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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2401.17326 |
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| _version_ | 1866913216153518080 |
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| author | Hawker, Molly Cao, Pengxing Sneyd, James Siekmann, Ivo |
| author_facet | Hawker, Molly Cao, Pengxing Sneyd, James Siekmann, Ivo |
| contents | The calcium (Ca$^{2+}$) signalling system is important for many cellular processes within the human body. Signals are transmitted within the cell by releasing Ca$^{2+}$ from the endoplasmic reticulum (ER) into the cytosol via clusters of Ca$^{2+}$ channels. Mathematical models of Ca$^{2+}$ release via inositol 1,4,5-trisphosphate receptors (IP$_{3}$R) help with understanding underlying Ca$^{2+}$ dynamics but data-driven modelling of stochastic Ca$^{2+}$ release events, known as Ca$^{2+}$ puffs, is a difficult challenge. Parameterising Markov models for representing the IP$_{3}$R with steady-state single channel data obtained at fixed combinations of the ligands Ca$^{2+}$ and inositol-trisphosphate (IP$_{3}$) has previously been demonstrated to be insufficient. However, by extending an IP$_{3}$R model based on steady-state data with an integral term that incorporates the delayed response of the channel to varying Ca$^{2+}$ concentrations we succeed in generating realistic Ca$^{2+}$ puffs. By interpreting the integral term as a weighted average of Ca$^{2+}$ concentrations that extend over a time interval of length $τ$ into the past we conclude that the IP$_{3}$R requires a certain amount of memory of past ligand concentrations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_17326 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Ca$^{2+}$ puff model based on integrodifferential equations Hawker, Molly Cao, Pengxing Sneyd, James Siekmann, Ivo Quantitative Methods The calcium (Ca$^{2+}$) signalling system is important for many cellular processes within the human body. Signals are transmitted within the cell by releasing Ca$^{2+}$ from the endoplasmic reticulum (ER) into the cytosol via clusters of Ca$^{2+}$ channels. Mathematical models of Ca$^{2+}$ release via inositol 1,4,5-trisphosphate receptors (IP$_{3}$R) help with understanding underlying Ca$^{2+}$ dynamics but data-driven modelling of stochastic Ca$^{2+}$ release events, known as Ca$^{2+}$ puffs, is a difficult challenge. Parameterising Markov models for representing the IP$_{3}$R with steady-state single channel data obtained at fixed combinations of the ligands Ca$^{2+}$ and inositol-trisphosphate (IP$_{3}$) has previously been demonstrated to be insufficient. However, by extending an IP$_{3}$R model based on steady-state data with an integral term that incorporates the delayed response of the channel to varying Ca$^{2+}$ concentrations we succeed in generating realistic Ca$^{2+}$ puffs. By interpreting the integral term as a weighted average of Ca$^{2+}$ concentrations that extend over a time interval of length $τ$ into the past we conclude that the IP$_{3}$R requires a certain amount of memory of past ligand concentrations. |
| title | A Ca$^{2+}$ puff model based on integrodifferential equations |
| topic | Quantitative Methods |
| url | https://arxiv.org/abs/2401.17326 |