Modelling spatio-temporal interactions between second messengers Ca 2 + and cAMP in a pancreatic β -cell

Calcium serves as a widespread second messenger in almost every human and animal cell. The regulation of various cellular processes, such as transcriptional control and the kinetics of membrane channels, is significantly influenced by intracellular calcium ions (Ca2 + ), and linkages between Ca2 + and other second messengers should activate signaling networks. The passage of ions across the cell membrane regulates Ca2 + levels in pancreatic β -cells and requires the coordinated interaction of various ion transport mechanisms and organelles. The signaling of Ca2 + in β -cells and its interactions with the intracellular dynamics of cyclic adenosine monophosphate (cAMP) is poorly understood. Therefore, the current investigation proposes a mathematical model to illustrate the spatiotemporal dynamical interaction between Ca2 + and cAMP. In order to construct a one-dimensional mathematical model, the fundamental initial and boundary conditions derived from the physiological characteristics of the β -cell are incorporated. The numerical results were obtained by MATLAB simulations using the finite element method and the Crank-Nicolson method. The current study aims to offer an update on regulation between Ca2 + and cAMP signaling circuits, with a focus on interactions that occur in localized areas of the β -cell. The model gives the individual effect of each parameter on the regulation of Ca2 + and cAMP profiles in a β -cell. Evidently, impairments in the regulation of messenger pathways contribute to the pathological conditions, as demonstrated by the results obtained.

Cross Talking Calcium, IP3 and Buffer Dynamics Alters ATP and NADH Level in Obese and Normal Hepatocyte Cell

The cross talk between calcium (Ca2+), IP3 and buffer dynamics regulate various mechanisms in hepatocyte cells. The study of independent systems of calcium, IP3, and buffer signaling provides limited information about cell dynamics. In the current study, coupled reaction-diffusion equations are used to design a cross-talk model for IP3, buffer, and calcium dynamics in a hepatocyte cell. The one-way feedback of calcium, buffer, and IP3 in ATP production, ATP degradation, and NADH production rate is incorporated into the model. Numerical simulation has been done using the Finite Element Method (FEM) along the spatial direction and the Crank-Nicolson (C-N) method along the temporal direction. The numerical results are analysed to determine the effects of alterations in processes of cross-talking dynamics of IP3, buffer, and calcium on ATP and NADH production and degradation rate of ATP in a hepatocyte cell under normal and obesity conditions. The comparative analysis of these findings unveils notable distinctions induced by obesity in calcium dynamics, ATP and NADH synthesis, and ATP degradation kinetics.

Regulatory disturbances in the dynamical signaling systems of C a 2 + and NO in fibroblasts cause fibrotic disorders

Studying the calcium dynamics within a fibroblast cell individually has provided only a restricted understanding of its functions. However, research efforts focusing on systems biology approaches for such investigations have been largely neglected by researchers until now. Fibroblast cells rely on signaling from calcium ( C a 2 + ) and nitric oxide (NO) to maintain their physiological functions and structural stability. Various studies have demonstrated the correlation between NO and the control of C a 2 + dynamics in cells. However, there is currently no existing model to assess the disruptions caused by various factors in regulatory dynamics, potentially resulting in diverse fibrotic disorders. A mathematical model has been developed to investigate the effects of changes in parameters such as buffer, receptor, sarcoplasmic endoplasmic reticulum C a 2 + -ATPase (SERCA) pump, and source influx on the regulation and dysregulation of spatiotemporal calcium and NO dynamics in fibroblast cells. This model is based on a system of reaction-diffusion equations, and numerical simulations are conducted using the finite element method. Disturbances in key processes related to calcium and nitric oxide, including source influx, buffer mechanism, SERCA pump, and inositol trisphosphate ( I P 3 ) receptor, may contribute to deregulation in the calcium and NO dynamics within fibroblasts. The findings also provide new insights into the extent and severity of disorders resulting from alterations in various parameters, potentially leading to deregulation and the development of fibrotic disease.

A Comprehensive Fuzzy Model for Understanding Neuronal Calcium Distribution in Presence of VGCC, Na+/Ca2+ Exchanger, Buffer, and ER Fluxes

Free Calcium ions in the cytosol are essential for many physiological and physical functions. The free calcium ions are commonly regarded as a second messenger, are an essential part of brain communication. Numerous physiological activities, such as calcium buffering and calcium ion channel flow, etc. influence the cytosolic calcium concentration. In light of the above, the primary goal of this study is to develop a model of calcium distribution in neuron cells when a Voltage-Gated Calcium Channel and Sodium Calcium Exchanger are present. As we know, decreased buffer levels and increased calcium activity in the Voltage-Gated Calcium Channel and Sodium Calcium Exchanger lead to Alzheimer's disease. Due to these changes, the calcium diffusion in that location becomes disrupted and impacted by Alzheimer's disease. The model has been constructed by considering key factors like buffers and ER fluxes when Voltage-Gated Calcium Channels and Sodium Calcium Exchangers are present. Based on the physiological conditions of the parameters, appropriate boundary conditions have been constructed in the fuzzy environment. This model is considered a fuzzy boundary value problem with the source term and initial boundary conditions are modeled by triangular fuzzy functions. In this, paper we observed the approximate solution of the mathematical model which was investigated by the fuzzy undetermined coefficient method. The solution has been performed through MATLAB and numerical results have been computed using simulation. The observation made that the proper operation of the Voltage-Gated Calcium Channel and Sodium Calcium Exchanger is critical for maintaining the delicate equilibrium of calcium ions, which regulates vital cellular activities. Dysregulation of Voltage-Gated Calcium Channel and Sodium Calcium Exchanger activity has been linked to neurodegenerative illnesses like Alzheimer's disease.

Impact of Interdependent Ca2+ and IP3 Dynamics On ATP Regulation in A Fibroblast Model

The vital participation of Ca2+ in human organ functions such as muscular contractions, heartbeat, brain functionality, skeletal activity, etc, motivated the scientists to thoroughly research the mechanisms of calcium (Ca2+) signalling in distinct human cells. Ca2+, inositol triphosphate (IP3), and adenosine triphosphate (ATP) play important roles in cell signaling and physiological processes. ATP and its derivatives are hypothesized to be important in the pathogenic process that leads to fibrotic illnesses like fibrosis. Fluctuations in Ca2+ and IP3 in a fibroblast cell influence ATP production. To date, no evidence of coupled Ca2+ and IP3 mechanics regulating ATP generation in a fibroblast cell during fibrotic disease has been found. The current work suggests an integrated mechanism for Ca2+ and IP3 dynamics in a fibroblast cell that regulates ATP generation. Simulation has been carried out using the finite element approach. The mechanics of interdependent systems findings vary dramatically from the results of basic independent system mechanics and give fresh information about the two systems' activities. The numerical results provide new insights into the impacts of disturbances in source influx, the serca pump, and buffers on interdependent Ca2+ and IP3 dynamics and ATP synthesis in a fibroblast cell. According to the findings of this study, fibrotic disorders cannot be attributed solely to disruptions in the processes of calcium signaling mechanics but also to disruptions in IP3 regulation mechanisms affecting the regulation of calcium in the fibroblast cell and ATP release.

Numerical simulation of calcium dynamics dependent ATP degradation, IP3 and NADH production due to obesity in a hepatocyte cell

Calcium (Ca[Formula: see text]) signals have a crucial role in regulating various processes of almost every cell to maintain its structure and function. Calcium dynamics has been studied in various cells including hepatocytes by many researchers, but the mechanisms of calcium signals involved in regulation and dysregulation of various processes like ATP degradation rate, IP[Formula: see text] and NADH production rate respectively in normal and obese cells are still poorly understood. In this paper, a reaction diffusion equation of calcium is employed to propose a model of calcium dynamics by coupling ATP degradation rate, IP[Formula: see text] and NADH production rate in hepatocyte cells under normal and obese conditions. The processes like source influx, buffer, endoplasmic reticulum (ER), mitochondrial calcium uniporters (MCU) and Na[Formula: see text]/Ca[Formula: see text] exchanger (NCX) have been incorporated in the model. Linear finite element method is used along spatial dimension, and Crank-Nicolson method is used along temporal dimension for numerical simulation. The results have been obtained for the normal hepatocyte cells and for cells due to obesity. The comparative study of these results reveal significant difference caused due to obesity in Ca[Formula: see text] dynamics as well as in ATP degradation rate, IP[Formula: see text] and NADH production rate.

Simulation of biochemical dynamics of [Formula: see text] and [Formula: see text] in fibroblast cell

Calcium dynamics is not only responsible for maintaining the framework and functions of the cell but also plays a role in the dynamics of other biochemical systems in the cell. Phospholipase C-[Formula: see text] l ([Formula: see text]) has a crucial role in the function of fibroblast cells. Experiments have shown that [Formula: see text] and [Formula: see text] have interdependent dynamics in fibroblast cells. However, no reaction-diffusion model exists for the two-way feedback system dynamics of [Formula: see text] and [Formula: see text] in fibroblasts till date. The computational model is designed to investigate the impact of variations in several processes, such as the [Formula: see text] pump, buffer process, source inflow, etc., on the system dynamics of [Formula: see text] and [Formula: see text] in fibroblast cells. The computational findings are obtained using finite element techniques, and the consequences of dysregulation in various processes on the spatiotemporal calcium and [Formula: see text] dynamics in fibroblasts are investigated. The results lead to the conclusion that the effects of buffer, source influx, diffusion, and [Formula: see text] pump can cause fluctuations in the dynamics of [Formula: see text] and [Formula: see text] in fibroblasts. Disruptions in these constitutive processes can result in changes in the dynamics of calcium and [Formula: see text]. Thus, the current model provides new/novel information regarding the precise dysregulatory constitutive systems that regulate calcium and [Formula: see text] kinetics, such as source inflow, diffusion, [Formula: see text], and buffer, can be responsible for excessive calcium and [Formula: see text] concentrations leading to fibrotic illnesses such as cancer and fibrosis.

Spatio temporal interdependent calcium and buffer dynamics regulating DAG in a hepatocyte cell due to obesity

Calcium ions (Ca2+) serve as a crucial signaling mechanism in almost all cells. The buffers are proteins that bind free Ca2+ to reduce the cell's Ca2+ concentration. The most studies reported in the past on calcium signaling in various cells have considered the buffer concentration as constant in the cell. However, buffers also diffuse and their concentration varies dynamically in the cells. Almost no work has been reported on interdependent calcium and buffer dynamics in the cells. In the present study, a model is proposed for inter-dependent spatio-temporal dynamics of calcium and buffer by coupling reaction-diffusion equations of Ca2+ and buffer in a hepatocyte cell. Boundary and initial conditions are framed based on the physiological state of the cell. The effect of various parameters viz. inositol 1,4,5-triphosphate receptor (IP3R), diffusion coefficient, SERCA pump and ryanodine receptor (RyR) on spatio-temporal dynamics of calcium and buffer regulating diacylglycerol (DAG) in a normal and obese hepatocyte cell has been studied using finite element simulation. From the results, it is concluded that the dynamics of calcium and buffer impact each other significantly along the spatio-temporal dimensions, thereby affecting the regulation of all the processes including DAG in a hepatocyte cell. The proposed model is more realistic than the existing ones, as the interdependent system dynamics of calcium and buffer have different regulatory impacts as compared to the individual and independent dynamics of these signaling processes in a hepatocyte cell.

Disturbances in system dynamics of [Formula: see text] and [Formula: see text] perturbing insulin secretion in a pancreatic [Formula: see text]-cell due to type-2 diabetes

The individual study of [Formula: see text] and [Formula: see text] dynamics respectively in a [Formula: see text]-cell has yielded limited information about the cell functions. But the systems biology approaches for such studies have received very little attention by the research workers in the past. In the present work, a system-dynamics model for the interdependent [Formula: see text] and [Formula: see text] signaling that controls insulin secretion in a [Formula: see text]-cell has been suggested. A two-way feedback system of [Formula: see text] and [Formula: see text] has been considered and one-way feedback between [Formula: see text] and insulin has been implemented in the model. The finite element method along with the Crank-Nicolson method have been applied for simulation. Numerical results have been used to analyze the impact of perturbations in [Formula: see text] and [Formula: see text] dynamics on insulin secretion for normal and Type-2 diabetic conditions. The results reveal that Type-2 diabetes comes from abnormalities in insulin secretion caused by the perturbation in buffers and pumps (SERCA and PMCA).

Cellular nitric oxide synthesis is affected by disorders in the interdependent [Formula: see text] and [Formula: see text] dynamics during cystic fibrosis disease

Calcium ([Formula: see text]), inositol trisphosphate ([Formula: see text]), and nitric oxide (NO) signaling are essential to maintain the structural integrity and physiological activity of fibroblast cells. The accumulation of excess quantity of NO for longer periods can lead to a variety of fibrotic disorders, including heart disease, penile fibrosis in Peyronie's disease (PD), and cystic fibrosis. The dynamics of these three signaling processes and their interdependence in fibroblast cells are not clearly known to date. A systems biology model is proposed using reaction-diffusion equations for calcium, [Formula: see text], and calcium-dependent NO synthesis in fibroblast cells. The finite element method (FEM) is used to examine [Formula: see text], [Formula: see text], and NO regulation and dysregulation in cells. The results throw light on the conditions that disturb the coupled [Formula: see text] and [Formula: see text] dynamics and the influence of these factors on the levels of NO concentration in the fibroblast cell. The findings suggest that changes in source inflow, buffers, and diffusion coefficient might induce an increase or reduction in nitric oxide and [Formula: see text] synthesis, resulting in fibroblast cell diseases. Furthermore, the findings provide new information regarding the size and intensity of diseases in response to changes in several factors of their dynamics, which has been linked to the development of cystic fibrosis and cancer. This knowledge could be valuable for developing novel approaches to the diagnosis of diseases and therapies for various disorders of fibroblast cells.

Mathematical Modeling of Calcium Oscillatory Patterns in a Neuron

Calcium oscillations are an imperative mode of signaling phenomenon. These oscillations are due to the active interactions taking place between some of the parameters like voltage gated calcium channels (VGCC), sodium calcium exchanger (NCX), calcium binding buffers, endoplasmic reticulum (ER) and mitochondria. The present paper focuses on the problem of higher level of calcium concentration in neurons which may further result into Alzheimer's Disease (AD). For this, a three-dimensional mathematical model having a system of differential equations depicting the changes in cytosolic calcium (in presence of buffers, VGCC and NCX), ER calcium and mitochondrial calcium, is formulated. A three-dimensional neuronal structure is targeted as the domain which is further discussed and solved using finite element technique in Comsol Multiphysics 5.4. Apposite boundary conditions matching well with the in-situ conditions are assumed. The obtained results clearly show the significance of the lower amount of the buffer and higher calcium mediated activities of VGCC, NCX, ER and mitochondria on calcium profile. These changes may lead to AD. To transit from AD condition to normal, exogenous buffers are added to check their significance. The results thus show that the replenishment of buffer may balance the amount of cell calcium and hence can affect positively on Alzheimer's affected cells.

Modeling the mechanics of calcium regulation in T lymphocyte: A finite element method approach

Changes in cellular Ca[Formula: see text] concentration control a variety of physiological activities including hormone and neurotransmitter release, muscular contraction, synaptic plasticity, ionic channel permeability, apoptosis, enzyme activity, gene transcription and reproduction process. Spatial–temporal Ca[Formula: see text] dynamics due to Ca[Formula: see text] release, buffering and re-uptaking plays a central role in studying the Ca[Formula: see text] regulation in T lymphocytes. In most cases, Ca[Formula: see text] has its major signaling function when it is elevated in the cytosolic compartment. In this paper, a two-dimensional mathematical model to study spatiotemporal variations of intracellular Ca[Formula: see text] concentration in T lymphocyte cell is proposed and investigated. The cell is assumed to be a circular shaped geometrical domain for the representation of properties of Ca[Formula: see text] dynamics within the cell including important parameters. Ca[Formula: see text] binding proteins for the dynamics of Ca[Formula: see text] are itself buffer and other physiological parameters located in Ca[Formula: see text] stores. The model incorporates the important biophysical processes like diffusion, reaction, voltage-gated Ca[Formula: see text] channel, leak from endoplasmic reticulum (ER), efflux from cytosol to ER via sarco–ER Ca[Formula: see text] adenosine triphosphate (SERCA) pumps, buffers and Na[Formula: see text] exchanger. The proposed mathematical model is solved using a finite difference method and the finite element method. Appropriate initial and boundary conditions are incorporated in the model based on biophysical conditions of the problem. Computer simulations in MATLAB R2019b are employed to investigate mathematical models of reaction–diffusion equation. The effect of source, buffer, Na[Formula: see text]/Ca[Formula: see text] exchanger, etc. on spatial and temporal patterns of Ca[Formula: see text] in T lymphocyte has been studied with the help of numerical results. From the obtained results, it is observed that, the coordinated combination of the incorporated parameters plays a significant role in Ca[Formula: see text] regulation in T lymphocytes. ER leak and voltage-gated Ca[Formula: see text] channel provides the necessary Ca[Formula: see text] to the cell when required for its proper functioning, while on the other side buffers, SERCA pump and Na[Formula: see text]/Ca[Formula: see text] exchanger makes balance in the Ca[Formula: see text] concentration, so as to prevent the cell from death as higher concentration for longer time is harmful for the cell and can cause cell death.

Modeling and simulation of spatial-temporal calcium distribution in T lymphocyte cell by using a reaction-diffusion equation

T lymphocytes are white blood cells that play a central role in cell-mediated immunity. Ca2+ has its major signaling function when it is elevated in the cytosolic compartment. The free cytosolic Ca2+ dynamics plays a very important role in the activation, and fate decision process in the T lymphocytes. Here, we develop a quantitative spatio-temporal Ca2+ dynamic model which includes, the Ca2+ releasing channels ER leak and voltage-gated Ca2+ channel, buffering and re-uptaking mechanism in the T lymphocytes. In this model, the cell is represented as a circular-shaped geometrical domain. This representation introduces modeling flexibility needed for detailed representation of the properties of Ca2+ dynamics in the cell including important parameters. The proposed mathematical model is solved using a finite difference method and the finite element method. Appropriate initial and boundary conditions are incorporated in the model based on biophysical conditions of the problem. Computer simulations in MATLAB R2010a are employed to investigate mathematical models of reaction-diffusion equation. The estimation is based on reaction-diffusion equation associated with biophysical and biochemical reactions taking place in the cell. From our results, it is observed that, the coordinated combination of the incorporated parameters plays a significant role in Ca2+ regulation in T lymphocytes. ER leak and voltage-gated Ca2+ channel provides the necessary Ca2+ to the cell when required for its proper functioning, while on the other side buffers and Na+/Ca2+ exchanger makes balance in the Ca2+ concentration, so as to prevent the cell from death as higher concentration for longer time is harmful for the cell and can cause cell death. These results have been used to study the relationship of Ca2+ concentration with parameters like VGCC, Na+/Ca2+ exchanger, ER leak and buffers. The significance of the study reveals that there is a significant variation in Ca2+ profiles due to the effect of VGCC, Na+/Ca2+ exchanger, ER leak, and buffers. The results give us better insights of coordinated effect of VGCC, Na+/Ca2+ exchanger, ER leak, and buffers on Ca2+ distribution in T lymphocytes. T lymphocytes are the primary host cells to receive the viral infections which transmits the signal then to other cell types. The proper quantity of Ca2+ concentration makes T lymphocytes more active and healthier to fight the infection properly and can protect the immune system from various fatal viral infections. Thus, the application of the study lies in the field of immunology to protect a susceptible from various viral infectious diseases like HIV, HBV, HINI, etc. by strengthening the immune system. The outcomes of the study reveal that the applied finite element method is computationally very strong and effective to analyze differential equations that arise in Ca2+ dynamics.