Agarwal SR, Clancy CE, Harvey RD (2016) Mechanisms restricting diffusion of intracellular \(cAMP\). Sci Rep 6(1):19577. https://doi.org/10.1038/srep19577

Bhardwaj H, Adlakha N (2022) Radial basis function based differential quadrature approach to study reaction diffusion of \(Ca^\) in T Lymphocyte. Int J Comput Methods. https://doi.org/10.1142/S0219876222500591

Bhardwaj H, Adlakha N (2023) Fractional order reaction diffusion of calcium regulating NFAT production in T Lymphocyte. Int J Biomath. https://doi.org/10.1142/S1793524523500547

Bhardwaj H, Adlakha N (2023) Model to study interdependent calcium and \(IP_\) distribution regulating NFAT production in T lymphocyte. J Mech Med Biol. https://doi.org/10.1007/s00249-023-01660-1

Dave DD, Jha BK (2021) Mathematical modeling of calcium oscillatory patterns in a neuron. Interdiscip Sci Comput Life Sci 13:12–24. https://doi.org/10.1007/s12539-020-00401-8

Dupont G, Falcke M, Kirk V, Sneyd J (2016) Models of calcium signalling, vol 43. Springer, New York, USA

Falcke M (2003) Buffers and oscillations in intracellular \(Ca^\) dynamics. Biophys J 84(1):28–41

Article  CAS  PubMed  PubMed Central  Google Scholar 

Fridlyand LE, Harbeck MC, Roe MW, Philipson LH (2007) Regulation of \(cAMP\) dynamics by \(Ca^\) and G protein-coupled receptors in the pancreatic \(\beta \)-cell: a computational approach. Am J Physiol-Cell Physiol 293(6):C1924–C1933. https://doi.org/10.1152/ajpcell.00555.2006

Article  CAS  PubMed  Google Scholar 

Fridlyand LE, Philipson LH (2016) Pancreatic beta cell G-protein coupled receptors and second messenger interactions: a systems biology computational analysis. PloS One 11(5):e0152869. https://doi.org/10.1371/journal.pone.0152869

Gorbunova YV, Spitzer NC (2002) Dynamic interactions of cyclic AMP transients and spontaneous \(Ca^\) spikes. Nature 418(6893):93–96. https://doi.org/10.1038/nature00835

Higgins ER, Cannell MB, Sneyd J (2006) A buffering SERCA pump in models of calcium dynamics. Biophys J 91(1):151–163. https://doi.org/10.1529/biophysj.105.075747

Jagtap YD, Adlakha N (2018) Simulation of buffered advection diffusion of calcium in a hepatocyte cell. Math Biol Bioinform 13(2):609–619. https://doi.org/10.17537/2018.13.609

Jagtap Y, Adlakha N (2023) Numerical model of hepatic glycogen phosphorylase regulation by nonlinear interdependent dynamics of calcium and \(IP_ \). Eur Phys J Plus 138(5):1–13. https://doi.org/10.1140/epjp/s13360-023-03961-y

Jha A, Adlakha N (2014) Finite element model to study the effect of exogenous buffer on calcium dynamics in dendritic spines. Int J Model Simul Sci Comput 5(02):1350027. https://doi.org/10.1142/S179396231350027X

Jha A, Adlakha N, Jha BK (2016) Finite element model to study effect of \(Na^/Ca^\) exchangers and source geometry on calcium dynamics in a neuron cell. J Mech Med Biol 16(02):1650018. https://doi.org/10.1142/S0219519416500184

Jha BK, Adlakha N, Mehta MN (2013) Two-dimensional finite element model to study calcium distribution in astrocytes in presence of VGCC and excess buffer. Int J Model Simul Sci Comput 4(02):1250030. https://doi.org/10.1142/S1793962312500304

Jha BK, Adlakha N, Mehta MN (2014) Two-dimensional finite element model to study calcium distribution in astrocytes in presence of excess buffer. Int J Biomath 7(03):1450031. https://doi.org/10.1142/S1793524514500314

Jha BK, Joshi H, Dave DD (2018) Portraying the effect of calcium-binding proteins on cytosolic calcium concentration distribution fractionally in nerve cells. Interdiscip Sci Comput Life Sci 10:674–685. https://doi.org/10.1007/s12539-016-0202-7

Joshi H, Jha BK (2021) On a reaction-diffusion model for calcium dynamics in neurons with Mittag-Leffler memory. Eur Phys J Plus 136(6):623. https://doi.org/10.1140/epjp/s13360-021-01610-w

Keener J, Sneyd J (2009) Mathematical physiology. Springer, New York

Book  Google Scholar 

Kothiya AB, Adlakha N (2023) Cellular nitric oxide synthesis is affected by disorders in the interdependent \(Ca^\) and \(IP_3\) dynamics during cystic fibrosis disease. J Biol Phys 1–26. https://doi.org/10.1007/s10867-022-09624-w

Kothiya A, Adlakha N (2023) Simulation of biochemical dynamics of \(Ca^\) and \(PLC\) in fibroblast cell. J Bioenerg Biomembr 1–21. https://doi.org/10.1007/s10863-023-09976-5

Kothiya A, Adlakha N (2022) Model of Calcium Dynamics Regulating \(IP_3\) and \(ATP\) Production in a Fibroblast Cell. Adv Syst Sci Appl 22(3):49–69. https://doi.org/10.25728/assa.2022.22.3.1219

Kothiya A, Adlakha N (2023) Computational investigations of the and TGF-\(\beta \) dynamics in a fibroblast cell. Eur Phys J Plus 138(10):878. https://doi.org/10.1140/epjp/s13360-023-04508-x

Li YX, Rinzel J (1994) Equations for \(InsP_3\) receptor-mediated \([Ca^]_i\) oscillations derived from a detailed kinetic model: a Hodgkin-Huxley like formalism. J Theor Biol 166(4):461–473. https://doi.org/10.1006/jtbi.1994.1041

M Hofer A (2012) Interactions between calcium and cAMP signaling. Curr Med Chem 19(34):5768–5773. https://doi.org/10.2174/092986712804143286

Manhas N, Anbazhagan N (2021) A mathematical model of intricate calcium dynamics and modulation of calcium signalling by mitochondria in pancreatic acinar cells. Chaos Solit Fractals 145:110741. https://doi.org/10.1016/j.chaos.2021.110741

Manhas N, Pardasani KR (2014) Modelling mechanism of calcium oscillations in pancreatic acinar cells. J Bioenerg Biomembr 46:403–420. https://doi.org/10.1007/s10863-014-9561-0

Manhas N, Pardasani KR (2014) Mathematical model to study IP3 dynamics dependent calcium oscillations in pancreatic acinar cells. J Med Imaging Health Inf 4(6):874–880. https://doi.org/10.1166/jmihi.2014.1333

Manhas N, Sneyd J, Pardasani KR (2014) Modelling the transition from simple to complex \(Ca^\) oscillations in pancreatic acinar cells. J Biosci 39:463–484. https://doi.org/10.1007/s12038-014-9430-3

Marhl M, Haberichter T, Brumen M, Heinrich R (2000) Complex calcium oscillations and the role of mitochondria and cytosolic proteins. Biosystems 57(2):75–86. https://doi.org/10.1016/S0303-2647(00)00090-3

Mishra V, Adlakha N (2023) Numerical simulation of calcium dynamics dependent ATP degradation, \(IP_3\) and NADH production due to obesity in a hepatocyte cell. J Biol Phys 1–28. https://doi.org/10.1007/s10867-023-09639-x

Mishra V, Adlakha N (2023) Spatio temporal interdependent calcium and buffer dynamics regulating DAG in a hepatocyte cell due to obesity. J Bioenerg Biomembr 1–18. https://doi.org/10.1007/s10863-023-09973-8

Naik PA (2020) Modeling the mechanics of calcium regulation in T lymphocyte: a finite element method approach. Int J Biomath 13(05):2050038. https://doi.org/10.1142/S1793524520500382

Naik PA, Pardasani KR (2014) Finite Element Model to Study Effect of \(Na^/K^\) Pump and \(Na^/Ca^\) Exchanger on Calcium Distribution in Oocytes in Presence of Buffers. Asian J Math Stat 7(1):21

Naik PA, Pardasani KR (2016) Finite element model to study calcium distribution in oocytes involving voltage gated \(Ca^\) channel, ryanodine receptor and buffers. Alexandria J Med 52(1):43–49. https://doi.org/10.1016/j.ajme.2015.02.002

Naik PA, Pardasani KR (2019) Three-dimensional finite element model to study effect of RyR calcium channel, ER leak and SERCA pump on calcium distribution in oocyte cell. Int J Comput Methods 16(01):1850091. https://doi.org/10.1142/S0219876218500913

Panday S, Pardasani KR (2013) Finite element model to study effect of advection diffusion and \(Na^/Ca^\) exchanger on \(Ca^\) distribution in oocytes. J Medical Imaging Health Inf 3(3):374–379. https://doi.org/10.1166/jmihi.2013.1184

Pawar A, Pardasani KR (2022) Effect of disturbances in neuronal calcium and IP\(_3\) dynamics on \(\beta \)-amyloid production and degradation. Cogn Neurodynamics 1–18. https://doi.org/10.1142/S0219519414500225

Pawar A, Pardasani KR (2022) Simulation of disturbances in interdependent calcium and \(\beta \)-amyloid dynamics in the nerve cell. Eur Phys J Plus 137(8):1–23. https://doi.org/10.1140/epjp/s13360-022-03164-x

Pawar A, Pardasani KR (2022) Study of disorders in regulatory spatiotemporal neurodynamics of calcium and nitric oxide. Cogn Neurodynamics 1:1–22. https://doi.org/10.1007/s11571-022-09902-2

Pawar A, Pardasani KR (2023) Mechanistic insights of neuronal calcium and IP3 signaling system regulating ATP release during ischemia in progression of Alzheimer’s disease. Eur Biophys J 52(3):153–173. https://doi.org/10.1007/s00249-023-01660-1

Pawar A, Pardasani KR (2023) Computational model of calcium dynamics-dependent dopamine regulation and dysregulation in a dopaminergic neuron cell. Eur Phys J Plus 138(1):30. https://doi.org/10.1140/epjp/s13360-023-03691-1

Pawar A, Pardasani KR (2023) Fractional-order reaction-diffusion model to study the dysregulatory impacts of superdiffusion and memory on neuronal calcium and \(IP_3\) dynamics. Eur Phys J Plus 138(9):1–17. https://doi.org/10.1140/epjp/s13360-023-04410-6

Pawar A, Raj Pardasani K (2022) Effects of disorders in interdependent calcium and IP\(_3\) dynamics on nitric oxide production in a neuron cell. Eur Phys J Plus 137(5):1–19. https://doi.org/10.1140/epjp/s13360-022-02743-2

Peercy BE, Sherman AS, Bertram R (2015) Modeling of glucose-induced \(cAMP\) oscillations in pancreatic \(\beta \)-cells: \(cAMP\) rocks when metabolism rolls. Biophys J 109(2):439–449. https://doi.org/10.1016/j.bpj.2015.06.024

Perl W (1962) Heat and matter distribution in body tissues and the determination of tissue blood flow by local clearance methods. J Theor Biol 2(3):201–235. https://doi.org/10.1016/0022-5193(62)90025-5

Singh T, Adlakha N (2023) Numerical investigations and simulation of calcium distribution in the alpha-cell. Bull Biomath 1(1):40–57. https://doi.org/10.59292/bulletinbiomath.2023003

Smith GD (1996) Analytical steady-state solution to the rapid buffering approximation near an open \(Ca^\) channel. Biophys J 71(6):3064–3072. https://doi.org/10.1016/S0006-3495(96)79500-0

Stozer A, Paradiz Leitgeb E, Pohorec V, Dolensek J, Krizancic Bombek L, Gosak M, Skelin Klemen M (2021) The role of \(cAMP\) in beta cell stimulus-secretion and intercellular coupling. Cells 10(7):1658. https://doi.org/10.3390/cells10071658

Swaminathan D (2010) Mathematical modeling of intracellular calcium signaling: A study of \(IP_3\) receptor models. Ohio University

Tang Y, Othmer HG (1995) Frequency encoding in excitable systems with applications to calcium oscillations. Proc Natl Acad Sci 92(17):7869–7873. https://doi.org/10.1073/pnas.92.17.7869

Tengholm A, Gylfe E (2017) \(cAMP\) signalling in insulin and glucagon secretion. Diabetes Obes Metab 19:42–53. https://doi.org/10.1111/dom.12993

Tenner B, Getz M, Ross BL, Ohadi D, Mehta S, Rangamani P, Zhang J (2020) Spatially compartmentalized phase regulation in the \(Ca^\)-\(cAMP\)-\(PKA\)-oscillatory circuit. Biophys J 118(3):175a. https://doi.org/10.7554/eLife.55013

Tewari SG, Pardasani KR (2011) Finite element model to study two dimensional unsteady state cytosolic calcium diffusion. J Appl Math Inf 29(12):427–442

Tewari SG, Pardasani KR (2012) Modeling effect of sodium pump on calcium oscillations in neuron cells. J Multiscale Model 4(03):1250010. https://doi.org/10.1142/S1756973712500102

Tomas A, Jones B, Leech C (2020) New insights into beta-cell GLP-1 receptor and cAMP signaling. J Mol Biol 432(5):1347–1366. https://doi.org/10.1016/j.jmb.2019.08.009

Vaishali, Adlakha N (2023) Disturbances in system dynamics of \(Ca^\) and \(IP_\) perturbing insulin secretion in a pancreatic \(\beta \)-cell due to type-2 diabetes. J Bioenerg Biomembr. https://doi.org/10.1007/s10863-023-09966-7

Vaishali, Adlakha N (2024) Model of Calcium Dynamics Regulating \(IP_\), ATP and Insulin Production in a Pancreatic \(\beta \)-Cell. Acta Biotheor 72(1):2. https://doi.org/10.1007/s10441-024-09477-x

Vatsal VH, Jha BK, Singh TP (2023) To study the effect of ER flux with buffer on the neuronal calcium. Eur Phys J Plus 138(6):1–14. https://doi.org/10.1140/epjp/s13360-023-04077-z

Wagner J, Fall CP, Hong F, Sims CE, Allbritton NL, Fontanilla RA, Nuccitelli R (2004) A wave of \(IP_3\) production accompanies the fertilization \(Ca^\) wave in the egg of the frog, Xenopus laevis: theoretical and experimental support. Cell Calcium 35(5):433–447. https://doi.org/10.1016/j.ceca.2003.10.009

Yu X, Byrne JH, Baxter DA (2004) Modeling interactions between electrical activity and second-messenger cascades in Aplysia neuron R15. J Neurophysiol 91(5):2297–2311. https://doi.org/10.1152/jn.00787.2003

Zimny ML, Blackard WG (1975) The surface structure of isolated pancreatic islet cells. Cell Tissue Res 164(4):467–471. https://doi.org/10.1007/BF00219938