Modelling spatio-temporal interactions between second messengers Ca 2 + and cAMP in a pancreatic ß -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 (Ca 2 + ), and linkages between Ca 2 + and other second messengers should activate signaling networks. The passage of ions across the cell membrane regulates Ca 2 + levels in pancreatic ß -cells and requires the coordinated interaction of various ion transport mechanisms and organelles. The signaling of Ca 2 + in ß -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 Ca 2 + and cAMP. In order to construct a one-dimensional mathematical model, the fundamental initial and boundary conditions derived from the physiological characteristics of the ß -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 Ca 2 + and cAMP signaling circuits, with a focus on interactions that occur in localized areas of the ß -cell. The model gives the individual effect of each parameter on the regulation of Ca 2 + and cAMP profiles in a ß -cell. Evidently, impairments in the regulation of messenger pathways contribute to the pathological conditions, as demonstrated by the results obtained.

Model of Calcium Dynamics Regulating [Formula: see text], ATP and Insulin Production in a Pancreatic [Formula: see text]-Cell.

The calcium signals regulate the production and secretion of many signaling molecules like inositol trisphosphate ([Formula: see text]) and adenosine triphosphate (ATP) in various cells including pancreatic [Formula: see text]-cells. The calcium signaling mechanisms regulating [Formula: see text], ATP and insulin responsible for various functions of [Formula: see text]-cells are still not well understood. Any disturbance in these mechanisms can alter the functions of [Formula: see text]-cells leading to diabetes and metabolic disorders. Therefore, a mathematical model is proposed by incorporating the reaction-diffusion equation for calcium dynamics and a system of first-order differential equations for [Formula: see text], ATP-production and insulin secretion with initial and boundary conditions. The model incorporates the temporal dependence of [Formula: see text]-production and degradation, ATP production and insulin secretion on calcium dynamics in a [Formula: see text]-cell. The piecewise linear finite element method has been used for the spatial dimension and the Crank-Nicolson scheme for the temporal dimension to obtain numerical results. The effect of changes in source influxes and buffers on calcium dynamics and production of [Formula: see text], ATP and insulin levels in a [Formula: see text]-cell has been analyzed. It is concluded that the dysfunction of source influx and buffers can cause significant variations in calcium levels and dysregulation of [Formula: see text], ATP and insulin production, which can lead to various metabolic disorders, diabetes, obesity, etc. The proposed model provides crucial information about the changes in mechanisms of calcium dynamics causing proportionate disturbances in [Formula: see text], ATP and insulin levels in pancreatic cells, which can be helpful for devising protocols for diagnosis and treatment of various metabolic diseases.

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.

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).

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.

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.

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.

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.

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.

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.

Three dimensional coupled reaction-diffusion modeling of calcium and inositol 1,4,5-trisphosphate dynamics in cardiomyocytes.

Nanoparticles have shown great promise in improving cancer treatment efficacy by changing the intracellular calcium level through activation of intracellular mechanisms. One of the mechanisms of the killing of the cancerous cell by a nanoparticle is through elevation of the intracellular calcium level. Evidence accumulated over the past decade indicates a pivotal role for the IP3 receptor mediated Ca2+ release in the regulation of the cytosolic and the nuclear Ca2+ signals. There have been various studies done suggesting the role of IP3 receptors (IP3R) and IP3 production and degradation in cardiomyocytes. In the present work, we have proposed a three-dimensional unsteady-state mathematical model to describe the mechanism of cardiomyocytes which focuses on evaluation of various parameters that affect these coupled dynamics and elevate the cytosolic calcium concentration which can be helpful to search for novel therapies to cure these malignancies by targeting the complex calcium signaling process in cardiomyocytes. Our study suggests that there are other factors involved in this signaling which can increase the calcium level, which can help in finding treatment for cancer. The cytosolic calcium level may be controlled by IP3 signaling, leak, source influx of calcium (σ) and maximum production of IP3 (V P). We believe that the proposed model suggests new insight into finding treatment for cancer in cardiomyocytes through elevation of the cytosolic Ca2+ concentration by various parameters like leak, σ, V P and especially by other complex cell signaling dynamics, namely IP3 dynamics.

Quantitative Study of Thermal Disturbances Due to Nonuniformly Perfused Tumors in Peripheral Regions of Women's Breast.

BACKGROUND: Mathematical modeling of biothermal processes is widely used to enhance the quantitative understanding of thermoregulation system of human body organs. This quantitative knowledge of thermal information of various human body organs can be used for developing clinical applications. In the past, investigators have studied thermal distribution in hemisphere-shaped human breast in the presence of sphere-shaped tumor. The shape and size of the breast as well as tumor may also affect thermal distribution which can have serious implications in thermography. In this article, a model of thermal disturbances in peripheral regions of ellipsoid-shaped human breast involving ellipse-shaped nonuniformly perfused tumor has been developed for a 2-dimensional steady-state case. The modeling study will provide biomedical scientists vital insights of thermal changes occurring due to the shape and size of breast and tumor which can influence the development of protocols of thermography for diagnosis of tumors in women's breast. METHOD: We have incorporated the significant parameters such as blood flow, metabolic activity, and thermal conductivity in the thermal model for normal and malignant tissues. The controlled metabolic activity has been incorporated for normal tissues, and uncontrolled metabolic activity has been incorporated for tumor regions. The peripheral regions of breast are divided into 3 major layers, namely, epidermis, dermis, and subdermal tissues. An ellipse-shaped nonuniformly perfused tumor is assumed to be present in dermal layers. The nonuniformly perfused tumor is divided into 2 natural components, namely, the necrotic core and tumor periphery. The outer surface of the breast is assumed to be exposed to the environment, and the heat loss takes place by conduction, convection, radiation, and evaporation. The finite element approach is used to obtain the solution. The numerical results have been used to study the effect of shape and size of tumor on temperature distribution in matured breast of different shapes. RESULTS: By selecting appropriate model parameters, we have shown the spatial thermal variation in matured breast of different shapes which could be replicated by the proposed model. We have also shown the thermal disturbances caused by different shapes and sizes of tumors by selecting appropriate values of parameters. In addition, the thermal information from our model provides us the basis for prediction of shape and size of tumors in terms of change of the slope of temperature profiles at the junction of tumor and normal tissues and tumor periphery and tumor core. CONCLUSIONS: The proposed model was successfully used to study the impact of different sizes and shapes of nonuniformly perfused tumor on thermograms in peripheral regions of ellipse-shaped woman's breast. The proposed model is more realistic in terms of shape and size of tumors and woman's breast in comparison with earlier models reported in the literature. The finite element discretization of breast into large number of triangular ring elements effectively models the heterogeneity of region. The changes in slope of the thermal curves at the junctions of various peripheral and tumor layers are due to the nonhomogeneous nature of the region. The location of major thermal disturbances in the tissues indicates the presence of tumor. The change in the slope of the thermal curves gives us idea about the position, type, and size of the tumors in the peripheral tissues. This thermal information can be exploited for detection of tumors by thermographic techniques.

Linear programming model to construct phylogenetic network for 16S rRNA sequences of photosynthetic organisms and influenza viruses.

Phylogenetic trees give the information about the vertical relationships of ancestors and descendants but phylogenetic networks are used to visualize the horizontal relationships among the different organisms. In order to predict reticulate events there is a need to construct phylogenetic networks. Here, a Linear Programming (LP) model has been developed for the construction of phylogenetic network. The model is validated by using data sets of chloroplast of 16S rRNA sequences of photosynthetic organisms and Influenza A/H5N1 viruses. Results obtained are in agreement with those obtained by earlier researchers.