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Molecules Bio

Mathematical Modelling of the Cell Cycle

As the design for a piece of software, hardware, or model becomes more elaborate, it becomes difficult to ensure that it's really working how you think it's working.  Process algebras (or process calculi) are tools from computer science that allow you to prove whether a certain process can ever exhibit a behaviour.  This is particularly useful for reasoning about systems in where processes can happen in parallel, which makes them well-suited for studying biological systems: many processes occur simultaneously within a cell, and these processes can have an important impact on one another.

We created the Beacon Calculus, a process algebra for modelling biological systems.  Models written in the Beacon Calculus are concise, easy to encode, and straightforward to communicate to experimentalists.  It is also straightforward to modify and extend models written in the Beacon Calculus so that users can freely experiment with different hypotheses about how a mechanism might work by only changing a term or two.


The above snippet shows source code for a model of DNA replication: firing factors (FF) cause replication origins (ORI) to fire, at which time they start a leftward-moving replication fork (FL) and a rightward-moving replication fork (FR) that replicates the chromosome. In our Beacon Calculus language, this complex behaviour is expressed in only six lines of code and thousands of simulations can be run in seconds. With these six lines of code and a button click, we can simulate the replication of the entire budding yeast genome:


The above plot shows all 16 budding yeast chromosomes, but zooming in on chromosome II shows the quality of the fit between our simulation (blue) and replication timing data (grey):


This example has focused on DNA replication, but the Beacon Calculus can be used across diverse areas of biological research.  Thus far, the topics that the Beacon Calculus has been used to study include:

  • DNA replication,

  • multisite phosphorylation and ultrasensitive receptors,

  • transcription (including replication-transcription interactions),

  • DNA damage response,

  • regulatory network of centriole growth.

This list is rapidly expanding as our developers continue to improve the technology, allowing us to push forward into new biological applications.​

Corresponding software: 

bcs is available on GitHub and we maintain a manual with examples.

Corresponding publications:

Boemo, M.A.†, Cardelli, L., Nieduszynski, C.A. (2020) The Beacon Calculus: A formal method for the flexible and concise modelling of biological systems. PLoS Computational Biology 16:e1007651.  [DOI:​10.1371/journal.pcbi.1007651]

Aydogan, M.G.*†, Steinacker, T.L.*, Mofatteh, M., Wilmott, Z.M., Zhou, F.Y., Gartenmann, L., Wainman, A., Saurya, S., Novak, Z.A., Wong, S., Goriely, A., Boemo, M.A.†, Raff, J.W.† (2020) A free-running oscillator times and executes centriole biogenesis. Cell 181:1-16. [DOI:10.1016/j.cell.2020.05.018]

Boemo, M.A.†, Byrne, H.M.† (2018) Mathematical modelling of a hypoxia-regulated oncolytic virus delivered by tumour-associated macrophages. Journal of Theoretical Biology 461:102-116. [DOI:10.1016/j.jtbi.2018.10.044]

Developers and Scientists:

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