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Kojic M, Milosevic M, Simic V, Geroski V, Ziemys A, Filipovic N, Ferrari M. Smeared multiscale finite element model for electrophysiology and ionic transport in biological tissue. Comput Biol Med 2019; 108:288-304. [PMID: 31015049 DOI: 10.1016/j.compbiomed.2019.03.023] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/29/2018] [Revised: 03/22/2019] [Accepted: 03/23/2019] [Indexed: 10/27/2022]
Abstract
Basic functions of living organisms are governed by the nervous system through bidirectional signals transmitted from the brain to neural networks. These signals are similar to electrical waves. In electrophysiology the goal is to study the electrical properties of biological cells and tissues, and the transmission of signals. From a physics perspective, there exists a field of electrical potential within the living body, the nervous system, extracellular space and cells. Electrophysiological problems can be investigated experimentally and also theoretically by developing appropriate mathematical or computational models. Due to the enormous complexity of biological systems, it would be almost impossible to establish a detailed computational model of the electrical field, even for only a single organ (e.g. heart), including the entirety of cells comprising the neural network. In order to make computational models feasible for practical applications, we here introduce the concept of smeared fields, which represents a generalization of the previously formulated multiscale smeared methodology for mass transport in blood vessels, lymph, and tissue. We demonstrate the accuracy of the smeared finite element computational models for the electric field in numerical examples. The electrical field is further coupled with ionic mass transport within tissue composed of interstitial spaces extracellularly and by cytoplasm and organelles intracellularly. The proposed methodology, which couples electrophysiology and molecular ionic transport, is applicable to a variety of biological systems.
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Affiliation(s)
- M Kojic
- Houston Methodist Research Institute, The Department of Nanomedicine, 6670 Bertner Ave., R7-117, Houston, TX, 77030, USA; Bioengineering Research and Development Center BioIRC Kragujevac, Prvoslava Stojanovica 6, 3400, Kragujevac, Serbia; Serbian Academy of Sciences and Arts, Knez Mihailova 35, 11000, Belgrade, Serbia.
| | - M Milosevic
- Bioengineering Research and Development Center BioIRC Kragujevac, Prvoslava Stojanovica 6, 3400, Kragujevac, Serbia; Belgrade Metropolitan University, Tadeuša Košćuška 63, 11000, Belgrade, Serbia
| | - V Simic
- Bioengineering Research and Development Center BioIRC Kragujevac, Prvoslava Stojanovica 6, 3400, Kragujevac, Serbia
| | - V Geroski
- Bioengineering Research and Development Center BioIRC Kragujevac, Prvoslava Stojanovica 6, 3400, Kragujevac, Serbia
| | - A Ziemys
- Houston Methodist Research Institute, The Department of Nanomedicine, 6670 Bertner Ave., R7-117, Houston, TX, 77030, USA
| | - N Filipovic
- University of Kragujevac, Faculty for Engineering Sciences, Sestre Janic 6, 34000, Kragujevac, Serbia
| | - M Ferrari
- Houston Methodist Research Institute, The Department of Nanomedicine, 6670 Bertner Ave., R7-117, Houston, TX, 77030, USA
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Colman MA, Pinali C, Trafford AW, Zhang H, Kitmitto A. A computational model of spatio-temporal cardiac intracellular calcium handling with realistic structure and spatial flux distribution from sarcoplasmic reticulum and t-tubule reconstructions. PLoS Comput Biol 2017; 13:e1005714. [PMID: 28859079 PMCID: PMC5597258 DOI: 10.1371/journal.pcbi.1005714] [Citation(s) in RCA: 39] [Impact Index Per Article: 5.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/17/2017] [Revised: 09/13/2017] [Accepted: 08/08/2017] [Indexed: 12/28/2022] Open
Abstract
Intracellular calcium cycling is a vital component of cardiac excitation-contraction coupling. The key structures responsible for controlling calcium dynamics are the cell membrane (comprising the surface sarcolemma and transverse-tubules), the intracellular calcium store (the sarcoplasmic reticulum), and the co-localisation of these two structures to form dyads within which calcium-induced-calcium-release occurs. The organisation of these structures tightly controls intracellular calcium dynamics. In this study, we present a computational model of intracellular calcium cycling in three-dimensions (3-D), which incorporates high resolution reconstructions of these key regulatory structures, attained through imaging of tissue taken from the sheep left ventricle using serial block face scanning electron microscopy. An approach was developed to model the sarcoplasmic reticulum structure at the whole-cell scale, by reducing its full 3-D structure to a 3-D network of one-dimensional strands. The model reproduces intracellular calcium dynamics during control pacing and reveals the high-resolution 3-D spatial structure of calcium gradients and intracellular fluxes in both the cytoplasm and sarcoplasmic reticulum. We also demonstrated the capability of the model to reproduce potentially pro-arrhythmic dynamics under perturbed conditions, pertaining to calcium-transient alternans and spontaneous release events. Comparison with idealised cell models emphasised the importance of structure in determining calcium gradients and controlling the spatial dynamics associated with calcium-transient alternans, wherein the probabilistic nature of dyad activation and recruitment was constrained. The model was further used to highlight the criticality in calcium spark propagation in relation to inter-dyad distances. The model presented provides a powerful tool for future investigation of structure-function relationships underlying physiological and pathophysiological intracellular calcium handling phenomena at the whole-cell. The approach allows for the first time direct integration of high-resolution images of 3-D intracellular structures with models of calcium cycling, presenting the possibility to directly assess the functional impact of structural remodelling at the cellular scale. The organisation of the membrane and sub-cellular structures of cells in the heart closely controls the coupling between its electrical and mechanical function. Computational models of the cellular calcium handling system, which is responsible for this electro-mechanical coupling, have been developed in recent years to study underlying structure-function relationships. Previous models have been largely idealised in structure; we present a new model which incorporates experimental data describing the high-resolution organisation of the primary structures involved in calcium dynamics. Significantly, the structure of the intracellular calcium store is modelled for the first time. The model is shown to reproduce calcium dynamics in control cells in both normal and abnormal conditions, demonstrating its suitability for future investigation of structure-function relationships. Thus, the model presented provides a powerful tool for the direct integration of experimentally acquired structural data in healthy and diseased cells and assessment of the role of structure in regulating normal and abnormal calcium dynamics.
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Affiliation(s)
- Michael A. Colman
- School of Biomedical Sciences, Faculty of Biological Sciences, University of Leeds, Leeds, United Kingdom
- School of Physics and Astronomy, Faculty of Engineering and Physical Sciences, University of Manchester, Manchester, United Kingdom
- * E-mail:
| | - Christian Pinali
- Division of Cardiovascular Sciences, Faculty of Biology, Medicine and Health Sciences, University of Manchester, Manchester, United Kingdom
| | - Andrew W. Trafford
- Division of Cardiovascular Sciences, Faculty of Biology, Medicine and Health Sciences, University of Manchester, Manchester, United Kingdom
| | - Henggui Zhang
- School of Physics and Astronomy, Faculty of Engineering and Physical Sciences, University of Manchester, Manchester, United Kingdom
| | - Ashraf Kitmitto
- Division of Cardiovascular Sciences, Faculty of Biology, Medicine and Health Sciences, University of Manchester, Manchester, United Kingdom
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Hake J, Kekenes-Huskey PM, McCulloch AD. Computational modeling of subcellular transport and signaling. Curr Opin Struct Biol 2014; 25:92-7. [PMID: 24509246 PMCID: PMC4040296 DOI: 10.1016/j.sbi.2014.01.006] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/01/2013] [Accepted: 01/07/2014] [Indexed: 11/19/2022]
Abstract
Numerous signaling processes in the cell are controlled in microdomains that are defined by cellular structures ranging from nm to μm in size. Recent improvements in microscopy enable the resolution and reconstruction of these micro domains, while new computational methods provide the means to elucidate their functional roles. Collectively these tools allow for a biophysical understanding of the cellular environment and its pathological progression in disease. Here we review recent advancements in microscopy, and subcellular modeling on the basis of reconstructed geometries, with a special focus on signaling microdomains that are important for the excitation contraction coupling in cardiac myocytes.
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Affiliation(s)
- Johan Hake
- Center for Biomedical Computing, Simula Research Laboratory, P.O. Box 134, 1325 Lysaker, Norway.
| | | | - Andrew D McCulloch
- Department of Bioengineering and Medicine, University of California San Diego, CA, USA
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Kekenes-Huskey PM, Cheng Y, Hake JE, Sachse FB, Bridge JH, Holst MJ, McCammon JA, McCulloch AD, Michailova AP. Modeling effects of L-type ca(2+) current and na(+)-ca(2+) exchanger on ca(2+) trigger flux in rabbit myocytes with realistic T-tubule geometries. Front Physiol 2012; 3:351. [PMID: 23060801 PMCID: PMC3463892 DOI: 10.3389/fphys.2012.00351] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/13/2012] [Accepted: 08/16/2012] [Indexed: 12/26/2022] Open
Abstract
The transverse tubular system of rabbit ventricular myocytes consists of cell membrane invaginations (t-tubules) that are essential for efficient cardiac excitation-contraction coupling. In this study, we investigate how t-tubule micro-anatomy, L-type Ca2+ channel (LCC) clustering, and allosteric activation of Na+/Ca2+ exchanger by L-type Ca2+ current affects intracellular Ca2+ dynamics. Our model includes a realistic 3D geometry of a single t-tubule and its surrounding half-sarcomeres for rabbit ventricular myocytes. The effects of spatially distributed membrane ion-transporters (LCC, Na+/Ca2+ exchanger, sarcolemmal Ca2+ pump, and sarcolemmal Ca2+ leak), and stationary and mobile Ca2+ buffers (troponin C, ATP, calmodulin, and Fluo-3) are also considered. We used a coupled reaction-diffusion system to describe the spatio-temporal concentration profiles of free and buffered intracellular Ca2+. We obtained parameters from voltage-clamp protocols of L-type Ca2+ current and line-scan recordings of Ca2+ concentration profiles in rabbit cells, in which the sarcoplasmic reticulum is disabled. Our model results agree with experimental measurements of global Ca2+ transient in myocytes loaded with 50 μM Fluo-3. We found that local Ca2+ concentrations within the cytosol and sub-sarcolemma, as well as the local trigger fluxes of Ca2+ crossing the cell membrane, are sensitive to details of t-tubule micro-structure and membrane Ca2+ flux distribution. The model additionally predicts that local Ca2+ trigger fluxes are at least threefold to eightfold higher than the whole-cell Ca2+ trigger flux. We found also that the activation of allosteric Ca2+-binding sites on the Na+/Ca2+ exchanger could provide a mechanism for regulating global and local Ca2+ trigger fluxes in vivo. Our studies indicate that improved structural and functional models could improve our understanding of the contributions of L-type and Na+/Ca2+ exchanger fluxes to intracellular Ca2+ dynamics.
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