Coupling particle-based reaction-diffusion simulations with reservoirs mediated by reaction-diffusion PDEs
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2020
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| _version_ | 1866911209450635264 |
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| author | Kostré, Margarita Schütte, Christof Noé, Frank del Razo, Mauricio J. |
| author_facet | Kostré, Margarita Schütte, Christof Noé, Frank del Razo, Mauricio J. |
| contents | Open biochemical systems of interacting molecules are ubiquitous in life-related processes. However, established computational methodologies, like molecular dynamics, are still mostly constrained to closed systems and timescales too small to be relevant for life processes. Alternatively, particle-based reaction-diffusion models are currently the most accurate and computationally feasible approach at these scales. Their efficiency lies in modeling entire molecules as particles that can diffuse and interact with each other. In this work, we develop modeling and numerical schemes for particle-based reaction-diffusion in an open setting, where the reservoirs are mediated by reaction-diffusion PDEs. We derive two important theoretical results. The first one is the mean-field for open systems of diffusing particles; the second one is the mean-field for a particle-based reaction-diffusion system with second-order reactions. We employ these two results to develop a numerical scheme that consistently couples particle-based reaction-diffusion processes with reaction-diffusion PDEs. This allows modeling open biochemical systems in contact with reservoirs that are time-dependent and spatially inhomogeneous, as in many relevant real-world applications. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2006_00003 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Coupling particle-based reaction-diffusion simulations with reservoirs mediated by reaction-diffusion PDEs Kostré, Margarita Schütte, Christof Noé, Frank del Razo, Mauricio J. Quantitative Methods Chemical Physics Computational Physics 92C40, 92C45, 60J70, 60Gxx, 70Lxx Open biochemical systems of interacting molecules are ubiquitous in life-related processes. However, established computational methodologies, like molecular dynamics, are still mostly constrained to closed systems and timescales too small to be relevant for life processes. Alternatively, particle-based reaction-diffusion models are currently the most accurate and computationally feasible approach at these scales. Their efficiency lies in modeling entire molecules as particles that can diffuse and interact with each other. In this work, we develop modeling and numerical schemes for particle-based reaction-diffusion in an open setting, where the reservoirs are mediated by reaction-diffusion PDEs. We derive two important theoretical results. The first one is the mean-field for open systems of diffusing particles; the second one is the mean-field for a particle-based reaction-diffusion system with second-order reactions. We employ these two results to develop a numerical scheme that consistently couples particle-based reaction-diffusion processes with reaction-diffusion PDEs. This allows modeling open biochemical systems in contact with reservoirs that are time-dependent and spatially inhomogeneous, as in many relevant real-world applications. |
| title | Coupling particle-based reaction-diffusion simulations with reservoirs mediated by reaction-diffusion PDEs |
| topic | Quantitative Methods Chemical Physics Computational Physics 92C40, 92C45, 60J70, 60Gxx, 70Lxx |
| url | https://arxiv.org/abs/2006.00003 |