Glycine receptors (GlyRs) mediate fast inhibitory neurotransmission in the brain and have been recognized as key pharmacological targets for pain. A large number of chemically diverse compounds that are able to modulate GlyR function both positively and negatively have been reported, which provides useful information for the development of pharmacological strategies and models for the allosteric modulation of these ion channels.in silico methodologies for allosteric drug discovery and boost the development of conformation-based pharmacological approaches.Based on existing literature, we have collected 218 unique chemical entities with documented modulatory activities at homomeric GlyR-α1 and -α3 and built a database named GRALL. This collection includes agonists, antagonists, positive and negative allosteric modulators and a number of experimentally inactive compounds. Most importantly, for a large fraction of them a structural annotation based on their putative binding site on the receptor is provided. This type of annotation, which is currently missing in other drug banks, along with the availability of cooperativity factors from radioligand displacement experiments are expected to improve the predictivity of https://ifm.chimie.unistra.fr/grall. For each molecular entry, it provides information on the chemical structure, the ligand-binding site, the direction of modulation, the potency, the 3D molecular structure and quantum-mechanical charges as determined by our in-house pipeline.The GRALL library is distributed as a web-accessible database at the following link: mcecchini@unistra.frBioinformatics online. Glycine receptors (GlyRs) are pentameric ligand-gated ion channels (pLGICs) that mediate fast inhibitory neurotransmission in the spinal cord, brainstem and the retina . Glycinezebrafish was solved in complex with the endogenous agonist glycine, the competitive agonist strychnine, or the allosteric agonist ivermectin (human GlyR-α3 provided the details of glycine binding (AR) , the potency and the 3D molecular structure and charge distribution in the most likely protonation and tautomeric state , cannabinoids (11), glutamate analogs (9), phenylalanine derivatives (8), general anesthetics (5), ginkgolic-acid (1), gelsemine (1) and 32 chemically diverse compounds recently discovered by high-throughput screening (HTS) see . The claKd or Ki), whereas the rest as half-maximal effective concentrations, i.e. EC50 or IC50. Although measured EC50 or IC50 values depend on the actual concentration of neurotransmitter in the assay, which would prevent a direct comparison of results collected from different publications, these data are still amenable to a coarse classification. By grouping ligands into four classes  to 97, whose binding sites have been assigned using a level of confidence from 1 to 5. The classification of compounds based on their putative binding site highlights the extreme chemical diversity of GlyR modulators that bind to distinct regulatory sites, which needs to be accounted for in drug-discovery campaigns targeting GlyR or analogous channels. Therefore, the structural annotation along with the availability of experimentally inactive compounds in GRALL is expected to facilitate the development of predictive models for allosteric drug design in neurotransmitter receptors.We have reported on the GRALL database, which is a carefully curated, web-accessible library of small-molecule modulators of GlyRs. The library contains 218 unique chemical entities including agonists, antagonists, positive and negative allosteric modulators with documented activity and potency, which are ready for use in Straightforward statistics on GRALL highlights: (i) the lack of structural information concerning pharmacologically relevant classes of GlyR modulators such as tropeines (i.e. the high-affinity site) and cannabinoids; (ii) a striking paucity of potent NAMs targeting GlyR; and (iii) the lack of cooperativity factors e.g. extracted from radioligand displacement experiments for the majority of known modulators. These observations along with the intriguing finding that the (+)-neurosteroid site is the only allosteric site that is so far able to accommodate both PAMs and NAMs, are genuine results from GRALL, which provide clear directions for future research.Overall, the manually curated information in GRALL, i.e. the annotation of the binding site, the modulatory activity, the 3D structure and quantum charges per molecular entry, will be instrumental for the development of predictive pharmacological approaches for the allosteric modulation of GlyR, pLGICs and allosteric proteins more generally.Kd/Ki over EC50/IC50 over mean/maximum potentiation. When multiples publications were found that report on the activity of one given compound, the value in the publication that included the largest number of activity measurements was kept for reasons of consistency; this choice allows for a fair comparison and ranking of congeneric compounds. Standardization into canonical SMILES (Simplified Molecular Input Line Entry Specification) was achieved using RDKit , protect aromaticity (default: true), protect charge (default: true), exclude antiaromatic compounds (default: true), protect ester groups (default: true).The dominant tautomeric state of the ligand was determined using n cxcalc . For thicxcalc stereoisomers of Marvin  protocol  of 0.4 used as a distance threshold between Morgan fingerprints is appropriate to group congeneric compounds that exert comparable modulation at GlyR. Therefore, compounds with a maximal pair-wise Tc > 0.4 relative to ligands in Level 1 to 4 were annotated to the same binding site with a level of confidence 5. We note that this protocol produced no unexpected annotation, while rationalizing the assumption of similarity made by the authors in the various publications. One peculiarity concerns the neurosteroid compounds, for which the threshold Tc > 0.4 with Morgan fingerprints was not able to discriminate between (+)- and (−)-neurosteroid-site binders. Since it was found that negatively charged neurosteroids tend to act as negative modulators (AR and GlyR) of positively charged residues in the lower part of the (−)-neurosteroid site and their absence at the (+)-neurosteroid site. Therefore, in addition to the Tanimoto coefficient a filter based on the formal charge of the molecule was introduced to assign negatively charged ligands to the (−)-neurosteroids site and all others to the (+)-neurosteroid site with a level of confidence 5.Congeneric compounds with high-structural similarity or consistent Structure-Activity Relationship (SAR) with one lead compound annotated at Level 1, 2, 3, or 4 have not been necessarily explored by structural biology or site-directed mutagenesis, although they are likely to bind to the same regulatory site. In order to provide an objective annotation for these compounds the Morgan/Circular fingerprints as implemented in RDKit . Upon verification, the transmitted information will be added to the database and published online.GRALL aims at being a curated and up-to-date database of GlyR modulators. For this purpose, special care was taken to develop automated procedures to process new molecular entities and update the database. Because human processing of a constantly growing literature is challenging but critical to ensure the highest level of accuracy, we encourage researchers to contact us and submit missing information  via the preformatted form available on the website (btaa170_Supplementary_DataClick here for additional data file.


Pygoscelis adeliae) is constrained by the sea-ice cover during the breeding season. We estimated the population-level repeatability in foraging trip parameters and sea-ice conditions encountered by birds across successive trips over several years, and we examined their foraging site fidelity linked to sea-ice concentrations throughout the chick-rearing season. Penguins’ foraging activity was repeatable despite varying annual sea-ice conditions. Birds’ site fidelity is constrained by both sea-ice conditions around the colony that limit movements and resources availability, and also behavioural repeatability of individuals driven by phenological constraints. Adélie penguins favoured sea-ice concentrations between 20–30%, as these facilitate access to open water while opening multiple patches for exploration in restricted areas in case of prey depletion. When the sea-ice concentration became greater than 30%, foraging site fidelity decreased and showed higher variability, while it increased again after 60%. Between two trips, the foraging site fidelity remained high when sea-ice concentration changed by ± 10% but showed greater variability when sea-ice concentrations differed on a larger range. In summary, Adélie penguins specialize their foraging behaviour during chick-rearing according to sea-ice conditions to enhance their reproductive success. The balance between being consistent under favourable environmental conditions vs. being flexible under more challenging conditions may be key to improving foraging efficiency and reproductive success to face fast environmental changes.There is a growing interest in studying consistency and site fidelity of individuals to assess, respectively, how individual behaviour shapes the population response to environmental changes, and to highlight the critical habitats needed by species. In Antarctica, the foraging activity of central place foragers like Adélie penguins ( The marine environment is highly dynamic. Although direct observations of predation are rarely possible, foraging behaviour of predators such as seabirds is often used as an indicator of resource-enriched areas and prey availability ,2. SeabiHigh plasticity in phenological responses under a changing environment is thought to improve a species’ breeding success and increased their fitness . FlexibiIn dynamic environments, individual’s behavioural consistency indicates how it copes with constraints, for example, during the succession of foraging trips throughout a breeding season ,15. To tPygoscelis adeliae) are good models to study the effect of spatial and temporal environmental variations on the consistency or flexibility of their foraging behaviour, as well as on their foraging site fidelity. Their foraging success is highly dependent on sea-ice conditions. Sea-ice conditions vary significantly during a breeding season, leading to a highly dynamic foraging environment in terms of prey availability [Euphausia superba) [E. crystallorophias) and juveniles of Antarctic silverfish (Pleuragramma antarctica) in the more neritic waters of the continental shelf [In Antarctica, Adélie penguins  . Later, superba) ,27. At tal shelf ,28. Howeal shelf ,30.In East Antarctica, sea-ice cover along the coastline has increased in recent years ,32. ReceHere, we aimed to study the repeatability in Adélie penguins’ foraging trip parameters during successive chick-rearing trips across years, when birds experienced contrasted sea-ice scapes. We also aimed to assess foraging site fidelity between trips, and relate these to environmental conditions and their spatio-temporal variations within and across years. The Adélie penguins’ repeatability has–to the best of our knowledge–only been studied in terms of their diving behaviour .Our main hypothesis was that repeatability in foraging efforts and foraging site fidelity should be high under optimal conditions. Optimal sea-ice conditions for Adélie penguins are thought to be when the sea-ice concentration is around 20–30%, i.e. a state of diffuse sea-ice in which food availability is expected to be high, leading to enhanced foraging success –38. In sInversely, under more challenging conditions (high sea-ice concentration and large extent around the colony), sea-ice cover constrains birds from traveling farther. We expect penguins to return to the same foraging grounds around the colony until prey depletion occurs, from which point we expect them to expand their exploration range to find new profitable foraging areas, thereby increasing their foraging effort ,38,39.This study was conducted in Terre Adélie (East Antarctica), on the Ile des Pétrels, near Dumont d’Urville French station . This study was approved by the ethic committee of the Terres Australes et Antarctiques Françaises (TAAF) and the French regional ethic committee 54. Adélie penguins were equipped with GPS loggers over several successive trips during the chick-rearing season (late December to mid-January), from 2010–11 to 2017–18 (except 2012–13 and 2013–14) , Table 1We calculated the peak hatching date from the Adélie penguin colony, as the median date of hatching where 50% of the first laid egg have hatched . Excredisltraj function from the “adehabitatLT” R package [i) the total trip duration, ii) the total trip distance , iii) the maximal distance from the colony  and iv) the heading (bearing angle) between the colony and the most distal point of a trip , between the starting and returning date of each bird’s trip for all years. In 2012, AMSR data were not available. We thus downloaded daily satellite imagery data collected via SSM/I (ftp://ftp.ifremer.fr/ifremer/cersat/products/gridded/psi-concentration/data/antarctic/daily) with a 12.5 km grid cell resolution, for all years.Daily sea-ice concentration data  were downloaded from the website of the University of Bremen, Germany . The correlation was > 0.63, we thus kept daily raster maps with the finest resolution for all years  except 2012. On that particular year, we rasterized the maps from SSM/I data (res. 12.5 km) on a grid with a resolution of 6.25 km.For each bird’s trip, daily sea-ice concentration data were extracted and transformed into raster maps with the “raster” R package, with the two types of data at both 6.25 and 12.5 km grid cell resolution (except 2012 for which 6.25 km resolution was not available). Each GPS location was associated with the relevant daily sea-ice concentration in the given cell at the two resolutions. For all years except 2012, we compared the values at each GPS location of the two resolutions with a correlation test  at two spatial-scales (defined below) to have a global view of the overall conditions in the region  but also to test the conditions encountered at the trip scale :2 . It repThe second scale corresponds to the annually prospected area, defined by the annual maximal extent of all penguins’ trips  and is tWe used the Spearman correlation test to assess if the mean sea-ice conditions in the annually prospected area were representative of the conditions in the whole study area, and if the sea-ice concentrations changed in the same direction using the two scales. We used a Generalized Linear Model  to test the effect of the year in interaction with the spatial scale and the timing in the season (the time elapsed between the peak hatching date and the trip departure date) on the mean sea-ice concentration over each trip duration. This helps to compare the inter- and intra-annual variation of the sea-ice scape in the whole study area and to see how it varied around the colony .We measured the repeatability of the four foraging parameters (defined in 2.1) calculated from the entire foraging trip: the total trip duration, the cumulative distance travelled, the maximal distance and the bearing angle between the colony and the most distal point reached during the trip.To perform repeatability analyses, we first fitted Generalized Linear Mixed Models (GLMMs) with a Gaussian error distribution. All parameters were log-transformed except the bearing angle, to approximate normality of residuals . For eacNote that bearing angle was considered as a linear variable, and not as a circular variable, because penguins covered only 44% of the full degree circle (between -71.8° W to 87.8° E).R) with the “rptR” R package using the rptGaussian function [2 the global within-group variance. Here, a “group” stands for an individual bird with a set of consecutive trips, so that within and between group variances reflect the variances between trips of a same bird and between individuals, respectively. The repeatability index ranges from 0 to 1: a low repeatability (near 0) reflects either a high within-individual variation or a low between-individual variation. A high repeatability corresponds to a low within-individual variance. Here, we classified the repeatability into three categories (following [R < 0.25), moderate (0.25 >R > 0.5) and high (R> 0.5). To disentangle what part of the repeatability is explained by external factors (fixed effects) from what is explained by the individual, we compared the adjusted repeatability : lowi) the distance to the colony (as a straight line) and the percentage of the maximal distance reached during the trip that it represented, and ii) the duration elapsed since the departure, as the percentage of the total trip duration. These two variables are related by a bell-shaped curve  and that of the following trip . For each location of the central phase of the trip n+1, we calculated the distance to the nearest location of the central phase of the trip n. We then calculated the cumulative distance (i.e. the sum of the distances between each location of the trip n+1 with the nearest location on the previous trip). Finally, we divided the cumulative distance by the number of locations on the focal trip segment (trip n+1), giving a mean distance (the NND) between the two central phases. The greater the fidelity between the foraging areas of two trips, the lower the NND.To assess whether individuals targeted the same foraging areas from one trip to another, we calculated the nearest-neighbour distance (NND), adapted from , and folemmeans function, “emmeans” R package, [We first tested the effect of year on the average annual NND values to assess for inter-annual differences in the foraging site fidelity with a linear model. We then tested the effect of the year in interaction with the timing in the season on the log-transformed NND of the compared trips, using GLMs. We applied a post-hoc test to perform pairwise comparison between years  and a TWe then tested the effect of the mean sea-ice concentration in the annually prospected area over two trips on the NND. We aimed to test if birds returned to close areas–or not–to the location they visited during their previous trip under specific sea-ice conditions. We concomitantly examined variations in sea-ice concentrations between successive trips  to account for the potential geographical barriers that sea ice could represent to the movements of the birds from one trip to the next. A positive difference meant that mean sea-ice concentration in the prospected area during the second trip was lower than during the first one (i.e. sea-ice receded), and inversely: a negative sea-ice concentration difference indicates a higher mean sea-ice concentration during the second trip than the previous one. Models were fitted using Generalized Additive Mixed Models  to allow for non-linear relationships. The response variable  was log-transformed and bird ID was added as a random effect.-1 on average, except in 2016–17 where the speed was about 0.5 km.h-1.Adélie penguins performed longer/farther trips and reached a greater maximal distance in 2011–12 than in other years . For all2), and the smallest in 2016–17 (740.12 km2).The surface of the area prospected by birds differed annually , with thMean sea-ice concentration in the whole study area was highly variable among years, except between 2010–11 and 2015–16 which had the lowest values throughout the season . At each scale, sea-ice concentrations changed throughout the seasons, but with different directions or amplitudes  and the maximal distance the least repeatable (R = 0.26 ± 0.06). However, during the foraging phase of trips, the sea-ice concentrations encountered by Adélie penguins were poorly repeatable (R = 0.17 ± 0.06).Adjusted repeatability  was moderately high for all foraging parameters (R > 0.50) for all parameters measured, except for the bearing angle which had approximately the same value as in the adjusted model (R = 0.40).Non-adjusted repeatability values (model including only the ID as random effect and no fixed effect) were higher  [Trip duration and bearing angle were the most repeatable parameters for Adélie penguins in our study. Moreover, repeatability in the bearing angle did not differ between years  . Such a s papua) ,13. ThisHowever, the repeatability in sea-ice conditions in the non-adjusted model was higher than that in the adjusted model, reflecting a low intra-individual variability and/or a high inter-individual variability across years. Said differently, penguins faced different conditions among years, but individuals used similar sea-ice conditions under given annual conditions and from one individual trip to another.Seabirds select their foraging habitats according to prey availability ,58. In EIn our study, while environmental constraints may predominantly explain the high fidelity in foraging areas during years of intensive sea-ice concentration, it is noteworthy that the fidelity is also high in years with no physical constraints to movements. Non-extreme sea-ice conditions, with diffuse sea-ice concentrations around the colony, but enough to enable the resources’ development, offer then the best option for exploration while remaining consistent in respect to phenological time constraint and reproductive effort.Optimal foraging activity, growth rate and breeding success of Adélie penguins are associated with moderate (up to 20%) sea-ice cover around the colony ,37,63. TWhen sea-ice concentration is low around the colony from the beginning of the season, penguins have direct access to suitable foraging grounds and exhibit a high site fidelity, like in 2015–16 in our study. However, this takes place in a reduced area of prospection–the smallest after the one prospected in 2016–17 –in which resource availability probably decreased rapidly throughout the season .In another case, intermediate but constant sea-ice concentrations throughout the season lead to the adoption of an “exploration-refinement” strategy ,54, wherOppositely, under high sea-ice concentrations, penguins have limited access to open water and must concentrate their foraging effort to the only accessible areas from one trip to the next, as already seen in Lützow-Holm Bay . Yet, prOur results concur with others . When sea-ice conditions become more variable and resource availability consequently becomes less predictable, birds have to intensify explorative behaviour if they are to optimize prey encounter. Indeed, being flexible may be favourable for individuals to adjust their strategies according to food availability when their habitats undergo fast changes, like is the case in East Antarctica. Bearing in mind the two recent massive breeding failures of the Adélie penguins colony of Pétrels Island that were due to extreme environmental conditions , their Central-place foragers perform their foraging activity around their breeding colony and are thus constrained in the habitat range available in its vicinity ,64. TherS1 File(DOCX)Click here for additional data file.S2 File(DOCX)Click here for additional data file.


The isoenzymes-enriched preparations from the rat tissues with different expression of OADH and OGDH are used to characterize their interaction with 2-oxoglutarate (OG), 2-oxoadipate (OA) and the phosphonate analogs. Despite a 100-fold difference in the isoenzymes ratio in the heart and liver, similar Michaelis saturations by OG are inherent in the enzyme preparations from these tissues (in vivo inhibition of the DHTKD1-encoded OADH, a new member of mammalian family of 2-oxo acid dehydrogenases, up-regulated in some cancers and associated with diabetes and obesity.Phosphonate analogs of pyruvate and 2-oxoglutarate are established specific inhibitors of cognate 2-oxo acid dehydrogenases. The present work develops application of this class of compounds to specific  Reactions were started by addition of the enzyme preparations to the assay media. The amount of enzyme preparations (0.074 mg protein for the preparation from liver and 0.023 mg protein for the preparation from heart) were chosen to induce the lowest reliably measured reaction rate (ΔA340 = 0.001/min) at 0.01 mM OA without the phosphonates.The enzyme activities were assayed in the medium (pH 7.0) containing 50 mM MOPS, 1 mM ThDP, 1 mM MgClReaction rates were calculated from linear parts of the product accumulation curves , excluding the initial region, where mixing the reagents and solubilization of the preparation affected the optical density.v or its maximal value Vmax, attained at the substrate saturation, throughout this study. Accordingly, a and Amax are used as the equivalents of v and Vmax, in the text.To compare the catalytic rates of the non-homogeneous preparations, their specific activity, i.e., the reaction rate normalized per mg of protein in the assay system, was used as a measure of the reaction rate R2 < 0.98), the data were approximated by the model assuming the two independent types of the active sites with different affinities toward 2-oxo substrates . The assumption was based on the presence of the two enzymes, OGDH and OADH, in the employed preparations.Non-linear regression was used to approximate the experimental dependences of the reaction rates on the OG or OA concentration according to the Michaelis-Menten equation , the effective values of Km/Amax) and Slope (Km/(Amax*Ki)) of a dependence. The values of Ki were determined as the ratio of the corresponding Intercepts to the Slopes. In the two-site model, the vs. [I] and vs. [I] dependences, respectively. The standard errors of Ki were determined from means and standard errors of the Intercepts and the Slopes, using the previously described formula for standard deviation of a fraction  or ambient (air) atmosphere and in water solutions. R2), equivalent to a coefficient of correlation (r) used in linear regression.Data are presented as Mean ± Standard Error of Mean. Regression analysis was done in GraphPad Prism 8, Fitting the experimental data to a model by non-linear regression was estimated by coefficients of determination , while the liver contains comparable levels of the two isoenzymes (DHTKD1/OGDH ≈ 1.6). In view of the similar substrate specificity of OGDH and another, the OGDHL-encoded isoenzymes  in either the heart or liver  and protein (10.5-times higher) levels , compared to −1)  by the Michaelis-Menten equation  are satisfactorily approximated , the R2 values characterizing the fitting of the experimental data to the model vary, depending on the phosphonate used and its concentration. For instance, at a fixed concentration of 0.05 mM, R2 decreases to 0.822 at 50 μM SP, remains unchanged with GP (R2 = 0.930) and improves with AP (R2 = 0.998). This finding indicates that the preferential inhibition of the low-affinity sites by SP increases the relative contribution of the high-affinity sites to the OADH reaction, thus reducing R2 for the one-site model. In contrast, preferential inhibition by AP of the high-affinity OA-binding sites decreases their contribution to the catalysis, leading to the improved fitting of the experimental data in the presence of AP to the one-site model. No changes in R2 suggest similar reactivity of the different sites to GP. Thus, in general, the substrate saturation curves in the presence of the increasing concentrations of SP, GP and AP have been approximated by a sum of two Michaelis-Menten equations. Considering the difference in However, the two types of the OA-binding sites in the enzyme preparation from liver , are disagnitude , the inhagnitude .To investigate the mechanism of inhibition, changes in the effective kinetic parameters  and GP  demonstrate Ki values in micromolar range, whereas AP  is about two orders of magnitude less effective (Ki = 7.1 ± 1.6 μM) and GP (Ki = 2.8 ± 0.8 μM) more efficiently than by AP (Ki = 49 ± 5 μM)  . Thus, tKi values for SP (2.8 ± 0.5 μM) and GP (1.3 ± 0.02 μM) are more than an order of magnitude lower than that for AP (47 ± 1 μM). However, up to 0.05 mM 2-oxoadipate, the opposite inhibitory pattern is observed: the lowest Ki value is for AP (0.048 ± 0.004 μM), followed by those for GP (2.0 ± 0.2 μM) and SP (116 ± 6 μM). This finding corroborates the existence of two independent types of the active sites, binding OA, and phosphonates. Compared to the high-affinity OA-binding sites, more sensitive to AP, those with the low affinity to OA have a higher affinity to SP. As shown above, the former sites correspond to OADH catalysis by the DHTKD1-encoded protein (OADH), whereas the latter—by the OGDH(L)-encoded protein (OGDH). GP binding at both types of the active sites does not differ as significantly as the binding of SP or AP.The data on the SP, GP, and AP inhibition in the different ranges of OA concentrations in the hepatic preparation were analyzed separately at the low (0–0.05 mM) and high (0.1–10 mM) ranges of OA concentrations. At 0.1–10 mM 2-oxoadipate, the inhibitory pattern of OADH reaction in hepatic preparation is similar to that of cardiac preparation: The presence of the two types of independent OA-binding sites in the hepatic preparation results in an interesting inhibition pattern, when the competitive action of SP vs. OA in each of the sites  is accomM. smegmatis OGDH in complex with the post-decarboxylation ThDP adduct formed after addition of OG [PDB ID: 2Y0P  and substitution of SP in this complex by GP and AP, as described in Methods, allows one to assess potential interactions of the phosphonate ligands with the active site of the rat OGDH physiological states, which is currently required for understanding the significance of OADH function at an organism level. In fact, unlike the well-studied and ubiquitous OGDH, which function is critical for the organism survival, the expression of the f 10−5 M  may sileand OADH . Remarkaand OADH . Our finOGDH(L)-encoded 2-oxoglutarate dehydrogenase and adipoyl phosphonate with the DHTKD1-encoded 2-oxoadipate dehydrogenase is shown by the kinetic and structural analyses. The preferred binding of the bulkier ligands to 2-oxoadipate dehydrogenase is mediated by the active site serine residue substituting the tyrosine residue in 2-oxoglutarate dehydrogenase. Glutaryl phosphonate shows comparable efficiency in inhibiting both the 2-oxoadipate and 2-oxoglutarate dehydrogenases in vitro. Application of adipoyl phosphonate in vivo may be used to reveal physiological significance of the DHTKD1-encoded 2-oxoadipate dehydrogenase and fight malignant transformations with overexpressed DHTKD1.The phosphonate analogs of dicarboxylic 2-oxo acids are quantified as competitive vs. the 2-oxo acid substrates inhibitors of the 2-oxoadipate and 2-oxoglutarate dehydrogenases. Remarkable selectivity of the interactions of succinyl phosphonate with the The original contributions presented in the study are included in the article/The animal study was reviewed and approved by Bioethics Comittee of Lomonosov Moscow State University.AK and NL synthesized the phosphonate analogs. AA performed the kinetic experiments. MB and AA performed structural analysis. VB and AA analyzed the results and wrote the manuscript. All authors reviewed and edited the manuscript.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


Multisite phosphorylation  is a basic way of encoding substrate function and circuits/networks of post-translational modifications (PTM) are ubiquitous in cell signalling. The information processing characteristics of PTM systems are a focal point of broad interest. The ordering of modifications is a key aspect of multisite modification, and a broad synthesis of the impact of ordering of modifications is still missing. We focus on a basic class of multisite modification circuits: the cyclic mechanism, which corresponds to the same ordering of phosphorylation and dephosphorylation, and examine multiple variants involving common/separate kinases and common/separate phosphatases. This is of interest both because it is encountered in concrete cellular contexts, and because it serves as a bridge between ordered  mechanisms (representing one type of ordering) and random mechanisms (which have no ordering). We show that bistability and biphasic dose response curves of the maximally modified phosphoform are ruled out for basic structural reasons independent of parameters, while oscillations can result with even just one shared enzyme. We then examine the effect of relaxing some basic assumptions about the ordering of modification. We show computationally and analytically how bistability, biphasic responses and oscillations can be generated by minimal augmentations to the cyclic mechanism even when these augmentations involved reactions operating in the unsaturated limit. All in all, using this approach we demonstrate (1) how the cyclic mechanism (with single augmentations) represents a modification circuit using minimal ingredients (in terms of shared enzymes and sequestration of enzymes) to generate bistability and oscillations, when compared to other mechanisms, (2) new design principles for rationally designing PTM systems for a variety of behaviour, (3) a basis and a necessary step for understanding the origins and robustness of behaviour observed in basic multisite modification systems. Multisite phosphorylation wherein substrates are modified at multiple sites by kinases/phosphatases is fundamental to cellular biology. It represents a basic way of encoding substrate function in cellular systems, and is encountered in a wide variety of cellular contexts. The interest in multisite phosphorylation stems from the convergence of two distinct aspects: as a mechanism for conferring substrate identity and function on one hand, and as a complex biochemical information processor on the other. Multisite phosphorylation  represent basic circuits/networks of post-translational modification (PTM), which are encountered in many cellular contexts, and consequently understanding their information processing characteristics is of broad relevance and interest.5, while serving to encode substrate function8. It has important roles in a range of contexts such as the cell cycle regulatory system, Alzheimer’s disease and inflammation12. A key focal point involves multisite modification where the kinases and/or the phosphatases are the same. An examination of double-site modification with a common kinase and phosphatase reveals variations along different axes. One axis is the ordering of modifications: the modification may be ordered  or random depending on whether or not a specific order of modification is imposed. Another axis of classification stems from the modification mechanism itself: if the enzyme is released after every modification, it is called distributive, whereas if the enzyme remains bound it is referred to as processive. Combinations of both mechanisms may also be observed. Depending on combinations of the above features (modification network “topology” and enzymatic mechanism) and the commonality of kinases and/or phosphatases, multiple basic modification scenarios can be isolated even in the double site modification system. With an increase in number of modification sites, many more variations are possible.Multisite phosphorylation is a recurrent feature of cell signalling networks13 for a recent survey). It is worth pointing out that basic chemical and physical factors along with sequestration of species are key ingredients responsible for the complexity of the resulting behaviour. There are many studies focussing on different aspects of information processing in multisite phosphorylation. The capability of exhibiting threshold-like behaviour even with similar catalytic constants for multiple modifications by an enzyme was shown in14. The surprising feature that bistability could be seen in double site modification was shown in15 and this was generalized to reveal an unlimited multistability as the number of modification sites was increased16. A range of related systems have been studied in this context17. The fact that simple ordered distributive mechanism contained an in-built trade-off creating the possibility of biphasic responses was demonstrated in18. Oscillatory behaviour has been revealed in different cases: in random mechanisms with a single kinase/phosphatase pair, and also resulting from the interplay of distributive and processive mechanisms in ordered modification systems, or even arising from an enzyme activation step21. Other studies have focussed on the presence or absence of oscillations in these systems23. Processive systems by contrast behave in a simpler way and exhibit a unique asymptotically stable steady state26. In a recent paper we examined multiple transitions in intrinsic behaviour which emerged as a consequence of modification mechanisms being part of pathways21. Other studies have studied a range of related aspects33.Elucidating the dynamics and information processing characteristics of post-translational modification networks and circuits, presents many challenges, and is the focus of a number of studies , embedded in a transcription–translation feedback loop38 . Thirdly, there are other ways in which a circuit very similar to the cyclic network can arise: this can happen if for instance the phosphorylation involves substrate binding to a scaffold, while dephophorylation occurs without binding to a scaffold. If an intermediate phosphoform is not released from the scaffold during phosphorylation, then we have a mechanism which is structurally essentially the same as the cyclic mechanism , with minor augmentations. Another way in which a similar modification logic as the cyclic mechanism can be generated is phosphorylation and dephosphorylation occur in different compartments, with only unmodified and fully modified forms shuttling (eg. see40). In our paper, we examine relaxations of the basic cyclic structure, to create a bridge between ordered and random mechanisms. This line of investigation may be relevant in multiple contexts which involve random mechanisms with some modification steps irreversible. In particular, the ERK signalling network involves phosphorylation at two sites, with phosphorylation (mediated by MEK) proceeding in the same order as dephosphorylation (mediated by MKP3)41. This ordering corresponds to a cyclic network, and different studies have considered other additional reactions built on to this42. Finally, our study serves as a basis for engineering chemical modification in synthetic biology to achieve specific information processing tasks44.There are multiple reasons which justify the focus and approach of the study. Firstly cyclic mechanisms represent a very basic variant of multisite phosphorylation (based on a specific ordering of modifications). Thus they represent a basic model PTM system. Secondly, cyclic multisite phosphorylation/dephosphorylation are seen in multiple natural cellular contexts. One example is rhodopsin phosphorylation, which is responsible for dark adaptationBy examining cyclic models with different variants with separate/common kinases and phosphatases, we can obtain basic design insights into which combinations of basic ingredients enable or prevent certain types of behaviour. By systematically augmenting these circuits, we can identify the minimum augmentations (and the specific nature of the augmentations of the circuit) to enable different kinds of behaviour. Through this approach we can also study the relationship between the cyclic mechanism, the ordered sequential mechanism and the random mechanism, recognizing that the cyclic mechanism is a bridge between those well-studied mechanisms. In this way, we are able to elucidate and synthesize the impact of ordering of modifications of these systems on the overall behaviour. All in all, we are also able to draw a sharp boundary between the impossibility and possibility of different types of behaviour, and distill the interplay between reaction topology, commonality and sequestration of enzymes which enables different behaviour, through our approach. In addition to the relevance to systems and synthetic biology, the study also has relevance to the broader field of chemical information processing, which aims to dissect and engineer different patterns of information processing in chemical systems, with applications as diverse as analytical chemistry and chemical computation.A  ordered mechanism  of double site modification where the order of phosphorylation is exactly opposite to the order of dephosphorylation is a mechanism which results in only one partial phosphoform Fig. a. The raA) modified by a kinase in sequence to give We use a double-site modification with a cyclic mechanism, as a basic focal point throughout the paper. We also briefly examine, cyclic mechanisms involving more than two site modifications. The basic cyclic mechanism Fig. b involveThe model of the cyclic modification network is built up as follows. All models of individual modification steps  are described through widely-used models involving the relevant enzyme binding to substrate to form the complex which irreversibly modifies the substrate to the modified form .We examine multiple variants of cyclic mechanisms, based on the identities of the enzymes involved in multiple modifications, whether common or distinct Fig. b. Thus wWe also examine specific relaxations of the assumptions of the cyclic mechanisms see Fig. c. For inThe models for all these variations are built up in the same way, implementing a mass action description for the kinetics of the individual modification steps. The mass action description does not make a-priori assumptions regarding regimes of enzyme activity and thus offers a comphrehensive model of the original system. These models  are presented in the “Our focal point is a range of specific qualitative behaviour  all of which are of experimental interest in natural or engineered biology. Our primary goal is to establish unambiguously, the presence or absence of these characteristics in the various networks considered. Thus our results involve a combination of computational results which demonstrate the possibility of such behaviour on one hand, along with analytical results which establish the absence of behaviour for structural reasons, independent of parameters. In the former case we briefly discuss the ranges of parameters which enable the behaviour to be seen. Through a combination of the two approaches, and by applying this to multiple variants of the cyclic multisite module, we are able to sharpen the boundary between the absence and presence of different types of behaviour. This directly reveals what modification network characteristics  enables certain behavior to be seen and allows us to determine minimum requirements for a network to demonstrate the behaviour.In our computational work, enzyme-substrate unbinding constants are fixed at the same value for all enzyme substrate pairs. This does not introduce any essential restriction and allows for the entire range of qualitative behaviour we focus on, to be seen in the models considered. The remaining parameters are the catalytic constants, the enzyme substrate binding constants, and total amounts of enzymes and substrate. We choose representative values for these parameters within plausible ranges studied in the literature, and study their effect if this results in the qualitative behaviour of interest. Our main computational goal is to establish the presence of different characteristic behaviour in the networks under consideration.46. These MATLAB models were cross-validated with simulations of the same network in COPASI47. Note that the latter requires only specification of the network, parameters, and kinetics of individual steps. Bifurcation analysis of these models is performed using MATCONT48, after incorporating conservation conditions and eliminating certain variables. Computational studies are complemented by analytical approaches both on a given model, as well as variations  and the other which is monotonically increasing  mechanism can result in bistabilityity Fig. a. In facity Fig. ” reveals18.Another behaviour of interest is biphasic dose responses in the maximally modified phosphoform , which have been shown both experimentally and theoretically. We had shown that the biphasic behaviour arises in the ordered distributive mechanism, because increasing kinase concentrations can sequester partial phosphoforms in complexes, thus allowing more phosphatase to target the fully modified formFor corresponding parameters (where an ordered model exhibits a biphasic dose response), the cyclic model only exhibits a monotonically increasing dose response curve for the fully modified phosphoform Fig. b. Direct21, though oscillations in the intrinsic ordered distributive model have been elusive. The cyclic model does not require an explicit enzyme activation step to produce oscillations. Oscillations were found to occur in regimes where the sequential distributive model exhibited bistability, though this is neither necessary nor sufficient.The previous results point to structural features of the cyclic model, which result in complex information processing characteristic of sequential (and random) distributive models being prevented, and suggests that the cyclic model behaves in a very simple way. This is in line with the intuition that the cyclic model which have “disconnected” forward and reverse modification pathways, might behave comparably to a single site modification system. However, Fig. We then explored other aspects of the cyclic mechanism to isolate requirements for oscillations. We found Fig. b that a 20. The mixed mechanism for the ordered distributive double site modification has only one partial phosphoform, and this phosphoform is directly created and released only in one modification direction. The cyclic model has two different phosphoforms, and furthermore the structure allows for having common enzymes in one direction and separate enzymes in the other, generating oscillation, something which does not happen in the analogous mixed model. The mixed model has a processive step, associated with a common enzyme: if the opposing modification is mediated by separate enzymes, oscillations will not result as the system is similar to a three step irreversible reaction network with separate enzymes . In such a network there is no common enzyme shared between phosphoforms (while acting distributively). This indicates an essential extra flexibility inherent in the cyclic mechanism vis-a-vis the mixed mechanism.The behaviour of the cyclic model, preventing multistability, but generating oscillations is reminiscent of another mechanism we have studied, the mixed-mechanism21. The ordered (distributive) model exhibits bistability, but has not been shown to intrinsically exhibit oscillations . The basic cyclic model exhibits oscillations but not bistability or biphasic behaviour. We explored the minimum additions to the cyclic model to obtain bistability and biphasic dose response curves. This amounts to relaxing some restrictive assumptions regarding ordering in the basic cyclic model. To do this, we examined the augmentation of either a single phosphorylation step (opposite a given dephosphorylation step) or a single dephosphorylation step (opposite a phosphorylation step). This is done for three classes of cyclic models . This results in a series of six models . In such cases the rate of substrate modification is linearly proportional to the relevant free enzyme and substrate concentration . Computational analysis shows that in fact bistability can be obtained in all these cases , having one additional reaction (see Model C31) can give rise to oscillations. Furthermore this is true even if this extra reaction is in the unsaturated limit see “”.18 and is seen in model C12, since the phosphatase targets Table Model C21 exhibits biphasic response in relationship to both total kinase concentrations. Particularly noteworthy here is the response to variation in the second kinase (K2) concentration. Here we find a robust biphasic response for all other parameter values. Furthermore, as the total concentration of K2 is increased towards infinity, the Both models C31 and C32 can exhibit a biphasic response to variation of K2 but not to K1 see “”. This aWe probed the cases where biphasic responses could be obtained, by examining whether this remained true even if the augmented reaction was in the unsaturated regime (negligible sequestration). We found that the biphasic response to K2 in models C12, C22 and C32 was completely eliminated, and analytical results demonstrated this. The biphasic response to K1 in model C21 could still be obtained. The biphasic response to K2 of models C21 and C31 could also still be obtained. This is consistent with a demonstration of robust biphasic responses in these models, which results from a direct competing effect due to the action of K2 on two legs of the network. This is demonstrated analytically in the “The landscape of biphasic responses Table  can be vOur results show how a single augmentation to the cyclic mechanism can enable bistability and biphasic dose–response curves. Similarly, as seen in Fig. We discuss cyclic mechanisms involving more than two modification sites. Recall that we described the cyclic mechanism in double site phosphorylation as an ordered mechanism where the order of phosphorylation and dephosphorylation are the same: this implies that the first site to be phosphorylated is the first to be dephosphorylated and the last site to be phosphorylated is the last to be dephosphorylated. This gave rise to a characteristic cyclic (irreversible) network structure seen previously, which was the basis of the observed behaviour. Now when we examine a larger number of modification sites, having the same order of phosphorylation and dephosphorylation still gives cyclic mechanisms, similar to what we have seen. However it is possible to have mechanisms where the order of phosphorylation and dephosporylation are not the same, still giving rise to cyclic networks of the type we have encountered.We can summarize the overall result as follows: in a three site modification system, cyclic mechanisms require either (1) the first site phosphorylated to be the first site dephosphorylated or (2) the last site phosphorylated to be the last site dephosphorylated. In only such cases do we have the phosphoforms in phosphorylation and dephosphorylations to be distinct, with the reaction network having a cyclic structure as seen above.This can be justified as follows. Without loss of generality, assuming the order of phosphorylation involves the first site  and dephosphorylation (in the reverse cycle) are associated with a common phosphoform. Thus no cyclic mechanism arises in this case. Figure The above characterization of the cyclic mechanism for three site modifications does not account for all cyclic mechanisms, when the number of modification sites is greater than 3. To see this, we focus on a four site modification mechanism and assume without loss of generality that the phosphorylation order is first site followed by second site followed by third site followed by fourth site. Thus the reaction pathway can be described as Our computational results above are complemented by analytical work. Typically we use analytical approaches for questions which cannot be addressed conclusively by computations. Thus we focus on cases where particular types of behaviour are ruled out irrespective of parameters. We also use analytical work in some cases to demonstrate the presence of specific kinds of behaviour .The approach to the analysis is as follows. After writing down the steady state equations for all species , and incorporating the conservation conditions for enzymes and substrate, a number of variables can be eliminated. This is done as follows. (1) Firstly, at steady state the concentration of complexes is proportional to the product of concentrations of the relevant (free) enzymes and substrates. (2) Using the conservation conditions for enzymes, and the expression for the complexes as discussed above, the free enzyme concentrations can be written in terms of substrate concentrations. This can be done for all relevant enzymes. (3) Substrate variables can all be written in terms of one substrate variable  Absence of biphasic responses in models C12, C22 and C32 with respect to K or K2 when the additional reaction acted in the unsaturated limit. These various cases are studied in the “From our analytical studies we demonstrate. (1) Absence of multistationarity in cyclic mechanisms with distinct/common kinases and distinct/common phosphatases. (2) Absence of the biphasic dose response curve for 41, giving rise to a cyclic network core. It is also known that different kinases modifying the same substrate can also involve specific ordering50. This is by no means restricted to the same kinase performing multiple modifications: in fact ordering can also be observed with multiple kinases51. Finally, the same insights also apply to dephosphorylation, which can also be ordered or random52.Ordering of modifications is a fundamental aspect of multisite modification and in present in a range of contexts and guises. An example involving common kinases and phosphatases in double site modification is ERK phosphorylation/dephosphorylation by MEK/MKP3 where the order of phosphorylation is the same as that of dephosphorylationThis paper explores the impact of ordering of modifications in multisite phosphorylation and focusses on cyclic distributive double site modification models, which represent a particular ordering of modifications where the order of phosphorylation and dephosphorylation are the same, resulting in two partial phosphoforms. Cyclic mechanisms are of interest because (1) they represent a particular ordering and consequently a model system for enzymatic multisite modification, and a basic post-translation modification network and can be a reference for engineering synthetic multisite modification (2) they are found in natural systems (3) they are, from a network perspective, a bridge between ordered sequential and random mechanisms (4) analysis of this system provides and consolidates insights into the origins of different types of information processing characteristics observed in ordered and random distributive mechanisms.Our goal was to characterize the presence or absence of basic information processing characteristics, specifically multistability, oscillation and biphasic responses of the maximally modified form, and thus evaluate the impact of the ordering of modifications. To do this we aim to draw a sharp boundary between the presence or absence of a given behaviour and how it depends on network interactions (and any augmentations), as well as other ingredients  and thus infer the minimum requirements for a given behaviour. Our analysis is performed in double site modification networks (involving different variants of common/separate kinases/phosphatases) both because of the relevance to specific contexts, and because they represent tractable networks which can be transparently analyzed to reveal basic insights which generalize to a greater number of modification sites. The results are summarized in Fig. 20 that oscillations can occur in networks where multistationarity is precluded for basic structural reasons.Cyclic mechanisms with a common kinase and common phosphatase or separate kinases and a common phosphatase are able to readily give oscillations. In fact, even with separate kinases and phosphatases, an extra reversible reaction in the unsaturated regime can give rise to oscillations. The former cases are strictly monostable, reinforcing an aspect seen elsewhereHaving a single reversible reaction augmenting the cyclic mechanism is sufficient for bistability. Furthermore this does not even require sufficient sequestration of enzymes/substrates in this extra reaction. All in all, a cyclic mechanism where one enzyme acts on two modification reactions, even if one of them is in the unsaturated limit, is sufficient for obtaining bistability.Biphasic responses in the maximally modified phosphoform stem from an in-built trade-off. This is absent in the basic cyclic mechanisms and consequently such biphasic responses are ruled out. With the presence of a single reversible reaction, we identify multiple categories of responses: (1) those where biphasic responses are ruled out for the kinase enzyme(s): in the case where there are two kinase enzymes, they are ruled out for both. In the case of two kinase enzymes, (2) those where biphasic responses are seen for one of the kinase enzymes but not the other (3) those where they are seen for both kinase enzymes. Viewed from another axes (the requirements on the augmented reaction), these biphasic responses can be categorized as either requiring the augmented reaction to be acting far from then unsaturated limit, to existing even if the augmented reaction is in the unsaturated limit, and in some of the latter cases, exhibiting robust biphasic responses. The existence of robust biphasic responses stems from a basic structural feature in the network realizing a robust trade-off .55. Bistability and oscillations have not yet been demonstrated for the basic modification systems in isolation, but are predicted from very basic considerations.Biphasic responses have been experimentally observed in multiple contexts21.Ordered sequential models with purely processive mechanisms of enzymatic modification result in a single globally stable steady state. The ordered sequential model with distributive modification can result in bistability with one or both enzymes being common to the different modifications. Ordered sequential models with common kinases and phosphatases can generate biphasic responses. Oscillations have thus far been elusive. The random mechanism readily provides multistability and oscillations, with separate/common kinases and separate/common phosphatasesThe ordered sequential mechanism with mixed mechanisms of modification (one direction of modification is distributive and the other processive), share a common characteristic of the basic cyclic mechanisms, of having a single steady state which can lose stability to a Hopf bifurcation. There too, biphasic responses are ruled out. The effective separation of phosphorylation and dephosphorylation legs , is a common feature of the two systems. We find oscillations possible in the cyclic system even when the binding constants of the partial phosphoforms to relevant enzymes, is relatively low. If these binding constants for one of the partial phosphoforms were high, then the relevant partial phosphoform would hardly be present in free form (assuming moderate unbinding rates and sufficient enzyme), a feature reminiscent of the processive leg of the mixed mechanism model. We thus conclude that oscillations in the cyclic mechanism are not merely a simple echo of those in mixed mechanisms.The contrast with the ordered sequential distributive model shows straightaway that the presence of different phosphoforms, eliminates a trade-off responsible for biphasic responses, and also multistationarity, but interestingly that this very feature can readily generate oscillations. The contrast with random modification mechanisms highlights that behaviour such as bistability and oscillations actually requires only a small number of underlying factors present in the random mechanism to achieve. It also straightaway points to multiple regions/corners in the parameter space where such behaviour is achieved.Non-trivial dynamical characteristics such as bistability and oscillations in multisite modification ultimately rely on (1) a common enzyme in more than one modification step and (2) sequestration of enzymes in complexes, which is the source of non-linearity. Our analysis of cyclic mechanisms with a single augmented step in an unsaturated regime shows that it is possible  to realize both bistability and oscillations in networks with a single common enzyme acting in only two steps, with one of them in the unsaturated limit. This represents a minimum combination of the factors outlined above. Random mechanisms have more than one enzyme acting in multiple steps, while sequential ordered mechanisms (1) need at least one common enzyme for bistability and (2) have not been shown to exhibit oscillations intrinsically even with greater degrees of coupling of enzymes and sequestration.The above results are relevant to both systems and synthetic biology, and their intersection. All the types of basic behaviour considered here  are being investigated experimentally in either natural or engineered contexts involving multisite modification.37, where the compromising of phosphorylation is associated with certain disorders), and is also an example of different basic circuit containing multisite phosphorylation. It provides insights into the behaviour of circuits (for example random modification mechanisms), which we discuss below. In addition, it also provides insights into variants or augmentations of multisite modification , which exhibit a similar chemical modification logic.Since multisite modification systems are part of signalling networks, there is a need to understand in detail (1) the intrinsic characteristics of multisite modification and (2) how they function as part of signalling pathways. In the context of (1), analyzing cyclic mechanisms is of interest, because it is encountered naturally , with respect to the introduction of new information processing characteristics.Random mechanisms of multisite modification with different degrees of commonality of enzymes are fundamental PTM circuits. Characterizing their behaviour, their dependence on parameters and “design principles” underlying different characteristic behaviour they exhibit is fundamental to understanding multisite modification systems in systems biology. While some aspects can be studied to an extent by exhaustive parametric scanning, understanding the sources and origins of different behaviour needs a much more concerted effort and prompts multiple questions. Do these arise from dominant interactions/subnetworks? Do they arise from non-trivial interactions between different sub-networks? What type of sequestration effects are important? What impact do these aspects have on the robustness of behaviour? As part of this effort, one needs to consider stripped down versions of the full random mechanism, where it is possible to characterize both the presence and absence of behaviour, as well as parametric dependence clearly. Cyclic mechanisms  represent extreme stripped down versions in this regard. They represent tractable starting points from which augmentations can be added step by step (towards full random mechanisms), along with a clearer characterization of parametric dependence in these simpler networks at every stage. Such a bottom-up approach implemented in stages can provide a distinct systematic way of understanding in depth the behaviour and its origins in random mechanisms. In this context, we also point out that the ERK phosphorylation/dephosphorylation by MEK/MKP3, involves a specific ordering giving rise to a cyclic network core, in addition to which other reactions are considered56, we can say that the construction of such circuits in-silico is an example of building basic ingredients with a view towards understanding the origins of different kinds of behaviour in more complex post-translational modification circuits. The engineering of multisite phosphorylation in synthetic biology is being pursued in multiple directions experimentally44, and this in turn is one aspect of the engineering of reaction networks58. Our analysis shows that separating phosphorylation/dephosphorylation steps is a key enabler of oscillations. Implementing such a design principle , could facilitate the creation of oscillatory circuits in cellular and cell-free systems. Our analysis in this paper also provides a template for the engineering of different circuits with different combinations of information processing characteristics.Viewed from a bottom-up synthetic chemical approach, we are able to isolate fairly simple circuits which can in principle, be engineered to achieve circuit behaviour. From the perspective of building life to understand it61.The results are also relevant to chemical information processing more generally. While complex behaviour in chemical pathways and circuits has been long established, the fact that such behaviour can occur in more basic chemical modification scenarios, with the crucial role of species sequestration, is of more recent vintage. In such systems, determining the effect of sequestration and how it combines with basic chemical modification mechanisms, as well as the underlying modification network has led to multiple basic unanswered questions. By examining very basic modification networks and circuits therein, we are able to more sharply define the interplay between network ingredients, topology and sequestration to achieve certain behaviour. In this regard, being able to rule out the presence of such behaviour in circuits independent of parameters is important, as it allows us to more sharply draw the boundary between the presence and absence of such behaviour. Further analysis can build on this to examine robustness of behaviour and how additional ingredients contribute to this. The role of different ingredients such as the commonality or distinctness of modification enzymes and how they contribute to the tuneability of the circuits is another important aspect. The realization of new chemical circuits to achieve different information processing tasks  is being pursued in a range of non-biological avenues as wellAll in all, the results are relevant to understanding important aspects of the chemical underpinning of signalling circuits and their complexity, how they can be used to building new information processing circuits, and also in emerging areas which aim to bridge the living and the non-living, with a chemical focus.Supplementary Information 1Supplementary Information 2Supplementary Information 3Supplementary Information 4Supplementary Information 5


Climate change is altering the biogeochemical and physical characteristics of the Arctic marine environment, which impacts sea ice algal and phytoplankton bloom dynamics and the vertical transport of these carbon sources to benthic communities. Little is known about whether the contribution of sea ice-derived carbon to benthic fauna and nitrogen cycling has changed over multiple decades in concert with receding sea ice. We combined compound-specific stable isotope analysis of amino acids with highly branched isoprenoid diatom lipid biomarkers using archived (1982–2016) tissue of benthivorous Atlantic walrus to examine temporal trends of sea ice-derived carbon, nitrogen isotope baseline and trophic position of Atlantic walrus at high- and mid-latitudes in the Canadian Arctic. Associated with an 18% sea ice decline in the mid-Arctic, sea ice-derived carbon contribution to Atlantic walrus decreased by 75% suggesting a strong decoupling of sea ice-benthic habitats. By contrast, a nearly exclusive amount of sea ice-derived carbon was maintained in high-Arctic Atlantic walrus (98% in 1996 and 89% in 2006) despite a similar percentage in sea ice reduction. Nitrogen isotope baseline or the trophic position of Atlantic walrus did not change over time at either location. These findings indicate latitudinal differences in the restructuring of carbon energy sources used by Atlantic walrus and their benthic prey, and in turn a change in Arctic marine ecosystem functioning between sea ice–pelagic–benthic habitats. First, Odobenus rosmarus rosmarus) to test for changes in the relative importance of sea ice algae versus phytoplankton carbon sources that fuel benthic communities. Atlantic walruses are central place foragers that are stenophagous and reside near shallow (less than 80 m) bivalve-rich benthic communities, their main prey  × 10−3, where X is 13C or 15N and R equals 13C/12C or 15N/14N.The δion 13C of phenylalanine (δ13CPhe) and sea ice-derived carbon from H-print estimates—two variables that have been used to discriminate between sea ice-derived carbon and phytoplankton-derived carbon [13CPhe value represents a higher contribution of phytoplankton-derived carbon to the diet of the consumer. A Pearson correlation was used to examine the correlation between summer sea ice concentration and sea ice breakup date. We also used linear regression analysis to investigate temporal trends of sea ice concentration in Jones Sound and Foxe Basin. To test for changes across years in Foxe Basin, mean annual values of δ13CPhe (i.e. baseline δ13C), δ15NPhe (i.e. baseline δ15N) and sea ice-derived carbon  were used in linear regressions to meet the assumption of independent data for this time series  since one value of sea ice concentration was estimated for each year and generally five Atlantic walrus individuals were collected per year, except in 1987 (n = 4), 2013 (n = 2) and 2016 (n = 2). Including each individual within each sampling year violates the assumption of independent errors and allows pseudoreplication where observations from the same year are more likely to be similar than observations from other years. We used a similar analytical approach to investigate relationships of δ13CPhe and sea ice-derived carbon relative to sea ice concentration of Atlantic walruses in Foxe Basin. Student t-tests were used to determine a significant difference in δ13CPhe, δ15NPhe and sea ice-derived carbon between 1996 versus 2006 for individuals collected in Jones Sound.We used linear regression analysis to investigate the relationship between δd carbon ,37. A loGlu-Phe) related to a species' mode of nitrogen excretion and diet quality [15NGlu and δ15NPhe represent the stable isotope nitrogen values of glutamic acid and phenylalanine of the consumer, β represents the difference in δ15NGlu and δ15NPhe of primary producers (3.4‰) [Glu-Phe is the seal-specific TDF value of 4.3‰. Alternative methods for calculated trophic position of Atlantic walrus provided differences in absolute values but similar trends over time . To test for temporal changes in trophic position of Atlantic walruses in Foxe Basin, linear regression was used on mean annual values of trophic position over time. A student t-test was used to determine a significant difference in trophic position of Jones Sound Atlantic walrus between 1996 and 2006. All statistical analyses were performed in R v. 3.6.1 [There are several trophic position (TP) equations derived from compound-specific stable isotope analysis of individual amino acids that provide a range in trophic position estimates for marine mammals and seabirds ,39. Give quality , multi-T quality ,31,39, a quality . Therefo quality )2.3TP=2+s (3.4‰)  and TDFGv. 3.6.1 .3.(a)t33 = −3.81, r2 = 0.31, p < 0.001) and 18% in Foxe Basin  and 17 days earlier in Foxe Basin  each year from 1982 to 2016. However, over this 35-year record, summer sea ice concentration decreased by approximately 26% in Jones Sound 13CPhe (r = 0.67). Furthermore, a significant increase in δ13CPhe relative to sea ice-derived carbon occurred  with estimated sea ice-derived carbon values ranging from 30% to greater than 100% in association with δ13CPhe values ranging from −29.4‰ to −24.7‰ t8 = 1.35, p = 0.25), δ15NPhe  and trophic position  of Atlantic walrus between 1996 and 2006  when sea ice concentration was 70% in 1996 and only 40% in 2006  and trophic position  of Atlantic walrus did not change over time, whereas significant decreases occurred for sea ice-derived carbon  and δ13CPhe  and δ13CPhe  were significantly higher in years of higher sea ice concentration  in the contribution of sea ice-derived carbon to Atlantic walrus, a benthic fauna consumer, in Foxe Basin. This pattern was associated with a dramatic decline in sea ice cover where Atlantic walrus shifted from a nearly exclusive contribution of sea ice-derived carbon in their diet to more phytoplankton-derived carbon. In Jones Sound, a slight decrease of sea ice-derived carbon to the benthic environment occurred between 1996 versus 2006, though Atlantic walrus in this area have maintained a nearly exclusive amount of sea ice-derived carbon in their diet (98% in 1996 and 89% in 2006) despite a large difference in summer sea ice concentration between sampling years (70% in 1996 versus 40% in 2006). We found strong support of a decoupling of sea ice–benthic habitats. Less sea ice-derived carbon now reaches benthic fauna at mid-Arctic, but not high-Arctic, latitudes which suggests spatial variation in fundamental alterations of carbon energy dynamics and ecosystem functioning due to climate change. This result aligns with observed changes in sea ice algal bloom phenology and production in that the sea ice algal bloom is occurring earlier in the year across the Arctic, but there is latitudinal heterogeneity in the amount of sea ice algal production . In the (a)Delphinapterus leucas) and ringed seals (Pusa hispida), predators who mainly consume prey within the epipelagic portion of the water column, has declined over a 27-year study period in Cumberland Sound, Nunavut [Sea ice-derived carbon estimated from highly branched isoprenoids has been observed across all consumer trophic levels from primary and secondary consumers to near-top and top predators –24,43, s Nunavut ,23. UsinIn the 1980s in the more-southern area of Foxe Basin, the contribution of sea ice-derived carbon (i.e. highly branched isoprenoid diatom lipids from liver) in the diet of Atlantic walrus was similar to that of the more-northern area of Jones Sound in the 1990s and 2000s (88% versus 94%), but then decreased dramatically in the 1990s and 2000s where sea ice-derived carbon became 1.8 times lower (52%) than in Jones Sound. More rapid declines in summer sea ice concentration and earlier sea ice breakup in Jones Sound relative to Foxe Basin from 1982 to 2016 (this study) is consistent with observations of greater susceptibility of northern Arctic regions to reduced springtime ice seasons than more-southern areas . DespiteThe Arctic seafloor and its sediments act as a long-term repository for sea ice-derived carbon where benthic heterotrophs feed on these sedimentary stores of sea ice-derived carbon which can then be transferred back up to the pelagic environment via fishes, marine mammals and seabirds who consume benthic fauna . Therefo13CPhe of Atlantic walrus in Foxe Basin declined at a rate of 0.6‰ per decade from 1982 to 2016 in association with a decreasing sea ice concentration and earlier sea ice breakup, and was 0.8‰ lower in 2006 than in 1996 in Jones Sound, suggesting less sea ice-derived carbon in the benthos over time in both areas which aligns with our H-Print estimates. The decadal declines of δ13CPhe in Atlantic walrus from both study areas is six to eight times higher than the decrease of δ13C of dissolved inorganic carbon in Arctic marine waters (−0.11‰ per decade) attributed to increasing concentrations of anthropogenic CO2 in the atmosphere known as the Suess effect [13CPhe parallel estimates from [13C of particulate organic carbon in the Arctic Ocean decreased by 0.6‰ per decade with declining sea ice in combination with increased phytoplankton primary productivity [13CPhe values over time [13CPhe corresponded to that of temporal declines in H-Print values. From 1998 to 2018, both Jones Sound and Foxe Basin have undergone an increase in phytoplankton biomass [The δs effect . Additiotes from  where thuctivity . It is uver time  since te biomass  which in biomass , however biomass  due to t biomass ,51. Ther(b)15N reflects the δ15N of seawater nitrate [15N of the baseline in Jones Sound and Foxe Basin occurred suggesting that water circulation, nitrogen cycling and nitrate assimilation by primary producers from both areas have remained consistent over time.Nitrogen is a key element of life and is one of the major elements required for primary production in marine environments . Nitroge nitrate . Both Jo nitrate ,54. Thou nitrate , no longTrophic position estimates revealed that Atlantic walrus in Jones Sound and Foxe Basin have consistently played the same trophic role in each area over time. Equation (2.3) provided a trophic position of Atlantic walrus (range = 2.8–3.2) that is in better agreement with estimates derived from stomach contents (3.4)  compared(c)15N of the baseline and trophic position of Atlantic walrus did not change over time indicating consistent nitrogen cycling and trophic roles of high bivalve consumption. We identified spatio-temporal changes in the carbon source that fuels benthic communities in the Arctic, suggesting a continuing decrease and thinning of sea ice cover will influence species interactions, benthic community biomass and structure, and Arctic ecosystem functioning. Long-term monitoring of Atlantic walrus biological parameters, such as body condition, is required to determine how Atlantic walrus and potentially other benthic consumers are responding to these changing carbon sources to gain insight into the modifications in ecosystem dynamics across the rapidly warming Arctic.Our novel biochemical trophodynamic approach using compound-specific stable isotope analysis of amino acids in combination with highly branched isoprenoids revealed that: (1) both analytical approaches are complementary to each other with moderate explanatory power, (2) in association with an earlier sea ice breakup and declining sea ice concentration, a strong decoupling of sea ice-benthic habitats occurred at mid-Arctic latitudes where less sea ice algae is now incorporated into benthic fauna, (3) sea ice algae is the nearly exclusive carbon source for benthic fauna in the high-Arctic and (4) the δ