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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. Author summary: Simulating a model of a biological system can suggest ideas for future experiments and help ensure that conclusions about a mechanism 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. This simplicity is critical as it allows users the freedom to come up with new ideas and rapidly test them. Models written in the Beacon Calculus are also easy to modify and extend, allowing users to add new features to the model or incorporate it into a larger biological system. 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. We also apply it to multisite phosphorylation, which is important for cellular signalling. To enable users to create their own models, we created the open-source Beacon Calculus simulator bcs (https://github.com/MBoemo/bcs.git) which is easy to install and is well-supported by documentation and examples. [ABSTRACT FROM AUTHOR]

Achieving a complete understanding of cellular signal transduction requires deciphering the relation between structural and biochemical features of a signaling system and the shape of the signal-response relationship it embeds. Using explicit analytical expressions and numerical simulations, we present here this relation for four-layered phosphorelays, which are signaling systems that are ubiquitous in prokaryotes and also found in lower eukaryotes and plants. We derive an analytical expression that relates the shape of the signal-response relationship in a relay to the kinetic rates of forward, reverse phosphorylation and hydrolysis reactions. This reveals a set of mathematical conditions which, when satisfied, dictate the shape of the signal-response relationship. We find that a specific topology also observed in nature can satisfy these conditions in such a way to allow plasticity among hyperbolic and sigmoidal signal-response relationships. Particularly, the shape of the signal-response relationship of this relay topology can be tuned by altering kinetic rates and total protein levels at different parts of the relay. These findings provide an important step towards predicting response dynamics of phosphorelays, and the nature of subsequent physiological responses that they mediate, solely from topological features and few composite measurements; measuring the ratio of reverse and forward phosphorylation rate constants could be sufficient to determine the shape of the signal-response relationship the relay exhibits. Furthermore, they highlight the potential ways in which selective pressures on signal processing could have played a role in the evolution of the observed structural and biochemical characteristic in phosphorelays. [ABSTRACT FROM AUTHOR]

DNA replication, mitosis and mitotic exit are critical transitions of the cell cycle which normally occur only once per cycle. A universal control mechanism was proposed for the regulation of mitotic entry in which Cdk helps its own activation through two positive feedback loops. Recent discoveries in various organisms showed the importance of positive feedbacks in other transitions as well. Here we investigate if a universal control system with transcriptional regulation(s) and post-translational positive feedback(s) can be proposed for the regulation of all cell cycle transitions. Through computational modeling, we analyze the transition dynamics in all possible combinations of transcriptional and post-translational regulations. We find that some combinations lead to 'sloppy' transitions, while others give very precise control. The periodic transcriptional regulation through the activator or the inhibitor leads to radically different dynamics. Experimental evidence shows that in cell cycle transitions of organisms investigated for cell cycle dependent periodic transcription, only the inhibitor OR the activator is under cyclic control and never both of them. Based on these observations, we propose two transcriptional control modes of cell cycle regulation that either STOP or let the cycle GO in case of a transcriptional failure. We discuss the biological relevance of such differences. [ABSTRACT FROM AUTHOR]

Major Histocompatibility Complex (MHC) class I molecules enable cytotoxic T lymphocytes to destroy virus-infected or cancerous cells, thereby preventing disease progression. MHC class I molecules provide a snapshot of the contents of a cell by binding to protein fragments arising from intracellular protein turnover and presenting these fragments at the cell surface. Competing fragments (peptides) are selected for cell-surface presentation on the basis of their ability to form a stable complex with MHC class I, by a process known as peptide optimization. A better understanding of the optimization process is important for our understanding of immunodominance, the predominance of some T lymphocyte specificities over others, which can determine the efficacy of an immune response, the danger of immune evasion, and the success of vaccination strategies. In this paper we present a dynamical systems model of peptide optimization by MHC class I. We incorporate the chaperone molecule tapasin, which has been shown to enhance peptide optimization to different extents for different MHC class I alleles. Using a combination of published and novel experimental data to parameterize the model, we arrive at a relation of peptide filtering, which quantifies peptide optimization as a function of peptide supply and peptide unbinding rates. From this relation, we find that tapasin enhances peptide unbinding to improve peptide optimization without significantly delaying the transit of MHC to the cell surface, and differences in peptide optimization across MHC class I alleles can be explained by allele-specific differences in peptide binding. Importantly, our filtering relation may be used to dynamically predict the cell surface abundance of any number of competing peptides by MHC class I alleles, providing a quantitative basis to investigate viral infection or disease at the cellular level. We exemplify this by simulating optimization of the distribution of peptides derived from Human Immunodeficiency Virus Gag-Pol polyprotein. INSET: Author Summary. [ABSTRACT FROM AUTHOR]

Competing Interests: The authors have declared that no competing interests exist.