Incorporating chemical signalling factors into cell-based models of growing epithelial tissues

In this paper we present a comprehensive computational framework within which the effects of chemical signalling factors on growing epithelial tissues can be studied. The method incorporates a vertex-based cell model, in conjunction with a solver for the governing chemical equations. The vertex model provides a natural mesh for the finite element method (FEM), with node movements determined by force laws. The arbitrary Lagrangian–Eulerian formulation is adopted to account for domain movement between iterations. The effects of cell proliferation and junctional rearrangements on the mesh are also examined. By implementing refinements of the mesh we show that the finite element (FE) approximation converges towards an accurate numerical solution. The potential utility of the system is demonstrated in the context of Decapentaplegic (Dpp), a morphogen which plays a crucial role in development of the Drosophila imaginal wing disc. Despite the presence of a Dpp gradient, growth is uniform across the wing disc. We make the growth rate of cells dependent on Dpp concentration and show that the number of proliferation events increases in regions of high concentration. This allows hypotheses regarding mechanisms of growth control to be rigorously tested. The method we describe may be adapted to a range of potential application areas, and to other cell-based models with designated node movements, to accurately probe the role of morphogens in epithelial tissues

Colloquium: Mechanical formalisms for tissue dynamics

The understanding of morphogenesis in living organisms has been renewed by tremendous progressin experimental techniques that provide access to cell-scale, quantitative information both on theshapes of cells within tissues and on the genes being expressed. This information suggests that ourunderstanding of the respective contributions of gene expression and mechanics, and of their crucialentanglement, will soon leap forward. Biomechanics increasingly benefits from models, which assistthe design and interpretation of experiments, point out the main ingredients and assumptions, andultimately lead to predictions. The newly accessible local information thus calls for a reflectionon how to select suitable classes of mechanical models. We review both mechanical ingredientssuggested by the current knowledge of tissue behaviour, and modelling methods that can helpgenerate a rheological diagram or a constitutive equation. We distinguish cell scale ("intra-cell")and tissue scale ("inter-cell") contributions. We recall the mathematical framework developpedfor continuum materials and explain how to transform a constitutive equation into a set of partialdifferential equations amenable to numerical resolution. We show that when plastic behaviour isrelevant, the dissipation function formalism appears appropriate to generate constitutive equations;its variational nature facilitates numerical implementation, and we discuss adaptations needed in thecase of large deformations. The present article gathers theoretical methods that can readily enhancethe significance of the data to be extracted from recent or future high throughput biomechanicalexperiments.Comment: 33 pages, 20 figures. This version (26 Sept. 2015) contains a few corrections to the published version, all in Appendix D.2 devoted to large deformation

Regge Field Theory in zero transverse dimensions: loops versus "net" diagrams

Toy models of interacting Pomerons with triple and quaternary Pomeron vertices in zero transverse dimension are investigated. Numerical solutions for eigenvalues and eigenfunctions of the corresponding Hamiltonians are obtained, providing the quantum solution for the scattering amplitude in both models. The equations of motion for the Lagrangians of the theories are also considered and the classical solutions of the equations are found. Full two-point Green functions ("effective" Pomeron propagator) and amplitude of diffractive dissociation process are calculated in the framework of RFT-0 approach. The importance of the loops contribution in the amplitude at different values of the model parameters is discussed as well as the difference between the models with and without quaternary Pomeron vertex.Comment: 34 pages, 36 figure

Global carbon budget 2022

Accurate assessment of anthropogenic carbon dioxide (CO2) emissions and their redistribution among the atmosphere, ocean, and terrestrial biosphere in a changing climate is critical to better understand the global carbon cycle, support the development of climate policies, and project future climate change. Here we describe and synthesize data sets and methodologies to quantify the five major components of the global carbon budget and their uncertainties. Fossil CO2 emissions (EFOS) are based on energy statistics and cement production data, while emissions from land-use change (ELUC), mainly deforestation, are based on land use and land-use change data and bookkeeping models. Atmospheric CO2 concentration is measured directly, and its growth rate (GATM) is computed from the annual changes in concentration. The ocean CO2 sink (SOCEAN) is estimated with global ocean biogeochemistry models and observation-based data products. The terrestrial CO2 sink (SLAND) is estimated with dynamic global vegetation models. The resulting carbon budget imbalance (BIM), the difference between the estimated total emissions and the estimated changes in the atmosphere, ocean, and terrestrial biosphere, is a measure of imperfect data and understanding of the contemporary carbon cycle. All uncertainties are reported as ±1σ. For the year 2021, EFOS increased by 5.1% relative to 2020, with fossil emissions at 10.1±0.5GtCyr-1 (9.9±0.5GtCyr-1 when the cement carbonation sink is included), and ELUC was 1.1±0.7GtCyr-1, for a total anthropogenic CO2 emission (including the cement carbonation sink) of 10.9±0.8GtCyr-1 (40.0±2.9GtCO2). Also, for 2021, GATM was 5.2±0.2GtCyr-1 (2.5±0.1ppmyr-1), SOCEAN was 2.9 ±0.4GtCyr-1, and SLAND was 3.5±0.9GtCyr-1, with a BIM of -0.6GtCyr-1 (i.e. the total estimated sources were too low or sinks were too high). The global atmospheric CO2 concentration averaged over 2021 reached 414.71±0.1ppm. Preliminary data for 2022 suggest an increase in EFOS relative to 2021 of +1.0% (0.1% to 1.9%) globally and atmospheric CO2 concentration reaching 417.2ppm, more than 50% above pre-industrial levels (around 278ppm). Overall, the mean and trend in the components of the global carbon budget are consistently estimated over the period 1959-2021, but discrepancies of up to 1GtCyr-1 persist for the representation of annual to semi-decadal variability in CO2 fluxes. Comparison of estimates from multiple approaches and observations shows (1) a persistent large uncertainty in the estimate of land-use change emissions, (2) a low agreement between the different methods on the magnitude of the land CO2 flux in the northern extratropics, and (3) a discrepancy between the different methods on the strength of the ocean sink over the last decade. This living data update documents changes in the methods and data sets used in this new global carbon budget and the progress in understanding of the global carbon cycle compared with previous publications of this data set. The data presented in this work are available at 10.18160/GCP-2022 (Friedlingstein et al., 2022b)

Toward community standards and software for whole-cell modeling

Whole-cell (WC) modeling is a promising tool for biological research, bioengineering, and medicine. However, substantial work remains to create accurate, comprehensive models of complex cells. Methods: We organized the 2015 Whole-Cell Modeling Summer School to teach WC modeling and evaluate the need for new WC modeling standards and software by recoding a recently published WC model in SBML. Results: Our analysis revealed several challenges to representing WC models using the current standards. Conclusion: We, therefore, propose several new WC modeling standards, software, and databases. Significance:We anticipate that these new standards and software will enable more comprehensive models

Global Carbon Budget 2020

Accurate assessment of anthropogenic carbon dioxide (CO$_{2}$) emissions and their redistribution among the atmosphere, ocean, and terrestrial biosphere in a changing climate – the “global carbon budget” – is important to better understand the global carbon cycle, support the development of climate policies, and project future climate change. Here we describe and synthesize data sets and methodology to quantify the five major components of the global carbon budget and their uncertainties. Fossil CO$_{2}$ emissions (E$_{FOS}$) are based on energy statistics and cement production data, while emissions from land-use change (E$_{LUC}$), mainly deforestation, are based on land use and land-use change data and bookkeeping models. Atmospheric CO$_{2}$ concentration is measured directly and its growth rate (G$_{ATM}$) is computed from the annual changes in concentration. The ocean CO$_{2}$ sink (S$_{OCEAN}$) and terrestrial CO$_{2}$ sink (S$_{LAND}$) are estimated with global process models constrained by observations. The resulting carbon budget imbalance (B$_{IM}$), the difference between the estimated total emissions and the estimated changes in the atmosphere, ocean, and terrestrial biosphere, is a measure of imperfect data and understanding of the contemporary carbon cycle. All uncertainties are reported as ±1σ. For the last decade available (2010–2019), E$_{FOS}$ was 9.6 ± 0.5 GtC yr$^{-1}$ excluding the cement carbonation sink (9.4 ± 0.5 GtC yr−1 when the cement carbonation sink is included), and E$_{LUC}$ was 1.6 ± 0.7 GtC yr$^{-1}$. For the same decade, G$_{ATM}$ was 5.1 ± 0.02 GtC yr$^{-1}$ (2.4 ± 0.01 ppm yr$_{-1}$), S$_{OCEAN}$ 2.5 ±  0.6 GtC yr$^{-1}$, and S$_{LAND}$ 3.4 ± 0.9 GtC yr$^{-1}$, with a budget imbalance B$_{IM}$ of −0.1 GtC yr$^{-1}$ indicating a near balance between estimated sources and sinks over the last decade. For the year 2019 alone, the growth in E$_{FOS}$ was only about 0.1 % with fossil emissions increasing to 9.9 ± 0.5 GtC yr$^{-1}$ excluding the cement carbonation sink (9.7 ± 0.5 GtC yr$^{-1}$ when cement carbonation sink is included), and E$_{LUC}$ was 1.8 ± 0.7 GtC yr$^{-1}$, for total anthropogenic CO$_{2}$ emissions of 11.5 ± 0.9 GtC yr$^{-1}$ (42.2 ± 3.3 GtCO$_{2}$). Also for 2019, G$_{ATM}$ was 5.4 ± 0.2 GtC yr$^{-1}$ (2.5 ± 0.1 ppm yr$^{-1}$), S$_{OCEAN}$ was 2.6 ± 0.6 GtC yr$^{-1}$, and S$_{LAND}$ was 3.1 ± 1.2 GtC yr$^{-1}$, with a B$_{IM}$ of 0.3 GtC. The global atmospheric CO$_{2}$ concentration reached 409.85 ± 0.1 ppm averaged over 2019. Preliminary data for 2020, accounting for the COVID-19-induced changes in emissions, suggest a decrease in E$_{FOS}$ relative to 2019 of about −7 % (median estimate) based on individual estimates from four studies of −6 %, −7 %, −7 % (−3 % to −11 %), and −13 %. Overall, the mean and trend in the components of the global carbon budget are consistently estimated over the period 1959–2019, but discrepancies of up to 1 GtC yr$^{-1}$ persist for the representation of semi-decadal variability in CO$_{2}$ fluxes. Comparison of estimates from diverse approaches and observations shows (1) no consensus in the mean and trend in land-use change emissions over the last decade, (2) a persistent low agreement between the different methods on the magnitude of the land CO$_{2}$ flux in the northern extra-tropics, and (3) an apparent discrepancy between the different methods for the ocean sink outside the tropics, particularly in the Southern Ocean. This living data update documents changes in the methods and data sets used in this new global carbon budget and the progress in understanding of the global carbon cycle compared with previous publications of this data set (Friedlingstein et al., 2019; Le Quéré et al., 2018b, a, 2016, 2015b, a, 2014, 2013). The data presented in this work are available at https://doi.org/10.18160/gcp-2020 (Friedlingstein et al., 2020)

Global Carbon Budget 2022

Accurate assessment of anthropogenic carbon dioxide (CO$_2$) emissions and their redistribution among the atmosphere, ocean, and terrestrial biosphere in a changing climate is critical to better understand the global carbon cycle, support the development of climate policies, and project future climate change. Here we describe and synthesize data sets and methodologies to quantify the five major components of the global carbon budget and their uncertainties. Fossil CO$_2$ emissions (E$_{FOS}$) are based on energy statistics and cement production data, while emissions from land-use change (E$_{LUC}$), mainly deforestation, are based on land use and land-use change data and bookkeeping models. Atmospheric CO$_2$ concentration is measured directly, and its growth rate (G$_{ATM}$) is computed from the annual changes in concentration. The ocean CO$_2$ sink (S$_{OCEAN}$) is estimated with global ocean biogeochemistry models and observation-based data products. The terrestrial CO$_2$ sink (S$_{LAND}$) is estimated with dynamic global vegetation models. The resulting carbon budget imbalance (B$_{IM}$), the difference between the estimated total emissions and the estimated changes in the atmosphere, ocean, and terrestrial biosphere, is a measure of imperfect data and understanding of the contemporary carbon cycle. All uncertainties are reported as ±1σ. For the year 2021, E$_{FOS}$ increased by 5.1 % relative to 2020, with fossil emissions at 10.1 ± 0.5 GtC yr$^{−1}$ (9.9 ± 0.5 GtC yr$^{−1}$ when the cement carbonation sink is included), and E$_{LUC}$ was 1.1 ± 0.7 GtC yr$^{−1}$, for a total anthropogenic CO$_2$ emission (including the cement carbonation sink) of 10.9 ± 0.8 GtC yr$^{−1}$ (40.0 ± 2.9 GtCO$_2$). Also, for 2021, G$_{ATM}$ was 5.2 ± 0.2 GtC yr$^{−1}$ (2.5 ± 0.1 ppm yr$^{−1}$), S$_{OCEAN}$ was 2.9  ± 0.4 GtC yr$^{−1}$, and S$_{LAND}$ was 3.5 ± 0.9 GtC yr$^{−1}$, with a B$_{IM}$ of −0.6 GtC yr$^{−1}$ (i.e. the total estimated sources were too low or sinks were too high). The global atmospheric CO$_2$ concentration averaged over 2021 reached 414.71 ± 0.1 ppm. Preliminary data for 2022 suggest an increase in E$_{FOS}$ relative to 2021 of +1.0 % (0.1 % to 1.9 %) globally and atmospheric CO$_2$ concentration reaching 417.2 ppm, more than 50 % above pre-industrial levels (around 278 ppm). Overall, the mean and trend in the components of the global carbon budget are consistently estimated over the period 1959–2021, but discrepancies of up to 1 GtC yr$^{−1}$ persist for the representation of annual to semi-decadal variability in CO$_2$ fluxes. Comparison of estimates from multiple approaches and observations shows (1) a persistent large uncertainty in the estimate of land-use change emissions, (2) a low agreement between the different methods on the magnitude of the land CO$_2$ flux in the northern extratropics, and (3) a discrepancy between the different methods on the strength of the ocean sink over the last decade. This living data update documents changes in the methods and data sets used in this new global carbon budget and the progress in understanding of the global carbon cycle compared with previous publications of this data set. The data presented in this work are available at https://doi.org/10.18160/GCP-2022 (Friedlingstein et al., 2022b)

The annual update GLODAPv2.2023: the global interior ocean biogeochemical data product

The Global Ocean Data Analysis Project (GLODAP) is a synthesis effort providing regular compilations of surface to bottom ocean biogeochemical bottle data, with an emphasis on seawater inorganic carbon chemistry and related variables determined through chemical analysis of seawater samples. GLODAPv2.2023 is an update of the previous version, GLODAPv2.2022 (Lauvset et al., 2022). The major changes are as follows: data from 23 new cruises were added. In addition, a number of changes were made to the data included in GLODAPv2.2022. GLODAPv2.2023 includes measurements from more than 1.4 million water samples from the global oceans collected on 1108 cruises. The data for the now 13 GLODAP core variables (salinity, oxygen, nitrate, silicate, phosphate, dissolved inorganic carbon, total alkalinity, pH, chlorofluorocarbon-11 (CFC-11), CFC-12, CFC-113, CCl4, and SF6) have undergone extensive quality control with a focus on the systematic evaluation of bias. The data are available in two formats: (i) as submitted by the data originator but converted to World Ocean Circulation Experiment (WOCE) exchange format and (ii) as a merged data product with adjustments applied to minimize bias. For the present annual update, adjustments for the 23 new cruises were derived by comparing those data with the data from the 1085 quality-controlled cruises in the GLODAPv2.2022 data product using crossover analysis. SF6 data from all cruises were evaluated by comparison with CFC-12 data measured on the same cruises. For nutrients and ocean carbon dioxide (CO2), chemistry comparisons to estimates based on empirical algorithms provided additional context for adjustment decisions. The adjustments that we applied are intended to remove potential biases from errors related to measurement, calibration, and data-handling practices without removing known or likely time trends or variations in the variables evaluated. The compiled and adjusted data product is believed to be consistent to better than 0.005 in salinity, 1 % in oxygen, 2 % in nitrate, 2 % in silicate, 2 % in phosphate, 4 µmol kg−1 in dissolved inorganic carbon, 4 µmol kg−1 in total alkalinity, 0.01–0.02 in pH (depending on region), and 5 % in the halogenated transient tracers. The other variables included in the compilation, such as isotopic tracers and discrete CO2 fugacity (fCO2), were not subjected to bias comparison or adjustments. The original data, their documentation, and DOI codes are available at the Ocean Carbon and Acidification Data System of NOAA National Centers for Environmental Information (NCEI), which also provides access to the merged data product. This is provided as a single global file and as four regional ones – the Arctic, Atlantic, Indian, and Pacific oceans – under https://doi.org/10.25921/zyrq-ht66 (Lauvset et al., 2023). These bias-adjusted product files also include significant ancillary and approximated data, which were obtained by interpolation of, or calculation from, measured data. This living data update documents the GLODAPv2.2023 methods and provides a broad overview of the secondary quality control procedures and results

GLODAPv2.2022: the latest version of the global interior ocean biogeochemical data product

The Global Ocean Data Analysis Project (GLODAP) is a synthesis effort providing regular compilations of surface-to-bottom ocean biogeochemical bottle data, with an emphasis on seawater inorganic carbon chemistry and related variables determined through chemical analysis of seawater samples. GLODAPv2.2022 is an update of the previous version, GLODAPv2.2021 (Lauvset et al., 2021). The major changes are as follows: data from 96 new cruises were added, data coverage was extended until 2021, and for the first time we performed secondary quality control on all sulfur hexafluoride (SF6) data. In addition, a number of changes were made to data included in GLODAPv2.2021. These changes affect specifically the SF6 data, which are now subjected to secondary quality control, and carbon data measured on board the RV Knorr in the Indian Ocean in 1994–1995 which are now adjusted using certified reference material (CRM) measurements made at the time. GLODAPv2.2022 includes measurements from almost 1.4 million water samples from the global oceans collected on 1085 cruises. The data for the now 13 GLODAP core variables (salinity, oxygen, nitrate, silicate, phosphate, dissolved inorganic carbon, total alkalinity, pH, chlorofluorocarbon-11 (CFC-11), CFC-12, CFC-113, CCl4, and SF6) have undergone extensive quality control with a focus on systematic evaluation of bias. The data are available in two formats: (i) as submitted by the data originator but converted to World Ocean Circulation Experiment (WOCE) exchange format and (ii) as a merged data product with adjustments applied to minimize bias. For the present annual update, adjustments for the 96 new cruises were derived by comparing those data with the data from the 989 quality-controlled cruises in the GLODAPv2.2021 data product using crossover analysis. SF6 data from all cruises were evaluated by comparison with CFC-12 data measured on the same cruises. For nutrients and ocean carbon dioxide (CO2) chemistry comparisons to estimates based on empirical algorithms provided additional context for adjustment decisions. The adjustments that we applied are intended to remove potential biases from errors related to measurement, calibration, and data handling practices without removing known or likely time trends or variations in the variables evaluated. The compiled and adjusted data product is believed to be consistent to better than 0.005 in salinity, 1 % in oxygen, 2 % in nitrate, 2 % in silicate, 2 % in phosphate, 4 µmol kg−1 in dissolved inorganic carbon, 4 µmol kg−1 in total alkalinity, 0.01–0.02 in pH (depending on region), and 5 % in the halogenated transient tracers. The other variables included in the compilation, such as isotopic tracers and discrete CO2 fugacity (fCO2), were not subjected to bias comparison or adjustments. The original data, their documentation, and DOI codes are available at the Ocean Carbon and Acidification Data System of NOAA NCEI (https://www.ncei.noaa.gov/access/ocean-carbon-acidification-data-system/oceans/GLODAPv2_2022/, last access: 15 August 2022). This site also provides access to the merged data product, which is provided as a single global file and as four regional ones – the Arctic, Atlantic, Indian, and Pacific oceans – under https://doi.org/10.25921/1f4w-0t92 (Lauvset et al., 2022). These bias-adjusted product files also include significant ancillary and approximated data, which were obtained by interpolation of, or calculation from, measured data. This living data update documents the GLODAPv2.2022 methods and provides a broad overview of the secondary quality control procedures and results.</p