Model Reduction Tools For Phenomenological Modeling of Input-Controlled Biological Circuits

Pandey, Ayush; Murray, Richard M.

doi:10.1101/2020.02.15.950840

Cited by 6 publications

(7 citation statements)

References 35 publications

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“…This can impede generalization of the obtained results, which might strongly depend on the particular set of chosen parameter values. Therefore, techniques for reducing the complexity of mathematical models while preserving their most fundamental characteristics have been a topic of great interest for several decades, ranging from the well-established quasi-steady-state assumption to more advanced mathematical algorithms [87][88][89][90].…”

Section: Discussionmentioning

confidence: 99%

A modular approach for modeling the cell cycle based on functional response curves

2021

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Modeling biochemical reactions by means of differential equations often results in systems with a large number of variables and parameters. As this might complicate the interpretation and generalization of the obtained results, it is often desirable to reduce the complexity of the model. One way to accomplish this is by replacing the detailed reaction mechanisms of certain modules in the model by a mathematical expression that qualitatively describes the dynamical behavior of these modules. Such an approach has been widely adopted for ultrasensitive responses, for which underlying reaction mechanisms are often replaced by a single Hill function. Also time delays are usually accounted for by using an explicit delay in delay differential equations. In contrast, however, S-shaped response curves, which by definition have multiple output values for certain input values and are often encountered in bistable systems, are not easily modeled in such an explicit way. Here, we extend the classical Hill function into a mathematical expression that can be used to describe both ultrasensitive and S-shaped responses. We show how three ubiquitous modules (ultrasensitive responses, S-shaped responses and time delays) can be combined in different configurations and explore the dynamics of these systems. As an example, we apply our strategy to set up a model of the cell cycle consisting of multiple bistable switches, which can incorporate events such as DNA damage and coupling to the circadian clock in a phenomenological way.

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Section: Discussionmentioning

confidence: 99%

A modular approach for modeling the cell cycle based on functional response curves

2021

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Section: Discussionmentioning

confidence: 99%

A modular approach for modeling the cell cycle based on functional response curves

Boeck

Rombouts

Gelens

2021

Preprint

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Modeling biochemical reactions by means of differential equations often results in systems with a large number of variables and parameters. As this might complicate the interpretation and generalization of the obtained results, it is often desirable to reduce the complexity of the model. One way to accomplish this is by replacing the detailed reaction mechanisms of certain modules in the model by a mathematical expression that qualitatively describes the dynamical behavior of these modules. Such an approach has been widely adopted for ultrasensitive responses, for which underlying reaction mechanisms are often replaced by a single Hill equation. Also time delays are usually accounted for by using an explicit delay in delay differential equations. In contrast, however, S-shaped response curves, which are often encountered in bistable systems, are not easily modeled in such an explicit way. Here, we extend the classical Hill function into a mathematical expression that can be used to describe both ultrasensitive and S-shaped responses. We show how three ubiquitous modules (ultrasensitive responses, S-shaped responses and time delays) can be combined in different configurations and explore the dynamics of these systems. As an example, we apply our strategy to set up a model of the cell cycle consisting of multiple bistable switches, which can account for events such as DNA damage and coupling to the circadian clock in a phenomenological way.

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“…This has been explored in the literature using various approaches such as by direct mathematical comparison of mechanistic and phenomenological models [46][47][48] or by studying particular examples of reduced models.…”

Section: Mechanisms Are Reaction Schemasmentioning

confidence: 99%

“…45–47 Bridging the connections between the different modeling abstractions is a challenging research problem. This has been explored in the literature using various approaches such as by direct mathematical comparison of mechanistic and phenomenological models 48–50 or by studying particular examples of reduced models. 2 BioCRNpyler provides a computational approach using reaction schemas to easily change the mechanisms used in compilation from detailed mass-action to coarse-grained at various level of complexity.…”

Section: Framework and Compilation Overviewmentioning

confidence: 99%

BioCRNpyler: Compiling Chemical Reaction Networks from Biomolecular Parts in Diverse Contexts

Poole

Pandey

Shur

et al. 2020

Preprint

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Biochemical interactions in systems and synthetic biology are often modeled with Chemical Reaction Networks (CRNs). CRNs provide a principled modeling environment capable of expressing a huge range of biochemical processes. In this paper, we present a software toolbox, written in python, that complies high-level design specifications to CRN representations. This compilation process offers three advantages. First, the building of the actual CRN representation is automatic and outputs Systems Biology Markup Language (SBML) models compatible with numerous simulators. Second, a library of modular biochemical components allows for different architectures and implementations of biochemical circuits to represented succinctly with design choices propogated throughout the underlying CRN automatically. This prevents the often occurring mismatch between high-level designs and model dynamics. Third, high-level design specification can be embedded into diverse biomolecular environments, such as cell-free extracts and in vivo milieus. With these advantages offered by BioCRNpyler, users can quickly build and test multitude of models in different environments. Finally, our software toolbox has a parameter database, which allows users to rapidly prototype large models using very few parameters which can be customized later.

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Model Reduction Tools For Phenomenological Modeling of Input-Controlled Biological Circuits

Cited by 6 publications

References 35 publications

A modular approach for modeling the cell cycle based on functional response curves

A modular approach for modeling the cell cycle based on functional response curves

A modular approach for modeling the cell cycle based on functional response curves

BioCRNpyler: Compiling Chemical Reaction Networks from Biomolecular Parts in Diverse Contexts

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