Finite volume simulation of calcium distribution in a cholangiocyte cell

Year 2023, , 17 - 32, 31.03.2023

Nakul Nakul Vedika Mishra Neeru Adlakha

https://doi.org/10.53391/mmnsa.1273945

Cited By: 5

Abstract

Cholangiocytes are the cells of the liver having a major role in the conditioning of bile used in digestion. Other functions of cholangiocytes are in apoptosis and bicarbonate secretion. The Calcium in the intracellular environment of various cells including cholangiocytes regulates a large number of functions. This regulating mechanism in cholangiocytes has been poorly understood to date. In order to analyze the calcium regulation in cholangiocyte cells, a mathematical model for a one-dimensional steady-state case is constructed in this study. This involves a non-linear reaction-diffusion equation with appropriate boundary conditions. The influx from IP$_{3}$ receptor, ryanodine receptor (RYR), and plasma membrane as well as the efflux of calcium from SERCA pump and plasma membrane have been employed in the model. The finite volume method and Newton-Raphson method have been used to solve the problem. Numerical findings have been used to examine the effects of parameters like diffusion coefficient, rate of SERCA pump efflux, buffer, and influx from plasma membrane on calcium concentration in cholangiocyte cells. The information generated from the model can be useful for understanding the mechanism of cholestatic disorders which can be further useful in the diagnosis and treatment of these disorders.

Keywords

Liver, reaction-diffusion equation, calcium, finite volume method, Newton-Raphson method

References

• Wake, K. Perisinusoidal stellate cells (fat-storing cells, interstitial cells, lipocytes), their related structure in and around the liver sinusoids, and vitamin A-storing cells in extrahepatic organs. International review of cytology, 66, 303-353, (1980).
• Tabibian, J.H., Masyuk, A.I., Masyuk, T.V., O’Hara, S.P., & LaRusso, N.F. Physiology of cholangiocytes. Comprehensive Physiology, 3(1), (2013).
• Wang, D.Q.H., Neuschwander-Tetri, B.A., & Portincasa, P. The Biliary System, Colloquium Series on Integrated Systems Physiology: From Molecule to Function. Morgan & Claypool, 109-145, (2012).
• Bouwens, L., De Bleser, P., Vanderkerken, K., Geerts, B., & Wisse, E. Liver cell heterogeneity: functions of non-parenchymal cells. Enzyme, 46, 155-168, (1992).
• Strazzabosco, M., & Fabris, L. Functional anatomy of normal bile ducts. The Anatomical Record: Advances in Integrative Anatomy and Evolutionary Biology, 291(6), 653-660, (2008).
• Minagawa, N., Kruglov, E.A., Dranoff, J.A., Robert, M.E., Gores, G.J., & Nathanson, M.H. The anti-apoptotic protein Mcl-1 inhibits mitochondrial Ca2+ signals. Journal of Biological Chemistry, 280(39), 33637-33644, (2005).
• Fiorotto, R., Spirlì, C., Fabris, L., Cadamuro, M., Okolicsanyi, L., & Strazzabosco, M. Ursodeoxycholic acid stimulates cholangiocyte fluid secretion in mice via CFTR-dependent ATP secretion. Gastroenterology, 133(5), 1603-1613, (2007).
• Li, Q., Dutta, A., Kresge, C., Bugde, A., & Feranchak, A.P. Bile acids stimulate cholangiocyte fluid secretion by activation of transmembrane member 16A Cl− channels. Hepatology, 68(1), 187-199, (2018).
• Hirata, K., Dufour, J.F., Shibao, K., Knickelbein, R., O’Neill, A.F., Bode, H.P., ... & Nathanson, M.H. Regulation of Ca2+ signaling in rat bile duct epithelia by inositol 1, 4, 5-trisphosphate receptor isoforms. Hepatology, 36(2), 284-296, (2002).
• Kotwani, M., & Adlakha, N. Modeling of endoplasmic reticulum and plasma membrane Ca2+ uptake and release fluxes with excess buffer approximation (EBA) in fibroblast cell. International Journal of Computational Materials Science and Engineering, 6(01), 1750004, (2017).
• Panday, S., & Pardasani, K. R. Finite element model to study effect of advection diffusion and Na+/Ca2+ exchanger on Ca2+ distribution in oocytes. Journal of medical imaging and health informatics, 3(3), 374-379, (2013).
• Naik, P.A., & Pardasani, K.R. One dimensional finite element model to study calcium distribution in oocytes in presence of VGCC, RyR and buffers. Journal of Medical Imaging and Health Informatics, 5(3), 471-476, (2015).
• Naik, P.A., & Pardasani, K.R. Finite element model to study calcium distribution in oocytes involving voltage gated Ca2+ channel, ryanodine receptor and buffers. Alexandria Journal of Medicine, 52(1), 43-49, (2016).
• Naik, P.A., & Pardasani, K.R. Three-dimensional finite element model to study effect of RyR calcium channel, ER leak and SERCA pump on calcium distribution in oocyte cell. International Journal of Computational Methods, 16(01), 1850091, (2019).
• Jha, B.K., Adlakha, N., & Mehta, M.N. Finite element model to study calcium diffusion in astrocytes. Int. J. of Pure and Appl. Math, 78(7), 945-955, (2012).
• Jha, A., & Adlakha, N. Finite element model to study the effect of exogenous buffer on calcium dynamics in dendritic spines. International Journal of Modeling, Simulation, and Scientific Computing, 5(02), 1350027, (2014).
• Jha, A., Adlakha, N., & Jha, B.K. Finite element model to study effect of Na+-Ca2+ exchangers and source geometry on calcium dynamics in a neuron cell. Journal of Mechanics in Medicine and Biology, 16(02), 1650018, (2016).
• Jha, A., & Adlakha, N. Two-dimensional finite element model to study unsteady state Ca2+ diffusion in neuron involving ER LEAK and SERCA. International Journal of Biomathematics, 8(01), 1550002, (2015).
• Pathak, K.B., & Adlakha, N. Finite element model to study calcium signalling in cardiac myocytes involving pump, leak and excess buffer. Journal of Medical Imaging and Health Informatics, 5(4), 683-688, (2015).
• Manhas, N., & Anbazhagan, N. A mathematical model of intricate calcium dynamics and modulation of calcium signalling by mitochondria in pancreatic acinar cells. Chaos, Solitons & Fractals, 145, 110741, (2021).
• Manhas, N., & Pardasani, K.R. Mathematical model to study IP3 dynamics dependent calcium oscillations in pancreatic acinar cells. Journal of Medical Imaging and Health Informatics, 4(6), 874-880, (2014).
• Manhas, N., & Pardasani, K.R. Modelling mechanism of calcium oscillations in pancreatic acinar cells. Journal of bioenergetics and biomembranes, 46, 403-420, (2014).
• Tewari, S.G., & Pardasani, K.R. Modeling effect of sodium pump on calcium oscillations in neuron cells. Journal of Multiscale Modelling, 4(03), 1250010, (2012).
• Tewari, S., & Pardasani, K.R. Finite element model to study two dimensional unsteady state cytosolic calcium diffusion in presence of excess buffers. IAENG International Journal of Applied Mathematics, 40(3), 108-112, (2010).
• Jagtap, Y., & Adlakha, N. Numerical study of one-dimensional buffered advection–diffusion of calcium and IP3 in a hepatocyte cell. Network Modeling Analysis in Health Informatics and Bioinformatics, 8(1), 25, (2019).
• Jagtap, Y., & Adlakha, N. Finite volume simulation of two dimensional calcium dynamics in a hepatocyte cell involving buffers and fluxes. Communications in Mathematical Biology and Neuroscience, (2018).
• Kumar, H., Naik, P.A., & Pardasani, K.R. Finite element model to study calcium distribution in T lymphocyte involving buffers and ryanodine receptors. Proceedings of the National Academy of Sciences, India Section A: Physical Sciences, 88, 585-590, (2018).
• Kothiya, A., & Adlakha, N. Model of Calcium Dynamics Regulating IP3 and ATP Production in a Fibroblast Cell. Advances in Systems Science and Applications, 22(3), 49-69, (2022).
• Kothiya, A.B., & Adlakha, N. Cellular nitric oxide synthesis is affected by disorders in the interdependent Ca2+ and IP3 dynamics during cystic fibrosis disease. Journal of Biological Physics, 1-26, (2023).
• Bhardwaj, H., & Adlakha, N. Radial Basis Function Based Differential Quadrature Approach to Study Reaction Diffusion of Ca2+ in T Lymphocyte. International Journal of Computational Methods, (2022).
• Minagawa, N., Nagata, J., Shibao, K., Masyuk, A.I., Gomes, D.A., Rodrigues, M.A., ... & Nathanson, M.H. Cyclic AMP regulates bicarbonate secretion in cholangiocytes through release of ATP into bile. Gastroenterology, 133(5), 1592-1602, (2007).
• Nathanson, M.H., Burgstahler, A.D., Mennone, A.L.B.E.R.T., & Boyer, J.L. Characterization of cytosolic Ca2+ signaling in rat bile duct epithelia. American Journal of Physiology-Gastrointestinal and Liver Physiology, 271(1), G86-G96, (1996).
• Woo, K., Dutta, A.K., Patel, V., Kresge, C., & Feranchak, A.P. Fluid flow induces mechanosensitive ATP release, calcium signalling and Cl− transport in biliary epithelial cells through a PKCγ-dependent pathway. The Journal of physiology, 586(11), 2779-2798, (2008).
• Weerachayaphorn, J., Amaya, M.J., Spirli, C., Chansela, P., Mitchell-Richards, K.A., Ananthanarayanan, M., & Nathanson, M.H. Nuclear factor, erythroid 2-like 2 regulates expression of type 3 inositol 1, 4, 5-trisphosphate receptor and calcium signaling in cholangiocytes. Gastroenterology, 149(1), 211-222, (2015).
• Ueasilamongkol, P., Khamphaya, T., Guerra, M. T., Rodrigues, M.A., Gomes, D.A., Kong, Y., ... & Weerachayaphorn, J. Type 3 inositol 1, 4, 5-trisphosphate receptor is increased and enhances malignant properties in cholangiocarcinoma. Hepatology, 71(2), 583-599, (2020).
• Shibao, K., Hirata, K., Robert, M.E., & Nathanson, M.H. Loss of inositol 1, 4, 5-trisphosphate receptors from bile duct epithelia is a common event in cholestasis. Gastroenterology, 125(4), 1175-1187, (2003).
• Rodrigues, M.A., Gomes, D.A., & Nathanson, M.H. Calcium signaling in cholangiocytes: methods, mechanisms, and effects. International Journal of Molecular Sciences, 19(12), 3913, (2018).
• Masyuk, A.I., Masyuk, T.V., Splinter, P.L., Huang, B.Q., Stroope, A.J., & LaRusso, N.F. Cholangiocyte cilia detect changes in luminal fluid flow and transmit them into intracellular Ca2+ and cAMP signaling. Gastroenterology, 131(3), 911-920, (2006).
• Marzioni, M., Alpini, G., Saccomanno, S., Candelaresi, C., Venter, J., Rychlicki, C., ... & Benedetti, A. Glucagon-like peptide-1 and its receptor agonist exendin-4 modulate cholangiocyte adaptive response to cholestasis. Gastroenterology, 133(1), 244-255, (2007).
• Martin, J., & Dufour, J.F. Cholestasis shuts down calcium signaling in cholangiocytes. Hepatology, 39(1), 248-249, (2004).
• Maroni, L., Haibo, B., Ray, D., Zhou, T., Wan, Y., Meng, F., ... & Alpini, G. Functional and structural features of cholangiocytes in health and disease. Cellular and molecular gastroenterology and hepatology, 1(4), 368-380, (2015).
• Lazaridis, K.N., Strazzabosco, M., & LaRusso, N.F. The cholangiopathies: disorders of biliary epithelia. Gastroenterology, 127(5), 1565-1577, (2004).
• Jung, J., & Lee, M.G. Role of calcium signaling in epithelial bicarbonate secretion. Cell Calcium, 55(6), 376-384, (2014).
• Guerra, M.T., & Nathanson, M.H. Calcium signaling and secretion in cholangiocytes. Pancreatology, 15(4), S44-S48, (2015).
• Amaya, M.J., & Nathanson, M.H. Calcium signaling and the secretory activity of bile duct epithelia. Cell Calcium, 55(6), 317-324, (2014).
• Shin, D.H., Kim, M., Kim, Y., Jun, I., Jung, J., Nam, J.H., ... & Lee, M.G. Bicarbonate permeation through anion channels: its role in health and disease. Pflügers Archiv-European Journal of Physiology, 472, 1003-1018, (2020).
• Alpini, G., Glaser, S.S., Rodgers, R., Phinizy, J.L., Robertson, W.E., Lasater, J., ... & LeSage, G.D. Functional expression of the apical Na+-dependent bile acid transporter in large but not small rat cholangiocytes. Gastroenterology, 113(5), 1734-1740, (1997).
• Lopez-Caamal, F., Oyarzún, D.A., Middleton, R. H., & García, M.R. Spatial Quantification of Cytosolic Ca2+ Accumulation in Non excitable Cells: An Analytical Study. IEEE/ACM Transactions on Computational Biology and Bioinformatics, 11(3), 592-603, (2014).
• Pawar, A., & Pardasani, K.R. Effect of disturbances in neuronal calcium and IP3 dynamics on β-amyloid production and degradation. Cognitive Neurodynamics, 1-18, (2022).
• Pawar, A., & Pardasani, K.R. Simulation of disturbances in interdependent calcium and β-amyloid dynamics in the nerve cell. The European Physical Journal Plus, 137(8), 1-23, (2022).
• Pawar, A., & Pardasani, K.R. Study of disorders in regulatory spatiotemporal neurodynamics of calcium and nitric oxide. Cognitive Neurodynamics, 1-22, (2022).
• Pawar, A., & Pardasani, K.R. Computational model of calcium dynamics-dependent dopamine regulation and dysregulation in a dopaminergic neuron cell. The European Physical Journal Plus, 138(1), 30, (2023).
• Pawar, A., & Raj Pardasani, K. Effects of disorders in interdependent calcium and IP3 dynamics on nitric oxide production in a neuron cell. The European Physical Journal Plus, 137(5), 1-19, (2022).
• Pankratova, E.V., Sinitsina, M.S., Gordleeva, S., & Kazantsev, V.B. Bistability and Chaos Emergence in Spontaneous Dynamics of Astrocytic Calcium Concentration. Mathematics, 10(8), 1337, (2022).
• Joshi, H., & Jha, B.K. 2D dynamic analysis of the disturbances in the calcium neuronal model and its implications in neurodegenerative disease. Cognitive Neurodynamics, 1-12, (2022).
• Joshi, H., & Jha, B.K. 2D memory-based mathematical analysis for the combined impact of calcium influx and efflux on nerve cells. Computers & Mathematics with Applications, 134, 33-44, (2023).
• Tarifa, C., Vallmitjana, A., Jiménez-Sábado, V., Marchena, M., Llach, A., Herraiz-Martínez, A., ... & Hove-Madsen, L. Spatial distribution of calcium sparks determines their ability to induce afterdepolarizations in human atrial myocytes. Basic to Translational Science, 8(1), 1-15, (2023).
• Chang, Y., Funk, M., Roy, S., Stephenson, E., Choi, S., Kojouharov, H. V., ... & Pan, Z. Developing a mathematical model of intracellular calcium dynamics for evaluating combined anticancer effects of afatinib and RP4010 in esophageal cancer. International Journal of Molecular Sciences, 23(3), 1763, (2022).55(6), 376-384, (2014).
• Joshi, H., & Jha, B.K. Chaos of calcium diffusion in Parkinson’s infectious disease model and treatment mechanism via Hilfer fractional derivative. Mathematical Modelling and Numerical Simulation with Applications, 1(2), 84-94, (2021).
• Naik, P.A. Modeling the mechanics of calcium regulation in T lymphocyte: a finite element method approach. International Journal of Biomathematics, 13(05), 2050038, (2020).
• Naik, P.A., Eskandari, Z., & Shahraki, H.E. Flip and generalized flip bifurcations of a twodimensional discrete-time chemical model. Mathematical Modelling and Numerical Simulation with Applications, 1(2), 95-101, (2021).
• Naik, P.A., & Pardasani, K.R. Two dimensional finite element model to study calcium distribution in oocytes. Journal of Multiscale Modelling, 6(01), 1450002, (2015).
• Jha, B.K., & Joshi, H. A Fractional Mathematical Model to Study the Effect of Buffer and Endoplasmic Reticulum on Cytosolic Calcium Concentration in Nerve Cells. In Fractional Calculus in Medical and Health Science (pp. 211-227), CRC Press, (2020).