The time-changed stochastic approach and fractionally integrated processes to model the actin-myosin interaction and dwell times
We propose two stochastic models for the interaction between the myosin head and the actin filament, the physio-chemical mechanism triggering muscle contraction and that is not yet completely understood. We make use of the fractional calculus approach with the purpose of constructing non-Markov proc...
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AIMS Press
2025-03-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2025037 |
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| author | Nikolai Leonenko Enrica Pirozzi |
| author_facet | Nikolai Leonenko Enrica Pirozzi |
| author_sort | Nikolai Leonenko |
| collection | DOAJ |
| description | We propose two stochastic models for the interaction between the myosin head and the actin filament, the physio-chemical mechanism triggering muscle contraction and that is not yet completely understood. We make use of the fractional calculus approach with the purpose of constructing non-Markov processes for models with $ memory. $ A time-changed process and a fractionally integrated process are proposed for the two models. Each of these includes memory effects in a different way. We describe such features from a theoretical point of view and with simulations of sample paths. Mean functions and covariances are provided, considering constant and time-dependent tilting forces by which effects of external loads are included. The investigation of the dwell time of such phenomenon is carried out by means of density estimations of the first exit time (FET) of the processes from a strip; this mimics the times of the Steps of the myosin head during the sliding movement outside a potential well due to the interaction with actin. For the case of time-changed diffusion process, we specify an equation for the probability density function of the FET from a strip. The schemes of two simulation algorithms are provided and performed. Some numerical and simulation results are given and discussed. |
| format | Article |
| id | doaj-art-69eff89a229c45d5abbc24c51d7acd18 |
| institution | DOAJ |
| issn | 1551-0018 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | AIMS Press |
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| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-69eff89a229c45d5abbc24c51d7acd182025-08-20T03:16:58ZengAIMS PressMathematical Biosciences and Engineering1551-00182025-03-012241019105410.3934/mbe.2025037The time-changed stochastic approach and fractionally integrated processes to model the actin-myosin interaction and dwell timesNikolai Leonenko0Enrica Pirozzi1School of Mathematics, Cardiff University, Cardiff CF24 4AG, UKDipartimento di Matematica e Fisica, Università della Campania Luigi Vanvitelli, Caserta, ItalyWe propose two stochastic models for the interaction between the myosin head and the actin filament, the physio-chemical mechanism triggering muscle contraction and that is not yet completely understood. We make use of the fractional calculus approach with the purpose of constructing non-Markov processes for models with $ memory. $ A time-changed process and a fractionally integrated process are proposed for the two models. Each of these includes memory effects in a different way. We describe such features from a theoretical point of view and with simulations of sample paths. Mean functions and covariances are provided, considering constant and time-dependent tilting forces by which effects of external loads are included. The investigation of the dwell time of such phenomenon is carried out by means of density estimations of the first exit time (FET) of the processes from a strip; this mimics the times of the Steps of the myosin head during the sliding movement outside a potential well due to the interaction with actin. For the case of time-changed diffusion process, we specify an equation for the probability density function of the FET from a strip. The schemes of two simulation algorithms are provided and performed. Some numerical and simulation results are given and discussed.https://www.aimspress.com/article/doi/10.3934/mbe.2025037fractional diffusionsfirst exit timecaputo fractional derivativediscretization schemesstochastic simulations |
| spellingShingle | Nikolai Leonenko Enrica Pirozzi The time-changed stochastic approach and fractionally integrated processes to model the actin-myosin interaction and dwell times Mathematical Biosciences and Engineering fractional diffusions first exit time caputo fractional derivative discretization schemes stochastic simulations |
| title | The time-changed stochastic approach and fractionally integrated processes to model the actin-myosin interaction and dwell times |
| title_full | The time-changed stochastic approach and fractionally integrated processes to model the actin-myosin interaction and dwell times |
| title_fullStr | The time-changed stochastic approach and fractionally integrated processes to model the actin-myosin interaction and dwell times |
| title_full_unstemmed | The time-changed stochastic approach and fractionally integrated processes to model the actin-myosin interaction and dwell times |
| title_short | The time-changed stochastic approach and fractionally integrated processes to model the actin-myosin interaction and dwell times |
| title_sort | time changed stochastic approach and fractionally integrated processes to model the actin myosin interaction and dwell times |
| topic | fractional diffusions first exit time caputo fractional derivative discretization schemes stochastic simulations |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2025037 |
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