Abstract
Biological systems are made up of components that change their actions (and interactions) over time and coordinate with other components nearby. Together with a large state space, the complexity of this behaviour can make it difficult to create concise mathematical models that can be easily extended or modified. This paper introduces the Beacon Calculus, a process algebra designed to simplify the task of modelling interacting biological components. Its breadth is demonstrated by creating models of DNA replication dynamics, the gene expression dynamics in response to DNA methylation damage, and a multisite phosphorylation switch. The flexibility of these models is shown by adapting the DNA replication model to further include two topics of interest from the literature: cooperative origin firing and replication fork barriers. The Beacon Calculus is supported with the open-source simulator bcs (https://github.com/MBoemo/bcs.git) to allow users to develop and simulate their own models.
Highlights
The ability to quickly create flexible and concise models of biological systems makes mathematical modelling more practical, enables rapid hypothesis testing, and increases the likelihood that modelling will be used to ensure that conclusions drawn from experiments are consistent with data
The Beacon Calculus is a new language that makes modelling simple by allowing users to simulate a biological system in only a few lines of code
We demonstrate the breadth of applications in this paper by applying the Beacon Calculus to DNA replication and DNA damage repair, both of which have implications for genome stability and cancer
Summary
The ability to quickly create flexible and concise models of biological systems makes mathematical modelling more practical, enables rapid hypothesis testing, and increases the likelihood that modelling will be used to ensure that conclusions drawn from experiments are consistent with data. Process calculi (or process algebras) are valuable tools for assessing the performance, reliability, and behaviour of a system. Communication actions allow processes to interact with one another to perform coordinated behaviours. The semantics of a process calculus sets rigorous rules that govern which actions that processes can perform, enabling formal reasoning about whether a system is ever capable of performing (or not performing) a certain sequence of actions. While process calculi have been historically developed to formally reason about programs and algorithms, they are applicable to any concurrent system (such as biological systems)
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