Metabolic regulation of mitochondrial morphologies in pancreatic beta cells: coupling of bioenergetics and mitochondrial dynamics

Tilokani, L., Nagashima, S., Paupe, V. & Prudent, J. Mitochondrial dynamics: Overview of molecular mechanisms. Essays Biochem 62, 341–360 (2018).Article 
PubMed 
PubMed Central 

Google Scholar 
Stiles, L. & Shirihai, O. S. Mitochondrial dynamics and morphology in beta-cells. Best. Pract. Res. Clin. Endocrinol. Metab. 26, 725–738 (2012).Article 
CAS 
PubMed 
PubMed Central 

Google Scholar 
Fu, W., Liu, Y. & Yin, H. Mitochondrial dynamics: biogenesis, fission, fusion, and mitophagy in the regulation of stem cell behaviors. Stem Cells Int 2019, 9757201 (2019).Article 
PubMed 
PubMed Central 

Google Scholar 
Chan, D. C. Mitochondrial dynamics and its involvement in disease. Annu. Rev. Pathol. 15, 235–259 (2020).Article 
CAS 
PubMed 

Google Scholar 
Bereiter-Hahn, J., Vöth, M., Mai, S. & Jendrach, M. Structural implications of mitochondrial dynamics. Biotechnol. J. 3, 765–780 (2008).Article 
CAS 
PubMed 

Google Scholar 
Pickles, S., Vigié, P. & Youle, R. J. Mitophagy and quality control mechanisms in mitochondrial maintenance. Curr. Biol. 28, R170–R185 (2018).Article 
CAS 
PubMed 
PubMed Central 

Google Scholar 
Montemurro, C. et al. Cell cycle-related metabolism and mitochondrial dynamics in a replication-competent pancreatic beta-cell line. Cell Cycle 16, 2086–2099 (2017).Article 
CAS 
PubMed 
PubMed Central 

Google Scholar 
Pernas, L. & Scorrano, L. Mito-morphosis: Mitochondrial fusion, fission, and cristae remodeling as key mediators of cellular function. Annu. Rev. Physiol. 78, 505–531 (2016).Article 
CAS 
PubMed 

Google Scholar 
Twig, G., Hyde, B. & Shirihai, O. S. Mitochondrial fusion, fission and autophagy as a quality control axis: The bioenergetic view. Biochim. Biophys. Acta 1777, 1092–1097 (2008).Article 
CAS 
PubMed 

Google Scholar 
Molina, A. J. A. et al. Mitochondrial networking protects beta-cells from nutrient-induced apoptosis. Diabetes 58, 2303–2315 (2009).Article 
CAS 
PubMed 
PubMed Central 

Google Scholar 
Mouli, P. K., Twig, G. & Shirihai, O. S. Frequency and selectivity of mitochondrial fusion are key to its quality maintenance function. Biophys. J. 96, 3509–3518 (2009).Article 
CAS 
PubMed 
PubMed Central 

Google Scholar 
Alavi, M. V. & Fuhrmann, N. Dominant optic atrophy, OPA1, and mitochondrial quality control: understanding mitochondrial network dynamics. Mol. Neurodegener. 8, 32 (2013).Article 
PubMed 
PubMed Central 

Google Scholar 
Sharma, A., Smith, H. J., Yao, P. & Mair, W. B. Causal roles of mitochondrial dynamics in longevity and healthy aging. EMBO Rep. 20, e48395 (2019).Article 
CAS 
PubMed 
PubMed Central 

Google Scholar 
Meyer, J. N., Leuthner, T. C. & Luz, A. L. Mitochondrial fusion, fission, and mitochondrial toxicity. Toxicology 391, 42–53 (2017).Article 
CAS 
PubMed 

Google Scholar 
Youle, R. J. & van der Bliek, A. M. Mitochondrial fission, fusion, and stress. Science 337, 1062–1065 (2012).Article 
CAS 
PubMed 
PubMed Central 

Google Scholar 
Song, Z., Ghochani, M., McCaffery, J. M., Frey, T. G. & Chan, D. C. Mitofusins and OPA1 mediate sequential steps in mitochondrial membrane fusion. Mol. Biol. Cell 20, 3525–3532 (2009).Article 
CAS 
PubMed 
PubMed Central 

Google Scholar 
Song, Z., Chen, H., Fiket, M., Alexander, C. & Chan, D. C. OPA1 processing controls mitochondrial fusion and is regulated by mRNA splicing, membrane potential, and Yme1L. J. Cell Biol. 178, 749–755 (2007).Article 
CAS 
PubMed 
PubMed Central 

Google Scholar 
Yu, R., Jin, S.-B., Lendahl, U., Nistér, M. & Zhao, J. Human Fis1 regulates mitochondrial dynamics through inhibition of the fusion machinery. EMBO J. 38, e99748 (2019).Article 
PubMed 
PubMed Central 

Google Scholar 
van der Bliek, A. M., Shen, Q. & Kawajiri, S. Mechanisms of mitochondrial fission and fusion. Cold Spring Harb. Perspect. Biol. 5, a011072 (2013).PubMed 
PubMed Central 

Google Scholar 
Smirnova, E., Griparic, L., Shurland, D. L. & van der Bliek, A. M. Dynamin-related protein Drp1 is required for mitochondrial division in mammalian cells. Mol. Biol. Cell 12, 2245–2256 (2001).Article 
CAS 
PubMed 
PubMed Central 

Google Scholar 
Losón, O. C., Song, Z., Chen, H. & Chan, D. C. Fis1, Mff, MiD49, and MiD51 mediate Drp1 recruitment in mitochondrial fission. Mol. Biol. Cell 24, 659–667 (2013).Article 
PubMed 
PubMed Central 

Google Scholar 
Liesa, M. & Shirihai, O. S. Mitochondrial dynamics in the regulation of nutrient utilization and energy expenditure. Cell Metab. 17, 491–506 (2013).Article 
CAS 
PubMed 
PubMed Central 

Google Scholar 
Mishra, P. & Chan, D. C. Metabolic regulation of mitochondrial dynamics. J. Cell Biol. 212, 379–387 (2016).Article 
CAS 
PubMed 
PubMed Central 

Google Scholar 
Wai, T. & Langer, T. Mitochondrial dynamics and metabolic regulation. Trends Endocrinol. Metab. 27, 105–117 (2016).Article 
CAS 
PubMed 

Google Scholar 
Dai, W. & Jiang, L. Dysregulated mitochondrial dynamics and metabolism in obesity, diabetes, and cancer. Front Endocrinol. (Lausanne) 10, 570 (2019).Article 
PubMed 

Google Scholar 
Glancy, B., Kim, Y., Katti, P. & Willingham, T. B. The functional impact of mitochondrial structure across subcellular scales. Front. Physiol. 11, 541040 (2020).Article 
PubMed 
PubMed Central 

Google Scholar 
Chen, H. & Chan, D. C. Mitochondrial dynamics in regulating the unique phenotypes of cancer and stem cells. Cell Metab. 26, 39–48 (2017).Article 
CAS 
PubMed 
PubMed Central 

Google Scholar 
Ma, Y., Wang, L. & Jia, R. The role of mitochondrial dynamics in human cancers. Am. J. Cancer Res. 10, 1278–1293 (2020).CAS 
PubMed 
PubMed Central 

Google Scholar 
Srinivasan, S., Guha, M., Kashina, A. & Avadhani, N. G. Mitochondrial dysfunction and mitochondrial dynamics-The cancer connection. Biochim. Biophys. Acta Bioenerg. 1858, 602–614 (2017).Article 
CAS 
PubMed 

Google Scholar 
Kennedy, E. D. et al. Glucose-stimulated insulin secretion correlates with changes in mitochondrial and cytosolic Ca2+ in aequorin-expressing INS-1 cells. J. Clin. Invest. 98, 2524–2538 (1996).Article 
CAS 
PubMed 
PubMed Central 

Google Scholar 
Wiederkehr, A. & Wollheim, C. B. Mitochondrial signals drive insulin secretion in the pancreatic β-cell. Mol. Cell. Endocrinol. 353, 128–137 (2012).Article 
CAS 
PubMed 

Google Scholar 
Jhun, B. S., Lee, H., Jin, Z.-G. & Yoon, Y. Glucose stimulation induces dynamic change of mitochondrial morphology to promote insulin secretion in the insulinoma cell line INS-1E. PLoS ONE 8, e60810 (2013).Article 
CAS 
PubMed 
PubMed Central 

Google Scholar 
Komatsu, M., Takei, M., Ishii, H. & Sato, Y. Glucose-stimulated insulin secretion: A newer perspective. J. Diabetes Investig. 4, 511–516 (2013).Article 
CAS 
PubMed 
PubMed Central 

Google Scholar 
Schultz, J. et al. Precise expression of Fis1 is important for glucose responsiveness of beta cells. J. Endocrinol. 230, 81–91 (2016).Article 
CAS 
PubMed 

Google Scholar 
Patel, P. K., Shirihai, O. & Huang, K. C. Optimal dynamics for quality control in spatially distributed mitochondrial networks. PLoS Comput. Biol. 9, e1003108 (2013).Article 
CAS 
PubMed 
PubMed Central 

Google Scholar 
Haythorne, E. et al. Diabetes causes marked inhibition of mitochondrial metabolism in pancreatic β-cells. Nat. Commun. 10, 2474 (2019).Article 
PubMed 
PubMed Central 

Google Scholar 
Szendroedi, J., Phielix, E. & Roden, M. The role of mitochondria in insulin resistance and type 2 diabetes mellitus. Nat. Rev. Endocrinol. 8, 92–103 (2011).Article 
PubMed 

Google Scholar 
Panchal, K. & Tiwari, A. K. Mitochondrial dynamics, a key executioner in neurodegenerative diseases. Mitochondrion 47, 151–173 (2019).Article 
CAS 
PubMed 

Google Scholar 
Rovira-Llopis, S. et al. Mitochondrial dynamics in type 2 diabetes: Pathophysiological implications. Redox Biol. 11, 637–645 (2017).Article 
CAS 
PubMed 
PubMed Central 

Google Scholar 
Rutter, G. A., Georgiadou, E., Martinez-Sanchez, A. & Pullen, T. J. Metabolic and functional specialisations of the pancreatic beta cell: gene disallowance, mitochondrial metabolism and intercellular connectivity. Diabetologia 63, 1990–1998 (2020).Article 
CAS 
PubMed 
PubMed Central 

Google Scholar 
Shah, S. I., Paine, J. G., Perez, C. & Ullah, G. Mitochondrial fragmentation and network architecture in degenerative diseases. PLoS ONE 14, e0223014 (2019).Article 
CAS 
PubMed 
PubMed Central 

Google Scholar 
Supale, S., Li, N., Brun, T. & Maechler, P. Mitochondrial dysfunction in pancreatic β cells. Trends Endocrinol. Metab. 23, 477–487 (2012).Article 
CAS 
PubMed 

Google Scholar 
Chaudhry, A., Shi, R. & Luciani, D. S. A pipeline for multidimensional confocal analysis of mitochondrial morphology, function, and dynamics in pancreatic β-cells. Am. J. Physiol. Endocrinol. Metab. 318, E87–E101 (2020).Article 
CAS 
PubMed 

Google Scholar 
Lovy, A., Molina, A. J. A., Cerqueira, F. M., Trudeau, K. & Shirihai, O. S. A faster, high resolution, mtPA-GFP-based mitochondrial fusion assay acquiring kinetic data of multiple cells in parallel using confocal microscopy. J. Vis. Exp. e3991 https://doi.org/10.3791/3991 (2012)Zhang, C.-L., Rodenkirch, L., Schultz, J. R. & Chiu, S. Y. A novel method to study the local mitochondrial fusion in myelinated axons in vivo. J. Neurosci. Methods 207, 51–58 (2012).Article 
CAS 
PubMed 
PubMed Central 

Google Scholar 
Cortassa, S. & Aon, M. A. Computational modeling of mitochondrial function. Methods Mol. Biol. 810, 311–326 (2012).Article 
CAS 
PubMed 
PubMed Central 

Google Scholar 
Cortassa, S., O’Rourke, B., Winslow, R. L. & Aon, M. A. Control and regulation of mitochondrial energetics in an integrated model of cardiomyocyte function. Biophys. J. 96, 2466–2478 (2009).Article 
CAS 
PubMed 
PubMed Central 

Google Scholar 
Gauthier, L. D., Greenstein, J. L. & Winslow, R. L. Toward an integrative computational model of the Guinea pig cardiac myocyte. Front. Physiol. 3, 244 (2012).Article 
PubMed 
PubMed Central 

Google Scholar 
Nguyen, M.-H. T., Dudycha, S. J. & Jafri, M. S. Effect of Ca2+ on cardiac mitochondrial energy production is modulated by Na+ and H+ dynamics. Am. J. Physiol., Cell Physiol. 292, C2004–C2020 (2007).Article 
CAS 
PubMed 

Google Scholar 
Wei, A.-C., Liu, T., Cortassa, S., Winslow, R. L. & O’Rourke, B. Mitochondrial Ca2+ influx and efflux rates in guinea pig cardiac mitochondria: low and high affinity effects of cyclosporine A. Biochim. Biophys. Acta 1813, 1373–1381 (2011).Article 
CAS 
PubMed 
PubMed Central 

Google Scholar 
Zhou, L. et al. Modeling cardiac action potential shortening driven by oxidative stress-induced mitochondrial oscillations in guinea pig cardiomyocytes. Biophys. J. 97, 1843–1852 (2009).Article 
CAS 
PubMed 
PubMed Central 

Google Scholar 
Magnus, G. & Keizer, J. Minimal model of beta-cell mitochondrial Ca2+ handling. Am. J. Physiol. 273, C717–C733 (1997).Article 
CAS 
PubMed 

Google Scholar 
Bertram, R., Gram Pedersen, M., Luciani, D. S. & Sherman, A. A simplified model for mitochondrial ATP production. J. Theor. Biol. 243, 575–586 (2006).Article 
CAS 
PubMed 

Google Scholar 
Saa, A. & Siqueira, K. M. Modeling the ATP production in mitochondria. Bull. Math. Biol. 75, 1636–1651 (2013).Article 
CAS 
PubMed 

Google Scholar 
Fridlyand, L. E. & Philipson, L. H. Glucose sensing in the pancreatic beta cell: a computational systems analysis. Theor. Biol. Med. Model. 7, 15 (2010).Article 
PubMed 
PubMed Central 

Google Scholar 
Fridlyand, L. E., Tamarina, N. & Philipson, L. H. Bursting and calcium oscillations in pancreatic beta-cells: specific pacemakers for specific mechanisms. Am. J. Physiol. Endocrinol. Metab. 299, E517–E532 (2010).Article 
CAS 
PubMed 
PubMed Central 

Google Scholar 
Fridlyand, L. E. & Philipson, L. H. Pancreatic beta cell G-protein coupled receptors and second messenger interactions: A systems biology computational analysis. PLoS ONE 11, e0152869 (2016).Article 
PubMed 
PubMed Central 

Google Scholar 
Fridlyand, L. E., Ma, L. & Philipson, L. H. Adenine nucleotide regulation in pancreatic beta-cells: modeling of ATP/ADP-Ca2+ interactions. Am. J. Physiol. Endocrinol. Metab. 289, E839–E848 (2005).Article 
CAS 
PubMed 

Google Scholar 
Dalmasso, G., Marin Zapata, P. A., Brady, N. R. & Hamacher-Brady, A. Agent-based modeling of mitochondria links sub-cellular dynamics to cellular homeostasis and heterogeneity. PLoS ONE 12, e0168198 (2017).Article 
PubMed 
PubMed Central 

Google Scholar 
Hoffman, T. E., Barnett, K. J., Wallis, L. & Hanneman, W. H. A multimethod computational simulation approach for investigating mitochondrial dynamics and dysfunction in degenerative aging. Aging Cell 16, 1244–1255 (2017).Article 
CAS 
PubMed 
PubMed Central 

Google Scholar 
Tam, Z. Y., Gruber, J., Halliwell, B. & Gunawan, R. Mathematical modeling of the role of mitochondrial fusion and fission in mitochondrial DNA maintenance. PLoS ONE 8, e76230 (2013).Article 
CAS 
PubMed 
PubMed Central 

Google Scholar 
Sukhorukov, V. M., Dikov, D., Reichert, A. S. & Meyer-Hermann, M. Emergence of the mitochondrial reticulum from fission and fusion dynamics. PLoS Comput. Biol. 8, e1002745 (2012).Article 
CAS 
PubMed 
PubMed Central 

Google Scholar 
Kornick, K., Bogner, B., Sutter, L. & Das, M. Population dynamics of mitochondria in cells: A minimal mathematical model. Front. Phys. 7, 146 (2019).Lefebvre, A. E. Y. T., Ma, D., Kessenbrock, K., Lawson, D. A. & Digman, M. A. Automated segmentation and tracking of mitochondria in live-cell time-lapse images. Nat. Methods 18, 1091–1102 (2021).Article 
CAS 
PubMed 

Google Scholar 
Gregg, T. et al. Pancreatic β-cells from mice offset age-associated mitochondrial deficiency with reduced KATP channel activity. Diabetes 65, 2700–2710 (2016).Article 
CAS 
PubMed 
PubMed Central 

Google Scholar 
Lowell, B. B. & Shulman, G. I. Mitochondrial dysfunction and type 2 diabetes. Science 307, 384–387 (2005).Article 
CAS 
PubMed 

Google Scholar 
Liesa, M., Palacín, M. & Zorzano, A. Mitochondrial dynamics in mammalian health and disease. Physiol. Rev. 89, 799–845 (2009).Article 
CAS 
PubMed 

Google Scholar 
Boissan, M. et al. Membrane trafficking. Nucleoside diphosphate kinases fuel dynamin superfamily proteins with GTP for membrane remodeling. Science 344, 1510–1515 (2014).Article 
CAS 
PubMed 
PubMed Central 

Google Scholar 
Lacombe, M.-L., Tokarska-Schlattner, M., Boissan, M. & Schlattner, U. The mitochondrial nucleoside diphosphate kinase (NDPK-D/NME4), a moonlighting protein for cell homeostasis. Lab. Invest. 98, 582–588 (2018).Article 
CAS 
PubMed 

Google Scholar 
Tokarska-Schlattner, M. et al. The nucleoside diphosphate kinase D (NM23-H4) binds the inner mitochondrial membrane with high affinity to cardiolipin and couples nucleotide transfer with respiration. J. Biol. Chem. 283, 26198–26207 (2008).Article 
CAS 
PubMed 
PubMed Central 

Google Scholar 
Schlattner, U. et al. NME4/nucleoside diphosphate kinase D in cardiolipin signaling and mitophagy. Lab. Invest. 98, 228–232 (2018).Article 
CAS 
PubMed 

Google Scholar 
Benard, G. et al. Mitochondrial bioenergetics and structural network organization. J. Cell Sci. 120, 838–848 (2007).Article 
CAS 
PubMed 

Google Scholar 
Koopman, W. J. H. et al. Inhibition of complex I of the electron transport chain causes O2-. -mediated mitochondrial outgrowth. Am. J. Physiol., Cell Physiol. 288, C1440–C1450 (2005).Article 
CAS 
PubMed 

Google Scholar 
Shiratori, R. et al. Glycolytic suppression dramatically changes the intracellular metabolic profile of multiple cancer cell lines in a mitochondrial metabolism-dependent manner. Sci. Rep. 9, 18699 (2019).Article 
CAS 
PubMed 
PubMed Central 

Google Scholar 
Anello, M. et al. Functional and morphological alterations of mitochondria in pancreatic beta cells from type 2 diabetic patients. Diabetologia 48, 282–289 (2005).Article 
CAS 
PubMed 

Google Scholar 
Sivitz, W. I. & Yorek, M. A. Mitochondrial dysfunction in diabetes: from molecular mechanisms to functional significance and therapeutic opportunities. Antioxid. Redox Signal. 12, 537–577 (2010).Article 
CAS 
PubMed 
PubMed Central 

Google Scholar 
Dlasková, A. et al. 4Pi microscopy reveals an impaired three-dimensional mitochondrial network of pancreatic islet beta-cells, an experimental model of type-2 diabetes. Biochim. Biophys. Acta 1797, 1327–1341 (2010).Article 
PubMed 

Google Scholar 
Amartuvshin, O. et al. Aging shifts mitochondrial dynamics toward fission to promote germline stem cell loss. Aging Cell 19, e13191 (2020).Article 
CAS 
PubMed 
PubMed Central 

Google Scholar 
Yu, T., Robotham, J. L. & Yoon, Y. Increased production of reactive oxygen species in hyperglycemic conditions requires dynamic change of mitochondrial morphology. Proc. Natl Acad. Sci. USA 103, 2653–2658 (2006).Article 
CAS 
PubMed 
PubMed Central 

Google Scholar 
Lien, E. C. & Vander Heiden, M. G. Pancreatic β cells put the glutamine engine in reverse. Cell Metab. 33, 702–704 (2021).Article 
CAS 
PubMed 

Google Scholar 
Stark, R. & Kibbey, R. G. The mitochondrial isoform of phosphoenolpyruvate carboxykinase (PEPCK-M) and glucose homeostasis: has it been overlooked? Biochim. Biophys. Acta 1840, 1313–1330 (2014).Article 
CAS 
PubMed 

Google Scholar 
Zhang, G.-F. et al. Reductive TCA cycle metabolism fuels glutamine- and glucose-stimulated insulin secretion. Cell Metab. 33, 804–817.e5 (2021).Article 
CAS 
PubMed 

Google Scholar 
Jesinkey, S. R. et al. Mitochondrial GTP links nutrient sensing to β cell health, mitochondrial morphology, and insulin secretion independent of oxphos. Cell Rep. 28, 759–772.e10 (2019).Article 
CAS 
PubMed 
PubMed Central 

Google Scholar 
Bertram, R., Sherman, A. & Satin, L. S. Electrical, calcium, and metabolic oscillations in pancreatic islets. in Islets of Langerhans (ed. Islam, Md. S.) 453–474 (Springer Netherlands). :https://doi.org/10.1007/978-94-007-6686-0_10 2015Klec, C., Ziomek, G., Pichler, M., Malli, R. & Graier, W. F. Calcium signaling in ß-cell physiology and pathology: A revisit. Int. J. Mol. Sci. 20, 6110 (2019).Kaddour-Djebbar, I. et al. Specific mitochondrial calcium overload induces mitochondrial fission in prostate cancer cells. Int. J. Oncol. 36, 1437–1444 (2010).CAS 
PubMed 

Google Scholar 
Zhou, X. et al. Mitochondrial dynamics: A potential therapeutic target for ischemic stroke. Front. Aging Neurosci. 13, 721428 (2021).Article 
CAS 
PubMed 
PubMed Central 

Google Scholar 
Curry, D. W., Stutz, B., Andrews, Z. B. & Elsworth, J. D. Targeting AMPK signaling as a neuroprotective strategy in parkinson’s disease. J. Parkinsons Dis. 8, 161–181 (2018).Article 
PubMed 
PubMed Central 

Google Scholar 
Lin, S.-C. & Hardie, D. G. AMPK: Sensing glucose as well as cellular energy status. Cell Metab. 27, 299–313 (2018).Article 
CAS 
PubMed 

Google Scholar 
Toyama, E. Q. et al. Metabolism. AMP-activated protein kinase mediates mitochondrial fission in response to energy stress. Science 351, 275–281 (2016).Article 
CAS 
PubMed 
PubMed Central 

Google Scholar 
Khacho, M. et al. Mitochondrial dynamics impacts stem cell identity and fate decisions by regulating a nuclear transcriptional program. Cell Stem Cell 19, 232–247 (2016).Article 
CAS 
PubMed 

Google Scholar 
Tseng, W.-W. ntumitolab/mitodyn-ode: 20240813. Zenodo https://doi.org/10.5281/zenodo.13309321 (2024).Dash, R. K. & Beard, D. A. Analysis of cardiac mitochondrial Na + -Ca2+ exchanger kinetics with a biophysical model of mitochondrial Ca2+ handling suggests a 3:1 stoichiometry. J. Physiol. (Lond.) 586, 3267–3285 (2008).Article 
CAS 
PubMed 

Google Scholar 
Golding, E. M., Teague, W. E. & Dobson, G. P. Adjustment of K’ to varying pH and pMg for the creatine kinase, adenylate kinase and ATP hydrolysis equilibria permitting quantitative bioenergetic assessment. J. Exp. Biol. 198, 1775–1782 (1995).Article 
CAS 
PubMed 

Google Scholar 
Nicholls, D. G. The pancreatic β-cell: A bioenergetic perspective. Physiol. Rev. 96, 1385–1447 (2016).Article 
CAS 
PubMed 

Google Scholar 
Bezanson, J., Edelman, A., Karpinski, S. & Shah, V. B. Julia: A fresh approach to numerical computing. SIAM Rev. 59, 65–98 (2017).Rackauckas, C. & Nie, Q. DifferentialEquations.jl – A performant and feature-rich ecosystem for solving differential equations in Julia. J. Open Res. Softw. 5, (2017).Ma, Y. et al. ModelingToolkit: A composable graph transformation system for equation-based modeling. arXiv https://doi.org/10.48550/arxiv.2103.05244 (2021).Hunter, J. D. Matplotlib: A 2D graphics environment. Comput. Sci. Eng. 9, 90–95 (2007).Article 

Google Scholar 
Tseng, W.-W. ntumitolab/Mitochondrial-Network-Model: 20240807. Zenodo https://doi.org/10.5281/zenodo.13254168 (2024).

Hot Topics

Related Articles