1
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Vatsal VH, Jha BK, Singh TP. Generalised Neuronal Calcium Dynamics of Membrane and ER in the Polar Dimension. Cell Biochem Biophys 2024:10.1007/s12013-024-01425-3. [PMID: 39106022 DOI: 10.1007/s12013-024-01425-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 07/10/2024] [Indexed: 08/07/2024]
Abstract
Calcium ions are the second messenger playing as regulators for various cellular activities. Its spatiotemporal control is critical for various brain functions, including neuroplasticity, apoptosis, and cell death. The Endoplasmic Reticulum (ER) plays an important role in determining these spatiotemporal calcium dynamics. Stromal interaction molecule (STIM) - Orai channel on the membrane generates additional calcium flow, whereas other membrane fluxes contribute to cytosolic flux. Due to their anomalous character, we used the Caputo fractional differential operator to mimic these interactions in polar coordinates. Solutions were generated using hybrid integral transform methods to control the analytical approach. Using Green's function yielded a closed-form solution for Mittag-Leffler-type functions. This work emphasizes the significant relationship between calcium and various buffer levels in neurons. The differential transition simulation of a time derivative with space across different parameters indicated a decrease in calcium concentration. Anomalously low buffer levels exhibited the impact of Alzheimer's disease on calcium higher concentration, leading to the death of neurons. Additionally, the research introduces a method involving S100B, BAPTA, and calmodulin buffers to uphold optimal calcium levels within the neuronal cytosol. The applicability of this model with different buffer properties and parameters and memory impacts the calcium concentration with the neurological disorder.
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Affiliation(s)
- Vora Hardagna Vatsal
- Department of Mathematics, School of Technology, Pandit Deendayal Energy University, Gandhinagar, Gujarat, India
| | - Brajesh Kumar Jha
- Department of Mathematics, School of Technology, Pandit Deendayal Energy University, Gandhinagar, Gujarat, India.
| | - Tajinder Pal Singh
- Department of Mathematics, School of Technology, Pandit Deendayal Energy University, Gandhinagar, Gujarat, India
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2
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Vaishali, Adlakha N. Modelling spatio-temporal interactions between second messengers Ca 2 + and cAMP in a pancreatic β -cell. J Bioenerg Biomembr 2024; 56:389-404. [PMID: 38771496 DOI: 10.1007/s10863-024-10021-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/13/2024] [Accepted: 05/06/2024] [Indexed: 05/22/2024]
Abstract
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.
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Affiliation(s)
- Vaishali
- Department of Mathematics, SVNIT, Surat, 395007, Gujarat, India.
| | - Neeru Adlakha
- Department of Mathematics, SVNIT, Surat, 395007, Gujarat, India
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3
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Mishra V, Adlakha N. Cross Talking Calcium, IP 3 and Buffer Dynamics Alters ATP and NADH Level in Obese and Normal Hepatocyte Cell. Cell Biochem Biophys 2024; 82:1537-1553. [PMID: 38789660 DOI: 10.1007/s12013-024-01306-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 05/08/2024] [Indexed: 05/26/2024]
Abstract
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.
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Affiliation(s)
- Vedika Mishra
- Department of Mathematics, SVNIT, Surat, 395007, Gujarat, India.
| | - Neeru Adlakha
- Department of Mathematics, SVNIT, Surat, 395007, Gujarat, India
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4
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Kothiya A, Adlakha N. Regulatory disturbances in the dynamical signaling systems of C a 2 + and NO in fibroblasts cause fibrotic disorders. J Biol Phys 2024; 50:229-251. [PMID: 38753214 PMCID: PMC11106231 DOI: 10.1007/s10867-024-09657-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/25/2023] [Accepted: 04/16/2024] [Indexed: 05/21/2024] Open
Abstract
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.
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Affiliation(s)
- Ankit Kothiya
- DoM, Sardar Vallabhbhai National Institute of Technology, Surat, 395007, Gujarat, India.
| | - Neeru Adlakha
- DoM, Sardar Vallabhbhai National Institute of Technology, Surat, 395007, Gujarat, India
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5
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Pawar A, Pardasani KR. Modelling Cross Talk in the Spatiotemporal System Dynamics of Calcium, IP 3 and Nitric Oxide in Neuron Cells. Cell Biochem Biophys 2024; 82:787-803. [PMID: 38376737 DOI: 10.1007/s12013-024-01229-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/11/2023] [Accepted: 02/05/2024] [Indexed: 02/21/2024]
Abstract
The bioenergetic system of calcium ([Ca2+]), inositol 1, 4, 5-trisphophate (IP3) and nitric oxide (NO) regulate the diverse mechanisms in neurons. The dysregulation in any or all of the calcium, IP3 and nitric oxide dynamics may cause neurotoxicity and cell death. Few studies are noted in the literature on the interactions of two systems like [Ca2+] with IP3 and [Ca2+] with nitric oxide in neuron cells, which gives limited insights into regulatory and dysregulatory processes in neuron cells. But, no study is available on the cross talk in dynamics of three systems [Ca2+], IP3 and NO in neurons. Thus, the cross talk in the system dynamics of [Ca2+], IP3 and NO regulation processes in neurons have been studied using mathematical model. The two-way feedback process between [Ca2+] and IP3 and two-way feedback process between [Ca2+] and NO through cyclic guanosine monophosphate (cGMP) with plasmalemmal [Ca2+]-ATPase (PMCA) have been incorporated in the proposed model. This coupling handles the indirect two-way feedback process between IP3 and nitric oxide in neuronal cells automatically. The numerical outcomes were acquired by employing the finite element method (FEM) with the Crank-Nicholson scheme (CNS). The present model incorporating the sodium-calcium exchanger (NCX) and voltage-gated calcium channel (VGCC) provides novel insights into the various regulatory and dysregulatory processes due to buffer, IP3-receptor, ryanodine receptor, cGMP kinetics through PMCA channel, etc. and their impacts on the interactive spatiotemporal system dynamics of [Ca2+], IP3 and NO in neurons. It is concluded that the behavior of different crucial mechanisms is quite different for interactions of two systems of [Ca2+] and NO and the interactions of three systems of [Ca2+], IP3 and nitric oxide in neuronal cell due to mutual regulatory adjustments. The association of several neurological disorders with the alterations in calcium, IP3 and NO has been explored in neurons.
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Affiliation(s)
- Anand Pawar
- Department of Mathematics, Bioinformatics and Computer Applications, Maulana Azad National Institute of Technology, Bhopal, 462003, Madhya Pradesh, India.
| | - Kamal Raj Pardasani
- Department of Mathematics, Bioinformatics and Computer Applications, Maulana Azad National Institute of Technology, Bhopal, 462003, Madhya Pradesh, India.
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6
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Jha BK, Bhattacharyya R. A Comprehensive Fuzzy Model for Understanding Neuronal Calcium Distribution in Presence of VGCC, Na +/Ca 2+ Exchanger, Buffer, and ER Fluxes. Cell Biochem Biophys 2024; 82:1367-1379. [PMID: 38743137 DOI: 10.1007/s12013-024-01291-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 04/20/2024] [Indexed: 05/16/2024]
Abstract
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.
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Affiliation(s)
- Brajesh Kumar Jha
- Department of Mathematics, School of Technology, Pandit Deendayal Energy University, Raisan, Gandhinagar, Gujarat, 382007, India.
| | - Rituparna Bhattacharyya
- Department of Mathematics, School of Technology, Pandit Deendayal Energy University, Raisan, Gandhinagar, Gujarat, 382007, India.
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7
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Vaishali, Adlakha N. Model of Calcium Dynamics Regulating [Formula: see text], ATP and Insulin Production in a Pancreatic [Formula: see text]-Cell. Acta Biotheor 2024; 72:2. [PMID: 38334878 DOI: 10.1007/s10441-024-09477-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/21/2023] [Accepted: 12/30/2023] [Indexed: 02/10/2024]
Abstract
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.
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Affiliation(s)
- Vaishali
- Department of Mathematics, SVNIT, Surat, Gujarat, 395007, India.
| | - Neeru Adlakha
- Department of Mathematics, SVNIT, Surat, Gujarat, 395007, India
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8
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Bhattacharyya R, Jha BK. Analyzing fuzzy boundary value problems: a study on the influence of mitochondria and ER fluxes on calcium ions in neuron cells. J Bioenerg Biomembr 2024; 56:15-29. [PMID: 38064155 DOI: 10.1007/s10863-023-09994-3] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/15/2023] [Accepted: 11/07/2023] [Indexed: 01/07/2024]
Abstract
Cytosolic-free calcium ions play an important role in various physical and physiological processes. A vital component of neural signaling is the free calcium ion concentration often known as the second messenger. There are many parameters that effect the cytosolic free calcium concentration like buffer, voltage-gated ion channels, Endoplasmic reticulum, Mitochondria, etc. Mitochondria are small organelles located within the nervous system that are involved in processes within cells such as calcium homeostasis management, energy generation, response to stress, and cell demise pathways. In this work, a mathematical model with fuzzy boundary values has been developed to study the effect of Mitochondria and ER fluxes on free Calcium ions. The intended findings are displayed utilizing the physiological understanding that amyloid beta plaques and tangles of neurofibrillary fibers have been identified as the two main causes of AD. The key conclusion of the work is the investigation of [Formula: see text] for healthy cells and cells affected by Alzheimer's disease, which may aid in the study of such processes for computational scientists and medical practitioners. Also, it has been shown that when a unique solution is found for a specific precise problem, it also successfully deals with any underlying ambiguity within the problem by utilizing a technique based on the principles of linear transformation. Furthermore, the comparison between the analytical approach and the generalized hukuhara derivative approach is shown here, which illustrates the benefits of the analytical approach. The simulation is carried out in MATLAB.
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Affiliation(s)
- Rituparna Bhattacharyya
- Department of Mathematics, School of Technology, Pandit Deendayal Energy University, Raisan, Gandhinagar, Gujarat, 382007, India
| | - Brajesh Kumar Jha
- Department of Mathematics, School of Technology, Pandit Deendayal Energy University, Raisan, Gandhinagar, Gujarat, 382007, India.
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9
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Sanders KM, Drumm BT, Cobine CA, Baker SA. Ca 2+ dynamics in interstitial cells: foundational mechanisms for the motor patterns in the gastrointestinal tract. Physiol Rev 2024; 104:329-398. [PMID: 37561138 PMCID: PMC11281822 DOI: 10.1152/physrev.00036.2022] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/16/2022] [Revised: 06/29/2023] [Accepted: 08/06/2023] [Indexed: 08/11/2023] Open
Abstract
The gastrointestinal (GI) tract displays multiple motor patterns that move nutrients and wastes through the body. Smooth muscle cells (SMCs) provide the forces necessary for GI motility, but interstitial cells, electrically coupled to SMCs, tune SMC excitability, transduce inputs from enteric motor neurons, and generate pacemaker activity that underlies major motor patterns, such as peristalsis and segmentation. The interstitial cells regulating SMCs are interstitial cells of Cajal (ICC) and PDGF receptor (PDGFR)α+ cells. Together these cells form the SIP syncytium. ICC and PDGFRα+ cells express signature Ca2+-dependent conductances: ICC express Ca2+-activated Cl- channels, encoded by Ano1, that generate inward current, and PDGFRα+ cells express Ca2+-activated K+ channels, encoded by Kcnn3, that generate outward current. The open probabilities of interstitial cell conductances are controlled by Ca2+ release from the endoplasmic reticulum. The resulting Ca2+ transients occur spontaneously in a stochastic manner. Ca2+ transients in ICC induce spontaneous transient inward currents and spontaneous transient depolarizations (STDs). Neurotransmission increases or decreases Ca2+ transients, and the resulting depolarizing or hyperpolarizing responses conduct to other cells in the SIP syncytium. In pacemaker ICC, STDs activate voltage-dependent Ca2+ influx, which initiates a cluster of Ca2+ transients and sustains activation of ANO1 channels and depolarization during slow waves. Regulation of GI motility has traditionally been described as neurogenic and myogenic. Recent advances in understanding Ca2+ handling mechanisms in interstitial cells and how these mechanisms influence motor patterns of the GI tract suggest that the term "myogenic" should be replaced by the term "SIPgenic," as this review discusses.
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Affiliation(s)
- Kenton M Sanders
- Department of Physiology and Cell Biology, School of Medicine, University of Nevada-Reno, Reno, Nevada, United States
| | - Bernard T Drumm
- Smooth Muscle Research Centre, Dundalk Institute of Technology, Dundalk, Ireland
| | - Caroline A Cobine
- Smooth Muscle Research Centre, Dundalk Institute of Technology, Dundalk, Ireland
| | - Salah A Baker
- Department of Physiology and Cell Biology, School of Medicine, University of Nevada-Reno, Reno, Nevada, United States
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Kothiya A, Adlakha N. Impact of Interdependent Ca 2+ and IP 3 Dynamics On ATP Regulation in A Fibroblast Model. Cell Biochem Biophys 2023; 81:795-811. [PMID: 37749442 DOI: 10.1007/s12013-023-01177-6] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 09/12/2023] [Indexed: 09/27/2023]
Abstract
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.
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Affiliation(s)
- Ankit Kothiya
- DoM, S. V. National Institute of Technology, Surat, 395007, Gujarat, India.
| | - Neeru Adlakha
- DoM, S. V. National Institute of Technology, Surat, 395007, Gujarat, India
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11
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Pawar A, Pardasani KR. Study of disorders in regulatory spatiotemporal neurodynamics of calcium and nitric oxide. Cogn Neurodyn 2023; 17:1661-1682. [PMID: 37974582 PMCID: PMC10640555 DOI: 10.1007/s11571-022-09902-2] [Citation(s) in RCA: 9] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/01/2022] [Revised: 09/26/2022] [Accepted: 10/14/2022] [Indexed: 11/10/2022] Open
Abstract
Experimental studies have reported the dependence of nitric oxide (NO) on the regulation of neuronal calcium ([Ca2+]) dynamics in neurons. But, there is no model available to estimate the disorders caused by various parameters in their regulatory dynamics leading to various neuronal disorders. A mathematical model to analyze the impacts due to alterations in various parameters like buffer, ryanodine receptor, serca pump, source influx, etc. leading to regulation and dysregulation of the spatiotemporal calcium and NO dynamics in neuron cells is constructed using a system of reaction-diffusion equations. The numerical simulation is performed with the finite element approach. The disturbances in the different constitutive processes of [Ca2+] and nitric oxide including source influx, buffer mechanism, ryanodine receptor, serca pump, IP3 receptor, etc. can be responsible for the dysregulation in the [Ca2+] and NO dynamics in neurons. Also, the results reveal novel information about the magnitude and intensity of disorders in response to a range of alterations in various parameters of this neuronal dynamics, which can cause dysregulation leading to neuronal diseases like Parkinson's, cerebral ischemia, trauma, etc.
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Affiliation(s)
- Anand Pawar
- Department of Mathematics, Bioinformatics and Computer Applications, Maulana Azad National Institute of Technology, Bhopal, Madhya Pradesh 462003 India
| | - Kamal Raj Pardasani
- Department of Mathematics, Bioinformatics and Computer Applications, Maulana Azad National Institute of Technology, Bhopal, Madhya Pradesh 462003 India
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12
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Mishra V, Adlakha N. Spatio temporal interdependent calcium and buffer dynamics regulating DAG in a hepatocyte cell due to obesity. J Bioenerg Biomembr 2023; 55:249-266. [PMID: 37460636 DOI: 10.1007/s10863-023-09973-8] [Citation(s) in RCA: 5] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/14/2023] [Accepted: 06/23/2023] [Indexed: 09/12/2023]
Abstract
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.
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Affiliation(s)
- Vedika Mishra
- Department of Mathematics, SVNIT, Gujarat, 395007, Surat, India.
| | - Neeru Adlakha
- Department of Mathematics, SVNIT, Gujarat, 395007, Surat, India
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13
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Adlakha N. 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. J Bioenerg Biomembr 2023:10.1007/s10863-023-09966-7. [PMID: 37418135 DOI: 10.1007/s10863-023-09966-7] [Citation(s) in RCA: 6] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Key Words] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/27/2023] [Accepted: 04/27/2023] [Indexed: 07/08/2023]
Abstract
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).
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Affiliation(s)
- Neeru Adlakha
- Department of Mathematics and Humanities, SVNIT, Surat, 395007, Gujarat, India
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14
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Vatsal VH, Jha BK, Singh TP. To study the effect of ER flux with buffer on the neuronal calcium. EUROPEAN PHYSICAL JOURNAL PLUS 2023; 138:494. [PMID: 37304245 PMCID: PMC10240135 DOI: 10.1140/epjp/s13360-023-04077-z] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 03/10/2023] [Accepted: 05/07/2023] [Indexed: 06/13/2023]
Abstract
Calcium signaling is decisive for cellular functions. This calcium random walk stipulates neuronal functions. Calcium concentration could provoke gene transcription, apoptosis, neuronal plasticity, etc. A malformation in calcium could change the neuron's intracellular behavior. Calcium concentration balancing is a complex cellular mechanism. This occurrence can be handled with the Caputo fractional reaction-diffusion equation. In this mathematical modeling, we have included the STIM-Orai mechanism and Endoplasmic Reticulum (ER) flux, Inositol Triphosphate Receptor (IPR), SERCA, plasma membrane flux, voltage-gated calcium entry, and different buffer interactions. A hybrid integral transform and Green's function approach were taken to solve the initial boundary problem. A closed-form solution of a Mittag-Leffler family function plotted using MATLAB software. Different parameters impact changes in the spatiotemporal behavior of the calcium concentration. Specific roles of organelles involved in Alzheimer's disease-affected neurons are computed. Ethylene glycol tetraacetic acid (EGTA), 1,2-bis(o-aminophenoxy)ethane N,N,N,N-tetraacetic acid (BAPTA), and S100B protein effects are also observed. In all simulations, we can say S100B and the STIM-Orai effect cannot be neglected. This model lights up the different approaches for calcium signaling pathway simulation. As a consequence, we determine that a generalized reaction-diffusion approach is a better fit realistic model.
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Affiliation(s)
- Vora Hardagna Vatsal
- Department of Mathematics, Pandit Deendayal Energy University, Gandhinagar, 382007 Gujarat India
| | - Brajesh Kumar Jha
- Department of Mathematics, Pandit Deendayal Energy University, Gandhinagar, 382007 Gujarat India
| | - Tajinder Pal Singh
- Department of Mathematics, Pandit Deendayal Energy University, Gandhinagar, 382007 Gujarat India
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15
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Kothiya AB, Adlakha N. Cellular nitric oxide synthesis is affected by disorders in the interdependent [Formula: see text] and [Formula: see text] dynamics during cystic fibrosis disease. J Biol Phys 2023; 49:133-158. [PMID: 36811722 PMCID: PMC10160313 DOI: 10.1007/s10867-022-09624-w] [Citation(s) in RCA: 7] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/16/2022] [Accepted: 12/27/2022] [Indexed: 02/24/2023] Open
Abstract
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.
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16
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Pawar A, Pardasani KR. Mechanistic insights of neuronal calcium and IP 3 signaling system regulating ATP release during ischemia in progression of Alzheimer's disease. EUROPEAN BIOPHYSICS JOURNAL : EBJ 2023:10.1007/s00249-023-01660-1. [PMID: 37222773 DOI: 10.1007/s00249-023-01660-1] [Citation(s) in RCA: 6] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Key Words] [Subscribe] [Scholar Register] [Received: 12/05/2022] [Revised: 03/21/2023] [Accepted: 05/10/2023] [Indexed: 05/25/2023]
Abstract
The mechanisms of calcium ([Ca2+]) signaling in various human cells have been widely analyzed by scientists due to its crucial role in human organs like the heartbeat, muscle contractions, bone activity, brain functionality, etc. No study is reported for interdependent [Ca2+] and IP3 mechanics regulating the release of ATP in neuron cells during Ischemia in Alzheimer's disease advancement. In the present investigation, a finite element method (FEM) is framed to explore the interdependence of spatiotemporal [Ca2+] and IP3 signaling mechanics and its role in ATP release during Ischemia as well as in the advancement of Alzheimer's disorder in neuron cells. The results provide us insights of the mutual spatiotemporal impacts of [Ca2+] and IP3 mechanics as well as their contributions to ATP release during Ischemia in neuron cells. The results obtained for the mechanics of interdependent systems differ significantly from the results of simple independent system mechanics and provide new information about the processes of the two systems. From this study, it is concluded that neuronal disorders cannot only be simply attributed to the disturbance caused directly in the processes of calcium signaling mechanics, but also to the disturbances caused in IP3 regulation mechanisms impacting the calcium regulation in the neuron cell and ATP release.
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Affiliation(s)
- Anand Pawar
- Department of Mathematics, Bioinformatics and Computer Applications, Maulana Azad National Institute of Technology, Bhopal, Madhya Pradesh, 462003, India.
| | - Kamal Raj Pardasani
- Department of Mathematics, Bioinformatics and Computer Applications, Maulana Azad National Institute of Technology, Bhopal, Madhya Pradesh, 462003, India
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17
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Pawar A, Pardasani KR. Effect of disturbances in neuronal calcium and IP3 dynamics on β-amyloid production and degradation. Cogn Neurodyn 2023; 17:239-256. [PMID: 36704637 PMCID: PMC9871154 DOI: 10.1007/s11571-022-09815-0] [Citation(s) in RCA: 11] [Impact Index Per Article: 11.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/11/2022] [Revised: 04/12/2022] [Accepted: 04/21/2022] [Indexed: 01/29/2023] Open
Abstract
Overproduction and accumulation of β-amyloid and its improper clearance can cause neurotoxicity leading to Alzheimer's disease. The production and degradation of β-amyloid depend on the calcium ([Ca2+]) and IP3 dynamics in the nerve cells. Thus, there is a need to understand the impacts of disturbances in the processes of [Ca2+] and IP3 dynamics on β-amyloid production and its degradation. Here, a model is proposed to investigate the role of [Ca2+] and IP3 dynamics on β-amyloid production and degradation. The problem is formulated in terms of the initial boundary value problem involving the system of two reaction-diffusion equations respectively for [Ca2+] and IP3 in the nerve cell. The solution is obtained by employing the Finite element approach. The numerical results are used to analyze the impact of various mechanisms of calcium and IP3 dynamics on β-amyloid production and degradation in a neuron cell. The results indicate that disturbances in any of the constitutive processes of interdependent calcium and IP3 dynamics like source influx, buffering, serca pump, and IP3 dynamics, etc. can cause dynamic changes in β-amyloid production and degradation, which in turn can be the cause of neurotoxicity and neuronal disorders like Alzheimer's disease. Thus, the relationships obtained by the proposed model among various mechanisms can be useful in addressing the challenges of identifying specific constitutive processes causing neuronal disorders like Alzheimer's disease, etc., and developing the framework for their diagnosis and treatment.
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Affiliation(s)
- Anand Pawar
- Department of Mathematics, Bioinformatics, and Computer Applications, MANIT, Bhopal, Madhya Pradesh 462003 India
| | - Kamal Raj Pardasani
- Department of Mathematics, Bioinformatics, and Computer Applications, MANIT, Bhopal, Madhya Pradesh 462003 India
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18
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Agrawal A, Wang K, Polonchuk L, Cooper J, Hendrix M, Gavaghan DJ, Mirams GR, Clerx M. Models of the cardiac L-type calcium current: A quantitative review. WIREs Mech Dis 2023; 15:e1581. [PMID: 36028219 PMCID: PMC10078428 DOI: 10.1002/wsbm.1581] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/25/2022] [Revised: 06/16/2022] [Accepted: 07/19/2022] [Indexed: 01/31/2023]
Abstract
The L-type calcium current (I CaL ) plays a critical role in cardiac electrophysiology, and models ofI CaL are vital tools to predict arrhythmogenicity of drugs and mutations. Five decades of measuring and modelingI CaL have resulted in several competing theories (encoded in mathematical equations). However, the introduction of new models has not typically been accompanied by a data-driven critical comparison with previous work, so that it is unclear which model is best suited for any particular application. In this review, we describe and compare 73 published mammalianI CaL models and use simulated experiments to show that there is a large variability in their predictions, which is not substantially diminished when grouping by species or other categories. We provide model code for 60 models, list major data sources, and discuss experimental and modeling work that will be required to reduce this huge list of competing theories and ultimately develop a community consensus model ofI CaL . This article is categorized under: Cardiovascular Diseases > Computational Models Cardiovascular Diseases > Molecular and Cellular Physiology.
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Affiliation(s)
- Aditi Agrawal
- Computational Biology & Health Informatics, Department of Computer ScienceUniversity of OxfordOxfordUK
| | - Ken Wang
- Pharma Research and Early Development, Innovation Center BaselF. Hoffmann‐La Roche Ltd.BaselSwitzerland
| | - Liudmila Polonchuk
- Pharma Research and Early Development, Innovation Center BaselF. Hoffmann‐La Roche Ltd.BaselSwitzerland
| | - Jonathan Cooper
- Centre for Advanced Research ComputingUniversity College LondonLondonUK
| | - Maurice Hendrix
- Centre for Mathematical Medicine & Biology, School of Mathematical SciencesUniversity of NottinghamNottinghamUK
- Digital Research Service, Information SciencesUniversity of NottinghamNottinghamUK
| | - David J. Gavaghan
- Computational Biology & Health Informatics, Department of Computer ScienceUniversity of OxfordOxfordUK
| | - Gary R. Mirams
- Centre for Mathematical Medicine & Biology, School of Mathematical SciencesUniversity of NottinghamNottinghamUK
| | - Michael Clerx
- Centre for Mathematical Medicine & Biology, School of Mathematical SciencesUniversity of NottinghamNottinghamUK
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19
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Sneyd J, Rugis J, Su S, Suresh V, Wahl AM, Yule DI. Simulation of Calcium Dynamics in Realistic Three-Dimensional Domains. Biomolecules 2022; 12:1455. [PMID: 36291663 PMCID: PMC9599163 DOI: 10.3390/biom12101455] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/13/2022] [Revised: 10/01/2022] [Accepted: 10/04/2022] [Indexed: 11/16/2022] Open
Abstract
The cytosolic concentration of free calcium ions ([Ca2+]) is an important intracellular messenger in most cell types, and the spatial distribution of [Ca2+] is often critical. In a salivary gland acinar cell, a polarised epithelial cell, whose principal function is to transport water and thus secrete saliva, [Ca2+] controls the secretion of primary saliva, but increases in [Ca2+] are localised to the apical regions of the cell. Hence, any quantitative explanation of how [Ca2+] controls saliva secretion must take into careful account the spatial distribution of the various Ca2+ sources, Ca2+ sinks, and Ca2+-sensitive ion channels. Based on optical slices, we have previously constructed anatomically accurate three-dimensional models of seven salivary gland acinar cells, and thus shown that a model in which Ca2+ responses are confined to the apical regions of the cell is sufficient to provide a quantitative and predictive explanation of primary saliva secretion. However, reconstruction of such anatomically accurate cells is extremely time consuming and inefficient. Here, we present an alternative, mostly automated method of constructing three-dimensional cells that are approximately anatomically accurate and show that the new construction preserves the quantitative accuracy of the model.
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Affiliation(s)
- James Sneyd
- Department of Mathematics, University of Auckland, Auckland 1142, New Zealand
| | - John Rugis
- Department of Mathematics, University of Auckland, Auckland 1142, New Zealand
| | - Shan Su
- Department of Mathematics, University of Auckland, Auckland 1142, New Zealand
| | - Vinod Suresh
- Department of Engineering Science, University of Auckland, Auckland 1142, New Zealand
| | - Amanda M. Wahl
- Department of Pharmacology and Physiology, University of Rochester, Rochester, NY 14642, USA
| | - David I. Yule
- Department of Pharmacology and Physiology, University of Rochester, Rochester, NY 14642, USA
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20
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Chen Y, Matveev V. Stationary Ca 2+ nanodomains in the presence of buffers with two binding sites. Biophys J 2021; 120:1942-1956. [PMID: 33771472 DOI: 10.1016/j.bpj.2021.03.015] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/14/2020] [Revised: 03/06/2021] [Accepted: 03/11/2021] [Indexed: 10/21/2022] Open
Abstract
We examine closed-form approximations for the equilibrium Ca2+ and buffer concentrations near a point Ca2+ source representing a Ca2+ channel, in the presence of a mobile buffer with two Ca2+ binding sites activated sequentially and possessing distinct binding affinities and kinetics. This allows us to model the impact on Ca2+ nanodomains of realistic endogenous Ca2+ buffers characterized by cooperative Ca2+ binding, such as calretinin. The approximations we present involve a combination or rational and exponential functions, whose parameters are constrained using the series interpolation method that we recently introduced for the case of simpler Ca2+ buffers with a single Ca2+ binding site. We conduct extensive parameter sensitivity analysis and show that the obtained closed-form approximations achieve reasonable qualitative accuracy for a wide range of buffer's Ca2+ binding properties and other relevant model parameters. In particular, the accuracy of the derived approximants exceeds that of the rapid buffering approximation in large portions of the relevant parameter space.
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Affiliation(s)
- Yinbo Chen
- Department of Mathematical Sciences, New Jersey Institute of Technology, Newark, New Jersey
| | - Victor Matveev
- Department of Mathematical Sciences, New Jersey Institute of Technology, Newark, New Jersey.
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21
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Peng Z, Resnick A, Young YN. Primary cilium: a paradigm for integrating mathematical modeling with experiments and numerical simulations in mechanobiology. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2021; 18:1215-1237. [PMID: 33757184 PMCID: PMC8552149 DOI: 10.3934/mbe.2021066] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
Primary cilia are non-motile, solitary (one per cell) microtubule-based organelles that emerge from the mother centriole after cells have exited the mitotic cycle. Identified as a mechanosensing organelle that responds to both mechanical and chemical stimuli, the primary cilium provides a fertile ground for integrative investigations of mathematical modeling, numerical simulations, and experiments. Recent experimental findings revealed considerable complexity to the underlying mechanosensory mechanisms that transmit extracellular stimuli to intracellular signaling many of which include primary cilia. In this invited review, we provide a brief survey of experimental findings on primary cilia and how these results lead to various mathematical models of the mechanics of the primary cilium bent under an external forcing such as a fluid flow or a trap. Mathematical modeling of the primary cilium as a fluid-structure interaction problem highlights the importance of basal anchorage and the anisotropic moduli of the microtubules. As theoretical modeling and numerical simulations progress, along with improved state-of-the-art experiments on primary cilia, we hope that details of ciliary regulated mechano-chemical signaling dynamics in cellular physiology will be understood in the near future.
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Affiliation(s)
- Zhangli Peng
- Department of Bioengineering, University of Illinois at Chicago, 851 S. Morgan St., Chicago, IL 60607, USA
| | - Andrew Resnick
- Department of Physics, Center for Gene Regulation in Health and Disease, Cleveland State University, Cleveland, OH 44115, USA
| | - Y.-N. Young
- Department of Mathematical Sciences, New Jersey Institute of Technology, University Heights, Newark, NJ 07102, USA
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22
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Dave DD, Jha BK. Mathematical Modeling of Calcium Oscillatory Patterns in a Neuron. Interdiscip Sci 2020; 13:12-24. [PMID: 33170431 DOI: 10.1007/s12539-020-00401-8] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/15/2020] [Revised: 10/21/2020] [Accepted: 10/24/2020] [Indexed: 12/01/2022]
Abstract
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.
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Affiliation(s)
- Devanshi D Dave
- Department of Mathematics, School of Technology, PDPU, Gandhinagar, 382007, Gujarat, India.
| | - Brajesh Kumar Jha
- Department of Mathematics, School of Technology, PDPU, Gandhinagar, 382007, Gujarat, India
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23
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Chen Y, Muratov CB, Matveev V. Efficient Approximations for Stationary Single-Channel Ca 2+ Nanodomains across Length Scales. Biophys J 2020; 119:1239-1254. [PMID: 32877663 DOI: 10.1016/j.bpj.2020.06.038] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/16/2020] [Revised: 06/06/2020] [Accepted: 06/10/2020] [Indexed: 10/23/2022] Open
Abstract
We consider the stationary solution for the Ca2+ concentration near a point Ca2+ source describing a single-channel Ca2+ nanodomain in the presence of a single mobile Ca2+ buffer with 1:1 Ca2+ binding. We present computationally efficient approximants that estimate stationary single-channel Ca2+ nanodomains with great accuracy in broad regions of parameter space. The presented approximants have a functional form that combines rational and exponential functions, which is similar to that of the well-known excess buffer approximation and the linear approximation but with parameters estimated using two novel, to our knowledge, methods. One of the methods involves interpolation between the short-range Taylor series of the free buffer concentration and its long-range asymptotic series in inverse powers of distance from the channel. Although this method has already been used to find Padé (rational-function) approximants to single-channel Ca2+ and buffer concentrations, extending this method to interpolants combining exponential and rational functions improves accuracy in a significant fraction of the relevant parameter space. A second method is based on the variational approach and involves a global minimization of an appropriate functional with respect to parameters of the chosen approximations. An extensive parameter-sensitivity analysis is presented, comparing these two methods with previously developed approximants. Apart from increased accuracy, the strength of these approximants is that they can be extended to more realistic buffers with multiple binding sites characterized by cooperative Ca2+ binding, such as calmodulin and calretinin.
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Affiliation(s)
- Yinbo Chen
- Department of Mathematical Sciences, New Jersey Institute of Technology, Newark, New Jersey
| | - Cyrill B Muratov
- Department of Mathematical Sciences, New Jersey Institute of Technology, Newark, New Jersey
| | - Victor Matveev
- Department of Mathematical Sciences, New Jersey Institute of Technology, Newark, New Jersey.
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24
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Naik PA. Modeling the mechanics of calcium regulation in T lymphocyte: A finite element method approach. INT J BIOMATH 2020. [DOI: 10.1142/s1793524520500382] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
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.
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Affiliation(s)
- Parvaiz Ahmad Naik
- School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, P. R. China
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25
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Naik PA, Zu J. Modeling and simulation of spatial-temporal calcium distribution in T lymphocyte cell by using a reaction-diffusion equation. J Bioinform Comput Biol 2020; 18:2050013. [PMID: 32372713 DOI: 10.1142/s0219720020500134] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/03/2023]
Abstract
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.
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Affiliation(s)
- Parvaiz Ahmad Naik
- School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, Shaanxi 710049, P. R. China
| | - Jian Zu
- School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, Shaanxi 710049, P. R. China
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27
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Youm JB, Zheng H, Koh SD, Sanders KM. Na-K-2Cl Cotransporter and Store-Operated Ca 2+ Entry in Pacemaking by Interstitial Cells of Cajal. Biophys J 2019; 117:767-779. [PMID: 31400920 DOI: 10.1016/j.bpj.2019.07.020] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/18/2019] [Revised: 06/26/2019] [Accepted: 07/11/2019] [Indexed: 01/13/2023] Open
Abstract
Pacemaker depolarization in interstitial cells of Cajal (ICCs) is believed to be induced by Ca2+ transients and activation of anoctamin-1 (Ano1) channels in the plasma membrane. However, block of store-operated calcium entry (SOCE) or the Na-K-2Cl cotransporter (NKCC1) terminates pacemaker activity in ICC, indicating these transporters are involved in the initiation or maintenance of pacemaker activity. We hypothesized that SOCE contributes to pacemaker depolarization by maintaining [Ca2+] in the endoplasmic reticulum, which is the underlying source of Ca2+ transients for activation of Ano1. NKCC1 maintains the Cl- gradient supporting the driving force for inward current mediated by Ano1. Currently mechanisms sustaining release of Ca2+ and activation of Ano1 channels during the plateau phase of slow waves are unknown, but the reverse mode of the Na+/Ca2+ exchange may contribute. We generated a mathematical model of pacemaker activity based on current empirical observations from ICC of mouse small intestine that incorporates functions of SOCE and NKCC1. This model reproduces experimental findings, suggesting roles for SOCE and Ano1 channels: blocking of either NKCC1 or SOCE in our model terminates pacemaker activity. Direct contribution of NKCC1 to pacemaker activity in a beat-to-beat manner is not predicted by our model. Instead, NKCC1 plays a maintenance role supporting the driving force for Cl- efflux. Incorporation of SOCE allows the model to drive pacemaker activity without a diastolic depolarization, as observed in cardiac pacemaking. Further biological experiments are necessary to validate and further refine the roles of NKCC1, Na+/Ca2+ exchange, and Ano1 in the pacemaker mechanism of ICC.
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Affiliation(s)
- Jae Boum Youm
- Department of Physiology, College of Medicine, Cardiovascular and Metabolic Disease Center, Inje University, Busan, Korea
| | - Haifeng Zheng
- Department of Physiology and Cell Biology, University of Nevada, Reno School of Medicine, Reno, Nevada
| | - Sang Don Koh
- Department of Physiology and Cell Biology, University of Nevada, Reno School of Medicine, Reno, Nevada
| | - Kenton M Sanders
- Department of Physiology and Cell Biology, University of Nevada, Reno School of Medicine, Reno, Nevada.
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28
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Naik PA, Pardasani KR. Finite element model to study calcium distribution in oocytes involving voltage gated Ca2+ channel, ryanodine receptor and buffers. ALEXANDRIA JOURNAL OF MEDICINE 2019. [DOI: 10.1016/j.ajme.2015.02.002] [Citation(s) in RCA: 21] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 10/23/2022] Open
Affiliation(s)
- Parvaiz Ahmad Naik
- Department of Mathematics, Maulana Azad National Institute of Technology, Bhopal, 462051, India
| | - Kamal Raj Pardasani
- Department of Mathematics, Maulana Azad National Institute of Technology, Bhopal, 462051, India
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Abstract
Fundamental cell processes such as synaptic neurotransmitter release, endocrine hormone secretion, and myocyte contraction are controlled by highly localized calcium (Ca2+) signals resulting from brief openings of trans-membrane Ca2+ channels. On short temporal and spatial scales, the corresponding local Ca2+ nanodomains formed in the vicinity of a single or several open Ca2+ channels can be effectively approximated by quasi-stationary solutions. The rapid buffering approximation (RBA) is one of the most powerful of such approximations, and is based on the assumption of instantaneous equilibration of the bimolecular Ca2+ buffering reaction, combined with the conservation condition for the total Ca2+ and buffer molecule numbers. Previously, RBA has been generalized to an arbitrary arrangement of Ca2+ channels on a flat membrane, in the presence of any number of simple Ca2+ buffers with one-to-one Ca2+ binding stoichiometry. However, many biological buffers have multiple binding sites. For example, buffers and sensors phylogenetically related to calmodulin consist of two Ca2+-binding domains (lobes), with each domain binding two Ca2+ ions in a cooperative manner. Here we consider an extension of RBA to such buffers with two interdependent Ca2+ binding sites. We show that in the presence of such buffers, RBA solution is given by the solution to a cubic equation, analogous to the quadratic equation describing RBA in the case of a simple, one-to-one Ca2+ buffer. We examine in detail the dependence of RBA accuracy on buffering parameters, to reveal conditions under which RBA provides sufficient precision.
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Affiliation(s)
- Victor Matveev
- Department of Mathematical Sciences, New Jersey Institute of Technology, Newark, New Jersey.
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Joshi H, Jha BK. Fractionally delineate the neuroprotective function of calbindin-D28k in Parkinson’s disease. INT J BIOMATH 2019. [DOI: 10.1142/s1793524518501036] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022]
Abstract
Neuron is a fundamental unit of the brain, which is specialized to transmit information throughout the body through electrical and chemical signals. Calcium ([Formula: see text]) ions are known as second messengers which play important roles in the movement of the neurotransmitter. Calbindin-[Formula: see text] is a [Formula: see text] binding protein which is involved in regulation of intracellular [Formula: see text] ions and maintains [Formula: see text] homeostasis level, it also alters the cytosolic calcium concentration ([[Formula: see text]]) in nerve cells to keep the cell alive. Parkinson’s disease (PD) is a chronic progressive neurodegenerative brain disorder of the nervous system. Several regions of the brain indicate the hallmark of the PD. The symptoms of PD are plainly linked with the degeneration and death of dopamine neurons in the substantia nigra pars compacta located in midbrain which is accompanied by depletion in calbindin-[Formula: see text]. In the present paper, the neuroprotective role of calbindin-[Formula: see text] in the cytoplasmic [[Formula: see text]] distribution is studied. The elicitation in [[Formula: see text]] is due to the presence of low amount of calbindin-[Formula: see text] which can be portrayed and is a hallmark of PD. A one-dimensional space time fractional reaction diffusion equation is designed by keeping in mind the physiological condition taking place inside Parkinson’s brain. Computational results are performed in MATLAB.
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Affiliation(s)
- Hardik Joshi
- Department of Mathematics, School of Technology, Pandit Deendayal Petroleum University, Gandhinagar, Gujarat 382007, India
| | - Brajesh Kumar Jha
- Department of Mathematics, School of Technology, Pandit Deendayal Petroleum University, Gandhinagar, Gujarat 382007, India
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Abstract
Brain is the most complex structure of the human body. The processes going inside the brain and the mechanisms behind it have been unrevealed up to certain extent only. Out of the various physiological phenomena carried out by the brain, calcium signalling can be considered as one of the most important. Calcium being a second messenger plays an important role in transformation of various information. In view of above, an attempt has been made here to study calcium signalling in presence of buffers, i.e. one kind of proteins and endoplasmic reticulum (ER), which is also known as store house of the cell. Being the store house of the cell, it has very high amount of calcium, whereas buffers decrease the level of free calcium ions by binding calcium ions to it. A two-dimensional mathematical model has been developed to see the impact of these parameters on cytosolic calcium concentration. This mathematical model is solved analytically using Laplace transforms and similarity transforms. The simulations are carried out using MATLAB. It is observed that the impact of buffer and ER is significant on calcium signalling. The obtained results are interpreted with the Alzheimeric condition of the nerve cells.
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Affiliation(s)
- Devanshi D. Dave
- Department of Mathematics, School of Technology, Pandit Deendayal Petroleum University, Raisan, Gandhinagar, Gujarat 382007, India
| | - Brajesh Kumar Jha
- Department of Mathematics, School of Technology, Pandit Deendayal Petroleum University, Raisan, Gandhinagar, Gujarat 382007, India
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Abstract
Under the widespread umbrella of dementia, Alzheimer’s disease is the most common form of dementia. Most of the aged people are suffering from Alzheimer’s disease around the world. The reasons for the same are not known in detail and thus various experimental and computational attempts need to be carried out. Calcium, being a second messenger has an immense role in transformation of information. This transformation takes place in the form of signaling in which several parameters play an active role. In present work, an attempt has been made to describe the effect of calcium signaling in nerve cells for Alzheimer’s disease. Here, parameters like advection diffusion and buffering are taken into consideration to visualize the effects of the same on cytosolic calcium concentration. This physiological process is modeled two dimensionally and solved analytically. Laplace and similarity transforms are employed to obtain the desired results. The results are simulated and graphically plotted using MATLAB. The known fact that the higher concentration of calcium has adverse effects on the cell which may result into progression of AD is considered as a lantern in enlightening the physiology of Alzheimer’s disease.
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Affiliation(s)
- DEVANSHI D. DAVE
- Department of Mathematics, School of Technology, Pandit Deendayal Petroleum University, Gandhinagar 382007, Gujarat, India
| | - BRAJESH KUMAR JHA
- Department of Mathematics, School of Technology, Pandit Deendayal Petroleum University, Gandhinagar 382007, Gujarat, India
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Matveev V. Padé Approximation of a Stationary Single-Channel Ca 2+ Nanodomain. Biophys J 2017; 111:2062-2074. [PMID: 27806286 DOI: 10.1016/j.bpj.2016.09.019] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/28/2016] [Revised: 09/09/2016] [Accepted: 09/14/2016] [Indexed: 11/30/2022] Open
Abstract
We consider the stationary solution for the Ca2+ concentration near a point Ca2+ source describing a single-channel Ca2+ nanodomain, in the presence of a single mobile buffer with one-to-one Ca2+ binding stoichiometry. Previously, a number of Ca2+ nanodomains approximations have been developed, for instance the excess buffer approximation (EBA), the rapid buffering approximation (RBA), and the linear approximation (LIN), each valid for appropriate buffering conditions. Apart from providing a simple method of estimating Ca2+ and buffer concentrations without resorting to computationally expensive numerical solution of reaction-diffusion equations, such approximations proved useful in revealing the dependence of nanodomain Ca2+ distribution on crucial parameters such as buffer mobility and its Ca2+ binding properties. In this study, we present a different form of analytic approximation, which is based on matching the short-range Taylor series of the nanodomain concentration with the long-range asymptotic series expressed in inverse powers of distance from channel location. Namely, we use a "dual" Padé rational function approximation to simultaneously match terms in the short- and the long-range series, and we show that this provides an accurate approximation to the nanodomain Ca2+ and buffer concentrations. We compare this approximation with the previously obtained approximations and show that it yields a better estimate of the free buffer concentration for a wide range of buffering conditions. The drawback of our method is that it has a complex algebraic form for any order higher than the lowest bilinear order, and cannot be readily extended to multiple Ca2+ channels. However, it may be possible to extend the Padé method to estimate Ca2+ nanodomains in the presence of cooperative Ca2+ buffers with two Ca2+ binding sites, the case that existing methods do not address.
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Affiliation(s)
- V Matveev
- Department of Mathematical Sciences, New Jersey Institute of Technology, Newark, New Jersey.
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Finite Element Model to Study Calcium Distribution in T Lymphocyte Involving Buffers and Ryanodine Receptors. PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES INDIA SECTION A-PHYSICAL SCIENCES 2017. [DOI: 10.1007/s40010-017-0380-7] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
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Sigaut L, Villarruel C, Ponce Dawson S. FCS experiments to quantify Ca 2+ diffusion and its interaction with buffers. J Chem Phys 2017; 146:104203. [PMID: 28298094 DOI: 10.1063/1.4977586] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023] Open
Abstract
Ca2+ signals are ubiquitous. One of the key factors for their versatility is the variety of spatio-temporal distributions that the cytosolic Ca2+ can display. In most cell types Ca2+ signals not only depend on Ca2+ entry from the extracellular medium but also on Ca2+ release from internal stores, a process which is in turn regulated by cytosolic Ca2+ itself. The rate at which Ca2+ is transported, the fraction that is trapped by intracellular buffers, and with what kinetics are thus key features that affect the time and spatial range of action of Ca2+ signals. The quantification of Ca2+ diffusion in intact cells is quite challenging because the transport rates that can be inferred using optical techniques are intricately related to the interaction of Ca2+ with the dye that is used for its observation and with the cellular buffers. In this paper, we introduce an approach that uses Fluorescence Correlation Spectroscopy (FCS) experiments performed at different conditions that in principle allows the quantification of Ca2+ diffusion and of its reaction rates with unobservable (non-fluorescent) Ca2+ buffers. To this end, we develop the necessary theory to interpret the experimental results and then apply it to FCS experiments performed in a set of solutions containing Ca2+, a single wavelength Ca2+ dye, and a non-fluorescent Ca2+ buffer. We show that a judicious choice of the experimental conditions and an adequate interpretation of the fitting parameters can be combined to extract information on the free diffusion coefficient of Ca2+ and of some of the properties of the unobservable buffer. We think that this approach can be applied to other situations, particularly to experiments performed in intact cells.
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Affiliation(s)
- Lorena Sigaut
- Departamento de Física, FCEN-UBA, and IFIBA, CONICET, Ciudad Universitaria, Pabellón I, 1428 Buenos Aires, Argentina
| | - Cecilia Villarruel
- Departamento de Física, FCEN-UBA, and IFIBA, CONICET, Ciudad Universitaria, Pabellón I, 1428 Buenos Aires, Argentina
| | - Silvina Ponce Dawson
- Departamento de Física, FCEN-UBA, and IFIBA, CONICET, Ciudad Universitaria, Pabellón I, 1428 Buenos Aires, Argentina
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Jha BK, Joshi H, Dave DD. Portraying the Effect of Calcium-Binding Proteins on Cytosolic Calcium Concentration Distribution Fractionally in Nerve Cells. Interdiscip Sci 2016; 10:674-685. [DOI: 10.1007/s12539-016-0202-7] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/22/2016] [Revised: 10/02/2016] [Accepted: 11/08/2016] [Indexed: 10/20/2022]
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Cox DH. Modeling a Ca(2+) channel/BKCa channel complex at the single-complex level. Biophys J 2016; 107:2797-2814. [PMID: 25517147 DOI: 10.1016/j.bpj.2014.10.069] [Citation(s) in RCA: 28] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/10/2014] [Revised: 09/26/2014] [Accepted: 10/23/2014] [Indexed: 11/18/2022] Open
Abstract
BKCa-channel activity often affects the firing properties of neurons, the shapes of neuronal action potentials (APs), and in some cases the extent of neurotransmitter release. It has become clear that BKCa channels often form complexes with voltage-gated Ca(2+) channels (CaV channels) such that when a CaV channel is activated, the ensuing influx of Ca(2+) activates its closely associated BKCa channel. Thus, in modeling the electrical properties of neurons, it would be useful to have quantitative models of CaV/BKCa complexes. Furthermore, in a population of CaV/BKCa complexes, all BKCa channels are not exposed to the same Ca(2+) concentration at the same time. Thus, stochastic rather than deterministic models are required. To date, however, no such models have been described. Here, however, I present a stochastic model of a CaV2.1/BKCa(α-only) complex, as might be found in a central nerve terminal. The CaV2.1/BKCa model is based on kinetic modeling of its two component channels at physiological temperature. Surprisingly, The CaV2.1/BKCa model predicts that although the CaV channel will open nearly every time during a typical cortical AP, its associated BKCa channel is expected to open in only 30% of trials, and this percentage is very sensitive to the duration of the AP, the distance between the two channels in the complex, and the presence of fast internal Ca(2+) buffers. Also, the model predicts that the kinetics of the BKCa currents of a population of CaV2.1/BKCa complexes will not be limited by the kinetics of the CaV2.1 channel, and during a train of APs, the current response of the complex is expected to faithfully follow even very rapid trains. Aside from providing insight into how these complexes are likely to behave in vivo, the models presented here could also be of use more generally as components of higher-level models of neural function.
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Affiliation(s)
- Daniel H Cox
- Department of Neuroscience, Tufts University School of Medicine, Boston, Massachusetts.
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Toglia P, Ullah G. The gain-of-function enhancement of IP3-receptor channel gating by familial Alzheimer's disease-linked presenilin mutants increases the open probability of mitochondrial permeability transition pore. Cell Calcium 2016; 60:13-24. [PMID: 27184076 DOI: 10.1016/j.ceca.2016.05.002] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/26/2016] [Revised: 04/19/2016] [Accepted: 05/05/2016] [Indexed: 12/13/2022]
Abstract
Mutants in presenilins (PS1 or PS2) are the major cause of familial Alzheimer's disease (FAD). They affect intracellular Ca(2+) homeostasis by increasing the open probability (Po) of inositol 1,4,5-trisposphate (IP3) receptor (IP3R) Ca(2+) release channel located on the endoplasmic reticulum (ER) leading to exaggerated Ca(2+) release into a cytoplasmic microdomain formed by neighboring cluster of a few IP3R channels and mitochondrial Ca(2+) uniporter (MCU). Ca(2+) concentration in the microdomain ( [Formula: see text] ) depends on the distance between the cluster and MCU (r); the number of IP3R in the cluster releasing Ca(2+) to the cytoplasm ( [Formula: see text] ), and Po of IP3R. Using experimental whole-cell IP3R-mediated cytosolic Ca(2+) data, in conjunction with a computational model of cell bioenergetics, a data-driven Markov chain model for IP3R gating, and a model for the dynamics of the mitochondrial permeability transition pore (PTP), we explore differences in mitochondrial Ca(2+) uptake in cells expressing wild type (PS1-WT) and FAD-causing mutant (PS1-M146L) PS. We find that increased mitochondrial [Formula: see text] due to the gain-of-function enhancement of IP3R channels in the cells expressing PS1-M146L leads to the opening of PTP in high conductance state (PTPh), where the latency of opening is inversely correlated with r and proportional to [Formula: see text] . Furthermore, we observe diminished inner mitochondrial membrane potential (ΔΨm), [NADH], [Formula: see text] , and [ATP] when PTP opens. Additionally, we explore how parameters such as the pH gradient, inorganic phosphate concentration, and the rate of the Na(+)/Ca(2+)-exchanger affect the latency of PTP to open in PTPh.
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Affiliation(s)
- Patrick Toglia
- Department of Physics, University of South Florida, Tampa, FL 33620, USA
| | - Ghanim Ullah
- Department of Physics, University of South Florida, Tampa, FL 33620, USA.
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JHA AMRITA, ADLAKHA NEERU, JHA BRAJESHKUMAR. FINITE ELEMENT MODEL TO STUDY EFFECT OF Na+−Ca2+ EXCHANGERS AND SOURCE GEOMETRY ON CALCIUM DYNAMICS IN A NEURON CELL. J MECH MED BIOL 2016. [DOI: 10.1142/s0219519416500184] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
The study of calcium diffusion in neuron cells has gained interest among research workers during the last two decades, due to its wide variety of roles in human body like muscle contraction, secretion, metabolism, signal transduction etc. Na[Formula: see text] is the first ion that comes in the hierarchy of ions affecting cytosolic Ca[Formula: see text] concentration. This Na[Formula: see text] ion helps in intracellular Ca[Formula: see text] regulation in cytosol via Na[Formula: see text]/Ca[Formula: see text] exchanger protein (NCX protein). Most of the theoretical investigations on calcium diffusion in neuron cells have been carried out for one and two dimensional cases by various research workers and that too by incorporating a point source of influx. In order to have more realistic study the more details of geometry, microstructure and physiological parameters need to be incorporated in the models. In view of above a three dimensional unsteady state model of Calcium dynamics in a neuron cell has been developed. Apart from the point source, the line and surface sources of an influx of Ca[Formula: see text]as well as the Na[Formula: see text]/Ca[Formula: see text] exchanger, have been incorporated in the model. Appropriate initial and boundary conditions have been framed. The region is discretized using three dimensional circular sectoral elements. Variational finite element method has been employed to obtain the solution. The numerical results have been computed to study effect of Na[Formula: see text]/Ca[Formula: see text] exchanger, point source, line source and surface source of an influx on Ca[Formula: see text] distribution in a neuron cell.
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Affiliation(s)
- AMRITA JHA
- Department of Science & Humanities, Indus University, Ahmedabad, Gujarat, India
| | - NEERU ADLAKHA
- Department of Applied Mathematics & Humanities, SVNIT, Gujarat, India
| | - BRAJESH KUMAR JHA
- Department of Mathematics and Computer Science, SOT, Pandit Deendayal Petroleum University, Gandhinagar, Gujarat, India
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Wilson C, Saunter CD, Girkin JM, McCarron JG. Pressure-dependent regulation of Ca2+ signalling in the vascular endothelium. J Physiol 2015; 593:5231-53. [PMID: 26507455 PMCID: PMC4704526 DOI: 10.1113/jp271157] [Citation(s) in RCA: 31] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/26/2015] [Accepted: 10/19/2015] [Indexed: 12/19/2022] Open
Abstract
Key points Increased pressure suppresses endothelial control of vascular tone but it remains uncertain (1) how pressure is sensed by the endothelium and (2) how the vascular response is inhibited. This study used a novel imaging method to study large numbers of endothelial cells in arteries that were in a physiological configuration and held at normal blood pressures. Increased pressure suppressed endothelial IP3‐mediated Ca2+ signals. Pressure modulated endothelial cell shape. The changes in cell shape may alter endothelial Ca2+ signals by modulating the diffusive environment for Ca2+ near IP3 receptors. Endothelial pressure‐dependent mechanosensing may occur without a requirement for a conventional molecular mechanoreceptor.
Abstract The endothelium is an interconnected network upon which haemodynamic mechanical forces act to control vascular tone and remodelling in disease. Ca2+ signalling is central to the endothelium's mechanotransduction and networked activity. However, challenges in imaging Ca2+ in large numbers of endothelial cells under conditions that preserve the intact physical configuration of pressurized arteries have limited progress in understanding how pressure‐dependent mechanical forces alter networked Ca2+ signalling. We developed a miniature wide‐field, gradient‐index (GRIN) optical probe designed to fit inside an intact pressurized artery that permitted Ca2+ signals to be imaged with subcellular resolution in a large number (∼200) of naturally connected endothelial cells at various pressures. Chemical (acetylcholine) activation triggered spatiotemporally complex, propagating inositol trisphosphate (IP3)‐mediated Ca2+ waves that originated in clusters of cells and progressed from there across the endothelium. Mechanical stimulation of the artery, by increased intraluminal pressure, flattened the endothelial cells and suppressed IP3‐mediated Ca2+ signals in all activated cells. By computationally modelling Ca2+ release, endothelial shape changes were shown to alter the geometry of the Ca2+ diffusive environment near IP3 receptor microdomains to limit IP3‐mediated Ca2+ signals as pressure increased. Changes in cell shape produce a geometric microdomain regulation of IP3‐mediated Ca2+ signalling to explain macroscopic pressure‐dependent, endothelial mechanosensing without the need for a conventional mechanoreceptor. The suppression of IP3‐mediated Ca2+ signalling may explain the decrease in endothelial activity as pressure increases. GRIN imaging provides a convenient method that gives access to hundreds of endothelial cells in intact arteries in physiological configuration. Increased pressure suppresses endothelial control of vascular tone but it remains uncertain (1) how pressure is sensed by the endothelium and (2) how the vascular response is inhibited. This study used a novel imaging method to study large numbers of endothelial cells in arteries that were in a physiological configuration and held at normal blood pressures. Increased pressure suppressed endothelial IP3‐mediated Ca2+ signals. Pressure modulated endothelial cell shape. The changes in cell shape may alter endothelial Ca2+ signals by modulating the diffusive environment for Ca2+ near IP3 receptors. Endothelial pressure‐dependent mechanosensing may occur without a requirement for a conventional molecular mechanoreceptor.
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Affiliation(s)
- Calum Wilson
- Strathclyde Institute of Pharmacy and Biomedical Sciences, University of Strathclyde, SIPBS Building, 161 Cathedral Street, Glasgow, G4 0RE, UK
| | - Christopher D Saunter
- Centre for Advanced Instrumentation, Biophysical Sciences Institute, Department of Physics, Durham University, South Road, Durham, DH1 3LE, UK
| | - John M Girkin
- Centre for Advanced Instrumentation, Biophysical Sciences Institute, Department of Physics, Durham University, South Road, Durham, DH1 3LE, UK
| | - John G McCarron
- Strathclyde Institute of Pharmacy and Biomedical Sciences, University of Strathclyde, SIPBS Building, 161 Cathedral Street, Glasgow, G4 0RE, UK
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Bao G, de Jong D, Alevra M, Schild D. Ca(2+)-BK channel clusters in olfactory receptor neurons and their role in odour coding. Eur J Neurosci 2015; 42:2985-95. [PMID: 26452167 DOI: 10.1111/ejn.13095] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/10/2015] [Revised: 09/17/2015] [Accepted: 10/03/2015] [Indexed: 11/26/2022]
Abstract
Olfactory receptor neurons (ORNs) have high-voltage-gated Ca(2+) channels whose physiological impact has remained enigmatic since the voltage-gated conductances in this cell type were first described in the 1980s. Here we show that in ORN somata of Xenopus laevis tadpoles these channels are clustered and co-expressed with large-conductance potassium (BK) channels. We found approximately five clusters per ORN and twelve Ca(2+) channels per cluster. The action potential-triggered activation of BK channels accelerates the repolarization of action potentials and shortens interspike intervals during odour responses. This increases the sensitivity of individual ORNs to odorants. At the level of mitral cells of the olfactory bulb, odour qualities have been shown to be coded by first-spike-latency patterns. The system of Ca(2+) and BK channels in ORNs appears to be important for correct odour coding because the blockage of BK channels not only affects ORN spiking patterns but also changes the latency pattern representation of odours in the olfactory bulb.
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Affiliation(s)
- Guobin Bao
- Institute of Neurophysiology and Cellular Biophysics, University of Göttingen, Humboldtallee 23, 37073, Göttingen, Germany.,DFG Research Center for Nanoscale Microscopy and Molecular Physiology of the Brain (CNMPB), University of Göttingen, Göttingen, Germany
| | - Daniëlle de Jong
- Institute of Neurophysiology and Cellular Biophysics, University of Göttingen, Humboldtallee 23, 37073, Göttingen, Germany.,DFG Research Center for Nanoscale Microscopy and Molecular Physiology of the Brain (CNMPB), University of Göttingen, Göttingen, Germany
| | - Mihai Alevra
- Institute of Neurophysiology and Cellular Biophysics, University of Göttingen, Humboldtallee 23, 37073, Göttingen, Germany.,DFG Excellence Cluster 171, University of Göttingen, Göttingen, Germany
| | - Detlev Schild
- Institute of Neurophysiology and Cellular Biophysics, University of Göttingen, Humboldtallee 23, 37073, Göttingen, Germany.,DFG Research Center for Nanoscale Microscopy and Molecular Physiology of the Brain (CNMPB), University of Göttingen, Göttingen, Germany.,DFG Excellence Cluster 171, University of Göttingen, Göttingen, Germany
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Weinberg SH, Smith GD. The influence of Ca²⁺ buffers on free [Ca²⁺] fluctuations and the effective volume of Ca²⁺ microdomains. Biophys J 2015; 106:2693-709. [PMID: 24940787 DOI: 10.1016/j.bpj.2014.04.045] [Citation(s) in RCA: 26] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/12/2013] [Revised: 04/28/2014] [Accepted: 04/30/2014] [Indexed: 02/06/2023] Open
Abstract
Intracellular calcium (Ca(2+)) plays a significant role in many cell signaling pathways, some of which are localized to spatially restricted microdomains. Ca(2+) binding proteins (Ca(2+) buffers) play an important role in regulating Ca(2+) concentration ([Ca(2+)]). Buffers typically slow [Ca(2+)] temporal dynamics and increase the effective volume of Ca(2+) domains. Because fluctuations in [Ca(2+)] decrease in proportion to the square-root of a domain's physical volume, one might conjecture that buffers decrease [Ca(2+)] fluctuations and, consequently, mitigate the significance of small domain volume concerning Ca(2+) signaling. We test this hypothesis through mathematical and computational analysis of idealized buffer-containing domains and their stochastic dynamics during free Ca(2+) influx with passive exchange of both Ca(2+) and buffer with bulk concentrations. We derive Langevin equations for the fluctuating dynamics of Ca(2+) and buffer and use these stochastic differential equations to determine the magnitude of [Ca(2+)] fluctuations for different buffer parameters (e.g., dissociation constant and concentration). In marked contrast to expectations based on a naive application of the principle of effective volume as employed in deterministic models of Ca(2+) signaling, we find that mobile and rapid buffers typically increase the magnitude of domain [Ca(2+)] fluctuations during periods of Ca(2+) influx, whereas stationary (immobile) Ca(2+) buffers do not. Also contrary to expectations, we find that in the absence of Ca(2+) influx, buffers influence the temporal characteristics, but not the magnitude, of [Ca(2+)] fluctuations. We derive an analytical formula describing the influence of rapid Ca(2+) buffers on [Ca(2+)] fluctuations and, importantly, identify the stochastic analog of (deterministic) effective domain volume. Our results demonstrate that Ca(2+) buffers alter the dynamics of [Ca(2+)] fluctuations in a nonintuitive manner. The finding that Ca(2+) buffers do not suppress intrinsic domain [Ca(2+)] fluctuations raises the intriguing question of whether or not [Ca(2+)] fluctuations are a physiologically significant aspect of local Ca(2+) signaling.
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Affiliation(s)
- Seth H Weinberg
- Department of Applied Science, The College of William & Mary, Williamsburg, Virginia
| | - Gregory D Smith
- Department of Applied Science, The College of William & Mary, Williamsburg, Virginia.
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Optimal microdomain crosstalk between endoplasmic reticulum and mitochondria for Ca2+ oscillations. Sci Rep 2015; 5:7984. [PMID: 25614067 PMCID: PMC4303883 DOI: 10.1038/srep07984] [Citation(s) in RCA: 54] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/29/2014] [Accepted: 12/24/2014] [Indexed: 12/11/2022] Open
Abstract
A Ca2+ signaling model is proposed to consider the crosstalk of Ca2+ ions between endoplasmic reticulum (ER) and mitochondria within microdomains around inositol 1, 4, 5-trisphosphate receptors (IP3R) and the mitochondrial Ca2+ uniporter (MCU). Our model predicts that there is a critical IP3R-MCU distance at which 50% of the ER-released Ca2+ is taken up by mitochondria and that mitochondria modulate Ca2+ signals differently when outside of this critical distance. This study highlights the importance of the IP3R-MCU distance on Ca2+ signaling dynamics. The model predicts that when MCU are too closely associated with IP3Rs, the enhanced mitochondrial Ca2+ uptake will produce an increase of cytosolic Ca2+ spike amplitude. Notably, the model demonstrates the existence of an optimal IP3R-MCU distance (30–85 nm) for effective Ca2+ transfer and the successful generation of Ca2+ signals in healthy cells. We suggest that the space between the inner and outer mitochondria membranes provides a defense mechanism against occurrences of high [Ca2+]Cyt. Our results also hint at a possible pathological mechanism in which abnormally high [Ca2+]Cyt arises when the IP3R-MCU distance is in excess of the optimal range.
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Samigullin D, Fatikhov N, Khaziev E, Skorinkin A, Nikolsky E, Bukharaeva E. Estimation of presynaptic calcium currents and endogenous calcium buffers at the frog neuromuscular junction with two different calcium fluorescent dyes. Front Synaptic Neurosci 2015; 6:29. [PMID: 25709579 PMCID: PMC4285738 DOI: 10.3389/fnsyn.2014.00029] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/06/2014] [Accepted: 12/12/2014] [Indexed: 12/02/2022] Open
Abstract
At the frog neuromuscular junction, under physiological conditions, the direct measurement of calcium currents and of the concentration of intracellular calcium buffers—which determine the kinetics of calcium concentration and neurotransmitter release from the nerve terminal—has hitherto been technically impossible. With the aim of quantifying both Ca2+ currents and the intracellular calcium buffers, we measured fluorescence signals from nerve terminals loaded with the low-affinity calcium dye Magnesium Green or the high-affinity dye Oregon Green BAPTA-1, simultaneously with microelectrode recordings of nerve-action potentials and end-plate currents. The action-potential-induced fluorescence signals in the nerve terminals developed much more slowly than the postsynaptic response. To clarify the reasons for this observation and to define a spatiotemporal profile of intracellular calcium and of the concentration of mobile and fixed calcium buffers, mathematical modeling was employed. The best approximations of the experimental calcium transients for both calcium dyes were obtained when the calcium current had an amplitude of 1.6 ± 0.08 pA and a half-decay time of 1.2 ± 0.06 ms, and when the concentrations of mobile and fixed calcium buffers were 250 ± 13 μM and 8 ± 0.4 mM, respectively. High concentrations of endogenous buffers define the time course of calcium transients after an action potential in the axoplasm, and may modify synaptic plasticity.
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Affiliation(s)
- Dmitry Samigullin
- Laboratory of the Biophysics of Synaptic Processes, Kazan Scientific Centre, Kazan Institute of Biochemistry and Biophysics, Russian Academy of Sciences Kazan, Russia ; Open Laboratory of Neuropharmacology, Kazan Federal University Kazan, Russia ; Department of Radiophotonics and Microwave Technologies, Kazan National Research Technical University named after A. N. Tupolev Kazan, Russia
| | - Nijaz Fatikhov
- Laboratory of the Biophysics of Synaptic Processes, Kazan Scientific Centre, Kazan Institute of Biochemistry and Biophysics, Russian Academy of Sciences Kazan, Russia
| | - Eduard Khaziev
- Laboratory of the Biophysics of Synaptic Processes, Kazan Scientific Centre, Kazan Institute of Biochemistry and Biophysics, Russian Academy of Sciences Kazan, Russia ; Open Laboratory of Neuropharmacology, Kazan Federal University Kazan, Russia
| | - Andrey Skorinkin
- Laboratory of the Biophysics of Synaptic Processes, Kazan Scientific Centre, Kazan Institute of Biochemistry and Biophysics, Russian Academy of Sciences Kazan, Russia ; Department of Neurobiology and Radioelectronics, Kazan Federal University Kazan, Russia
| | - Eugeny Nikolsky
- Laboratory of the Biophysics of Synaptic Processes, Kazan Scientific Centre, Kazan Institute of Biochemistry and Biophysics, Russian Academy of Sciences Kazan, Russia ; Open Laboratory of Neuropharmacology, Kazan Federal University Kazan, Russia ; Department of Medical and Biological Physics, Kazan State Medical University Kazan, Russia
| | - Ellya Bukharaeva
- Laboratory of the Biophysics of Synaptic Processes, Kazan Scientific Centre, Kazan Institute of Biochemistry and Biophysics, Russian Academy of Sciences Kazan, Russia ; Open Laboratory of Neuropharmacology, Kazan Federal University Kazan, Russia
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Jha A, Adlakha N. Two-dimensional finite element model to study unsteady state Ca2+ diffusion in neuron involving ER LEAK and SERCA. INT J BIOMATH 2015. [DOI: 10.1142/s1793524515500023] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
In this paper, finite element approach using two-dimensional unsteady state problem has been developed to study radial and angular calcium diffusion problem in neurons. Calcium is responsible messenger for transmitting information in communication process between neurons. The most important Ca 2+ binding proteins for the dynamics of Ca 2+ is itself buffer and other physiological parameters are located in Ca 2+ stores. In this study, the model incorporates the physiological parameters like diffusion coefficient, receptors, exogenous buffers etc. Appropriate boundary conditions have been framed in view of the physiological conditions. Computer simulations in MATLAB 7.11 are employed to investigate mathematical models of reaction–diffusion equation, the details of the implementation can heavily affect the numerical solutions and, thus, the outcome simulated on Core(TM) i3 CPU M 330 @ 2.13 GHz processing speed and 3 GB memory.
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Affiliation(s)
- Amrita Jha
- Department of Science and Humanities, Indus University, Ahmedabad, India
| | - Neeru Adlakha
- Department of Applied Mathematics and Humanities, S. V. National Institute of Technology, Surat, India
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von Wegner F, Wieder N, Fink RHA. Microdomain calcium fluctuations as a colored noise process. Front Genet 2014; 5:376. [PMID: 25404938 PMCID: PMC4217525 DOI: 10.3389/fgene.2014.00376] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/28/2014] [Accepted: 10/10/2014] [Indexed: 12/02/2022] Open
Abstract
Calcium ions play a key role in subcellular signaling as localized transients of the intracellular calcium concentration modify the activity of ion channels, enzymes and transcription factors, among others. The intracellular calcium concentration is inherently noisy, as diffusion, the transient binding to and dissociation from buffer molecules and stochastically gating calcium channels contribute to the fluctuations of the local copy number of Ca2+ ions. We study the properties of the fluctuating calcium concentration in sub-femtoliter volumes using an exact stochastic simulation algorithm and approximations to the exact stochastic solution. It is shown that the time course of the local calcium concentration represents a colored noise process whose autocorrelation time is a function of buffer kinetics and diffusion constants. Using the chemical Langevin description and the excess buffer approximation of the process, fast approximative algorithms and theoretical connections to the Ornstein-Uhlenbeck process are obtained. In a generic example, we show how calcium noise can couple to the dynamics of a single variable moving in a double-well potential, leading to a colored noise induced transition. Our work shows how a multitude of intracellular signaling pathways may be influenced by the inherent stochasticity of calcium signals, a key messenger in virtually any cell type, and how the calcium signal can be implemented efficiently in cellular signaling models.
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Affiliation(s)
- Frederic von Wegner
- Medical Biophysics Group, Institute of Physiology and Pathophysiology, Heidelberg University Heidelberg, Germany
| | - Nicolas Wieder
- Medical Biophysics Group, Institute of Physiology and Pathophysiology, Heidelberg University Heidelberg, Germany
| | - Rainer H A Fink
- Medical Biophysics Group, Institute of Physiology and Pathophysiology, Heidelberg University Heidelberg, Germany
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Jha BK, Adlakha N, Mehta MN. Two-dimensional finite element model to study calcium distribution in astrocytes in presence of excess buffer. INT J BIOMATH 2014. [DOI: 10.1142/s1793524514500314] [Citation(s) in RCA: 30] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
In this paper a finite element model is developed to study cytosolic calcium concentration distribution in astrocytes for a two-dimensional steady-state case in presence of excess buffer. The mathematical model of calcium diffusion in astrocytes leads to a boundary value problem involving elliptical partial differential equation. The model consists of reaction–diffusion phenomena, association and dissociation rates and buffer. A point source of calcium is incorporated in the model. Appropriate boundary conditions have been framed. Finite element method is employed to solve the problem. A MATLAB program has been developed for the entire problem and simulated to compute the numerical results. The numerical results have been used to plot calcium concentration profiles in astrocytes. The effect of EGTA, BAPTA and σCa influx on calcium concentration distribution in astrocytes is studied with the help of numerical results.
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Affiliation(s)
- Brajesh Kumar Jha
- Department of Mathematics and Computer Science, School of Technology, Pandit Deendayal Petroleum University, Raisen, Gandhinagar, Gujarat 382007, India
| | - Neeru Adlakha
- Department of Mathematics, M. A. National Institute of Technology, Bhopal, India
| | - M. N. Mehta
- Department of Applied Mathematics, S. V. National Institute of Technology, Surat, India
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Lees-Green R, Gibbons SJ, Farrugia G, Sneyd J, Cheng LK. Computational modeling of anoctamin 1 calcium-activated chloride channels as pacemaker channels in interstitial cells of Cajal. Am J Physiol Gastrointest Liver Physiol 2014; 306:G711-27. [PMID: 24481603 PMCID: PMC3989704 DOI: 10.1152/ajpgi.00449.2013] [Citation(s) in RCA: 30] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 01/31/2023]
Abstract
Interstitial cells of Cajal (ICC) act as pacemaker cells in the gastrointestinal tract by generating electrical slow waves to regulate rhythmic smooth muscle contractions. Intrinsic Ca(2+) oscillations in ICC appear to produce the slow waves by activating pacemaker currents, currently thought to be carried by the Ca(2+)-activated Cl(-) channel anoctamin 1 (Ano1). In this article we present a novel model of small intestinal ICC pacemaker activity that incorporates store-operated Ca(2+) entry and a new model of Ano1 current. A series of simulations were carried out with the ICC model to investigate current controversies about the reversal potential of the Ano1 Cl(-) current in ICC and to predict the characteristics of the other ion channels that are necessary to generate slow waves. The model results show that Ano1 is a plausible pacemaker channel when coupled to a store-operated Ca(2+) channel but suggest that small cyclical depolarizations may still occur in ICC in Ano1 knockout mice. The results predict that voltage-dependent Ca(2+) current is likely to be negligible during the slow wave plateau phase. The model shows that the Cl(-) equilibrium potential is an important modulator of slow wave morphology, highlighting the need for a better understanding of Cl(-) dynamics in ICC.
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Affiliation(s)
- Rachel Lees-Green
- 1Auckland Bioengineering Institute, University of Auckland, Auckland, New Zealand;
| | - Simon J. Gibbons
- 2Enteric Neuroscience Program, Division of Gastroenterology and Hepatology, Mayo Clinic College of Medicine, Rochester, Minnesota; and
| | - Gianrico Farrugia
- 2Enteric Neuroscience Program, Division of Gastroenterology and Hepatology, Mayo Clinic College of Medicine, Rochester, Minnesota; and
| | - James Sneyd
- 3Department of Mathematics, University of Auckland, New Zealand; and
| | - Leo K. Cheng
- 1Auckland Bioengineering Institute, University of Auckland, Auckland, New Zealand; ,4Department of Surgery, Vanderbilt University, Nashville, Tennessee
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