Adv Syst Sci Appl 2022; 03:49–69 Published online at https://ijassa.ipu.ru. Model of Calcium Dynamics Regulating IP3 and ATP Production in a Fibroblast Cell Ankit Kothiya*, Neeru Adlakha Department of Mathematics and Humanities, SVNIT, Surat-395 007, Gujarat, India Abstract: Fibroblast cells are involved in the mechanism of growth and repair of tissue in human organs. Calcium (Ca2+) signaling is essentially required to maintain the microstructure and physiological function of the fibroblast cell. The study of Ca2+ signaling in fibroblast cells is crucial to understanding the mechanisms and disorders of fibroblast cells. The inositol 1,4,5- trisphosphate (IP3) participates in the release and extension of calcium from the endoplasmic reticulum (ER). Adenosine triphosphate (ATP ) also regulate various biological activity like proliferation, migration, stimulation of cell growth, etc. Any disturbance in Ca2+ can disturb the levels of IP3 and ATP in the cell. The Ca2+ dynamics and its relationship with IP3 and ATP production are not well understood. There is a need to understand the relationship among various parameters of Ca2+ dynamics and its role in IP3 and ATP production. The Ca2+ dynamics in fibroblast have been investigated by several researchers, but no attention is reported for analyzing Ca2+ dynamic production of IP3 and ATP . A mathematical model is proposed for analyzing the role of Ca2+ signaling in the production of IP3 and ATP in fibroblast cells. The model incorporates the effect of diffusion, buffer, leak, sarco endoplasmic reticulum calcium ATPase (SERCA) pump, etc. The model is formulated in the form of an initial-boundary problem. The solution is obtained using the finite element approach. The effects of excessive or low values of various parameters on Ca2+ dynamics, ATP production, IP3 production, and IP3 degradation have been analyzed for possible disorders in functions of a fibroblast cell. The alterations in these parameters cause alterations in ATP production, IP3 production and IP3 degradation and Ca2+ concentration profiles. This alteration in parameters can be responsible for the function and dysfunction of fibroblast cells, leading to cardiac disease, fibrosis, delayed wound healing, etc. The results lead to conclusion that the changes in source influx, buffers, and diffusion coefficient can cause an increase or decrease in ATP and IP3 production and IP3 degradation leading to disorders of fibroblast cells like cardiac fibroblast cell proliferation and migration, which have a role in wound healing, inflammation, and cancer . Obtained results provide insights into the Ca2+-dependent production of IP3 and ATP in a fibroblast cell. These insights can be useful for developing diagnostics and treating disorders of fibroblast cells. Keywords: IP3 receptor, SERCA pump, ATP , finite element method, calcium, fibroblast cell 1. INTRODUCTION Every system of an organism is made up of various types of cells. The functions of an organism are achieved by the cellular mechanism in the cell. One of the primary functions is to communicate with each part of the body and accomplish by Intra and inter-cellular calcium signaling [3]. A fibroblast is a kind of organic cell that originates locally from mesenchymal cells and is a permanent resident of connective tissue. These mesenchymal cells produce extracellular matrices such as collagens, fibronectin, tenascin and proteoglycans. It creates the auxiliary system for creature tissues and assumes a basic job in the healing of ∗Corresponding author: ankitkothiya1996@gmail.com 50 wounds [32]. Fibroblast cells are virtually present in every tissue of our body. They are responsible for the three-dimensional architecture and mechanical strength of the tissue. It maintains the structural framework in the tissue of animals by the synthesis of extracellular matrix molecules [33]. The change in fibroblast number and properties are associated with chronic lung diseases. The alteration in injury repair is responsible for asthma and pulmonary fibrosis [23]. Fibroblast cell plays a vital role in chronic lung disease. Transforming growth factor-beta (TGF -β) regulates the fibroblast function. Fibroblast response to cytokines, pro- inflammatory mediators and a variety of growth factors. The role of Ca2+ signaling in these responses is still not well explored [22]. Intracellular free Ca2+ is a ubiquitous secondary messenger, and it regulates various physiological processes like metabolism, differentiation, proliferation, signal transduction, secretion and contraction [15]. There are various types of buffers found in the fibroblast cell. Also, referred as proteins, buffer binds with Ca2+ to reduce the intracellular Ca2+ in fibroblast cells. There are many types of signaling processes in fibroblast cells that elevate intracellular Ca2+ and initiate activities of the cell. Two major mechanisms release Ca2+ from intracellular stores. These are the ryanodine receptor (RyR) and IP3 receptors activations in a cell. The RyR receptor is reported to be absent in humans and rate cardiac fibroblast [5]. However, TGF-β acts on ryanodine sensitive channel in human pulmonary fibroblast leading to Ca2+ wave activity [23]. The IP3 activation is the major Ca2+ release mechanism in fibroblast cells. When the legend bind to plasmalemma receptors, they cause the release of IP3, which in term causes the release of sequestered Ca2+ and influx of extracellular Ca2+. IP3 receptor and SERCA pump act as the source of Ca2+ from the ER which is used by the cell to initiate and sustain the signaling process required for smooth cellular functions. Adenosine triphosphate (ATP ) is an important signaling molecule that regulates various biological activities like increasing or reducing proliferation in various cells. Cardiac fibroblast cells are involved in maintaining structural, biochemistry, mechanical, and electrical characteristics of the heart [4]. ATP regulates the proliferation and migration of cardiac fibroblast cells. The cell migration was detected in a wound-healing assay. Cell proliferation increases with the increase in Ca2+ concentration. A significant effect of ATP at concentrations 0.1µM is observed in increasing the cell proliferation in cardiac fibroblast cells. But the extracellular ATP decreases cell proliferation in human cancer, endometrial stromal cells, respectively and neonatal fibroblast cells, the proliferation is reduced by extracellular ATP [19]. It stimulates cell growth in fibroblast cells. Approximately 1µM of ATP is present in the cell, and 1nM − 1µM is present outside the cell. ATP release and its metabolism dynamics regulate the intra and extracellular levels, which have a role in wound healing, contraction, relaxation, cell migration, differentiation, inflammation and cancer. Purinergic receptors (P2Y ) present on the cell membrane detect the ATP , thereby realizing IP3 present in the membrane, and it is moved into the cytoplasm. The IP3 then triggers the release of Ca2+ from the endoplasmic reticulum into the cytosol of the cell [19]. Therefore, it is of great interest to understand the functional aspects of Ca2+ signaling in a fibroblast cell [33]. A number of researchers have performed the study of Ca2+ distribution in various types of cells like neurons [13,43], astrocytes [12,41], myocytes [31,36,37], oocytes [24,28], acinar [20, 21], fibroblast [16], hepatocyte [11] cells, etc. Naik and Pardasani [25, 29] have studied a Ca2+ signaling in oocytes involving voltage-gated channel, buffer and RyR receptor. Harootunian et al. [7] explained the phenomena of oscillations in Ca2+ concentrations occurring due to the positive feedback between IP3 and Ca2+ in a fibroblast cell. They proposed four classes of models of generating mechanisms. Van Zoelen et al. [47] clarified the major discrepancies between transformed and normal cells anchorage-independent growth (AIG) and loss of density-dependent growth inhibition (DDGI). In this investigation, they Copyright © 2022 ASSA. Adv Syst Sci Appl (2022) 51 used normal rate kidney (NRK) fibroblast cell, which has been used widely as a model system for examining the role played by growth factors in phenotype transformation. Wagner and Keizer [48] analyzed the influence of buffer about Ca2+ release from internal stores. They also reported the effects of IP3, rapid stationary and mobile Ca2+ buffers. Jafri and Keizer [9] analyzed the influence of Ca2+ diffusion in the cytosol, and Ca2+ handling by the ER on IP3 affected Ca2+ wave propagation. Smith et al. [38] obtained an analytical solution to estimate the Ca2+ profile near the open Ca2+ channel for the steady- state condition of the transport equation proposed by Wagner and Keizer. Berridge et al. [2] reported that Ca2+ signaling in the cell triggers new life at fertilization control and controlling various development processes. Once the cells are differentiated, the Ca2+ functions to control processes like memory, secretion, proliferation, contraction and metabolism. They discussed the source of Ca2+, elementary Ca2+ signals, the role of the endoplasmic reticulum or sarcoplasmic reticulum, IP3 receptors and voltage-gated Ca2+ channel (V GCC) in Ca2+ signaling. Godefridus and Harks [6] performed investigations on excitable fibroblasts, including ion channels, action potential and IP3 signaling in NRK fibroblasts. Torres et al. [44] constructed a model for action potential generated in normal rate kidney fibroblasts. Kuster et al. [18] created a model for stabilizing the role of Ca2+/IP3 store-dependent plasma membrane and Ca2+/IP3 channels responsible for potential firing and intracellular Ca2+/IP3 fluctuations. Chen et al. [4] investigated the mechanism of ATP regulates the proliferation of human cardiac fibroblast. Sun et al. [40] gave a dynamic model that provides a constitutive way for controlling the Ca2+ dynamics and the electrical field-induced intracellular Ca2+ response. Schmitz et al. [34] investigated the whole-cell Ca2+ dynamics using models of single trans-membrane ion-conducting proteins. They successfully described several experimental stages and captured important characteristics of Ca2+ dynamics upon T-cell receptor (TCR) stimulation. Hao and Rovin et al. [8] represented a mathematical progress model from tubulointerstitial inflammation into fibrosis, which can be used for monitoring the treatment for interstitial fibrosis in lupus nephritis autoimmune disease (LNAD). Also, they give a mathematical model of idiopathic pulmonary fibrosis. Lembong et al. [19] performed experiments in fibroblast cells under a variety of tissue conditions to study ATP . Kumar and Pardasani [17] developed a one-dimensional mathematical model for T-lymphocytes representing the intracellular Ca2+ distribution using a finite element approach. They also obtained the effect of source influx, buffers, and RyR receptor for exceptional cases and SERCA pump for the temporal case. Kotwani and Adlakha [16] constructed an excess buffer approximated model of the plasma membrane and endoplasmic reticulum Ca2+ influx and efflux in fibroblast cell. Jagtap and Adlakha [10] constructed a framework to observe the impact of fluxes and buffer on Ca2+ dynamics in a hepatocyte cell. Naik, Pardasani [26] studied the relationship of intracellular Ca2+ with RyR receptor, Na+/Ca2+ exchanger, buffers, and SERCA pump, in oocytes cell. Jagtap and Adlakha [10, 11] studied the distribution of intracellular calcium in the presence of buffers by using the finite elements method (FEM ) in hepatocyte cells and concluded that calcium concentration decreases sharply for fast buffers, especially for endogenous and BAPTA buffer in compression with exogenous ethylene glycol tetraacetic acid (EGTA) Buffer. Also, they studied the IP3 and calcium association in hepatocyte cells involving SERCA pump, ER leak, buffer, IP3 diffusion and advection-diffusion of calcium. They concluded Ca2+ concentration increases due to the decrements in SERCA pump rate constant, buffer concentration, and increment in advection velocity. Joshi and Jha [14] studied the fractional reaction-diffusion model for the one-dimensional case involving RyR, V GCC and calbindin-D28k, and they obtained analytical explanations for the physiology of Parkinson’s brain. Martin Vaeth et al. [46] studied the effect of Ca2+ release-activated calcium (CRAC) channels and Stromal interacting molecule (STIM ) in T cell-mediated Copyright © 2022 ASSA. Adv Syst Sci Appl (2022) 52 immunity calcium signaling. Joshi and Jha [15], using the fractional reaction-diffusion model, showed the complex interaction between calbindin-D28k and Ca2+ in the presence of V GCC in neuron cells. They used Fourier and Laplace transformation in the fractional form to deduce the solution for the Spatio-temporal fractional reaction-diffusion equation. Bazhutina et al. [1] propose a mathematical model of human cardiomyocytes to study the mechanical and electrical response with cardiac fibroblast cells to its electronic interaction. No work is noticed for studying the influence of Ca2+ regulation on IP3 and ATP production in a fibroblast cell. The attempt has been made in this direction in the paper. 2. MATHEMATICAL MODEL The partial differential equation representing the one-dimensional Ca2+ dynamics in the presence of excess buffer and Ca2+ flux from the ER of the fibroblast cell is expressed below: [18, 44, 49] ∂[Ca2+] ∂t = DCa ∂2[Ca2+] ∂x2 − k+ j [B]∞([Ca2+]− [Ca2+]∞) + AER VCyt JER. (2.1) Here, [B]∞, [Ca2+]∞ are the steady-state buffer and calcium concentration respectively. The diffusion coefficient of calcium is denoted by DCa. The position variable and time-variable are denoted by ’x’ and ’t,’ respectively. The association rate of a buffer is denoted by k+ j . The area of the endoplasmic reticulum and volume of the cytosol of the fibroblast cell is denoted by AER and VCyt respectively. The various influx and outflux terms of equation (2.1) can be written as [16] JER = (JIP3R + JlkER − JSERCA). (2.2) JSERCA = Jmax SERCA [Ca2+cyt] 2 [Ca2+cyt] 2 +K2 SERCA , (2.3) JlkER = KlkER([Ca2+ER]− [Ca2+cyt]), (2.4) JIP3R = KIP3R([Ca2+ER]− [Ca2+cyt]). (2.5) To handle the nonlinearity in the equation (2.3), the following assumption [16] has been made. Let KSERCA >> [Ca2+cyt], (2.6) where KSERCA denotes the calcium dissociation constant. Then we have, [Ca2+cyt] [Ca2+cyt] +KSERCA << [Ca2+cyt] KSERCA . (2.7) Also, [Ca2+cyt] 2 [Ca2+cyt] 2 +K2 SERCA << [Ca2+cyt] K2 SERCA << [Ca2+cyt] KSERCA . (2.8) Substituting the values of equations (2.2) and (2.8) in (2.1), we get ∂[Ca2+] ∂t = DCa ∂2[Ca2+] ∂x2 − k+ j [B]∞([Ca2+]− [Ca2+]∞)+ AER Vcyt ( KIP3R([Ca2+ER]− [Ca2+cyt]) +KlkER([Ca2+ER]− [Ca2+cyt])− Jmac SERCA KSERCA [Ca2+cyt] ) . (2.9) Copyright © 2022 ASSA. Adv Syst Sci Appl (2022) 53 Calcium channels are presented on the ER membrane in fibroblast cells. In fibroblast cell intracellular calcium concentration is initially assumed at it’s resting condition and it’s value is 0.1µM . Thus the initial condition is [27, 45], [Ca2+](x, 0) = 0.1µM. (2.10) The boundary conditions for the cytosolic calcium at x = 0 and x = 10 are given by the following equations [16, 35] lim x→0 ( −DCa ∂[Ca2+] ∂x ) = σCa, (2.11) where σCa represents calcium flux on the left boundary of the fibroblast cell. lim x→10 [Ca2+] = [Ca2+]∞ = 0.1µM. (2.12) The calcium-dependent ATP release are defined as [39] ATP ([Ca2+]) = [( x0 x0 − 1 ) − 2 ( [Ca2+] [Ca2+]max )][( 1 x0 − 1 ) − ( [Ca2+] [Ca2+]max )2 ]−1 (2.13) and the calcium-dependent IP3 production is defined as [49] IP3([Ca2+]) = Vproduction ( [Ca2+]2 [Ca2+]2 +K2 pump ) . (2.14) Here, x0 is the constants for the ATP feedback and [Ca2+]max considered as a maximum value of calcium concentration of the cell. Therefore, the set of equations (2.9), (2.10), (2.11) and (2.12) form an initial boundary value problem. The equation (2.9) is written as 1 DCa ∂[Ca2+] ∂t = ( ∂2[Ca2+] ∂x2 ) − a1[Ca2+] + b1, (2.15) where a1 = k+ j [B]∞ DCa + 1 DCaFc ( KIP3R + Jmac SERCA KSERCA + VlkER ) , (2.16) b1 = k+ j [B]∞ DCa [Ca2+]∞ + 1 DCaFc ( KIP3R[Ca2+ER] +KlkER[Ca2+ER] ) . (2.17) If we assume that the value of KSERCA is very much less than the cytosolic calcium concentration. Then, the equation (2.15) is expressed as ∂2[Ca2+] ∂x2 − a2[Ca2+] + b2 − 1 DCa ∂[Ca2+] ∂t = 0, (2.18) where a2 = k+ j [B]∞ DCa + 1 DCaFc (KIP3R + VlkER) , (2.19) b2 = k+ j [B]∞ DCa [Ca2+]∞ + 1 DCaFc ( KIP3R[Ca2+ER] +KlkER[Ca2+ER]− KSERCA 1 +m2 ) (2.20) Copyright © 2022 ASSA. Adv Syst Sci Appl (2022) 54 with Fc= AER Vcyt and 0 < m < 1. From the equation (2.15) and equation (2.18), we get ∂2[Ca2+] ∂x2 − a[Ca2+] + b− 1 DCa ∂[Ca2+] ∂t = 0, (2.21) where a = a1, b = b1 for KSERCA >> [Ca2+cyt] and a = a2, b = b2 for KSERCA << [Ca2+cyt]. The equation (2.21) is solved by using the finite elements method [30]. Here ′v′ represent cytosolic calcium concentration. The equation (2.21) in discretized variational form is shown below: J (el) = 1 2 xj (el)∫ xi (el) [( ∂v(el) ∂x )2 + a(v(el))2 − 2bv(el) + 1 Dc ( ∂v(el) ∂t )2 ] dx− µ(el) ( σCa DCa v(el) ∣∣∣ x=0 ) . (2.22) Here, el = 1, 2....10. The constant term µ(el) = 1.0 for el = 1.0 and µ(el) = 0.0 for remaining elements. 3. SOLUTION The linear interpolation function is employed for field variable in each element as given below: v(el) = c1 + c2x, (3.23) where linear elements is denoted by ’el’ and c1, c2 are constants. The equation (3.23) is written as v(el) = P TC(el), (3.24) where P T = [1 x], C(el) = [ c1 c2 ] , v(el)(xi) = c1 + c2xi = vi, (3.25) v(el)(xj) = c1 + c2xj = vj. (3.26) Using equations (3.24) - (3.26), we get: v̄(el) = P (el)C(el), (3.27) where v̄(el) = [ vi vj ] , P (el) = [ 1 xi 1 xj ] , C(el) = (P (el))−1v̄(el). From equation (3.27), we have C(el) = R(el)v̄(el). (3.28) Thus, R(el) = (P (el))−1 = 1 xj − xi [ xj −xi −1 1 ] . Copyright © 2022 ASSA. Adv Syst Sci Appl (2022) 55 From equation (3.24) and (3.28) we get v(el) = P TR(el)v̄(el) (3.29) and v(el) ′ = P T x R (el)v̄(e), (3.30) where P T x = [0 1] . Substituting the equations (3.29) and (3.30) in equation (2.22) we get J (el) = 1 2 ∫ xj (el) xi (el) ( (P T x R (el)v̄(el))2 + a(P TR(el)v̄(el))2 − 2bP TR(el)v̄(el) + 1 Dc ∂(P TR(el)v̄(el))2 ∂t ) dx− µ(el) ( σCa DCa P TR(el)v̄(el)|x=0 ) . (3.31) ∂J (el) ∂v̄(el) = ∫ xj (el) xi (el) (R(el)TPxP T x R (el)v̄(el)) + a(R(el)TPP TR(el)v̄(el))− b(R(el)TP ) + 1 Dc ∂(P TR(el)v̄(el)) ∂t dx− µ(el) ( σCa DCa P TR(el)v̄(el)|x=0 ) . (3.32) We can write equation (3.32) as ∂J (el) ∂v̄(el) = ∂J (el) 1 ∂v̄(el) + ∂J (el) 2 ∂v̄(el) − ∂J (el) 3 ∂v̄(el) + ∂J (el) 4 ∂v̄(el) − ∂J (el) 5 ∂v̄(el) , (3.33) where ∂J (el) 1 ∂v̄(el) = ∫ xj (el) xi (el) (R(el)TPxP T x R (el)v̄(el))dx, (3.34) ∂J (el) 2 ∂v̄(el) = a ∫ xj (el) xi (el) (R(el)TPP TR(el)v̄(el))dx, (3.35) ∂J (el) 3 ∂v̄(el) = b ∫ xj (el) xi (el) (R(el)TP )dx, (3.36) ∂J (el) 4 ∂v̄(el) = 1 Dc ∫ xj (el) xi (el) ( ∂(P TR(el)v̄(el)) ∂t ) dx, ∂J (el) 5 ∂v̄(el) = µel ( σCa DCa R(el)TP |x=0 ) . Now the integral J (el) is minimized with respect to each nodal points as shown below: ∂I(el) ∂v̄(el) = 0, (3.37) ∂J (el) ∂v̄(el) = ∂J (el) 1 ∂v̄(el) + ∂J (el) 2 ∂v̄(el) − ∂J (el) 3 ∂v̄(el) + ∂J (el) 4 ∂v̄(el) − ∂J (el) 5 ∂v̄(el) = 0, (3.38) Copyright © 2022 ASSA. Adv Syst Sci Appl (2022) 56 ∂J ∂v̄ = ΣM̄ (el)∂J (el) dv̄(el) M̄ (el)T = 0, (3.39) where M (el) =  0 0 . . 1 0 0 1 . . 0 0  , u=  v1 v2 . . . v11 . Assembling the integral equations (3.39) we get J = ΣJ (el). (3.40) The equations (3.39) and (3.40) lead to the following system of linear differential equations [P ]11×11 [ ∂ū ∂t ] 11×1 + [Q]11×11[ū]11×1 = [R]11×1. (3.41) Here, [v̄] = [v1, v2, v3, ..., .v11], P is a system matrix, Q is the system vector and R is a force vector. The Crank Nicholson method is use for solving the system (3.41). Matlab has been used to simulate the problem and obtain numerical results. 4. RESULTS AND DISCUSSION The biophysical values and numerical constants used in computing the numerical results are shown in Table 4.2. Fig. 4.1 displays the spatial and temporal Ca2+, ATP , and IP3 concentration profiles for various values of time and positions. From fig. 4.1(A), it is clear that spatial Ca2+ concentration continuously decreases at each nodal point in the cytosol of the fibroblast cell with the increased distance from the source. This is due to the presence of source flux at x = 0.0µm and the diffusion of Ca2+ towards x = 10µm. In fig. 4.1(B), it is notice that the Ca2+ concentration is 0.1µM at t = 0msec and increases with increases in time. The rise in calcium concentration at the node at x = 0µm is more than other points and becomes lower as we move from x = 0µm to x = 10µm. It achieves a steady-state in time t = 150msec. Fig. 4.1(C, D) displays the calcium-dependent ATP production in space and time. It is evident from fig. 4.1(C) at the initial node, the concentration of ATP is higher and decreases gradually towards the ending node. From fig. 4.1(D), it is clear that the range of ATP varies from a lower concentration of 0.4µM to a higher concentration of 1µM , which depends on calcium concentration, in this case, when the initial concentration of calcium is 0.1µM then the ATP is 0.4µM . Therefore calcium and ATP are directly proportional and converge to a steady-state in time t = 150msec. Fig. 4.1(E, F) shows the calcium-dependent IP3 production for space and time. The concentration of IP3 is higher at the mouth of source influx. It decreases gradually on moving far from the source, and later it converges to the 0.005 µM. In fig. 4.1(F) it is notice that IP3 concentration is 0.005µM at t = 0msec and increases with an increase in time. The rise in IP3 concentration is more at x=0 µm and becomes lower as we move from x = 0µm to x = 10µm. It achieves a steady-state in time at 150msec. Therefore, it is clear that the IP3 production and Ca2+ concentration show similar behavior. Fig. 4.2 shows the profile of spatial and temporal Ca2+, ATP , and IP3 concentration for the different values of source amplitude along with the concentration of buffer 5µM and the value of diffusion coefficient 250µm2/s. In fig. 4.2, it is notice that the concentration of Ca2+, ATP , and IP3 is more for higher values of source amplitude. In fig. 4.2(A, C, E) Copyright © 2022 ASSA. Adv Syst Sci Appl (2022) 57 Distance (µm) 0 2 4 6 8 10 [C a 2 + ] C o n c e n tr a ti o n (µ M ) 0 0.2 0.4 0.6 (A). [Ca2+] Profile w.r.t space t =00ms t =10.0ms t =20.0ms t =30.0ms t =50.0ms t =100ms t =500ms Time (msec) 0 100 200 300 400 500 [C a 2 + ] C o n c e n tr a ti o n (µ M ) 0 0.2 0.4 0.6 (B). [Ca2+] Profile w.r.t time x=1.0µm x=2.0µm x=3.0µm x=4.0µm x=5.0µm x=6.0µm x=11µm Distance (µm) 0 2 4 6 8 10 A T P C o n c e n tr a ti o n (µ M ) 0.2 0.4 0.6 0.8 1 (C). ATP Profile w.r.t space t =00ms t =10.0ms t =20.0ms t =30.0ms t =50.0ms t =100ms t =500ms Time (msec) 0 100 200 300 400 500 A T P C o n c e n tr a ti o n (µ M ) 0.2 0.4 0.6 0.8 1 (D). ATP Profile w.r.t time x=1.0µm x=2.0µm x=3.0µm x=4.0µm x=5.0µm x=6.0µm x=11µm Distance (µm) 0 2 4 6 8 10 IP 3 C o n c e n tr a ti o n (µ M ) 0 0.02 0.04 0.06 (E). IP 3 Profile w.r.t space t =00ms t =10.0ms t =20.0ms t =30.0ms t =50.0ms t =100ms t =500ms Time (msec) 0 100 200 300 400 500 IP 3 C o n c e n tr a ti o n (µ M ) 0 0.02 0.04 0.06 (F). IP 3 Profile w.r.t time x=1.0µm x=2.0µm x=3.0µm x=4.0µm x=5.0µm x=6.0µm x=11µm Fig. 4.1. Calcium, ATP and IP3 concentration profile in a fibroblast cell at various time and positions for [B] = 5µM , Dc = 250µm2/s and σ = 20pA. the calcium, ATP , and IP3 concentration is higher at the source x = 0µm and decreases along the spatial direction and converges to 0.1µM , 0.25µM and 0.005µM at x = 10.0µm respectively. From fig. 4.2(B, D, F) it is clear that the calcium, ATP , and IP3 concentration achieves a steady-state in time t = 180msec. Therefore calcium, ATP , IP3 are dependent on the source amplitude. Fig. 4.3 displays the spatial and temporal calcium, ATP , and IP3 concentration for the various values of association rate of the buffer in the fibroblast cell. From fig. 4.3(A, C, E), it is noticed that as buffer binding rate increases calcium, ATP and IP3 concentration decreases. From fig. 4.3(B, D, F) it is clear that the calcium, ATP , and IP3 dynamics achieves a steady- state in time t = 175msec. Therefore calcium, ATP , IP3 are reliant on the association rate of the buffer in the fibroblast cell. Copyright © 2022 ASSA. Adv Syst Sci Appl (2022) 58 Distance (µm) 0 2 4 6 8 10[C a 2 + ] C o n c e n tr a ti o n ( µ M ) 0 0.2 0.4 0.6 0.8 (A). [Ca2+] Profile at t = 0.5 sec Sigma=10 pA Sigma=20 pA Sigma=30 pA Time (msec) 0 100 200 300 400 500[C a 2 + ] C o n c e n tr a ti o n ( µ M ) 0 0.2 0.4 0.6 0.8 (B). [Ca2+] Profile at x = 0 µm Sigma=10 pA Sigma=20 pA Sigma=30 pA Distance (µm) 0 2 4 6 8 10 A T P C o n c e n tr a ti o n ( µ M ) 0.2 0.4 0.6 0.8 1 (C). ATP Production at t = 0.5 sec Sigma=10 pA Sigma=20 pA Sigma=30 pA Time (msec) 0 100 200 300 400 500 A T P C o n c e n tr a ti o n ( µ M ) 0.2 0.4 0.6 0.8 1 (D). ATP Production at x = 0 µm Sigma=10 pA Sigma=20 pA Sigma=30 pA Distance (µm) 0 2 4 6 8 10 IP 3 C o n c e n tr a ti o n ( µ M ) 0 0.02 0.04 0.06 (E). IP 3 Production at t = 0.5 sec Sigma=10 pA Sigma=20 pA Sigma=30 pA Time (msec) 0 100 200 300 400 500 IP 3 C o n c e n tr a ti o n ( µ M ) 0 0.02 0.04 0.06 (F). IP 3 Production at x = 0 µm Sigma=10 pA Sigma=20 pA Sigma=30 pA Fig. 4.2. Ca2+-dependent ATP and IP3 concentration profile in fibroblast cell for different source influx for [B] = 5µM and Dc = 250µm2/s. Fig. 4.4 shows the differences in spatial and temporal calcium, ATP and IP3 concentration for the different values of diffusion coefficient i.e 220µm2/s, 270µm2/s, 320µm2/s. From fig. 4.4(A, C, E) it is notice that for the higher value of diffusion coefficient calcium, ATP , and IP3 ion move fast from apical to the basal region of the cell. Therefore, the concentration of calcium, ATP , and IP3 decreases with an increase in the value of diffusion coefficient near the source and calcium concentration uniformly converges to 0.1µM . ATP concentration and IP3 concentration converges to 0.22µM and 0.005µM respectively. The fig. 4.4(A, B) it is observed that calcium concentration is 0.58µM , 0.51µM , and 0.47µM for the diffusion coefficient 220µm2/s, 270µm2/s, 320µm2/s. Therefore diffusion and calcium concentration is inversely proportional to each other. In fig. 4.4(C, D, E, F) concentration of ATP and IP3 are inversely proportional to the value of diffusion coefficient and achieve a steady-state in time t = 125msec. Copyright © 2022 ASSA. Adv Syst Sci Appl (2022) 59 Distance (µm) 0 2 4 6 8 10[C a 2 + ] C o n c e n tr a ti o n ( µ M ) 0 0.2 0.4 0.6 0.8 (A). [Ca2+] Profile at t = 0.5 sec K j =0.32(µMsec) -1 K j =1.5(µMsec) -1 K j =13(µMsec) -1 Time (msec) 0 100 200 300 400 500[C a 2 + ] C o n c e n tr a ti o n ( µ M ) 0 0.2 0.4 0.6 0.8 (B). [Ca2+] Profile at x = 0 µm K j =0.32(µMsec) -1 K j =1.5(µMsec) -1 K j =13(µMsec) -1 Distance (µm) 0 2 4 6 8 10 A T P C o n c e n tr a ti o n ( µ M ) 0.2 0.4 0.6 0.8 1 (C). ATP Production at t = 0.5 sec K j =0.32(µMsec) -1 K j =1.5(µMsec) -1 K j =13(µMsec) -1 Time (msec) 0 100 200 300 400 500 A T P C o n c e n tr a ti o n ( µ M ) 0.2 0.4 0.6 0.8 1 (D). ATP Production at x = 0 µm K j =0.32(µMsec) -1 K j =1.5(µMsec) -1 K j =13(µMsec) -1 Distance (µm) 0 2 4 6 8 10 IP 3 C o n c e n tr a ti o n ( µ M ) 0 0.02 0.04 0.06 (E). IP 3 Production at t = 0.5 sec K j =0.32(µMsec) -1 K j =1.5(µMsec) -1 K j =13(µMsec) -1 Time (msec) 0 100 200 300 400 500 IP 3 C o n c e n tr a ti o n ( µ M ) 0 0.02 0.04 0.06 (F). IP 3 Production at x = 0 µm K j =0.32(µMsec) -1 K j =1.5(µMsec) -1 K j =13(µMsec) -1 Fig. 4.3. Ca2+-dependent ATP and IP3 concentration profile in fibroblast cell for different calcium binding association rate for [B] = 5µM , Dc = 250µm2/s and σ = 20pA. Fig. 4.5 displays the spatial and temporal distribution of Ca2+, ATP , and IP3 concentration for the different values of ethylene glycol tetraacetic acid (EGTA) buffers. From fig. 4.5, it is clear that the concentration of free Ca2+, ATP , and IP3 decreases at each nodal point of a fibroblast cell with the increase in the concentration of EGTA buffers 5µM , 10µM and 15µM . This EGTA binds with free Ca2+ makes a calcium-bound buffer in the cytosol and reduces the amount of free Ca2+. Thus, the increase in the concentration of buffer causes a decrease in the free Ca2+ concentration. The rate of decrease in Ca2+ concentration increases with the rise in EGTA buffer concentration. The Ca2+ concentration uniformly decreases towards the basal part of the fibroblast cell and attains a background equilibrium concentration of 0.1µM . It is clear from the results of fig. 4.1 and fig. 4.5 the behavior of calcium profiles are followed by the ATP and IP3 profiles. Ca2+, ATP , and IP3 concentrations are inversely proportional to buffer binding affinity. Copyright © 2022 ASSA. Adv Syst Sci Appl (2022) 60 Distance (µm) 0 2 4 6 8 10[C a 2 + ] C o n c e n tr a ti o n ( µ M ) 0 0.2 0.4 0.6 (A). [Ca2+] Profile at t = 0.5 sec D Ca =220µm 2 /s D Ca =270µm 2 /s D Ca =320µm 2 /s Time (msec) 0 100 200 300 400 500[C a 2 + ] C o n c e n tr a ti o n ( µ M ) 0 0.2 0.4 0.6 (B). [Ca2+] Profile at x = 0 µm D Ca =220µm 2 /s D Ca =270µm 2 /s D Ca =320µm 2 /s Distance (µm) 0 2 4 6 8 10 A T P C o n c e n tr a ti o n ( µ M ) 0.2 0.4 0.6 0.8 1 (C). ATP Production at t = 0.5 sec D Ca =220µm 2 /s D Ca =270µm 2 /s D Ca =320µm 2 /s Time (msec) 0 100 200 300 400 500 A T P C o n c e n tr a ti o n ( µ M ) 0.2 0.4 0.6 0.8 1 (D). ATP Production at x = 0 µm D Ca =220µm 2 /s D Ca =270µm 2 /s D Ca =320µm 2 /s Distance (µm) 0 2 4 6 8 10 IP 3 C o n c e n tr a ti o n ( µ M ) 0 0.02 0.04 0.06 (E). IP 3 Production at t = 0.5 sec D Ca =220µm 2 /s D Ca =270µm 2 /s D Ca =320µm 2 /s Time (msec) 0 100 200 300 400 500 IP 3 C o n c e n tr a ti o n ( µ M ) 0 0.02 0.04 0.06 (F). IP 3 Production at x = 0 µm D Ca =220µm 2 /s D Ca =270µm 2 /s D Ca =320µm 2 /s Fig. 4.4. Calcium, ATP and IP3 concentration profile in a fibroblast cell for the different values of diffusion coefficient at [B] = 5µM and σ = 20pA. The ratio of calcium and ATP in fig. 4.6(A) is highest at the calcium source and lowest along the spatial direction and became constant at the other end. They were comparing the fig. 4.6(A, B) with the calcium and ATP profiles of fig. 4.1, it shows that the sharpness of the curves in calcium and ATP profile in fig. 4.1 has got reduced in this fig. 4.6. This shows that the behavior of calcium and ATP is very close. In fig. 4.6(B), the ratio of calcium and ATP is lowest at time t = 0msec and increases with time and achieves a steady-state in 110msec. The steady-state time in fig. 4.6(B) is less in fig. 4.1(B, D) for the calcium and ATP . This shows that the temporal profile of calcium and ATP behavior is very close to each other. In fig. 4.6(C), the spatial profile of the ratio of calcium and IP3 is different from that in fig. 4.1 for calcium and IP3 profiles. For t = 25msec the special profile of calcium and IP3 ratio is increasing concave whereas for t = 500msec this ratio profile is increasing convex from x = 0µm to x = 10µm. Copyright © 2022 ASSA. Adv Syst Sci Appl (2022) 61 Distance (µm) 0 2 4 6 8 10[C a 2 + ] C o n c e n tr a ti o n ( µ M ) 0 0.2 0.4 0.6 (A). [Ca2+] Profile at t = 0.5 sec B=05µM B=10µM B=15µM Time (msec) 0 100 200 300 400 500[C a 2 + ] C o n c e n tr a ti o n ( µ M ) 0 0.2 0.4 0.6 (B). [Ca2+] Profile at x = 0 µm B=05µM B=10µM B=15µM Distance (µm) 0 2 4 6 8 10 A T P C o n c e n tr a ti o n ( µ M ) 0.2 0.4 0.6 0.8 1 (C). ATP Production at t = 0.5 sec B=05µM B=10µM B=15µM Time (msec) 0 100 200 300 400 500 A T P C o n c e n tr a ti o n ( µ M ) 0.2 0.4 0.6 0.8 1 (D). ATP Production at x = 0 µm B=05µM B=10µM B=15µM Distance (µm) 0 2 4 6 8 10 IP 3 C o n c e n tr a ti o n ( µ M ) 0 0.02 0.04 0.06 (E). IP 3 Production at t = 0.5 sec B=05µM B=10µM B=15µM Time (msec) 0 100 200 300 400 500 IP 3 C o n c e n tr a ti o n ( µ M ) 0 0.02 0.04 0.06 (F). IP 3 Production at x = 0 µm B=05µM B=10µM B=15µM Fig. 4.5. Calcium, ATP and IP3 concentration profile in a fibroblast cell for the different values of buffer for Dc = 250µm2/s and σ = 20pA. The calcium profile in fig. 4.1 is decreasing convex. The IP3 profiles in fig. 4.1 are also decreasing convex for t = 25msec and 50msec. But for t = 500msec the IP3 profile was decreasing concave. The drastic change in the ratio of calcium and IP3 profiles indicates a significant difference in the behavior of calcium and IP3 profiles. In fig. 4.6(D), the temporal profile ratio of calcium and IP3 is almost similar for x = 3µm and x = 6µm in behavior. Still, there is a change in behavior at x = 1µm compared to calcium and IP3 profiles in fig. 4.1 This shows that the behavior of curves of calcium and IP3 is very close at all spatial points for x > 1µm in fig. 4.1 but is different near the source. These fluctuations are due to a mismatch in calcium and IP3 profile near the source. The steady-state time of the ratio of calcium and IP3 profiles is less than the independent calcium and IP3 profiles. Fig. 4.7 shows the influence of calcium on the spatial and temporal flux of IP3 degradation profile in a fibroblast cell. The maximum concentration of degradation is observed at Copyright © 2022 ASSA. Adv Syst Sci Appl (2022) 62 Distance (µm) 0 2 4 6 8 10 R a ti o (C a 2 + /A T P ) 0.2 0.3 0.4 0.5 0.6 (A). Ratio(Ca2+/ATP) profile w.r.t space t =25 msec t =50 msec t =500 msec Time (msec) 0 100 200 300 400 500 R a ti o (C a 2 + /A T P ) 0.2 0.3 0.4 0.5 0.6 (B). Ratio(Ca2+/ATP) profile w.r.t time x=1 µm x=3 µm x=6 µm Distance (µm) 0 2 4 6 8 10 R a ti o (C a 2 + /I P 3 ) 10 15 20 25 (C). Ratio(Ca2+/IP 3 ) profile w.r.t space t =25 msec t =50 msec t =500 msec Time (msec) 0 100 200 300 400 500 R a ti o (C a 2 + /I P 3 ) 10 15 20 25 (D). Ratio(Ca2+/IP 3 ) profile w.r.t time x=1 µm x=3 µm x=6 µm Distance (µm) 0 2 4 6 8 10 R a ti o (A T P /I P 3 ) 0.01 0.02 0.03 0.04 0.05 (E). Ratio(ATP/IP 3 ) profile w.r.t space t =25 msec t =50 msec t =500 msec Time (msec) 0 100 200 300 400 500 R a ti o (A T P /I P 3 ) 0.01 0.02 0.03 0.04 0.05 (F). Ratio(ATP/IP 3 ) profile w.r.t time x=1 µm x=3 µm x=6 µm Fig. 4.6. Ratio of Ca2+-dependent ATP and IP3 with the calcium for different points of time and position for [B] = 5µM , Dc = 250µm2/s and σ = 20pA. x = 0.0µm and it reduces from x = 0.0µm to x = 10.0µm. In fig. 4.7, it is clear that the high value of calcium leads to the higher degradation of IP3. Further, it shows that IP3 concentration becomes low due to higher degradation of IP3. Fig. 4.8 shows the ratio of calcium, ATP , and IP3 concentrations for various values of source amplitude. It is noticed in fig. 4.8(A) that the peak value of calcium ratio for sigma 10pA and 20pA is 1.68 at x = 0µm. The peak value of ATP and IP3 ratios are notice at x = 1µm and x = 3µm respectively. At the initial node, calcium concentration is 68 percent higher than the ATP and lower than the IP3 percentage ratio, which is 81 percent. The minimum ratio is attained at the last node. In fig. 4.8(B) the ratio profile of calcium, ATP and IP3 for sigma 10pA and 20pA is minimum at time t = 0msec and increases with time from t = 0msec to t = 15msec for ATP and IP3. The calcium ratio gradually increases with Copyright © 2022 ASSA. Adv Syst Sci Appl (2022) 63 Distance (µm) 0 1 2 3 4 5 6 7 8 9 10 IP 3 C o n c e n tr a ti o n (µ M ) 0.09 0.095 0.1 0.105 0.11 0.115 0.12 0.125 0.13 0.135 0.14 (A). IP 3 Degradation profile with respect to (w.r.t) space t =00 msec t =10 msec t =20 msec t =30 msec t =50 msec t =100 msec t =500 msec Time (msec) 0 50 100 150 200 250 300 350 400 450 500 IP 3 c o n c e n tr a ti o n (µ M ) 0.09 0.095 0.1 0.105 0.11 0.115 0.12 0.125 0.13 0.135 0.14 (B). IP 3 Degradation Profile with respect to (w.r.t) time x=1 µm x=2 µm x=3 µm x=4 µm x=5 µm x=6 µm x=11 µm Fig. 4.7. [Ca2+]-dependent IP3 degradation for different points of time and position for [B] = 5µM , Dc = 250µm2/s and σ = 20pA. Distance (µm) 0 1 2 3 4 5 6 7 8 9 10 R a ti o C o n c e n tr a ti o n 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 (A). [Ca2+], IP 3 and ATP profile at t = 0.5 sec [Ca 2+ ] σ=20pA/σ=10pA [ATP] σ=20pA/σ=10pA [IP 3 ] σ=20pA/σ=10pA Time (msec) 0 50 100 150 200 250 300 350 400 450 500 R a ti o C o n c e n tr a ti o n 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 (B). [Ca2+], IP 3 and ATP profile at x = 0 µm [Ca 2+ ] σ=20pA/σ=10pA [ATP] σ=20pA/σ=10pA [IP 3 ] σ=20pA/σ=10pA Fig. 4.8. Ratio of Calcium, ATP and IP3 for different source influx for [B] = 5µM and Dc = 250µm2/s. time and achieves a steady-state in 90msec, ATP , and IP3 ratios for sigma 10pA and sigma 20pA also achieve steady state in 90msec. Fig. 4.9 shows the ratio graph of calcium, ATP , and IP3 concentrations for different values of the buffer. It is observed in fig. 4.9(A) that the peak value of calcium, ATP and IP3 ratios are at 4µm and 5µm respectively. Initial node calcium concentration is 26%, which is higher for buffer 5µM and 10µM than the ATP and IP3 ratio percentage. The minimum ratio is attained at the last node. In fig. 4.9(B), the ratio profile of calcium, ATP , and IP3 is Copyright © 2022 ASSA. Adv Syst Sci Appl (2022) 64 Distance (µm) 0 1 2 3 4 5 6 7 8 9 10 R a ti o C o n c e n tr a ti o n 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 (A). [Ca2+], IP 3 and ATP Profile at t = 0.5 sec [Ca 2+ ] [B]=5µM/[B]=10µM [ATP] [B]=5µM/[B]=10µM [IP 3 ] [B]=5µM/[B]=10µM Time (msec) 0 50 100 150 200 250 300 350 400 450 500 R a ti o C o n c e n tr a ti o n 1 1.05 1.1 1.15 1.2 1.25 1.3 (B). [Ca2+], IP 3 and ATP Profile at t = 0 µm [Ca 2+ ] [B]=5µM/[B]=10µM [ATP] [B]=5µM/[B]=10µM [IP 3 ] [B]=5µM/[B]=10µM Fig. 4.9. Ratio of Calcium, ATP and IP3 for different buffers for Dc = 250µm2/s and σ = 20pA. Table 4.1. Steady state time period for the Ca2+, IP3 and ATP Fig. No. Temporal Profile Time required to achieve steady state 1-B Calcium w.r.t time 150msec 1-D ATP w.r.t time 150msec 1-F IP3 w.r.t time 150msec 2-B Calcium at x = 0 180msec 2-D ATP at x = 0 180msec 2-F IP3 at x = 0 180msec 3-B Calcium at x = 0 175msec 3-D ATP at x = 0 175msec 3-F IP3 at x = 0 175msec 4-B Calcium 125msec 4-D ATP 115msec 4-F IP3 100msec 5-B Calcium 90msec 5-D ATP 95msec 5-F IP3 100msec 6-B Ratio Calcium/ATP 110msec 6-D Ratio Calcium/ IP3 100msec 6-F Ratio ATP / IP3 105msec 7 IP3 degradation 150msec 8 Ratio of Calcium, ATP , IP3 90msec 9 Ratio of Calcium, ATP , IP3 100msec lowest at time t = 0msec and increases with time and achieves a steady-state in 100msec for buffer 5µM and 10µM . In Figures 4.1 to 4.9 the profiles of calcium, IP3 and ATP are observed to be nonlinear which implies that the nonlinear phenomena is occurring due to changes in conditions like alteration in values of buffer, source influx, etc. to balance the effects of these alterations in parameters for regulating the concentrations of calcium, IP3 and ATP at appropriate levels to maintain the structure and function of the cell. Copyright © 2022 ASSA. Adv Syst Sci Appl (2022) 65 Table 4.2. List of physiological parameters [44] Symbol Parameters Values [Ca2+]∞ Background calcium concentration 0.1 µm Jmax SERCA Maximal pump rate of SERCA 8×10−5 µmol (s× dm2) KSERCA SERCA calcium dissociation constant 2.0µm KlkER Leak constant 2.0s−1 [Ca2+]ER ER calcium concentration 10.89 µm AER ER area 0.3 × 10−7dm2 VER Volume of ER 0.1 × 10−12dm3 Vcyt Volume of cytosol 1 × 10−12dm3 K+ j Association rate 1.5(mms)−1 [B]∞ Total buffer concentration 20 µm σ Source amplitude 15pA DCa Diffusion coefficient 250µm2/s Table 4.3. Error analysis of [Ca2+] concentration profile at x = 0µm Time N=10 elements N=20 elements Error Error % t = 100msec 0.7535093547 0.889250659 0.13574 0.15264 % t = 200msec 0.7638349682 0.994152451 0.23031 0.23165% t = 300msec 0.7640457957 1.015927426 0.25188 0.24794 % t = 500msec 0.7640501883 1.021388902 0.25739 0.25195 % t = 1000msec 0.7640501901 1.021634989 0.25758 0.25212% Table 4.4. Error analysis of ATP production profile at x = 1µm Time N=10 elements N=20 elements Error Error % t = 100msec 0.9892130695 0.918883410 0.07032 0.07653 % t = 200msec 0.9893086343 0.870996603 0.11831 0.13583% t = 300msec 0.9893087359 0.860896109 0.12841 0.14916 % t = 500msec 0.9893087360 0.858363403 0.13094 0.15255 % t = 1000msec 0.9893087361 0.858249304 0.13106 0.15270% Table 4.5. Error analysis of IP3 production profile at x = 2µm Time N=10 elements N=20 elements Error Error % t = 100msec 0.0371489218 0.058113011 0.020964 0.36075 % t = 200msec 0.0371770587 0.0612872185 0.024112 0.39341% t = 300msec 0.0371770887 0.0618411302 0.024664 0.39883 % t = 500msec 0.0371770888 0.0619751619 0.024798 0.40013 % t = 1000msec 0.0371770888 0.0619811563 0.024804 0.40019% For the time period t = 100, 200, 300, 500 and 1000 msec, the accuracy of the model for calcium are 99.84736 %, 99.76835 %, 99.975206 %, 99.74805 % and 99.74788 %, respectively, and for ATP production, the accuracy is 99.92347 %, 99.86417 %, 99.85084 %, 99.84745 % and 99.8473 %, respectively. For IP3 production, the accuracy is 99.63925 %, 99.60659 %, 99.60117 %, 99.59987 %, and 99.59981 %, respectively. Thus the minimum accuracy and maximum error % for this model are 99.75 % and 0.40 %, respectively. The grid sensitivity is negligible; this implies that the solution is independent of the grid. To perform stability analysis, calculated the spectral radius, and the system is said to be stable if the spectral radius is less than or equal to unity [50]. In this case, the spectral radius was 0.9619, which is less than unity. Thus the finite element solution in the present condition is stable. Copyright © 2022 ASSA. Adv Syst Sci Appl (2022) 66 5. CONCLUSION A one-dimensional model is proposed to investigate the impact of buffer, channel flux, and diffusion coefficient on spatial and temporal calcium profile in fibroblast cells and study their impact on ATP and IP3 production in the cell. It is concluded that spatial and temporal calcium distribution variation is proportional to the source influx and inversely proportional to diffusion coefficient and buffers. The variation in spatial and temporal profiles of ATP and IP3 production is also directly proportional to source influx and inversely proportional to buffer and diffusion coefficient. The IP3 degradation is also proportional to calcium distribution in the cell. The finite element simulation is quite effective in generating these insights, which may help frame measures for diagnosis and treatment. The outcomes of this study are in agreement with biological facts. The non-availability of the experimental results for the conditions of the present problem is constant, preventing validation impossible. The dysregulation effect of source influx, buffers, and diffusion coefficients calcium profiles are transferred to the ATP , IP3 production, and IP3 degradation profiles. Thus the changes in source influx, buffers, and diffusion coefficient can cause an increase or decrease in ATP and IP3 production and IP3 degradation. The IP3 is involved in the function of the SERCA pump. Therefore causes alteration in calcium profile due to the SERCA pump leading to dysregulation in calcium dynamics. 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