Comparison Theorems for Stochastic Chemical Reaction Networks
Abstract Continuous-time Markov chains are frequently used as stochastic models for chemical reaction networks, especially in the growing field of systems biology. A fundamental problem for these Stochastic Chemical Reaction Networks (SCRNs) is to understand the dependence of the stochastic behavior...
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| Autor*in: |
Campos, Felipe A. [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2023 |
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| Schlagwörter: |
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| Anmerkung: |
© The Author(s) 2023 |
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| Übergeordnetes Werk: |
Enthalten in: Bulletin of mathematical biology - Springer US, 1973, 85(2023), 5 vom: 31. März |
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| Übergeordnetes Werk: |
volume:85 ; year:2023 ; number:5 ; day:31 ; month:03 |
| Links: |
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| DOI / URN: |
10.1007/s11538-023-01136-5 |
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OLC2134607149 |
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| 520 | |a Abstract Continuous-time Markov chains are frequently used as stochastic models for chemical reaction networks, especially in the growing field of systems biology. A fundamental problem for these Stochastic Chemical Reaction Networks (SCRNs) is to understand the dependence of the stochastic behavior of these systems on the chemical reaction rate parameters. Towards solving this problem, in this paper we develop theoretical tools called comparison theorems that provide stochastic ordering results for SCRNs. These theorems give sufficient conditions for monotonic dependence on parameters in these network models, which allow us to obtain, under suitable conditions, information about transient and steady-state behavior. These theorems exploit structural properties of SCRNs, beyond those of general continuous-time Markov chains. Furthermore, we derive two theorems to compare stationary distributions and mean first passage times for SCRNs with different parameter values, or with the same parameters and different initial conditions. These tools are developed for SCRNs taking values in a generic (finite or countably infinite) state space and can also be applied for non-mass-action kinetics models. When propensity functions are bounded, our method of proof gives an explicit method for coupling two comparable SCRNs, which can be used to simultaneously simulate their sample paths in a comparable manner. We illustrate our results with applications to models of enzymatic kinetics and epigenetic regulation by chromatin modifications. | ||
| 650 | 4 | |a Stochastic chemical reaction networks | |
| 650 | 4 | |a Monotonicity | |
| 700 | 1 | |a Bruno, Simone |0 (orcid)0000-0001-9235-8226 |4 aut | |
| 700 | 1 | |a Fu, Yi |4 aut | |
| 700 | 1 | |a Del Vecchio, Domitilla |4 aut | |
| 700 | 1 | |a Williams, Ruth J. |4 aut | |
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10.1007/s11538-023-01136-5 doi (DE-627)OLC2134607149 (DE-He213)s11538-023-01136-5-p DE-627 ger DE-627 rakwb eng 570 510 VZ 12 ssgn BIODIV DE-30 fid 42.00 bkl Campos, Felipe A. verfasserin aut Comparison Theorems for Stochastic Chemical Reaction Networks 2023 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s) 2023 Abstract Continuous-time Markov chains are frequently used as stochastic models for chemical reaction networks, especially in the growing field of systems biology. A fundamental problem for these Stochastic Chemical Reaction Networks (SCRNs) is to understand the dependence of the stochastic behavior of these systems on the chemical reaction rate parameters. Towards solving this problem, in this paper we develop theoretical tools called comparison theorems that provide stochastic ordering results for SCRNs. These theorems give sufficient conditions for monotonic dependence on parameters in these network models, which allow us to obtain, under suitable conditions, information about transient and steady-state behavior. These theorems exploit structural properties of SCRNs, beyond those of general continuous-time Markov chains. Furthermore, we derive two theorems to compare stationary distributions and mean first passage times for SCRNs with different parameter values, or with the same parameters and different initial conditions. These tools are developed for SCRNs taking values in a generic (finite or countably infinite) state space and can also be applied for non-mass-action kinetics models. When propensity functions are bounded, our method of proof gives an explicit method for coupling two comparable SCRNs, which can be used to simultaneously simulate their sample paths in a comparable manner. We illustrate our results with applications to models of enzymatic kinetics and epigenetic regulation by chromatin modifications. Stochastic chemical reaction networks Monotonicity Bruno, Simone (orcid)0000-0001-9235-8226 aut Fu, Yi aut Del Vecchio, Domitilla aut Williams, Ruth J. aut Enthalten in Bulletin of mathematical biology Springer US, 1973 85(2023), 5 vom: 31. März (DE-627)129391719 (DE-600)184905-0 (DE-576)014776863 0092-8240 nnns volume:85 year:2023 number:5 day:31 month:03 https://doi.org/10.1007/s11538-023-01136-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC FID-BIODIV SSG-OLC-MAT SSG-OPC-MAT 42.00 VZ AR 85 2023 5 31 03 |
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10.1007/s11538-023-01136-5 doi (DE-627)OLC2134607149 (DE-He213)s11538-023-01136-5-p DE-627 ger DE-627 rakwb eng 570 510 VZ 12 ssgn BIODIV DE-30 fid 42.00 bkl Campos, Felipe A. verfasserin aut Comparison Theorems for Stochastic Chemical Reaction Networks 2023 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s) 2023 Abstract Continuous-time Markov chains are frequently used as stochastic models for chemical reaction networks, especially in the growing field of systems biology. A fundamental problem for these Stochastic Chemical Reaction Networks (SCRNs) is to understand the dependence of the stochastic behavior of these systems on the chemical reaction rate parameters. Towards solving this problem, in this paper we develop theoretical tools called comparison theorems that provide stochastic ordering results for SCRNs. These theorems give sufficient conditions for monotonic dependence on parameters in these network models, which allow us to obtain, under suitable conditions, information about transient and steady-state behavior. These theorems exploit structural properties of SCRNs, beyond those of general continuous-time Markov chains. Furthermore, we derive two theorems to compare stationary distributions and mean first passage times for SCRNs with different parameter values, or with the same parameters and different initial conditions. These tools are developed for SCRNs taking values in a generic (finite or countably infinite) state space and can also be applied for non-mass-action kinetics models. When propensity functions are bounded, our method of proof gives an explicit method for coupling two comparable SCRNs, which can be used to simultaneously simulate their sample paths in a comparable manner. We illustrate our results with applications to models of enzymatic kinetics and epigenetic regulation by chromatin modifications. Stochastic chemical reaction networks Monotonicity Bruno, Simone (orcid)0000-0001-9235-8226 aut Fu, Yi aut Del Vecchio, Domitilla aut Williams, Ruth J. aut Enthalten in Bulletin of mathematical biology Springer US, 1973 85(2023), 5 vom: 31. März (DE-627)129391719 (DE-600)184905-0 (DE-576)014776863 0092-8240 nnns volume:85 year:2023 number:5 day:31 month:03 https://doi.org/10.1007/s11538-023-01136-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC FID-BIODIV SSG-OLC-MAT SSG-OPC-MAT 42.00 VZ AR 85 2023 5 31 03 |
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10.1007/s11538-023-01136-5 doi (DE-627)OLC2134607149 (DE-He213)s11538-023-01136-5-p DE-627 ger DE-627 rakwb eng 570 510 VZ 12 ssgn BIODIV DE-30 fid 42.00 bkl Campos, Felipe A. verfasserin aut Comparison Theorems for Stochastic Chemical Reaction Networks 2023 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s) 2023 Abstract Continuous-time Markov chains are frequently used as stochastic models for chemical reaction networks, especially in the growing field of systems biology. A fundamental problem for these Stochastic Chemical Reaction Networks (SCRNs) is to understand the dependence of the stochastic behavior of these systems on the chemical reaction rate parameters. Towards solving this problem, in this paper we develop theoretical tools called comparison theorems that provide stochastic ordering results for SCRNs. These theorems give sufficient conditions for monotonic dependence on parameters in these network models, which allow us to obtain, under suitable conditions, information about transient and steady-state behavior. These theorems exploit structural properties of SCRNs, beyond those of general continuous-time Markov chains. Furthermore, we derive two theorems to compare stationary distributions and mean first passage times for SCRNs with different parameter values, or with the same parameters and different initial conditions. These tools are developed for SCRNs taking values in a generic (finite or countably infinite) state space and can also be applied for non-mass-action kinetics models. When propensity functions are bounded, our method of proof gives an explicit method for coupling two comparable SCRNs, which can be used to simultaneously simulate their sample paths in a comparable manner. We illustrate our results with applications to models of enzymatic kinetics and epigenetic regulation by chromatin modifications. Stochastic chemical reaction networks Monotonicity Bruno, Simone (orcid)0000-0001-9235-8226 aut Fu, Yi aut Del Vecchio, Domitilla aut Williams, Ruth J. aut Enthalten in Bulletin of mathematical biology Springer US, 1973 85(2023), 5 vom: 31. März (DE-627)129391719 (DE-600)184905-0 (DE-576)014776863 0092-8240 nnns volume:85 year:2023 number:5 day:31 month:03 https://doi.org/10.1007/s11538-023-01136-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC FID-BIODIV SSG-OLC-MAT SSG-OPC-MAT 42.00 VZ AR 85 2023 5 31 03 |
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10.1007/s11538-023-01136-5 doi (DE-627)OLC2134607149 (DE-He213)s11538-023-01136-5-p DE-627 ger DE-627 rakwb eng 570 510 VZ 12 ssgn BIODIV DE-30 fid 42.00 bkl Campos, Felipe A. verfasserin aut Comparison Theorems for Stochastic Chemical Reaction Networks 2023 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s) 2023 Abstract Continuous-time Markov chains are frequently used as stochastic models for chemical reaction networks, especially in the growing field of systems biology. A fundamental problem for these Stochastic Chemical Reaction Networks (SCRNs) is to understand the dependence of the stochastic behavior of these systems on the chemical reaction rate parameters. Towards solving this problem, in this paper we develop theoretical tools called comparison theorems that provide stochastic ordering results for SCRNs. These theorems give sufficient conditions for monotonic dependence on parameters in these network models, which allow us to obtain, under suitable conditions, information about transient and steady-state behavior. These theorems exploit structural properties of SCRNs, beyond those of general continuous-time Markov chains. Furthermore, we derive two theorems to compare stationary distributions and mean first passage times for SCRNs with different parameter values, or with the same parameters and different initial conditions. These tools are developed for SCRNs taking values in a generic (finite or countably infinite) state space and can also be applied for non-mass-action kinetics models. When propensity functions are bounded, our method of proof gives an explicit method for coupling two comparable SCRNs, which can be used to simultaneously simulate their sample paths in a comparable manner. We illustrate our results with applications to models of enzymatic kinetics and epigenetic regulation by chromatin modifications. Stochastic chemical reaction networks Monotonicity Bruno, Simone (orcid)0000-0001-9235-8226 aut Fu, Yi aut Del Vecchio, Domitilla aut Williams, Ruth J. aut Enthalten in Bulletin of mathematical biology Springer US, 1973 85(2023), 5 vom: 31. März (DE-627)129391719 (DE-600)184905-0 (DE-576)014776863 0092-8240 nnns volume:85 year:2023 number:5 day:31 month:03 https://doi.org/10.1007/s11538-023-01136-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC FID-BIODIV SSG-OLC-MAT SSG-OPC-MAT 42.00 VZ AR 85 2023 5 31 03 |
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10.1007/s11538-023-01136-5 doi (DE-627)OLC2134607149 (DE-He213)s11538-023-01136-5-p DE-627 ger DE-627 rakwb eng 570 510 VZ 12 ssgn BIODIV DE-30 fid 42.00 bkl Campos, Felipe A. verfasserin aut Comparison Theorems for Stochastic Chemical Reaction Networks 2023 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s) 2023 Abstract Continuous-time Markov chains are frequently used as stochastic models for chemical reaction networks, especially in the growing field of systems biology. A fundamental problem for these Stochastic Chemical Reaction Networks (SCRNs) is to understand the dependence of the stochastic behavior of these systems on the chemical reaction rate parameters. Towards solving this problem, in this paper we develop theoretical tools called comparison theorems that provide stochastic ordering results for SCRNs. These theorems give sufficient conditions for monotonic dependence on parameters in these network models, which allow us to obtain, under suitable conditions, information about transient and steady-state behavior. These theorems exploit structural properties of SCRNs, beyond those of general continuous-time Markov chains. Furthermore, we derive two theorems to compare stationary distributions and mean first passage times for SCRNs with different parameter values, or with the same parameters and different initial conditions. These tools are developed for SCRNs taking values in a generic (finite or countably infinite) state space and can also be applied for non-mass-action kinetics models. When propensity functions are bounded, our method of proof gives an explicit method for coupling two comparable SCRNs, which can be used to simultaneously simulate their sample paths in a comparable manner. We illustrate our results with applications to models of enzymatic kinetics and epigenetic regulation by chromatin modifications. Stochastic chemical reaction networks Monotonicity Bruno, Simone (orcid)0000-0001-9235-8226 aut Fu, Yi aut Del Vecchio, Domitilla aut Williams, Ruth J. aut Enthalten in Bulletin of mathematical biology Springer US, 1973 85(2023), 5 vom: 31. März (DE-627)129391719 (DE-600)184905-0 (DE-576)014776863 0092-8240 nnns volume:85 year:2023 number:5 day:31 month:03 https://doi.org/10.1007/s11538-023-01136-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC FID-BIODIV SSG-OLC-MAT SSG-OPC-MAT 42.00 VZ AR 85 2023 5 31 03 |
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Comparison Theorems for Stochastic Chemical Reaction Networks |
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Abstract Continuous-time Markov chains are frequently used as stochastic models for chemical reaction networks, especially in the growing field of systems biology. A fundamental problem for these Stochastic Chemical Reaction Networks (SCRNs) is to understand the dependence of the stochastic behavior of these systems on the chemical reaction rate parameters. Towards solving this problem, in this paper we develop theoretical tools called comparison theorems that provide stochastic ordering results for SCRNs. These theorems give sufficient conditions for monotonic dependence on parameters in these network models, which allow us to obtain, under suitable conditions, information about transient and steady-state behavior. These theorems exploit structural properties of SCRNs, beyond those of general continuous-time Markov chains. Furthermore, we derive two theorems to compare stationary distributions and mean first passage times for SCRNs with different parameter values, or with the same parameters and different initial conditions. These tools are developed for SCRNs taking values in a generic (finite or countably infinite) state space and can also be applied for non-mass-action kinetics models. When propensity functions are bounded, our method of proof gives an explicit method for coupling two comparable SCRNs, which can be used to simultaneously simulate their sample paths in a comparable manner. We illustrate our results with applications to models of enzymatic kinetics and epigenetic regulation by chromatin modifications. © The Author(s) 2023 |
| abstractGer |
Abstract Continuous-time Markov chains are frequently used as stochastic models for chemical reaction networks, especially in the growing field of systems biology. A fundamental problem for these Stochastic Chemical Reaction Networks (SCRNs) is to understand the dependence of the stochastic behavior of these systems on the chemical reaction rate parameters. Towards solving this problem, in this paper we develop theoretical tools called comparison theorems that provide stochastic ordering results for SCRNs. These theorems give sufficient conditions for monotonic dependence on parameters in these network models, which allow us to obtain, under suitable conditions, information about transient and steady-state behavior. These theorems exploit structural properties of SCRNs, beyond those of general continuous-time Markov chains. Furthermore, we derive two theorems to compare stationary distributions and mean first passage times for SCRNs with different parameter values, or with the same parameters and different initial conditions. These tools are developed for SCRNs taking values in a generic (finite or countably infinite) state space and can also be applied for non-mass-action kinetics models. When propensity functions are bounded, our method of proof gives an explicit method for coupling two comparable SCRNs, which can be used to simultaneously simulate their sample paths in a comparable manner. We illustrate our results with applications to models of enzymatic kinetics and epigenetic regulation by chromatin modifications. © The Author(s) 2023 |
| abstract_unstemmed |
Abstract Continuous-time Markov chains are frequently used as stochastic models for chemical reaction networks, especially in the growing field of systems biology. A fundamental problem for these Stochastic Chemical Reaction Networks (SCRNs) is to understand the dependence of the stochastic behavior of these systems on the chemical reaction rate parameters. Towards solving this problem, in this paper we develop theoretical tools called comparison theorems that provide stochastic ordering results for SCRNs. These theorems give sufficient conditions for monotonic dependence on parameters in these network models, which allow us to obtain, under suitable conditions, information about transient and steady-state behavior. These theorems exploit structural properties of SCRNs, beyond those of general continuous-time Markov chains. Furthermore, we derive two theorems to compare stationary distributions and mean first passage times for SCRNs with different parameter values, or with the same parameters and different initial conditions. These tools are developed for SCRNs taking values in a generic (finite or countably infinite) state space and can also be applied for non-mass-action kinetics models. When propensity functions are bounded, our method of proof gives an explicit method for coupling two comparable SCRNs, which can be used to simultaneously simulate their sample paths in a comparable manner. We illustrate our results with applications to models of enzymatic kinetics and epigenetic regulation by chromatin modifications. © The Author(s) 2023 |
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| title_short |
Comparison Theorems for Stochastic Chemical Reaction Networks |
| url |
https://doi.org/10.1007/s11538-023-01136-5 |
| remote_bool |
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| author2 |
Bruno, Simone Fu, Yi Del Vecchio, Domitilla Williams, Ruth J. |
| author2Str |
Bruno, Simone Fu, Yi Del Vecchio, Domitilla Williams, Ruth J. |
| ppnlink |
129391719 |
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| doi_str |
10.1007/s11538-023-01136-5 |
| up_date |
2024-07-04T01:52:09.581Z |
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