biomolecules47 .To develop a system of microbes representing major metabolic functions in the gut, we selected 25 prevalent bacterial species from all major phyla in the human gut microbiome47 Fig. . This co47 Fig. . Due to 49, we hypothesized that training our model on single and pairwise community measurements would provide an informative starting point for mapping composition–function relationships determining butyrate production. To do so, we first measured time-resolved growth of single species and observed a wide variety of growth dynamics within each phylum, including disparate growth rates and carrying capacities  and measured species abundance and the concentrations of organic acid fermentation products  after 48 h. The pairwise consortia displayed a broad range of butyrate concentrations of 0–50 mM . In stark contrast to the pairwise communities, the 24- and 25-species communities exhibited similar low butyrate production (~2–22 mM Butyrate). The absence of only two species Desulfovibrio piger (DP) (~22 mM Butyrate) and Anaerostipes caccae (AC) (~2 mM Butyrate) resulted in a significant increase or decrease in butyrate concentration compared to the remaining 24-member and 25-member communities , we estimated the parameters of our model based on experimental measurements. Our initial model was informed only by pairwise communities that contained at least one butyrate producer  pairwise community was lower than the AC monoculture, even though RI was low abundance, resulting in a high magnitude negative parameter in the regression model for a production interaction between AC and RI . The predicted butyrate production varied substantially based on the combination of butyrate producers present in each community Fig. . In addip = 9*10−43)   Fig.  and spec51, we first used model M2 to simulate the assembly of all communities containing all five butyrate producers  to map the composition–function landscape for butyrate production  using a model with updated parameters based on measurements of the 3–5 member communities  , suggesting that growth interactions dominated butyrate production  Fig. . By contion Fig. . The 5BPion Fig. , consistion Fig. .p = 0.043)  Fig. , demonst43) Fig.  and demop = 8*10−19), consistent with the strong correlation predicted by our model . We next tested if H2S contributed to the negative impact of DP on butyrate production. To test this hypothesis, each butyrate producer was grown in media supplemented with sulfide in a range of concentrations similar to those observed in DP monoculture. Notably, the butyrate concentration per unit biomass decreased with increasing sulfide concentration for CC, FP, ER, and RI  and species abundances  of the remaining high richness communities, demonstrating that our model could explain the quantitative trends in the high richness communities when provided with sufficiently informative training data −1) dominated the network, representing 49.8% of the interspecies interaction parameters −1)  in a different undefined media16 and found that 27 parameters with magnitude >0.1 h−1 (OD600 species j)−1 shared a sign and only five had opposite sign , Eggerthella lenta (EL), Dorea formicigenerans (DF), and Collinsella aerofaciens (CA) that enabled quantitatively accurate predictions of butyrate production  than in 4BP communities  . These observations combined with the fact that lactate-utilizing butyrate producers, including AC, have been shown to prefer glucose over lactate and produce ~5x more butyrate per unit biomass when grown on lactate versus glucose52, led us to develop the following mechanistic hypothesis: AC would switch between low butyrate (transformation of sugars into butyrate) and high butyrate (transformation of lactate into butyrate) producing states depending on the environmental pH and availability of key resources  were positively correlated with pH in the high richness communities and EL uniquely increased the pH in monoculture  and increased with the initial environmental pH Fig. . Based oIn sum, the proposed mechanism indicates that in a pH-buffered community, resource competition over energy-rich nutrients (i.e. sugars) could enhance butyrate production by AC by triggering a shift in the activity of metabolic pathways from a low to high butyrate-producing state. Environmental pH modification and strong resource competition are more likely to simultaneously occur in high richness communities, which may explain why models trained only on lower-richness communities (M1 and M2 models) were missing the positive production interactions attributed to the combination of these mechanisms. This analysis highlights that our interpretable modeling framework can provide key biological insights into ecological and molecular mechanisms driving community metabolic functions and can illuminate alternative metabolic states by separately quantifying growth and production interactions.62. However, the shape of this function depends on contributions of each species to the given ecosystem function and microbial interactions63. To provide insight into the design of communities that display an ecosystem function within desired specifications, we sought to understand the relationship between species richness and the distributions of butyrate and total biomass production by simulating all 33,554,431 possible sub-communities of our 25-species system  against similar DTL approaches for optimizing metabolite production by engineering individual microbes30 (Pearson r = 0.48–0.78) demonstrates that our model is quite accurate. We use our model to show that while ecosystem functions such as butyrate and total biomass production generally increase and saturate as a function of community richness as previously observed62, richness above a threshold can constrain the minimum and maximum achievable functional outputs of the system. Such constraints may limit the broad efficacy of interventions that attempt to alter microbiome functions and increase diversity without expanding the set of available organisms, such as autologous FMT64.We demonstrated that community-level functions can be designed using a modeling framework that predicts community assembly and then maps community composition to butyrate production. Our results showed that manipulating the presence/absence of species that do not directly contribute to butyrate production can cause butyrate concentration to vary over a wide range , highlighting the critical role of microbial interactions on a specialized metabolic function. Benchmarking our model’s butyrate prediction accuracy  required measurements of communities at similar richness. Since our model captured only pairwise interactions, a potential explanation of the improved performance of models trained on similar community richness is due to an increased number of observations of pairs of species, which in turn increases the statistical likelihood of accurately inferring a given pairwise interaction. However, an alternative interpretation of the importance of high richness community observations is that our model is approximating communities shaped by higher-order interactions with combinations of pairwise interaction terms. Corroborating the presence of higher-order interactions, butyrate production by AC was shaped by a combinatorial impact of environmental pH modification and competition over sugars. Therefore, the predictive capability of computational models of microbial communities could be improved by training on communities that span a range of species richness levels, rather than implementing a standard procedure of characterizing pairwise communities65, including butyrate producing bacteria41. Due to the plasticity of microbial metabolism in response to environmental stimuli, our results demonstrate that it is important to consider both how the resident community will enable growth of therapeutic bacteria as well as promote the desired metabolic states. Indeed, our results showed that the abundance of butyrate producers may not correlate with butyrate production in the presence of AC due to production interactions that influence the activity of metabolic pathways  compared to the DP deletion community . In this study, the butyrate concentration did not vary between conditions, which could have been masked by host butyrate consumption as the concentration was very low for both communities (<1 mM)68. These observations could be explained by H2S inhibition of bacterial production of butyrate and propionate, which share similar metabolic pathways, consistent with the accumulation of 3-hydroxybutyrate in the former case and decreased propionate production in the latter. In a separate study, a chemical inhibitor of H2S production resulted in enhanced butyrate production in an anaerobic digestor community, corroborating our results that H2S can inhibit butyrate production across a broad range of communities69. These mechanistic insights could explain associations between inflammatory diseases and other sulfur-reducing bacteria, such as Bilophila wadsworthia70, which is associated with reduced expression of microbial butyrate synthesis pathways in a mouse model of colitis71. At the molecular level, H2S has been observed to form CoA-persulfide through a reaction with coenzyme A, an essential cofactor for SCFA synthesis72. Also, H2S has recently been shown to modulate bacterial metabolism in the gut microbiome via post-translational modification of a wide range of enzymes73. These observations combined with our results provide a strong foundation for future work to understand the molecular basis by which H2S influences bacterial SCFA production and the resulting implications on the host physiology and disease states.While our approach lacks a host-interaction component, the mechanistic nature of insights derived from our model provide generalizable insight into understanding community-level functions in the mammalian gut environment. For instance, DP has been previously associated with IBD74. In this work, we constructed models of community dynamics and function in a single media under a batch growth period without considering additional physiologically relevant media factors such as dietary fibers and host-secreted factors. While the primary resources in our media comprise simple monomeric compounds rather than some complex substrates found in dietary components (i.e. sugars and amino acids rather than fiber and proteins/peptides), our understanding using this media environment provides a strong foundation which can be extended to understand the impacts of dietary variation on community function. Future work will extend our approach to build model-guided in vitro experimental pipelines for predicting microbiome function in vivo by incorporating these additional physiologically relevant factors as design variables to enable simultaneous exploration of the community and media factor design spaces. Such a model could be used to identify communities with functional responses that are robust to changes in the chemical environment, which may be good candidates for consistent function in vivo. Additionally, host–microbe interactions could be studied in a controlled manner by using co-cultures of synthetic microbiomes with host tissues75.The gut microbiome is exposed to a wide range of dietary substrates and the temporal changes in resource availability can dramatically shape community composition and metabolic activities76. Thus, designing microbiomes to elicit desired systemic responses from the host may require multifunctional bacterial therapeutic design. Our approach can be extended to design multiple functions by using a multi-output regression as the function model77. Alternatively, model interpretability could be sacrificed for potential increases in predictive ability by leveraging flexible machine learning78. An additional consideration for such design is that the underlying metabolic networks may drive tradeoffs between production of different molecules, thus constraining the design space. Such relationships could be quantified using flux variability analysis79 of genome-scale metabolic models80, providing potentially useful quantitative constraints for multifunctional synthetic microbiome design.While we focused on a predicting a single function (butyrate production), many microbial metabolites directly impact host physiology, with potential combinatorial effectsIn sum, our methods provide a flexible foundation to explore design strategies for building microbial communities with target functions from the bottom-up and to understand molecular and ecological mechanisms influencing community-level functions. Such methods will advance the design of synthetic microbiomes with predictable functions for deployment into real-world environments. Beyond understanding and manipulating the human gut microbiome to benefit human health, our approach could be used to harness microbiome properties to address numerous challenges facing society. For example, designing microbiomes for efficient nitrogen fixation to reduce the need for fertilizers, degradation of contaminants for detoxification of wastewater and environmental cleanup, and the production of high value compounds from renewable resources for sustainable bioprocessing applications.2, 15 ± 1% CO2 and balance N2. All prepared media and materials were placed in the chamber at least overnight before use to equilibrate with the chamber atmosphere. The strains used in this work were obtained from the sources listed in Supplementary Data Faecalibacterium prausnitzii.All anaerobic culturing was carried out in an anaerobic chamber with an atmosphere of 2.5 ± 0.5% H600 of 0.0066  in DM38 and aliquoted into three replicates of 1 mL each in a 96 Deep Well (96DW) plate and covered with a semi-permeable membrane (Diversified Biotech) and incubated at 37 °C without shaking. At each time point, samples were mixed and OD600 was measured by diluting an aliquot of each sample into phosphate-buffered saline (PBS) to be within the linear range of the plate reader.Each species’ preculture was diluted to an OD600 of 0.0066 in DM38. Community combinations were arrayed in 96DW plates by pipetting equal volumes of each species’ diluted preculture into the appropriate wells using a Tecan Evo Liquid Handling Robot inside an anaerobic chamber. Each 96DW plate was covered with a semi-permeable membrane and incubated at 37 °C. After 48 h, 96DW plates were removed from the incubator and samples were mixed. Cell density was measured by pipetting 200 μL of each sample into one microplate and diluting 20 μL of each sample into 180 μL of PBS in another microplate and measuring the OD600 of both plates (Tecan F200 Plate Reader). We selected the value that was within the linear range of the instrument for each sample. 200 μL of each sample was transferred to a new 96DW plate and pelleted by centrifugation at 2400×g for 10 min. A supernatant volume of 180 μL was removed from each sample and transferred to a 96-well microplate for storage at −20 °C and subsequent metabolite quantification by high performance liquid chromatography (HPLC). Cell pellets were stored at −80 °C for subsequent genomic DNA extraction and 16S rDNA library preparation for Illumina sequencing. In some experiments, 20 μL of each supernatant was used to quantify pH using a phenol Red assay81. Phenol red solution was diluted to 0.005% weight per volume in 0.9% w/v NaCl. Bacterial supernatant (20 μL) was added to 180 μL of phenol red solution, and absorbance was measured at 560 nm (Tecan Spark Plate Reader). A standard curve was produced by fitting the Henderson–Hasselbach equation to fresh media with a pH ranging between 3 and 11 measured using a standard electro-chemical pH probe (Mettler-Toledo). We used Eq.  with Amax representing the absorbance of the pH 11 standard, Amin denoting the absorbance of the pH 3 standard and A representing the absorbance of each condition.The parameters 600 of 0.0066 in DM38. Four falcon tubes of 1.11× concentrated DM38 were aliquoted, and brought to target sulfide concentration by adding an appropriate volume of sodium sulfide stock solution and a balance of sodium chloride solution, of equimolar sodium content, to a final media volume of 50 mL and DM38 of 1×. This procedure was performed one sulfide concentration at a time, followed by aliquoting into 1.6 mL microfuge tubes, inoculation of each strain, and capping to minimize sulfide volatizing during setup. FP cultures were supplemented with 1 g/L bacto yeast extract (BD) and 33 mM sodium acetate (Sigma Aldrich) prior to capping microfuge tubes. Capped microfuge tubes were incubated at 37 °C for 24 h at which point the OD600 was measured  and supernatants were collected for organic acid quantification via HPLC. Initial sulfide concentrations were measured in blank microfuge tube aliquots of each sulfide concentration via the Cline assay82, to account for degradation of the sulfide stock during experimental setup. Briefly, 14.8 μL of Cline reagent was added to 185.2 μL of culture supernatant and incubated in a sealed 96-Well Microplate for 2 h before diluting in 1% zinc acetate (Fisher) to the linear range of absorbance measurement at 667 nm (Tecan Spark Plate Reader). A standard curve was prepared similarly using sodium sulfide fixed in 1% zinc acetate. The Cline reagent was prepared by dissolving 1.6 g N,N-dimethyl-p-phenylenediamine sulfate (Acros Organics) and 2.4 g FeCl3 (Fisher) in 100 mL 50% v/v HCl (Fisher) in water.Sodium sulfide stock solution and standards were prepared in nitrogen purged water and 1% zinc acetate, respectively, and stored in stoppered, capped Hungate tubes at maximum fill volume to limit volatilizing and oxidizing of sulfide during setup. Each species’ preculture was diluted to an ODIn the pH and sugar titration experiment, the media DM38 was supplemented with 33 mM sodium acetate (Sigma) and excluded glucose, arabinose, and maltose. This media was split into four aliquots, each of which was pH adjusted to the specified pH using 5 M HCl. Each aliquot was then divided in half and glucose, arabinose, and maltose were added to one half to achieve the same concentrations as in DM38. For each pH, the media with and without sugars were serially diluted in ratios necessary to achieve the indicated fraction of sugars. AC was cultured in these media for 48 h, after which samples were collected and measured as described for the community culturing experiments.2SO4 to precipitate any components that might be incompatible with the running buffer. The samples were then centrifuged at 2400 × g for 10 min and then 150 μL of each sample was filtered through a 0.2 μm filter using a vacuum manifold before transferring 70 μL of each sample to an HPLC vial. HPLC analysis was performed using either a ThermoFisher  Ultimate 3000 UHPLC system equipped with a UV detector (210 nm) or a Shimadzu HPLC system equipped with a SPD-20AV UV detector (210 nm). Compounds were separated on a 250 × 4.6 mm Rezex© ROA-Organic acid LC column  run with a flow rate of 0.2 mL min−1 and at a column temperature of 50 °C. The samples were held at 4 °C prior to injection. Separation was isocratic with a mobile phase of HPLC grade water acidified with 0.015 N H2SO4 (415 µL L−1). At least two standard sets were run along with each sample set. Standards were 100, 20, and 4 mM concentrations of butyrate, succinate, lactate, and acetate, respectively. For most runs, the injection volume for both sample and standard was 25 µL. The resultant data was analyzed using the Thermofisher Chromeleon 7 software package or Shimadzu LabSolutions software package.Supernatant samples were thawed in a room temperature water bath before addition of 2 μL of H−1 Proteinase K (VWR) and 200 μL of Buffer AL (QIAGEN) were added to each sample before mixing with a pipette. Plates were then covered by a foil seal and incubated at 56 °C for 30 min with orbital shaking at 600 RPM. Next, 200 μL of 100% ethanol (Koptec) was added to each sample before mixing and samples were transferred to a nucleic acid binding (NAB) plate  on a vacuum manifold with a 96DW collection plate. Each well in the NAB plate was then washed once with 500 μL buffer AW1 (QIAGEN) and once with 500 μL of buffer AW2 (QIAGEN). A vacuum was applied to the Pall NAB plate for an additional 10 min to remove any excess ethanol. Samples were then eluted into a clean 96DW plate from each well using 110 μL of buffer AE (QIAGEN) preheated to 56 °C. Genomic DNA samples were stored at −20 °C until further processing.Genomic DNA was extracted from cell pellets using a modified version of the Qiagen DNeasy Blood and Tissue Kit protocol. First, pellets in 96DW plates were removed from −80 °C and thawed in a room temperature water bath. Each pellet was resuspended in 180 μL of enzymatic lysis buffer (20 mM Tris–HCl (Invitrogen), 2 mM sodium EDTA (Sigma-Aldrich), 1.2% Triton X-100 (Sigma-Aldrich), 20 mg/mL lysozyme from chicken egg white (Sigma-Aldrich)). Plates were then covered with a foil seal and incubated at 37 °C for 30 min with orbital shaking at 600 RPM. Then, 25 μL of 20 mg mL−1 by diluting in molecular grade water using a Tecan Evo Liquid Handling Robot. First, genomic DNA samples were removed from −20 °C and thawed in a room temperature water bath. Then, 1 μL of each sample was combined with 95 μL of SYBR Green (Invitrogen) diluted by a factor of 100 in TE buffer (Integrated DNA Technologies) in a black 384-well microplate. This process was repeated with two replicates of each DNA standard with concentrations of 0, 0.5, 1, 2, 4, and 6 ng μL−1. Each sample was then measured for fluorescence with an excitation/emission of 485/535 nm using a Tecan Spark plate reader. Concentrations of each sample were calculated using the standard curve and a custom Python script was used to compute the dilution factors and write a worklist for the Tecan Evo Liquid Handling Robot to normalize each sample to 1 ng μL−1 in molecular grade water. Samples with DNA concentration <1 ng μL−1 were not diluted. Diluted genomic DNA samples were stored at −20 °C until further processing.Genomic DNA concentrations were measured using a SYBR Green fluorescence assay and then normalized to a concentration of 1 ng μLMol. Syst. Biol., 2018). Primers were arrayed in skirted 96-well PCR plates (VWR) using an acoustic liquid handling robot (Labcyte Echo 550) such that each well received a different combination of one forward and one reverse primer (0.1 μL of each). After liquid evaporated, dry primers were stored at −20 °C. Primers were resuspended in 15 μL PCR master mix (0.2 μL Phusion High Fidelity DNA Polymerase (Thermo Scientific), 0.4 μL 10 mM dNTP solution (New England Biolabs), 4 μL 5× phusion HF buffer (Thermo Scientific), 4 μL 5 M Betaine (Sigma-Aldrich), 6.4 μL Water) and 5 μL of normalized genomic DNA to give a final concentration of 0.05 μM of each primer. Primer plates were sealed with Microplate B seals (Bio-Rad) and PCR was performed using a Bio-Rad C1000 Thermal Cycler with the following program: initial denaturation at 98 °C (30 s); 25 cycles of denaturation at 98 °C (10 s), annealing at 60 °C (30 s), extension at 72 °C (60 s); and final extension at 72 °C (10 min). 2 μL of PCR products from each well were pooled and purified using the DNA Clean & Concentrator (Zymo) and eluted in water. The resulting libraries were sequenced on an Illumina MiSeq using a MiSeq Reagent Kit v3 (600-cycle) to generate 2 × 300 paired-end reads.Amplicon libraries were generated from diluted genomic DNA samples by PCR amplification of the V3–V4 of the 16S rRNA gene using custom dual-indexed primers 16. Paired end reads were merged using PEAR (v0.9.10)83 after which reads without forward and reverse annealing regions were filtered out. A reference database of the V3–V5 16S rRNA gene sequences was created using consensus sequences from next-generation sequencing data or Sanger sequencing data of monospecies cultures. Sequences were mapped to the reference database using the mothur (v1.40.5)84 command classify.seqs . Relative abundance was calculated as the read count mapped to each species divided by the total number of reads for each condition. Absolute abundance of each species was calculated by multiplying the relative abundance by the OD600 measurement for each sample. Samples were excluded from further analysis if >1% of the reads were assigned to a species not expected to be in the community (indicating contamination) or if they had <1000 total reads and OD600 > 0.1 .Sequencing data were demultiplexed using Basespace Sequencing Hub’s FastQ Generation program. Custom python scripts were used for further data processing  without introducing an excessive number of parameters (e.g. mechanistic models85).The species PLoS Comput. Biol., 201944). Briefly, our method has a prior distribution for each model parameter and then varies the parameters to fit the model to the measured species abundances  while penalizing deviations from the parameter prior distributions. These penalties provide a regularization effect, which is necessary when the model is underdetermined. We used L2 regularization because we expected inter-species competition to be prevalent and thus did not expect many interaction parameters to be negligible. After an optimal parameter set is found, this process is repeated hundreds of times after applying random noise to the experimental data proportional to the measured experimental variance to generate an ensemble of parameter sets (i.e. the posterior distribution). This posterior distribution is then used as the prior distribution when updating the model with new data. We adapted a previous implementation of this method in Julia for this work.We used a Bayesian parameter inference approach to estimate parameters for the gLV model from experimental measurements . We used this posterior distribution as a prior distribution to update the model with the pairwise community data and generated the gLV module of Model M1, where posterior distributions were estimated from experimental data for ri, aii, and aij where species i and species j co-occurred in the experimental data and the posterior distribution of aij for unobserved pairs was equal to the prior. We similarly updated the model using the 3–5-member community experiments to generate Model M2. Regularization coefficients for each iteration of the model updating process are shown in Supplementary Data Before training the model on any data, we assumed a normally distributed prior for each parameter with mean of 0 and standard deviation equal to 1. We then trained the gLV model on time-series measurements of monoculture growth for each species, estimating a posterior distribution for each aij interaction parameter matrix such that the rows and columns occurred in the same order as the phylogenetic tree . This process was repeated independently for each parameter set in the posterior distribution.The gLV modules of Models M1 and M2 were underdetermined due to pairs of species never being observed in the same community within the training dataset. To generate parameters for these unobserved interactions, we used a matrix imputation approach to estimate the interaction parameters informed by the phylogenetic relatedness of species. First, we sorted the ree Fig. . Next, w44, we found that the optimization problem became intractable when attempting to estimate parameters from high richness community data (i.e. >10 species), due to infeasible memory requirements resulting in an inability to converge on a solution. To address this problem, we used the nonlinear programming solver FMINCON in MATLAB to generate the gLV module of Model M3 by training on all data simultaneously. While this approach is much less computationally efficient than the previous approach (taking hours rather than minutes to converge for datasets containing only low richness communities), it does not have the same memory-related convergence issues for datasets containing high richness communities and will find a solution given sufficient time. Using this method, the cost function for the optimization algorithm is computed using an ODE solver to simulate each community and the sum of mean squared errors for the community is computed and added to a L2 regularization term penalizing the magnitude of the parameter vector. To ensure that the model did not sacrifice the goodness of fit to the time-series monospecies data, the mean squared errors for these data were weighted more highly. The resulting optimization function was Eq. , Xi denotes the biomass concentration of species i, and i (mM OD600−1 h−1). If we assume that the specific productivity is proportional to the specific growth rate , we can define it as Eq.  yiel yiel6) yTo determine the product concentration at a specific time (e.g. 48 h as in our experiments), we can integrate Eq.  in time,aij) and metabolic shifts (via ρij) on the same species, thus their product would be small. Second, including such interactions would introduce 325 additional parameters to our model, reducing our ability to reasonably infer all parameter values and increasing the chances of overfitting. Together, these assumptions result in the linear regression model with interactions described in Eq. 10). Addid in Eq. .9\docume87). We used L1 regularization to minimize the number of nonzero parameters. Regularization coefficients were chosen by using 10-fold cross validation and choosing the coefficient value with the lowest median mean-squared error for the test data. For models M1 and M2, ensembles of regression models were generated, one for each possible combination of butyrate producers, where samples containing butyrate producers from outside of each set were excluded. In this case, butyrate production from less productive species (e.g. FP) were small compared to more productive species  thus reducing the model accuracy for communities lacking the high productivity species. For Model M3, one regression model was generated using all data because all communities of interest contained highly productive butyrate producers.Note that the summations in Eq.  refer onCustom MATLAB scripts were used to predict community assembly and butyrate production, for many communities as described in the text (e.g. all communities containing all 5 butyrate producers for Fig. 2S to the gas phase and the results agreed at least qualitatively with the data shown on each occasion.The experiments of various communities were performed in nine different batches and the full community was included in each of these batches to quantify variation across the different experimental batches. The 24-species “leave-one-out” communities were also repeated in three of the batches. The variance of these replicated communities can be seen in Figs. Further information on research design is available in the Supplementary InformationSupplementary Data 1Supplementary Data 2Supplementary Data 3Supplementary Data 4Supplementary Data 5Supplementary Data 6Reporting SummaryPeer Review FileDescription of Additional Supplementary Files