In this work, we fabricate microfluidic probes (MFPs) in a single step by stereolithographic 3D printing and benchmark their performance with standard MFPs fabricated via glass or silicon micromachining. Two research teams join forces to introduce two independent designs and fabrication protocols, using different equipment. Both strategies adopted are inexpensive and simple (they only require a stereolithography printer) and are highly customizable. Flow characterization is performed by reproducing previously published microfluidic dipolar and microfluidic quadrupolar reagent delivery profiles which are compared to the expected results from numerical simulations and scaling laws. Results show that, for most MFP applications, printer resolution artifacts have negligible impact on probe operation, reagent pattern formation, and cell staining results. Thus, any research group with a moderate resolution (≤100 µm) stereolithography printer will be able to fabricate the MFPs and use them for processing cells, or generating microfluidic concentration gradients. MFP fabrication involved glass and/or silicon micromachining, or polymer micromolding, in every previously published article on the topic. We therefore believe that 3D printed MFPs is poised to democratize this technology. We contribute to initiate this trend by making our CAD files available for the readers to test our “print & probe” approach using their own stereolithographic 3D printers. It operates under the well-known Hele-Shaw cell approximation, whereby a quasi-2D stokes flow is generated between two parallel flat plates separated by an arbitrarily small gap, and has been previously demonstrated in the microfluidic dipole (MD) and microfluidic quadrupole (MQ) configurations  is a non-contact microfluidic system that combines the concepts of hydrodynamic flow confinement (HFC)see Fig. . The tec12, such as high shear stress and tiny patterning areas, while allowing localized delivery of reagents for biological applications14. Another major advantage of the MFP is its ability to pattern large, open planar surfaces using conventional lab equipment (such as cells on Petri dishes)15.The main advantage of the MFP is that it overcomes major limitations of conventional channel-based microfluidics17. One of this barrier is the fact that MFPs cannot be easily produced on demand due to their typically complex fabrication procedures. For example, the technology was originally designed with a silicon tip and Polydimethylsiloxane (PDMS) chip-to-world connector, which requires bulk micromachining of the silicon chip, fabrication of the PDMS block using soft lithography or micro-molding techniques, alignment and assembly of the different layers, and separate machining of the probe holder3. An attempt to standardize this fabrication procedure introduced the glass-silicon hybrid vertical MFP (vMFP) concept, with a gasket-integrated probe holder for a more compact world-to-chip interface4. This technique has been demonstrated to be very effective in fabricating MFPs with all fluidic apertures placed along a straight line, and is currently one of the most commonly adopted. However, its procedure requires costly microfabrication facilities, implies wafer bonding steps, is difficult to implement for arbitrary aperture arrangements, and results in long prototyping cycles. The 3D printing technology, which is already positively disrupting the development cycles of conventional microfluidic devices19, is poised to overcome these challenges. Not only does it afford a relatively seamless connectivity of several parts, it also offers a straightforward, simple, rapid, inexpensive, and yet robust methodology to manufacture these devices on demand , as shown in Fig. ing Fig. . The proThe second MFP  aims at maximum design simplicity with a commercial 27 µm resolution stereolithography printer . There is no built-in reservoir in the MFP, and the fluidic connections are simply made by plugging commonly available 1/32” tubes into the probe and gluing them in place. The result minimizes probe size within the limits imposed by the printer Fig. . SpecialIn this design, the MFP and its adapter form a slider Fig. . This alAkin to classical MFPs, these 3D printed MFPs are connected to micro-positioners and goniometers, that can be controlled in one or more axes, to control the MFP-to-substrate gap and angle of inclination respectively Fig. . The MFPThe MD and MQ are produced using the 3D printed MFPs from both designs. The profiles were investigated as functions of MFP’s aperture Spacing to Diameter ratio (S/D), aspiration to injection flow rates ratio . Close inspection reveals that the location of the stagnation point was matched with a relative error of approximately 2%. This might be due to experimental inaccuracies such as an imperfect tip surface or small angle between the MFP and the bottom substrate. The analytical model also underestimates the HFC size by approximately 25 µm on all borders. This relatively small error (<5%) is explainable by the fact that the analytical solution considers point source approximation (and thus a S/D ≫ 1). For a similar S/D ratio than the one used in this experiment (S/D = 5.5), error of the same magnitude have been previously reported21. Also, the analytical model doesn’t consider the diffusion at the HFC interfaces. However, diffusion affects our experimental measurement and the threshold we used to determine the experimental HFC envelope might slightly overestimate it.Comparison between numerical simulations and experiments for the MQ profiles Fig.  shows thα of 5, an increasing HFC footprint was obtained when S/D is varied from 1.5 to 4  of the culture with a solution of CellTracker® Green fluorescence dye (10 μM concentration), using a MFP-substrate gap of 60 µm. As expected, an increase in staining intensity is observed as the exposure duration of the cells to the HFC (of the CellTracker solution) is increased from 15–120 s , are relatively inexpensive via 3D mail-order printing services, and are potentially as reusable as Si-based MFPs. This approach allowed for the integration of new components like inbuilt reservoirs, convenient MFP probe holders, and using commercially available tubing connectors for a straight forward connectivity and minimization of dead volume–that would have been otherwise complicated to achieve with conventional MFP microfabrication techniques. Moreover, this work demonstrated how 3D printing brings scalability and flexibility to the MFP in terms of producing different designs, different numbers of apertures, different aperture configurations, and different fluidic connectors. Using two independent MFP designs, proof-of-concepts were presented in the form of developing MDs, MQs, and selective labeling of adherent live cells within their culture medium in a “writing” mode. The MD and MQ profiles produced by the 3D printed MFPs closely matched numerical and analytical calculations – the same way micromachined MFPs do – thus confirming similarities in their accuracies. Furthermore, cell staining applications were demonstrated, which validate the applicability of the 3D printed MFPs in performing bioassays.10. (2) The printed MFPs contained some unavoidable channel artifacts – one design more than the other – that had minor effect on the accuracy of the produced profiles. However, with 3D printing technology currently undergoing intense development to bring down costs and increase resolution, these limits are expected to be continuously pushed back as new generations of 3D printers come to the market. In the case an MFP is required for an application that requires a single cell resolution, the same technology discussed here can be adapted to more advanced 3D printers capable of printing 3D nanostructures, such as those involving direct laser writing and two-photon polymerization technologies25. (3) Biocompatibility of the polymers and resins used in SLA is still a concern for applications where cells are directly cultured on the device26. However, in the case of MFPs, cells are cultured in Petri dishes, or microtiter plates, and are never in contact with the 3D printed device, which limit the biocompatibility problem. Furthermore, research on new post-processing and sterilization techniques, and on biocompatible resin formulation, have been demonstrated to reduce protein adsorption and improve long-term cell viability after experiments with 3D printed materials29.The use of affordable 3D printing in this field, however, comes with some drawbacks: (1) the current resolution of the affordable 3D printers limits the minimum aperture sizes of MFPs. However, this didn’t affect the capability of presented MFPs to target cluster of tens of cells and generate concentration gradients at resolutions similar to the original MQThe HFC concept behind the MD and MQ have numerous potential applications, which could become even more accessible to the research community with this new fabrication strategy, lessons learned from our experiments, and the presented proof of its practical applicability. By demonstrating the simplicity and customizability of 3D printed MFPs, we believe that the technology will help spread the concept outside microfabrication laboratories and make its potential and versatility as an open reagent delivery tool directly available to life-science laboratories. To support this assertion, all CAD and stl files used to print the above designs are made available  for any stereolithographic 3D printer owner to test.: Designs were performed using a commercial CAD software (SolidWorks) and the MFPs were printed using a commercially available stereolithographic 3D printer . The printer has a labeled XY resolution of 82 µm, and Z resolution of 25 µm but our parametric study with this specific MFP design showed that the minimum diameter resolution for repeatable 3D channels is 250 µm using a polymeric resin . After printing, the chip was washed with ethanol, placed in a UV flood light curing system for 2 min and then washed again with DI water. The MFP holder was separately 3D printed .Design 1Design 2: Designs were made using Catia v5  while abiding by two rules to minimize the risk of aperture clogging: 1) the length of apertures was kept the smallest possible  and 2) aperture size was kept over 6 printer’s pixel size (160 µm). The MFPs were printed using an Asiga freeform Pico with a resolution of 27 µm . The resins used were PlasCLEAR V2 and PlasGRAY V2 (Asiga). MFPs were briefly soaked in an isopropanol bath to remove uncured resin. To thoroughly clean the microchannels, the MFPs were then put in an isopropanol bath in a sonicator  for 20 minutes. Thereafter, MFPs were post-cured with UV light for 15 minutes to fully harden . MFPs were designed to fit widely available 1/16″ O.D. tubing. Tygon tubes  were plugged in the MFP and glued with cyanoacrylate glue. To insure no glue would enter inside the MFP apertures and tubing, each tube was filled with water during this step. MFP tips were manually polished using fiber optic lapping sheets . Sheet with 5 µm, 3 µm, 1 µm and 0.3 µm grits were used consecutively. Water was injected with the MFP’s apertures after each polishing steps to make sure no polishing residues would clog the apertures. MFPs made with clear resin were coated with black ink  using an airbrush. A layer of aerosol clear coat  was then sprayed on the tip.20H10Na2O5) . For the MQ, a solution of Rhodamine B (C28H31ClN2O3) (Sigma Aldrich) was injected through the second injection aperture. Injection and aspiration were driven using the MFCS®-EZ microfluidic pressure pump  or by the neMESYS high precision syringe pump  depending on the design used. Images of the profiles created by fluorescein and rhodamine B solutions were captured using their respective microscope’s fluorescent filter cubes, and then combined using Image J (Design 1)  and MATLAB (Design 2). For Design 2 MQ, a background image was subtracted on both fluorescein and Rhodamine B channels before they were merged in a single image. The background used corresponds to an image of the MFP with injection or aspiration turned off. To deduct the diffusion region from the overall profile, we used the “Minimum Threshold” function in ImageJ, which was derived from the thresholding technique adapted in reference30. Profiles were then traced out using a plot digitizer (GNU Library). For the dipole characterization, the experiment was repeated with at least 3 different MFPs per profile to test reproducibility. The dimensions for each interval was averaged to produce the final plot with standard error estimates used as the error bars.To characterize the MD and MQ, the MFP was positioned above a Petri dish or a microscope slide with custom walls (depending on the design) located on the stage of an inverted microscope. Upon aligning the MFP with the objective of the microscope, the Z stage  is used to slowly approach the substrate. When the MFP contacts the substrate, it is then lifted by the required gap-height to produce the Hele-Shaw two parallel plates configuration. The Design 1 MFPs were visualized using the Epi-fluorescence inverted ECLIPSE Ti microscope , and images were captured using the DS-Qi2 camera (NIKON). Design 2 MFPs were visualized and imaged using the epi-fluorescence inverted microscope Axio Observer.Z1  and the LaVision imager sCMOS camera . MD images were taken by injecting a solution of dissolved green fluorescein sodium salt  was used on the numerical simulation result.The 3D numerical models of the MD and MQ were developed using finite element simulations . The solutions were obtained using a direct and stationary solver to compute the Navier-Stokes equation  coupled with the convection-diffusion equations. MFPs were modeled as circular surfaces with inlets and outlets that correspond to the apertures. Dimensions used were those of the designed MFPs. Water was considered incompressible with a density of 998.2 kg/m21:x/S and 2y/S respectively  diluted in PBS buffer with a final concentration of 10 μM/mL. The solution was then mixed with fluorescein sodium salt  for visualizing the HFC using the microscope. The solution was then loaded into the MFP’s reservoir – by suction through the aperture of the MFP – and the MFP was positioned above the cell culture with a MFP-substrate gap of 60 µm. Monitoring of the cells’ exposure time was performed using a stopwatch. The calligraphic labeling was performed by programming (C#) the XY stage movements in the Zaber scripting environment. The spacing between each letter was achieved by rapid movement of the stages (~29 mm/s), from the end of one letter to the beginning of the other letter .HeLa cells  were cultured in sterile Petri Dishes (Thermo Scientific) in Dulbecco’s Modified Eagle Medium (DMEM) supplemented with 10% FBS, 100 U/mL penicillin, 100 μg/mL streptomycin and 0.2 mM L-glutamine  at 37 °C and 5% COMFPs used with cells were sterilized by soaking in 99% ethanol for 24 h. Washing with DI water, and curing, were then repeated and followed by soaking in DMEM for 12 h. Before preparing cell dishes used for the cell viability experiment, marks were randomly made at the bottom of the culture plates to ensure traceability of the target region. Cell viability was estimated by applying NucGreen™ Dead Cell Indicator (2 drops/mL of cell medium) to the cell culture dish already exposed to the HFC from the MFP. As control, a cell dish prepared with the same cell confluence as the processed dish, was kept in the incubator for the duration of the experiment and also processed with the NucGreen™ Dead Cell Indicator (Thermo Scientific) after 24 h. Counting of cells to evaluate death rate , was done manually using the ImageJ “Multi-Point” feature.Supplementary Figures and MaterialsAutomated cell labeling 1Automated cell labeling2


Factors associated with post-surgical pain are not fully explored. The aim of this study was to identify determinants of postoperative pain after arthroscopic surgery of the knee. Synovial tissue metabolism was analysed by microdialysis and the association with individual and peri-surgical factors to identify determinants important for pain management and thus patient satisfaction.2 (PGE2), glucose, and glycerol were measured by microdialysis in the knee synovium. Patients reporting VAS ≥ 4 received rescue pain medication with systemic opioids.Cross-sectional study of 57 patients (22 women) with median age of 39 years. All patients were operated on with arthroscopic surgery of the knee and monitored postoperatively with synovial microdialysis. The cross-sectional cohort was investigated to determine local tissue levels of inflammatory and metabolic compounds along with postoperative pain experience. Measurements: pain was determined by visual analogue scale (VAS). Postoperative synovial tissue levels of prostaglandin Ep = 0.04), lower body weight (p = 0.02), had a lower BMI (p = 0.04) and/or were smokers (p = 0.02). A closer analysis using multinomial logistic regression showed a significantly higher amount of pain in smokers (p = 0.01) and patients of a younger age (p = 0.02). A significant correlation was also found between VAS and duration of surgery (p = 0.007). No significant correlation could be found between VAS and synovial levels of PGE2, glycerol and glucose, but a statistically significant decline with time of PGE2 in both groups.Initial results indicated that patients with pain (interpreted as having VAS ≥ 4), i.e. those receiving rescue medication with systemic opioids, were of a younger age (p = 0.02) and smokers (p = 0.01), as well as an association between pain and length of surgery (p = 0.007). These findings point out individual factors useful for the prediction of postoperative pain after arthroscopic surgery and are clinically important for personalized pain management.The results from this study show a significantly higher frequency of pain, post-surgery among younger patients (II. In the c states –13. The The study design was observational cross-sectional cohort with surgery performed on eligible patients when operating room and laboratory personnel were available for performing microdialysis. The study period was between 2004 and 2013. The protocols for perioperative treatment, anaesthesia and the surgical procedures remained the same during the study. The study was conducted at the Department of Orthopaedic Surgery at Karolinska University Hospital in Huddinge, Sweden, with a catchment area representative of the general population.57 patients (22 women), healthy, apart from knee problems, were eligible for inclusion in the study. Informed written consent was obtained from each patient before inclusion.The inclusion criteria were indication for arthroscopic surgery of the knee due to intra-articular pathology  using the International Statistical Classification of Diseases and Related Health Problems (ICD-10). Patients with the following diagnoses were included in the study. patients undergoing arthroscopic surgery: derangement of meniscus due to old tear or injury (23), tear of meniscus, current injury (5), unilateral primary osteoarthritis of knee (2), other unilateral secondary osteoarthritis of knee (1), tear of articular cartilage of knee, current (3), damage to multiple structures of the knee joint (2), sprain of the superior tibiofibular joint and ligament (2), late-onset pain and discomfort after injury to the lower extremity (1), late-onset pain and discomfort after injury to tendon or muscle in the lower extremity (1), and sprain of cruciate ligament of knee (1).Performed type of arthroscopic surgery: arthroscopic partial excision of a meniscus in the knee joint (26), Arthroscopic partial excision of cartilage in the knee joint (2), arthroscopic synovectomy in the knee joint (1), arthroscopic exploration of the knee joint (8), arthroscopic or endoscopic reimplantation of a meniscus in the knee joint (3), other arthroscopic or endoscopic surgery on synovia or articulating surface (1).Diagnoses of patients with a cruciate ligament injury: sprain of cruciate ligament of knee 15) and damage to multiple structures of the knee joint (1). Performed surgery: arthroscopic reconstruction of a ligament in the knee joint without using a foreign material (16). ACL reconstructive surgery was done using the ipsilateral semitendinosus tendon as autograft. Exclusion criteria were known systemic inflammatory/metabolic diseases, or a regular intake of anti-inflammatory or other drugs known to or suspected of altering the metabolism of the knee joint. Patient characteristics are shown in Table 5 and damAll patients received a standardized premedication of paracetamol (2000 mg) and codeine (60 mg). The patients were not allowed glucose infusion, NSAID, or cortisone perioperatively. Anaesthesia was introduced and maintained using atropine 0.5 mg/ml, propofol 10 mg/ml, fentanyl 0.05 mg/ml and sevoflurane. The duration of the knee arthroscopic surgical procedure was 13–160 min.The method works by inserting a catheter with a tubular semipermeable membrane at its tip. When inserted, the catheter mimics the function of a capillary vessel by causing an equilibration across the semipermeable membrane between the interstitial fluid and dialysis fluid streaming through the probe. The equilibrated dialysis fluid is thereafter collected in a vial, and later analysed.2 using enzyme-linked immunosorbent assay ELISA  along with ethanol escape percentage measuring local blood flow. This was repeated five times. Microdialysis was done for a duration of 240 min (4 h) post-surgery. A total of six vials were collected from each patient  was injected into the knee joint, and a microdialysis catheter with a pore size of 20 kD  was introduced into the synovial membrane on the medial side of the knee under arthroscopic control. All catheters were perfused with a perfusion fluid  and the perfusion speed was 2.0 µl/min. The equilibration of the system started when a flush period of 40 min was finished. The first dialysate was collected after another 40 min. The samples were quickly frozen to minus 80 °C, and were later analysed together in the same assay for concentrations of glucose and glycerol with the CAM 600 , and PGEBlood flow was measured due to its regulating effect on cellular and extracellular substances through microcirculation. It was measured with the ethanol escape method (EtOH) , 15. TheMeasuring pain is commonly done using the visual analogue scale (VAS) , which is a subjective grading tool. The patients were asked to assess their VAS score every 40 min as the vials were collected. The patients who estimated their pain to be severe (VAS ≥ 4) postoperatively were offered pain medication (systemic ketobemidone). The patients were then divided into two groups depending on if they requested rescue medication (RM) or not (NRM). 47 of the patients had no need of rescue medication postoperatively. Ten patients had a higher degree of pain and required rescue medication. The first dose of pain medication was given at an average time point of 47 min post-surgery: a median of 2 mg of ketobemidone (1.5–3) iv. Four of the ten patients received a second dose on request: median 2 mg (1.5–3) iv. at average time 121 min post-surgery. One of the ten patients received a third dose of 2 mg iv. at 240 min post-surgery  and random effects . Variables showing significant univariate associations with pain were selected for a logistic regression analysis. Statistical analyses were performed using statistical software SAS version 9.4 .Continuous variables are expressed as median (10–90 percentile) and nominal and ordinal variables as percentage. The continuous variables were not normally distributed hence we expressed these variables as one standard deviation increase from the mean. Significance was set at the level of p = 0.04), with a lower body weight (p = 0.02), a lower BMI (p = 0.04) and a higher frequency of smoking (p = 0.02). There was a significant correlation between pain (VAS) and duration of surgery (p = 0.007) , based at study start Table . We foun07) Fig. . There wVAS Fig. .p = 0.02), gender (p = 0.15), smoking (p = 0.01) and 1-SD increase of BMI (p = 0.38) , with the RM group experiencing a higher degree of subjective pain. The curves differed significantly (< 0.0001).Factors that were associated with variability of VAS were evaluated using a multivariate mixed model. VAS showed a significant difference in subjective pain between the RM and NRM at 40 and 80 min (2. However, we found a statistically significant difference between the PGE2 levels at 40 min and the PGE2 levels between 120 and 240 min (Fig. Although a visual difference between curves, there was no statistically significant difference between the RM and NRM groups when using multivariate mixed model for the levels of PGEThe multivariate mixed models of glucose, glycerol and EtOH showed no statistically significant differences in or between groups. Overall the synovial tissue blood flow was stable.2, a mediator of central and peripheral pain sensitization [2, known as a pain mediator and a marker of inflammation, showed a visual difference between the NRM and the NRM group (Fig. 2 in patients requiring opioids [2 was significant in both groups post-surgery. This suggests a primary elevation associated with the initial pain and/or surgical trauma. Glucose levels showed no statistical difference between RM and NRM groups which is in contrast with other studies that demonstrate an increased consumption of glucose in the synovial membrane after minor arthroscopic surgery, but no change after ACL reconstruction [The most important finding of this study was that patients requiring rescue medication after arthroscopic knee surgery differed significantly in age, weight, BMI and smoking compared to those not requiring rescue medication. Multinomial logistic regression, showed a higher frequency of pain among young patients and smokers. These findings are in accordance with earlier studies , 5. The tization . The resoup Fig. . However opioids . The dectruction , 13, 19.The results of the present study show a higher degree of pain in younger patients, smokers, and after long-lasting arthroscopic surgery of the knee. This should be taken into consideration during planning and management of arthroscopic surgery to create a more effective and personalized pain management.


It is remarkable that the same transformation route is observed for phosphorus. Our theoretical analysis suggests that the sequence of structural transitions of CaBe2P2O8 is associated with the electronic transformation from predominantly molecular orbitals at low pressure to the state with overlapping electronic clouds of anions orbitals.Beryllium oxides have been extensively studied due to their unique chemical properties and important technological applications. Typically, in inorganic compounds beryllium is tetrahedrally coordinated by oxygen atoms. Herein based on results of in situ single crystal X-ray diffraction studies and ab initio calculations we report on the high-pressure behavior of CaBe 2P2O8 where Be coordination changes to trigonal-bipyramidal and octahedral, implying that d orbitals are not mandatory for high coordination.Beryllium in inorganic compounds is usually coordinated to four oxygen atoms, but higher coordination numbers have been predicted. Here the authors observe a pressure induced stepwise transition in CaBe Small atomic radius and high ionization energy of beryllium make covalent interactions playing the important role in stabilizing beryllium compounds, unlike other alkaline-earth elements. In contrast to MgO, CaO, SrO, and BaO, at ambient conditions BeO crystallizes in the hexagonal wurtzite structure, featuring tetrahedrally coordinated Be2+ and O2− ions4. Bonding of beryllium to four oxygen atoms with the formation of BeO46− tetrahedra is also exclusive for its natural occurrence5. Various molecular oxygen-rich composition compounds 2) demonstrating diverse Be–O bonding situations have been recently isolated within solid noble-gas matrices6. Cases with Be in coordination higher than four have not been observed experimentally for inorganic compounds, though recent ab initio calculation studies on BeO27 and BeO8 have predicted the formation of BeO6 octahedra with ionic Be–O bonding at high pressures.Due to the broad technological applications of beryllium oxocompounds11. High-pressure can effectively overcome reaction energy barriers and reorder atomic orbital energy levels so that new phases could reveal properties and stoichiometries unexpected from the viewpoint of conventional solid-state chemistry. Pressure-induced densification of matter is accompanied by the rearrangement of atomic bonds and structural units in order to fill the available space as effective as possible, which usually results in the increase of the atomic coordination numbers .Recent advances at third-generation synchrotron facilities made the in situ high-pressure X-ray diffraction a powerful tool in simultaneous synthesis and structural characterization of new compounds2Si2O819 has inspired us to probe high-pressure behavior of structurally similar compound CaBe2P2O8. The question whether beryllium could experience the same increase in coordination number is of general chemical interest as well as of particular importance for the understanding the nature of Be–O and P–O bonding. While the first experimental observations of P[V] and P[VI] have been recently reported for high-pressure phases of TiPO49 and AlPO424, the current study appears to the first reporting on the experimental observation of five- and six-fold coordinated beryllium. Here, we present results of high-pressure single-crystal X-ray diffraction (SCXRD) experiments conjoined with ab initio density functional theory (DFT) calculations that evidence a step-wise transition of Be and P coordination from tetrahedral to octahedral through trigonal bipyramidal.Recent discovery of five- and six-fold coordinated silicon in the high-pressure phases of CaB2Be2O8, possesses a monoclinic symmetry (space group P21/c) with a = 7.798(3), b = 8.782(2), c = 8.299(1) Å, β = 90.50(5)˚25. The asymmetric unit of hurlbutite contains four tetrahedrally coordinated T cations (two P and two Be), eight oxygen and one calcium atoms. Polymerization of PO4 and BeO4 tetrahedra through common vertices results in the formation of framework with four- and eight-membered channels running along the a-axis  and least (a-axis) compressible directions. The evolution of the new-forming contacts P1–O8* and Be2–O2* is shown in Supplementary Fig. 5 polyhedra possesses trigonal bipyramidal geometry with two long apical (1.70 and 1.92 Å) and three short equatorial bonds (1.50–1.53 Å), while P1 still preserves tetrahedral coordination. Upon further compression of hurlbutite-II, BeO5 evolves towards more regular trigonal bipyramid geometry by pronounced shortening of the Be–O2* bond.At pressures above 20 GPa the crystal structure again experiences conventional contraction with the preservation of the most , where the P1 and Be2 atoms fill trigonal bipyramidal voids and the P2 and Be1 atoms fill tetrahedral voids. Ca has 11-fold coordination manifesting distortion from an ideal close packing.At ~83 GPa the crystal structure undergoes another phase transition, which is reflected in an abrupt change of the unit-cell parameters Fig. . The higP-1 space group  and found an excellent agreement between measured and calculated unit-cell parameters, volume, atomic coordinates and interatomic distances 27. In inorganic oxocompounds this tendency is typically realized along with evolution of the oxygen sublattice toward the close packing arrangements41. This is also the case for hurlbutite: upon pressurizing O and Ca cations firstly arrange into close packing assembly consisting both of distorted HCP and CCP elements  and later into ABCACABCBCAB arrangement . While the cation coordination and oxygen sublattice are traditional determinants of a crystal structure, the alternative view on the crystal chemistry of oxides was proposed by O’Keeffe and Hyde by introducing terms cation packing and anion coordination44. While this approach was found to be effective for a number of cases , we find that the classical way of structure representation is more appropriate for our cases. By studying high-pressure behavior of a group of isotopological compounds with general formulae MT12T22O8 , we conclude that the crystal structure response (and particularly formation of TO5 species) is governed by interplay of two factors: compressibility of TO4 tetrahedra and size of large M cation. The chemistry of the T site governs T[IV] → T[V] transition pressure . The size of the M cation is responsible for formation of close packing arrangement with trigonal bipyramidal voids, i.e., TO5 species. Thus, in contrast to CaB2Si2O8, Si site in the structure of SrB2Si2O8 does not change coordination to five-fold upon pressurizing but instead undergoes a splitting into two sites45. Further increase of M cation size results in complete absence of Si[V]: the high-pressure polymorphism is realized via direct Si[IV] → Si[VI] transition in the crystal structure of BaB2Si2O845. In the upcoming review article on high-pressure behavior of MT12T22O8 compounds we are going to elaborate on the crystal chemical regularities in detail.Pressure-induced increase of cation coordination number is repeatedly observed tendencyThe present study further proves the powerful capabilities of high pressure as a tool for tuning chemical properties of matter. Growing interest of the chemical community in high-pressure SCXRD techniques using diamond anvil cells (DACs) ensures that the upcoming studies will bring further examples of unique phases as well as provide a solid experimental basis for the future development of novel high-pressure crystal chemistry.2P2O8, originating from Viitaniemi pegmatite  have been provided by Mineralogical Museum, CeNak, University of Hamburg. Three separate in situ high-pressure SCXRD were performed at the experimental station P02.2 (extreme conditions beamline) at synchrotron Petra III . Symmetric DACs with culets diameter of 300, 200, and 150 μm were used for pressure generation in experiments #1, #2, and #3, respectively. The sample chambers with approximate diameters of 150, 100, and 85 μm were obtained by drilling the preindented rhenium gasket. Hurlbutite crystals were placed inside the sample chambers along with a ruby sphere for pressure estimation  in the Perdew–Burke–Ernzerhof (PBE)56 parametrization was selected to treat the exchange and correlation effects. PBE-GGA belongs to the so-called semilocal DFT functionals, which are known to slightly underestimate bonding strength in solids and significantly underestimate band gaps in semicinductors and insulators. However, it is numerically efficient and provides accuracy, which is sufficient for the purposes of the present study. The integration over the Brillouin zone was performed using a gamma-centered mesh with a k-points grid 6 × 6 × 6. All the calculations were carried out using the Gaussian smearing with a broadening of σ = 0.05 eV. All properties were calculated at a given volumes (pressures) after the ion positions and cell shape were relaxed to achieve forces action on ions smaller then 10−2 eV/Å and hydrostatic conditions: |p − px|, |p − py|, |p − pz| < 0.5 kbar.Calculations of the electronic structure, total energies and structural parameters for all phases of hurlbutite were performed in the framework of the DFT using the Vienna ab initio simulation packageSupplementary informationPeer Review File


The emerging field of valleytronics aims to coherently manipulate an electron and/or hole’s valley pseudospin as an information bearing degree of freedom (DOF). Monolayer transition metal dichalcogenides, due to their strongly bound excitons, their degenerate valleys and their seamless interfacing with photons are a promising candidate for room temperature valleytronics. Although the exciton binding energy suggests room temperature valley coherence should be possible, it has been elusive to-date. A potential solution involves the formation of half-light, half-matter cavity polaritons based on 2D material excitons. It has recently been discovered that cavity polaritons can inherit the valley DOF. Here, we demonstrate the room temperature valley coherence of valley-polaritons by embedding a monolayer of tungsten diselenide in a monolithic dielectric cavity. The extra decay path introduced by the exciton-cavity coupling, which is free from decoherence, is the key to room temperature valley coherence preservation. These observations paves the way for practical valleytronic devices. 2 in a monolithic dielectric cavity, and observe room-temperature valley coherence of valley-polaritons.Owing to the presence of strongly bound excitons and degenerate valleys, monolayer transition metal dichalcogenides show promise for valleytronic applications. Here, the authors embed monolayer WSe Monolayer TMDCs are direct bandgap semiconductors that support stable room-temperature excitons (binding energy of 0.3–0.5 eV). The broken inversion symmetry and strong spin-orbit interaction give rise to pronounced optical selection rules at two energy-degenerate valleys6. The two valleys, K and K′, can be activated by circularly polarized light with opposite handedness. As a result of the previous, the binary valley pseudospin index has been identified as potential information bearing degree-of-freedom (DOF) giving birth to the field of valleytronics8.Nanoscale materials have attracted much attention in recent years for their potential to enable optoelectronic device architectures. Among these are monolayer transition metal dichalcogenides (TMDC)6 and the optical generation, and manipulation of valley coherence have been observed at cryogenic temperatures13. However, the major obstacle to coherently controlling the valley DOF at room temperature is the intervalley dephasing processes mediated by phonons, the electron-hole interaction or the Maialle-Silva-Sham mechanism (MSS mechanism)14.In analogy to spintronics, valleytronics relies on the ability to store, manipulate and readout information from the valley pseudospin. To date, the optical pumping of valley polarization18. It has been discovered that TMDC polaritons inherit the valley DOF and exhibit enhanced valley polarization at elevated temperature22. In this work we leverage polaritons based on the monolayer tungsten diselenide (WSe2) to circumvent intervalley dephasing and preserve finite valley coherence at room temperature. The polariton valley coherence is studied by steady-state angle-resolved Photoluminescence (PL) measurements  formed by a pair of dielectric distributed Bragg reflectors (DBRs) and a monolayer of WSe2 positioned at the cavity antinode (see Methods). In order to obtain strong coupling the cavity resonance is designed to be commensurate with the WSe2 neutral exciton energy. However, as shown in Fig. 2 deposition likely from strain induced by the deposition process or the dielectric environment change19, which results in an approximately 10 meV cavity-exciton detuning.The device used in this study, Fig. 18. Strong coupling is confirmed by the anti-crossing exhibited by the photonic and excitonic branches, see Fig. The device dispersion relation is measured by imaging the objective back focal plane onto the entrance slit of an imaging spectrometer22. A schematic of a coherent valley polariton state is illustrated in Fig. θ, is fitted to A cos (4θ + ϕ) + C0 as expected for measuring linear polarization. The fit is used to determine the output polarization angle ϕ0. Red arrows in each panel indicate the excitation polarization orientation. The relationship between the measured output linear polarization and the input linear polarization orientation is presented in Fig. Next, we study the room-temperature polariton valley coherence. A similar analysis of valley polariton polarization can be found in Supplementary Note 4ρl (l identifies linear) is used which can be expressed asI is the measured intensity and “co” (“cross”) means the input and output linear polarizers are parallel (perpendicular). Figure 2 monolayer flake. To gain insight into the valley coherence properties  to resonance (1.658 eV), ρl rises from 0% to ~9% for the polariton device. In contrast  ast Fig. , the unc22. In order to understand the observed polariton photo-physics, we build a valley-specific Jaynes–Cummings model . γ1 is the intervalley decoherence rate equal to the sum of γv and γdep. The incoherent intervalley scattering (γv) will lead to decoherence and so will the pure dephasing process (γdep). γ2 quantifies the population relaxation. In general, valley coherence is the result of competition between population relaxation and coherence decay. If particles (excitons or polaritons) in the two valleys decay to photons before their phase relation decoheres (γ1 < γ2), the output DOLP will be preserved. Particularly, by coupling to the cavity mode, polaritons will obtain an extra population relaxation path. This channel is free of decoherence because the cavity mode is immune to any intervalley scattering or pure dephasing processes  phonons are needed (one for each the electron and hole). The phonon mode occupation number is expressed asThe PLE results are explained with the previous model. At room temperature, the intervalley scattering is dominated by a phonon-assisted processωq represents the energy of the phonon modes involved in the process. We identify kT with ΔE − ℏωq26, which assumes the excess optical excitation energy ΔE, that is greater than ℏωq above the exciton energy gap, is assumed to generate phonons. The intervalley transition rate γv is then proportional to phonon population factor 〈n〉.ℏ14, the long-range part of the electron-hole interaction will generate a momentum-dependent effective magnetic field, around which the valley pseudospin of excitons with different center-of-mass momentum will precess with different frequencies. This will disturb the phase relation between the two valleys, leading to the following pure dephasing rate:As has already been described theoretically by Maialle et al.28, where the pseudospin relaxation time is directly related to the square of the precession frequency times the momentum relaxation time31. Ω(k) is the precession frequency caused by the momentum-related magnetic field, which can be written as C and α(1) are material-related constants. The center-of-mass momentum k obeys E is the energy difference between excitation and exciton bandgap. Assuming the momentum relaxation time τk is energy-independent, the dephasing rate γdep is proportional to the energy separation ΔE.The valley dynamics considered here is analogous to the motional narrowing effect observed in a metal or the D’yakonov–Perel (DP) mechanism in semiconductorA1 and A2 capture the relative magnitude of the intervalley scattering rate and the pure dephasing rate. The fit agrees well with the data as shown in Fig. 32. The fitting reveals that A1/A2 < 1, namely, the pure dephasing induced by the MSS mechanism (γdep) plays a more important role in the valley coherence dynamics when compared to the intervalley scattering (γv). Additionally, as shown in Fig. γc is much faster than the exciton decay rate γx, which is in good agreement with the fabricated device properties   5) allowentclass1pt{minimaρl as a function of in-plane momentum k|| (k|| = k0 sin θ where k0 is the photon wavenumber and θ is the incident angle). The results are shown in Fig. ρl exhibits strong angular dependence, maximizes at k|| = 0, and then diminishes as the in-plane momentum increases. Also, as the excitation energy is blueshifted from the exciton, the overall magnitude of valley coherence decreases.The polariton’s behavior is highly sensitive to the excitation laser’s angle of incidence due to its dispersive photonic constituent. We investigate polariton valley coherence δω. In our case, the cavity and exciton are positively detuned at k|| = 0, as a result, δω will monotonically increase as a parabola:δω(k||) as a function of in-plane momentum. The overall drop in observed valley coherence is a result in the energy detuning dependence as presented in Fig. Based on the model [see Supplementary Eq. 2-cavity polaritons at room temperature. We provide a Jaynes–Cummings inspired model to capture the polariton photo-physics. Important is that although the polariton’s excitonic component will undergo depolarization and dephasing processes its photonic counterpart offers a fast population decay channel that preserves the optically accessible valley coherence. We anticipate room-temperature polariton device will provide opportunities for valley-based switching architectures36, as well as provide potential approaches to valley-polaritonic circuitry38. Future work will focus on the time-resolved measurement of valley polariton devices to provide meaningful insight into polariton depolarization and dephasing dynamics.In summary, our results present evidence for valley coherence of WSe3 μW μm−2. The system is calibrated using a standard gold mirror and background is subtracted to avoid any leakage from the filter.A Fourier plane spectroscopy system is set-up for the sample under investigation  film. The other half cavity layer is deposited followed by the deposition of the top DBR mirror. Transfer matrix method is utilized to design geometry of the cavity (see Supplementary Note The DBR mirror is fabricated through physical vapor deposition of alternating layers of SiOSupplementary InformationPeer Review File


This article has been corrected: In Figure 2D, the panel for the loading control should be labeled ‘tubulin’, not ‘GAPD.’ We have corrected the legend to Figure 2D by updating this sentence: “Phospho-CrkL is a marker for Abl kinase activity while α-tubulin is a loading control.” In addition, we have added a sentence to the legend of Figure 5C to clarify the origin of the lysates: “C) Western blot  analysis showed no significant difference in total Yap1 protein expression in double treated mice compared to vehicle treated control mice.” The corrected Figure 2D and the corrected legend of Figure 5 are shown below. The authors declare that these corrections do not change the results or conclusions of this paper.1874-1886. https://doi.org/10.18632/oncotarget.26740Original article: Oncotarget. 2019; 10:1874–1886.


Deep brain stimulation (DBS) of the superolateral branch of the medial forebrain bundle (slMFB) emerges as a - yet experimental - treatment for major depressive disorder (MDD) and other treatment refractory psychiatric diseases. First experiences have been reported from two open label pilot trials in major depression (MDD) and long-term effectiveness for MDD (50 months) has been reported.To give a detailed description of the surgical technique for DBS of the superolateral branch of the medial forebrain bundle (slMFB) in MDD.n = 24 patients with MDD is reported. The detailed procedure of tractography-assisted targeting together with detailed electrophysiology in 144 trajectories in the target region (recording and stimulation) is described. Achieved electrode positions were evaluated based on postoperative helical CT and fused to preoperative high resolution anatomical magnetic resonance imaging , including the pre-operative diffusion tensor imaging (DTI) tractographic information . Midcommissural point (MCP) coordinates of effective contact (EC) location, together with angles of entry into the target region were evaluated. To investigate incidental stimulation of surrounding nuclei  as a possible mechanism, a therapeutic triangle (TT) was defined, located between these structures (based on MRI criteria in T2) and evaluated with respect to EC locations.Surgical experience from bilateral implantation procedures in Bilateral slMFB DBS was performed in all patients. We identified an electrophysiological environment  that helps to identify the proper target site on the operation table. Postoperative MCP-evaluation of effective contacts (EC) shows a significant variability with respect to localization. Evaluation of the TT shows that responders will typically have their active contacts inside the triangle and that surrounding nuclei  are not directly hit by EC, indicating a predominant white matter stimulation. The individual EC position within the triangle cannot be predicted and is based on individual slMFB (tractography) geometry. There was one intracranial bleeding (FORESEE I study) during a first implantation attempt in a patient who later received full bilateral implantation. Typical oculomotor side effects are idiosyncratic for the target region and at inferior contacts.The detailed surgical procedure of slMFB DBS implantation has not been described before. The slMFB emerges as an interesting region for the treatment of major depression (and other psychiatric diseases) with DBS. So far it has only been successfully researched in open label clinical case series and in 15 patients published. Stimulation probably achieves its effect through direct white-matter modulation of slMFB fibers. The surgical implantation comprises a standardized protocol combining tractographic imaging based on DTI, targeting and electrophysiological evaluation of the target region. To this end, slMFB DBS surgery is in technical aspects comparable to typical movement disorder surgery. In our view, slMFB DBS should only be performed under tractographic assistance.  •The slMFB is an emerging target for DBS in therapy refractory Depression.•The therapeutic effect is related to modulation of white matter.•Surgery for slMFB DBS is tractography assisted surgery.•DBS of the slMFB is in many aspects similar to movement disorder surgery. Despite effective therapies, 20% of patients will ultimately remain treatment resistant  in MDD. Our goal is to encourage other groups to research this target region.This article aims at sharing our detailed neurosurgical experience of slMFB DBS in 2We report our experience in 24 cases of bilateral slMFB DBS in MDD who were implanted during two open label trials (FORESEE & FORESEE II).2.1Both trials were conducted under the tenets of the Declaration of Helsinki. All patients gave written informed consent for participation in the studies. Both trials were reviewed and positively evaluated by the Bonn University Medical Center ethics committee.2.2MR imaging data were acquired on a whole-body 3 T MR system  by using an 8-element phased-array head coil. The MR imaging examination comprised an isotropic T2-weighted fast spin-echo sequence, a DTI sequence, and 2 magnetization-prepared rapid gradient- echo scans. The parameters were the following: fast spin-echo: repetition time (TR) = 12.650 ms, echo time (TE) = 100 ms, field of view (FOV) = 254 mm, matrix = 176 · 176, 120 sections, sections thickness = 1.44 mm, and acquisition time = 3 min and 44 s. The resulting data were reconstructed to isotropic (1.44 · 1.44 · 1.44)-mm3 voxels.Diffusion Tensor Imaging sequence: Single-shot spin-echo echo planar imaging pulse sequence with TR = 13.188 ms, TE = 84 ms,FOV = 256 mm,matrix = 128·128, 70 sections, section thickness = 2 mm, number of gradient directions = 32, b-value = 1000 s/mm2, sensitivity encoding factor 2.9, acquisition time = 7 min 54 s with isotropic reconstructed (2 · 2 · 2) mm3 voxels. A T1-weighted 3-D magnetization-prepared rapid gradient-echo sequence was acquired before  and after  contrast administration (gadolinium-diethylene-triamine pentaacetic acid) with a sensitivity encoding factor = 4, TR = 8.5 ms, TE = 3.8 ms, flip angle = 8, FOV = 256 mm, matrix = 256 · 256, 160 sections, section thickness = 2 mm, acquisition time = 4 min 17 s. It resulted in reconstructed isotropic (1 · 1 · 1) mm3 voxels. All images were obtained in axial orientation.Preoperative stereotactic computed tomography (CT) scans were acquired on a 16-row multidetector scanner  with a head mounted stereotactic frame. Parameters were as follows: tube voltage = 120 kV, tube current = 350 mA, collimation = 16 · 0.75 mm, tube rotation time = 1 s, pitch = 0.942, matrix = 512 · 512, section thickness = 1.5 mm, increment = 1.5 mm.Postoperative helical CT used the following parameters: tube voltage = 120 kV, tube current = 350 mA, collimation = 16 · 0.75 mm, tube rotation time = 0.75 s, pitch = 0.688, matrix = 512 · 512, section thickness = 2 mm, increment = 1 mm.2.3Deterministic FT was performed on a Linux workstation using StealthViz DTI . After Eddy-current correction for bulk motion of the patient between scans, the B0 sequence was co-registered to the T2W high resolution anatomical imaging.Fractional anisotropy was set at 0.2. Seed density was held at 5.0. Minimal fiber length was set to 20 mm. The MFB was tracked using a single rectangular region of interest  which was placed in the white matter just lateral to the ventral tegmental area (VTA), as identified in the T2W high-resolution MRI cf. . Essenti2.4Bilateral and pre-coronal  entry points were chosen. At first a trajectory was defined that entered the center of the TT based on T2W MRI information. The tip of the electrode was then defined as just reaching the VTA (according T2W MRI). The trajectory was then adjusted in order to penetrate the center of the string-like structure of the slMFB cf. . The def2.5After administration of standard antibiotic prophylaxis, a stereotactic frame  was placed under local anesthesia. A stereotactic CT scan was performed, and the image data were transferred to the planning workstation . The previously acquired MRI sequences and the DTI FT rendition of the slMFB were co-registered with the stereotactic CT scan and the frame coordinates were extracted.The first 9 patients were operated with a NexFrame head mounted and navigated stereotactic system . In these cases, 5 fiducial screws were placed, and CT scanning performed. All other patients were implanted using a Leksell G-Frame . The bilateral DBS electrode implantation was performed under local anesthesia with the patient in a semi-sitting position. Bi-coronal burr-holes were placed sequentially and the burr-hole was sealed with fibrin glue after introduction of the test electrodes in order to prevent CSF loss during surgery. Patients were video-recorded during stimulation.2.6In principle MER in this target region was used to define the white matter corridor between red nucleus (RN) medially and posteriorly, and the STN/SNr-complex, laterally cf. c. The ta2.7least cellular electro-physiological activity (MER) above the target region (inferior border of the slMFB). This position was typically found in the middle of the bundle . Macrostimulation was performed on the fully awake patient fulfilling two purposes: i) to look for acute stimulation effects , ii) look for physiological biomarkers that identify the implantation site and guide position of electrode implantation . Intra-operative stimulation settings were typically constant stimulation with 1–3 mA, 130 Hz, 60us for several (5–10) minutes. If oculomotor activity was seen in the middle of the bundle at a threshold <3 mA(test-stimulation for heartrate and appetitive motivation in the middle of the bundle) a different trajectory was chosen, still within the slMFB. Depth of final implantation was determined by looking for oculomotor activation at 1.5 mA at the inferior most point of the trajectory  was typically performed on the trajectory  and in a position that showed the 2.8DBS electrodes  were implanted on the chosen trajectory with the deepest point of implantation as described above (oculomotor effect at 1.5 mA). This electrode has 4 contacts (named 0–3) of 1.5 mm length each (1.27 mm diameter) and an interspacing of 0.5 mm. Electrodes were secured in the burr hole cap  and final position was checked with lateral fluoroscopy). In a second stage on the same day the patients were placed under general anesthesia and an IPG was placed subcutaneously either in the sub-clavicular or abdominal region. Post-operative helical CT on the day of surgery was performed as described above.2.9As shown in 2.10In order to record the position of effective contacts  in slMFB DBS we determined their spatial distribution (based on CT fused to the MR-planning) 1. in the mid-commissural point (MCP) coordinate system, 2. with respect to their individual anatomical environment (therapeutic triangle = TT).2.11we used the dead space between those two electrodes as the assumed center of the stimulation (assuming similar impedance of both). For illustration, electrode positions were plotted on standardized planes  from the Schaltenbrand and Wahren Atltas  in orthogonal views reconstructed parallel to the electrode (thus a view in direction of the electrode's length axis). Based on the geometry of the 3389 electrodes, the center of an individual EC was determined, and its MCP-coordinate was recorded cf.  a–d. Sinn Atltas .Fig. 6Re2.12The hypothesis for the optimal stimulation point is that it is located inside the slMFB (as a white matter structure) just lateral and above its exit from the ventral tegmental area. This region is individually determined and targeted with the DTI-tractographic approach (cf. above). However, since the stimulation region is located in a narrow corridor in proximity to the mammillothalamic tract (MTT), the anterior and inferior circumference of the red nucleus (RN) and the anterior and medial border of the subthalamic nucleus (STN)/substantia nigra (SNr) – complex cf. ,a–c. We 2.132-tests were performed comparing response in the different combinations of therapeutic areas. As these analyses are exploratory, there was no adjustment for multiple comparisons. Statistical programming was performed using STATA IC 12.1.Analyses were separated for left and right hemisphere. It was not considered that there could be possible interactions between the locations of the respective other electrode and the outcome. Chi3In total 24 patients  were implanted in two trials . All patients fulfilled the diagnostic criteria for therapy refractory major depression according to DSM V (for details of inclusion criteria cf. ).3.1n = 7 patients (FORESEE) have been published .Results of the first ublished . Long teublished  includinublished  of the sublished . Results3.2Adverse events are fully reported in 3.3DTI-FT was possible in all cases with an adequate quality that allowed implantation. A typical example is shown in 3.4Results of Micro-recording on 144 trajectories are presented in 3.5Results of intraoperative macrostimulation are shown in 3.63.6.1Detailed targeting coordinates (inferior border of slMFB according to DTI FT) and coordinates of the effective contacts are shown in 3.6.22-Test, p = .005). This might give a hint, that the left hemisphere could be of particular interest. However, due to the very small sample and multiple comparisons , this result should be interpreted with care.The definition and evaluation of the therapeutic triangle is presented in 44.1n = 24 patients with major depression in two open label trials FORESEE I  indicating proximity to the target structure, 4. acute effects which are typically lateralized and indicate an express a motivational response under stimulation and finally 5. an oculomotor response  we are not able to separate an area that needs to be stimulated in order to differentiate responders from non-responders. On the basis of the TT analysis, responding contacts are typically located inside the triangle. However, we cannot explain, why some non-responder contacts are also situated inside the TT. Moreover, we are not able to explain, why certain responders are situated more medial or lateral, anteriorly or posteriorly inside the triangle. Very likely this is a result of the variability of the slMFB which is targeted based on DTI FT. In this respect, we cannot answer the question if an electrode would be sufficiently placed if it were positioned “anywhere” inside the triangle. At this moment we have to conclude that this surgery should be performed under tractographic assistance since with the use of this technology we and others achieve a high efficacy.In the first cohort, we detected one left sided hemorrhage  and later argued that the slMFB was unilaterally destroyed in this case with the consequence of a lack of therapeutic efficacy . While t4.6We have speculated before, that slMFB-DBS addresses subcortical and cortical reward associated pathways – white matter, the slMFB - by activating descending and ascending fibers towards and from the VTA. We have previously speculated about the mechanism. It is likely that we ortho- and antidromically activate fibers that descend into the VTA and originate in the orbitofrontal and prefrontal cortex  . In thisA purely statistical comparative analysis of MER results together with typical electrode positions suggests that the medial and inferior STN might be co-stimulated with an up to 46.8% likelihood. This is a result of a statistical analysis combining the likelihood of the STN in a given trajectory and position with the likelihood of implanting such a trajectory. However, we typically selected the trajectory for implantation of the DBS electrode that showed the least MER activity (see above) and thus likely that our purely statistical estimation of co-stimulation might be too high. Furthermore, a co-stimulation of the STN becomes unlikely in the light of the results of our postoperative imaging and therapeutic triangle analysis cf.  which clOther circumstances might come into play for a lack of antidepressant efficacy like patient selection and phenotyping. Separation of responders and non-responders, however, is not the focus of this work but is the topic of our ongoing research.4.7Neuronavigated vs. stereotactic frames: The first cohort of patients was operated with a head mounted frame . We changed the procedure after these cases because a lack of confidence emerged in the accuracy of the neuro-navigated frame in a clinical case (not in this series). The procedure was adapted to a stereotactic frame. Besides some restrictions in the possible head movement with a stereotactic frame there were no gross differences in the procedure. The placement of the DBS electrodes did not show any obvious differences in placement accuracy between the two frame types.Microelectrode recording: In this work we present steps that lead to a safe and efficacious implantation of DBS electrodes in the slMFB. Therefore, we only qualitatively evaluated MER signals. A further evaluation of the electrophysiological characteristics - especially the SNR and VTA in major depression – is interesting and part of our future work but beyond the scope of this work.The use of deterministic tractography (DT) for targeting of the slMFB must be discussed, especially when looking at the many connections this structure makes cortically and subcortically. While on the group level DT might be able to show most of these distant projections  with DBS. So far it has only been successfully researched in open label clinical case series with results published from no >15 patients. The detailed surgical procedure of slMFB DBS implantation has not been described before. Stimulation produces its efficacy likely through direct white-matter modulation of slMFB fibers and not via a co-stimulation of the grey matter environment, although we cannot completely rule out such a possibility. The implantation procedure for slMFB DBS comprises a standardized protocol combining tractographic imaging based on DTI FT, targeting and electrophysiological evaluation of the target region. Our evaluation of MCP-coordinates shows a very wide interindividual range, making MCP-based targeting impossible. Therapeutically effective contacts need to be located in the therapeutic triangle but their individual detailed position inside the triangle is determined by individual DTI FT of the slMFB.Some informed features  help to readily identify the target region on the operation table. These aspects allow the neurosurgeon to directly control and optimize his part of the multidisciplinary approach to slMFB DBS in MDD. To this end, slMFB DBS surgery is in many aspects comparable to typical movement disorder surgery and form the viewpoint of implantation may be more advantageous then other target regions for MDD that lack such features. However, this advantage does not automatically imply a clinical superiority of slMFB in treating MDD and this latter aspect is currently being researched. In our view, slMFB DBS should only be performed under tractographic assistance. We have here described in detail our surgical experience in 24 cases of slMFB DBS in MDD. This description might in the future help other groups to successfully and safely implement the surgical approach to the slMFB for the treatment of psychiatric disorders.Medtronic (USA).This work is based on two Investigator Initiated Trials (FORESEE I & FORESEE II) that were partly funded (mainly generators) by


A fine tuning of the PMA is obtained using both epitaxial strain and growth-induced anisotropies. Both spontaneously in-plane and out-of-plane magnetized thin films can be elaborated. Ferromagnetic Resonance (FMR) measurements demonstrate the high-dynamic quality of these BiYIG ultrathin films; PMA films with Gilbert damping values as low as 3 × 10−4 and FMR linewidth of 0.3 mT at 8 GHz are achieved even for films that do not exceed 30 nm in thickness. Moreover, we measure inverse spin hall effect (ISHE) on Pt/BiYIG stacks showing that the magnetic insulator’s surface is transparent to spin current, making it appealing for spintronic applications.A magnetic material combining low losses and large perpendicular magnetic anisotropy (PMA) is still a missing brick in the magnonic and spintronic fields. We report here on the growth of ultrathin Bismuth doped Y A magnetic material combining both low losses and strong perpendicular magnetic anisotropy (PMA) was so far missing in the field of magnon-spintronics. The authors here report on Bismuth doped YIG nanometer thick films showing both PMA and low magnetic losses for ultra-thin PMA materials. Magnons, and their classical counterpart, the spin waves (SWs), can carry information over distances as large as millimeters in high-quality thick YIG films, with frequencies extending from the GHz to the THz regime7. The main figure of merit for magnonic materials is the Gilbert damping α8 which has to be as small as possible. This makes the number of relevant materials for SW propagation quite limited and none of them has yet been found to possess a large enough perpendicular magnetic anisotropy (PMA) to induce spontaneous out-of-plane magnetization. We report here on the Pulsed Laser Deposition (PLD) growth of ultra-low loss MI nanometers-thick films with large PMA: Bi substituted Yttrium Iron Garnet (BixYx3-Fe5O12 or BiYIG) where tunability of the PMA is achieved through epitaxial strain and Bi doping level. The peak-to-peak FMR linewidth (that characterize the losses) can be as low as μ0ΔHpp = 0.3 mT at 8 GHz for 30 nm thick films. This material thus opens new perspectives for both spintronics and magnonics fields as the SW dispersion relation can now be easily tuned through magnetic anisotropy without the need of a large bias magnetic field. Moreover, energy efficient data storage devices based on magnetic textures existing in PMA materials like magnetic bubbles, chiral domain walls, and magnetic skyrmions would benefit from such a low loss material for efficient operation9.Spintronics exploits the electron’s spin in ferromagnetic transition metals for data storage and data processing. Interestingly, as spintronics codes information in the angular momentum degrees of freedom, charge transport and therefore the use of conducting materials is not a requirement, opening thus electronics to insulators. In magnetic insulators (MI), pure spin currents are described using excitation states of the ferromagnetic background named magnons (or spin waves). Excitation, propagation and detection of magnons are at the confluent of the emerging concepts of magnonics11 even though it induces high uniaxial magnetic anisotropy14. Very recently, ultra-thin MI films showing PMA have been the subject of an increasing interest:16 Tm3Fe5O12 or BaFe12O19 (respectively a garnet and an hexaferrite) have been used to demonstrate spin-orbit-torque magnetization reversal using a Pt over-layer as a source of spin current18. However, their large magnetic losses prohibit their use as a spin-wave medium 19. Hence, whether it is possible to fabricate ultra-low loss thin films with a large PMA that can be used for both magnonics and spintronics applications remains to be demonstrated. Indeed, not only low losses are important for long range spin wave propagation but they are also necessary for spin transfer torque oscillators (STNOs) as the threshold current scales with the Gilbert damping20.The study of micron-thick YIG films grown by liquid phase epitaxy (LPE) was among the hottest topics in magnetism few decades ago. At this time, it has been already noticed that unlike rare earths  substitutions, Bi substitution does not overwhelmingly increase the magnetic lossesxYx3-IG  and having a thickness ranging between 8 and 50 nm. We demonstrate fine tuning of the magnetic anisotropy using epitaxial strain and measure ultra low Gilbert damping values (α = 3 × 10−4) on ultrathin films with PMA.In the quest for the optimal material platform, we explore here the growth of Bi doped YIG ultra-thin films using PLD with different substitution; BirBi = 113 pm and rY = 102 pm)21 leads to a linear increase of the BixY3-xIG bulk lattice parameter with Bi content  X-ray diffraction patterns  towards a compressive (x = 1.5) strain. Reciprocal space mapping of these BiYIG samples shown in Fig. The two substrates that are used are gallium gadolinium garnet (GGG), which is best lattice matched to pristine YIG and substituted GGG (sGGG) which is traditionally used to accommodate substituted YIG films for photonics applications. The difference between Bi and Y ionic radii  remains constant for all Bi content  when the film thickness (tfilm) increases as expected from magnetostatic energy considerations. In fact, as Dwidth is several orders of magnitude larger than tfilm, a domain wall energy of σDW ∼ 0.7 and 0.65 mJ m−2 (for x = 0.7 and 1 Bi doping) can inferred using the Kaplan and Gerhing model27 : HKU = MS–Meff  at different out-of-plane angle for a 30 nm thick perpendicularly magnetized Bi1Y2IG//sGGG film at 8 GHz  confirms the high films quality. We also derive the damping value of this film . For x = 0.7 Bi doping, the smallest observed FMR linewidth is 0.5 mT at 8 GHz.The most striking feature of these large PMA films is their extremely low magnetic losses that we characterize using Ferromagnetic Resonance (FMR) measurements. First of all, we quantify by in-plane FMR the anisotropy field PMA Fig. . We use GHz Fig. . This yi mT Fig.  for 27° ilm Fig.  by selec31. For such phenomenon interface transparency to spin current is then the critical parameter which is defined using the effective spin-mixing conductance (G↑↓). We use spin pumping experiments to estimate the increase of the Gilbert damping due to Pt deposition on Bi1Y2IG films. The spin-mixing conductance can thereafter be calculated using Ms and tfilm are the BiYIG magnetization and thickness, geff is the effective Landé factor (geff = 2), μB is the Bohr magneton and Δα is the increase in the Gilbert damping constant induced by the Pt top layer. We obtain G↑↓ = 3.9 × 1018 m−2 which is comparable to what is obtained on PLD grown YIG//GGG systems33. Consequently, the doping in Bi should not alter the spin orbit-torque efficiency and spin-torque devices made out of BiYIG will be as energy efficient as their YIG counterpart. To further confirm that spin current crosses the Pt/BiYIG interface, we measure Inverse Spin Hall Effect (ISHE) in Pt for a Pt/Bi1.5Y1.5IG(20 nm)//sGGG in-plane magnetized film (to fulfill the ISHE geometry requirements the magnetization needs to be in-plane and perpendicular to the measured voltage). We measure a characteristic voltage peak due to ISHE that reverses its sign when the static in-plane magnetic field is reversed . Innovative schemes for on-chip magnon-light coupler could be now developed bridging the field of magnonics to the one of photonics. From a practical point of view, the design of future active devices will be much more flexible as it is possible to easily engineer the spin waves dispersion relation through magnetic anisotropy tuning without the need of large bias magnetic fields. For instance, working in the forward volume waves configuration comes now cost free, whereas in standard in-plane magnetized media one has to overcome the demagnetizing field. As the development of PMA tunnel junctions was key in developing today scalable MRAM technology, likewise, we believe that PMA in nanometer-thick low loss insulators paves the path to new approaches where the magnonic medium material could also be used to store information locally combining therefore the memory and computational functions, a most desirable feature for the brain-inspired neuromorphic paradigm.In summary, this new material platform will be highly beneficial for magnon-spintronics and related research fields like caloritronics. In many aspects, ultra-thin BiYIG films offer new leverages for fine tuning of the magnetic properties with no drawbacks compared to the reference materials of these fields: YIG. BiYIG with its higher Faraday rotation coefficient  will increase the sensitivity of light based detection techniques that can be used (Brillouin light spectroscopy (BLS) or time resolved Kerr microscopyλ = 355 nm), of a 2.5 Hz repetition rate and a fluency varying from 0.95 to 1.43 J cm−2 depending upon the Bi doping in the target. The distance between target and substrate is fixed at 44 mm. Prior to the deposition the substrate is annealed at 700 °C under 0.4 mbar of O2. For the growth, the pressure is set at 0.25 mbar O2 pressure. The optimum growth temperature varies with the Bi content from 400 to 550 °C. At the end of the growth, the sample is cooled down under 300 mbar of O2.The PLD growth of BiYIG films is realized using stoichiometric BiYIG target. The laser used is a frequency tripled Nd:YAG laser (1 monochromator is used for measurement in Bragg-Brentano reflection mode to derive the (111) interatomic plan distance. Reciprocal Space Mapping is performed on the same diffractometer and we used the diffraction along the (642) plane direction which allow to gain information on the in-plane epitaxy relation along [20-2] direction.An Empyrean diffractometer with KαMs) by performing hysteresis curves along the easy magnetic direction at room temperature. The linear contribution of the paramagnetic (sGGG or GGG) substrate is linearly subtracted.A quantum design SQUID magnetometer was used to measure the films’ magnetic moment (Kerr microscope (Evico Magnetics) is used in the polar mode to measure out-of-plane hysteresis curves at room temperature. The same microscope is also used to image the magnetic domains structure after a demagnetization procedure. The spatial resolution of the system is 300 nm.θ out-of the stripline plane). For out-of-plane magnetized samples the Gilbert damping parameter has been obtained by studying the linewidth angular dependence. The procedure assumes that close to the minimum linewidth (Fig. Hpp.A broadband FMR setup with a motorized rotation stage was used. Frequencies from 1 to 20 GHz have been explored. The FMR is measured as the derivative of microwave power absorption via a low frequency modulation of the DC magnetic field. Resonance spectra were recorded with the applied static magnetic field oriented in different geometries (in-plane or tilted of an angle dth Fig.  most of For Inverse spin Hall effect measurements, the same FMR setup was used, however here the modulation is no longer applied to the magnetic field but to the RF power at a frequency of 5 kHz. A Stanford Research SR860 lock-in was used a signal demodulator.The data that support the findings of this study are available within the article or from the corresponding author upon reasonable request.Supplementary informationsPeer Review File


Coarse-grained rules are widely used in chemistry, physics and engineering. In biology, however, such rules are less common and under-appreciated. This gap can be attributed to the difficulty in establishing general rules to encompass the immense diversity and complexity of biological systems. Furthermore, even when a rule is established, it is often challenging to map it to mechanistic details and to quantify these details. Here we report a framework that addresses these challenges for mutualistic systems. We first deduce a general rule that predicts the various outcomes of mutualistic systems, including coexistence and productivity. We further develop a standardized machine-learning-based calibration procedure to use the rule without the need to fully elucidate or characterize their mechanistic underpinnings. Our approach consistently provides explanatory and predictive power with various simulated and experimental mutualistic systems. Our strategy can pave the way for establishing and implementing other simple rules for biological systems. Biological complexity has impeded our ability to predict the dynamics of mutualistic interactions. Here, the authors deduce a general rule to predict outcomes of mutualistic systems and introduce an approach that permits making predictions even in the absence of knowledge of mechanistic details. In marine ecosystems, coral reefs are based on mutualistic interactions between coral and algae, and provide ecosystem services for humans and habitats for diverse organisms2. Plant–bacterial mutualism is estimated to generate 60% of the annual terrestrial nitrogen input3. Mutualism also influences microbial community structures and is the cornerstone of various microbial metabolic tasks5. Although mutualistic coexistence is beneficial in maintaining the biodiversity, function and stability of ecosystems, under some conditions mutualistic systems can collapse, where one or more mutualistic partners is lost, and the persisting partners also experience a reduction in fitness. This perturbation can further trigger the loss or invasion of other populations and alter ecosystem functions9. A framework to interpret and predict mutualistic outcomes is useful to prevent undesirable system behaviors and provide guidance for modulating and engineering mutualistic systems.Mutualism, where two or more populations provide reciprocal benefit, is an essential type of ecological interaction13. However, such a framework is not yet available for determining mutualism outcomes. Main barriers in developing such a framework are the diversity of mutualistic interaction mechanisms and the complexity of underlying dynamics. Indeed, even engineered mutualistic systems that are by-design capable of cooperation, may not coexist. For example, it is still difficult to predict a priori whether an engineered microbial auxotrophic pair can persist or not16. Previously, theoretical criteria in the form of inequalities have been developed for specific mutualistic systems such as cross-feeding mutualisms17, plant–pollinator mutualisms18, seed-dispersal mutualisms19, ant–plant mutualisms20, and plant–mycorrhizal mutualisms21. These criteria depend on the underlying mechanisms assumed in the models and are not applicable to other types of mutualistic systems. General criteria have been developed25, such as the classic criterion which states that intraspecific competition must be greater than mutual benefit for a mutualistic system to be stable26. However, these usually describe transitions between stable coexistence and unbounded growth, and fail to address the transitions between coexistence and collapse and other mutualism dynamics28  to apply the rule to various simulated and experimental systems with different layers of complexities. The interpretation and predictability provided by our framework demonstrate the feasibility of describing a class of diverse biological systems with a simple quantitative rule.β) that reduces the other’s stress (δ) at a cost (ε) to itself. β, δ, and ε are universal features of mutualistic systems  represents the effective benefit produced through mutualistic interaction. Quantitatively, B(θ) increases with increasing β and decreasing ε and its structure differs depending on the specific model. δ represents stress; it is determined as 1 − rm, where rm is the growth rate of the population in the absence of its mutualistic partner and normalized by its maximum growth rate. The interpretation of our criterion is intuitive: mutualistic partners can coexist if the effective benefit exceeds stress, and the system collapses when the inequality is violated , mes Fig. , such asmes Fig. . Furthermes Fig. . The genB and δ are required to use the metric. Although δ is often easy to measure since it is a property of individual populations , quantification of its underlying parameters often requires nontrivial mechanistic characterizations, such as parameter fitting and specific biochemical assays. These mechanistic characterizations are especially challenging for cooperative traits, even in well-defined synthetic systems41. Applications of the criterion would thus be difficult for individual systems, let alone enabling streamlined applications for diverse mutualistic systems.Quantification of both B as an empirical function of experimentally controllable variables (v), denoted by B(v) ) that describes the diverse and complex interaction mechanisms without characterizing the specific mechanistic details. The calibrated B(v) along with δ, will serve as the basis for interpretation and prediction beyond initial data. Although the procedure requires initial measurements of qualitative outcomes, B(v)/δ can also provide predictive power for quantitative outcomes /δ to be positively related to the final density, probability of coexistence, and cheater resistance. Further, B(v) can be used to reveal how multiple system variables collectively alter the effectiveness of the interaction, which is a major challenge in studying context dependency of mutualistic outcomes42.To bypass these challenges, we developed a calibration procedure to use qualitative outcomes to directly quantify (v) Fig. . Specifimes Fig. . Based oY =  . Measurements of δ for the same observations are denoted as δ = . Note that theoretically, quantification of δ for any partner is sufficient. However, choosing the partner with a larger dynamic range of δ is preferable since it can contain more information content. The context variables are denoted by v = , where vi is a vector that contains the values of all system variables for observation i. With inputs Y, δ and v, we can establish a smooth boundary between coexistence and collapse described by F = 0. To ensure B > δ for coexistence and B < δ for collapse, we constrain F > 0 for coexistence and F < 0 for collapse. Because B = δ is true at the boundary, we can deduce that F = 0. According to the implicit function theorem, if F = 0 is continuously differentiable, the output B(v) is implied. A calibrated B(v) can then enable downstream interpretation and prediction.We first defined the input–output relationship of the calibration procedure Fig. . MeasureB(v), we used kernels that are separable in δ and v to obtain F = 0. We implemented linear, quadratic, cubic, and sigmoidal kernels to describe possible shapes of B(v). Because there are infinite number of B(v) that can provide equivalently high-classification accuracy, we ranked the B(v) obtained from different kernels and different kernel parameters to find the B(v) that are closer to the true B(θ(v)) ) is known, so that each B(v) can be evaluated against B(θ(v))by coefficient of determination (R2). We found that our procedure consistently optimizes for R2 , a machine-learning algorithm for supervised classification (see Supplementary Notes B(v)/δ can be applied to mutualism models in which no explicit form exists for B(θ). To do so, we constructed an overwhelmingly complex two-population model with competition, partner-density-dependent cost, high Hill coefficient and asymmetric function structures /δcorrectly predicts coexistence versus collapse for 97.2% of test data beyond the initial 100 data points. Detailed step-by-step calibration procedure is shown in Supplementary Note B(v)/δ provides predictive power for quantitative outcomes including total population size  at 32 h of culturing   is evaluated by the consistency of the top five B(v) and relative standard deviation of each B(v)  increases with increasing [aTc]. The calibration reveals that [IPTG] also modulates B(v), which indicates unintended system complexities, such as QS cross-talk and unequal fitness of the two populations. We used cross-validation to evaluate how well new observations can be predicted. We found that B(v)/δ provides an average cross-validation accuracy of 96.8% for coexistence versus collapse and it is also predictive of total final density  Fig. . The conity Fig. .Saccharomyces cerevisiae auxotrophs that is previously published37. In this system, one strain cannot produce tryptophan (Trp) and the other cannot produce leucine (Leu). The mutualistic interaction of this system is realized by the exchange of the two amino acids in cocultures  reveal that intermediate ratios of initial density and increasing amino acid concentrations elevate B(v)  have qualitatively different trends, indicating a low confidence of B(v) at high concentration /δ is still predictive of final densities with an average cross-validation accuracy of 95.0% /δ in this case can also predict the probability of coexistence as the ratio of initial densities varied  Fig. . However.0% Fig. . FurtherE. coli strains that compose 91 pairwise mutualistic systems44  generated a cross-validation accuracy of 91.8% and we verified that B(v)/δ is predictive of final total density /δ > 1, which can be due to system-specific properties that are not fully accounted for by mutualistic interactions.In the third example, we applied our framework to previously published measurements of 14 engineered auxotrophic s44 Fig. . The gens44 Fig. . δ of eagly Fig. . We usedity Fig. . We noti45. Thus, we tested our framework with simulations and experimental measurements of N-mutualist systems. Here, we show the calibration procedure with simulated data from a 5-mutualist system and found that the quality of the calibration results is well-maintained /δ provides an 89.3% cross-validation accuracy and remains predictive of the total density, which indicates the scalability of the framework in experimental settings  calibrated for pairwise interactions can be used to directly construct a metric for three-member systems, since theoretical analysis shows that n-member B(θ) can be approximated by pairwise B(θ) . For example, the context variable can be the seeding distance of two partners or the degree of intermixing of the seedings. Calibrated B(v) will then be dependent on these spatial variables. Alternatively, the criterion can be applied to local segments where the homogeneity assumption is appropriate. In general, it remains an open question whether and to what extent our approach would be applicable if the mutualistic system becomes much more complex than what we have tested, such as systems consisting of multiple attractors that all correspond to coexistence.In our demonstrations, we have focused on the analysis of homogenous systems. To account for the spatial dimension41. For many inequality-based simple rules that have been proposed and established58, our calibration procedure provides a generally applicable tool to apply these rules directly to experimental systems. If one side of the inequality and some final outcomes can be measured or have been observed historically, the other side can be calibrated as an empirical function. Although our procedure cannot further dissect the empirical function into specific mechanistic parameters, the function can serve as an overall summary of the underlying mechanistic details while bypassing the requirement of characterizing them individually. Our approach thus can enable the downstream interpretation and prediction by these simple rules with readily accessible measurements.Although simple general rules in biology can be powerful tools, their applicability to experimental systems can be limited by the difficulties in associating the abstracted parameters to lower-level mechanistic details and quantifying these details experimentally. This is evident in the application of Hamilton’s rule to experimental systemsBenefit shall increase growth rate or carrying capacity and is positively dependent on partner density.Cost shall decrease growth rate or carrying capacity.Stress shall produce negative growth of populations at some parameter combinations.Negative growth of a population shall be potentially counteracted by benefit provided by a partner, but further strengthened by cost.We built mutualism models based on four key assumptions:See Supplementary Note δ on one side. The other side of the inequality is then an expression of other parameters, which is expressed as B(θ). All criteria were verified using time course simulations. More details are presented in Supplementary Note We calculated the analytical solutions of fixed points of the 52 models using MATLAB R2017a. Then we identified the fixed points that represent stable coexistence. The coexistence criteria are derived by ensuring the fixed points are real positive numbers. We can then rearrange the inequality to have We used SVM algorithms in MATLAB to implement the calibration. The input data are formulated as following:n represents total number of observations and each index represents one observation. Y takes values of 1 or −1, which represent coexistence versus collapse for each observation. v contains the coordinates where observations are obtained and vi is a vector of which each element represents a context variable. For a system with two system variables,vi = . δ contains the stress level of the reference population for each observation i. v and δ are first standardized to vs and δs that have mean of 0 and standard deviation of 1. For simplicity of presentation, the following v and δ are standardized.In Eqs. –8), n r, n r8), v and δ, which can be expressed in a general form:We designed kernels that have additive separability between Kv is the kernel that dictates the shape of the empirical function of B and kδ is a kernel parameter. The predictor trained using SVM is:αi is the weight of observation i, and λ0 is the bias term. Both αi and λ0 are optimized by the SVM algorithm. yi, vi, and δi are input values for observation i.B = δ when f = 0. We can then derive B0(v), a primitive function of B, from Eq. , B0(v) is then adjusted for directionality and rescaled back according to mean and standard deviation of the original δ measurements.To obtain B(v), we used linear, quadratic, cubic, and sigmoidal kernels with a range of kernel parameters to train many different B(v). The optimal B(v) has the lowest overall cross-validation classification loss and bootstrapped variance. A final B(v) is then used along with δ measurements for interpretation and prediction. See Supplementary Note To find the optimal 60. Both populations carry two plasmids. Briefly, M1 carries plasmids identical to the predator plasmids, denoted A1 for the module carrying ccdA (tet promoter61 driving luxR and lasI followed by lux promoter driving ccdA) and B1 for the module carrying ccdB (Lac promoter61 upstream of ccdB followed by tet promoter upstream of gfp). To construct M2, A1 was used as backbone. To obtain orthogonal communication, KpnI and NotI restriction digest cloning was used to replace luxR/lasI genes from A1 with lasR/luxI genes from the previously published prey plasmid ). Reporter plasmid B1 is from59. To construct B2, enzymes XhoI and KpnI were used to replace the tet promoter on prey plasmid with the ccdB module from B1. All M1 and M2 plasmids were verified using restriction digest and sequencing.The two strains were constructed based on circuit components from a synthetic predator-prey system4, 0.1 mM CaCl2 and buffered with 100 mM MOPS with PH adjusted to 7.0) was used. Totally, 50 μg/ml kanamycin and 100 μg/ml chloramphenicol were added to the culture to maintain plasmids.The experiments of QS-based mutualistic system were done in 96-well microtiter plates. PH-buffered M9 medium  before use. Cocultures are created by mixing both strains in a 1:1 volume ratio. The culture is then diluted 10The code used for data generation and/or analysis in the study are available as Supplementary Software Supplementary InformationDescription of Additional Supplementary FilesSupplementary Movie 1Supplementary Movie 2Supplementary Movie 3Supplementary Movie 4Supplementary Software 1Peer Review File