Biologically relevant finite-size effects in a driven lattice gas with particle pausing and dynamical defects
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arXiv
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| Format: | Preprint |
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2024
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| author | Keisers, Johannes Zovo, Lorenzo Vito Dal Kern, Norbert Ciandrini, Luca |
| author_facet | Keisers, Johannes Zovo, Lorenzo Vito Dal Kern, Norbert Ciandrini, Luca |
| contents | In this article we present a comprehensive study of the totally asymmetric simple exclusion process with pausing particles (pTASEP), a model initially introduced to describe RNAP dynamics during transcription. We extend previous mean-field approaches and demonstrate that the pTASEP is equivalent to the exclusion process with dynamical defects (ddTASEP), thus broadening the scope of our investigation to a larger class of problems related to transcription and translation. We extend the mean-field theory to the open boundary case, revealing the system's phase diagram and critical values of entry and exit rates. However, we identify a significant discrepancy between theory and simulations in a region of the parameter space, indicating severe finite-size effects. To address this, we develop a single-cluster approximation that captures the relationship between current and lattice size, providing a more accurate representation of the system's dynamics. Finally, we extend our approach to open boundary conditions, demonstrating its applicability in different scenarios. Our findings underscore the importance of considering finite-size effects, often overlooked in the literature, when modelling biological processes such as transcription and translation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_16569 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Biologically relevant finite-size effects in a driven lattice gas with particle pausing and dynamical defects Keisers, Johannes Zovo, Lorenzo Vito Dal Kern, Norbert Ciandrini, Luca Statistical Mechanics Subcellular Processes In this article we present a comprehensive study of the totally asymmetric simple exclusion process with pausing particles (pTASEP), a model initially introduced to describe RNAP dynamics during transcription. We extend previous mean-field approaches and demonstrate that the pTASEP is equivalent to the exclusion process with dynamical defects (ddTASEP), thus broadening the scope of our investigation to a larger class of problems related to transcription and translation. We extend the mean-field theory to the open boundary case, revealing the system's phase diagram and critical values of entry and exit rates. However, we identify a significant discrepancy between theory and simulations in a region of the parameter space, indicating severe finite-size effects. To address this, we develop a single-cluster approximation that captures the relationship between current and lattice size, providing a more accurate representation of the system's dynamics. Finally, we extend our approach to open boundary conditions, demonstrating its applicability in different scenarios. Our findings underscore the importance of considering finite-size effects, often overlooked in the literature, when modelling biological processes such as transcription and translation. |
| title | Biologically relevant finite-size effects in a driven lattice gas with particle pausing and dynamical defects |
| topic | Statistical Mechanics Subcellular Processes |
| url | https://arxiv.org/abs/2406.16569 |