An agent-based modelling framework to study growth mechanisms in EGFR-L858R mutant cell alveolar type II cells.

Mutations in the epidermal growth factor receptor (EGFR) are common in non-small cell lung cancer (NSCLC), particularly in never-smoker patients. However, these mutations are not always carcinogenic, and have recently been reported in histologically normal lung tissue from patients with and without lung cancer. To investigate the outcome of EGFR mutation in healthy lung stem cells, we grow murine alveolar type II organoids monoclonally in a three-dimensional Matrigel. Our experiments show that the EGFR-L858R mutation induces a change in organoid structure: mutated organoids display more 'budding', in comparison with non-mutant controls, which are nearly spherical. We perform on-lattice computational simulations, which suggest that this can be explained by the concentration of division among a small number of cells on the surface of the mutated organoids. We are currently unable to distinguish the cell-based mechanisms that lead to this spatial heterogeneity in growth, but suggest a number of future experiments which could be used to do so. We suggest that the likelihood of L858R-fuelled tumorigenesis is affected by whether the mutation arises in a spatial environment that allows the development of these surface protrusions. These data may have implications for cancer prevention strategies and for understanding NSCLC progression.

Motility-Induced Phase Separation Mediated by Bacterial Quorum Sensing.

We study motility-induced phase separation (MIPS) in living active matter, in which cells interact through chemical signaling, or quorum sensing. In contrast to previous theories of MIPS, our multiscale continuum model accounts explicitly for genetic regulation of signal production and motility. Through analysis and simulations, we derive a new criterion for the onset of MIPS that depends on features of the genetic network. Furthermore, we identify and characterize a new type of oscillatory instability that occurs when gene regulation inside cells promotes motility in higher signal concentrations.

A Systematically Reduced Mathematical Model for Organoid Expansion.

Organoids are three-dimensional multicellular tissue constructs. When cultured in vitro, they recapitulate the structure, heterogeneity, and function of their in vivo counterparts. As awareness of the multiple uses of organoids has grown, e.g. in drug discovery and personalised medicine, demand has increased for low-cost and efficient methods of producing them in a reproducible manner and at scale. Here we focus on a bioreactor technology for organoid production, which exploits fluid flow to enhance mass transport to and from the organoids. To ensure large numbers of organoids can be grown within the bioreactor in a reproducible manner, nutrient delivery to, and waste product removal from, the organoids must be carefully controlled. We develop a continuum mathematical model to investigate how mass transport within the bioreactor depends on the inlet flow rate and cell seeding density, focusing on the transport of two key metabolites: glucose and lactate. We exploit the thin geometry of the bioreactor to systematically simplify our model. This significantly reduces the computational cost of generating model solutions, and provides insight into the dominant mass transport mechanisms. We test the validity of the reduced models by comparison with simulations of the full model. We then exploit our reduced mathematical model to determine, for a given inlet flow rate and cell seeding density, the evolution of the spatial metabolite distributions throughout the bioreactor. To assess the bioreactor transport characteristics, we introduce metrics quantifying glucose conversion (the ratio between the total amounts of consumed and supplied glucose), the maximum lactate concentration, the proportion of the bioreactor with intolerable lactate concentrations, and the time when intolerable lactate concentrations are first experienced within the bioreactor. We determine the dependence of these metrics on organoid-line characteristics such as proliferation rate and rate of glucose consumption per cell. Finally, for a given organoid line, we determine how the distribution of metabolites and the associated metrics depend on the inlet flow rate. Insights from this study can be used to inform bioreactor operating conditions, ultimately improving the quality and number of bioreactor-expanded organoids.

Emergent robustness of bacterial quorum sensing in fluid flow.

Bacteria use intercellular signaling, or quorum sensing (QS), to share information and respond collectively to aspects of their surroundings. The autoinducers that carry this information are exposed to the external environment; consequently, they are affected by factors such as removal through fluid flow, a ubiquitous feature of bacterial habitats ranging from the gut and lungs to lakes and oceans. To understand how QS genetic architectures in cells promote appropriate population-level phenotypes throughout the bacterial life cycle requires knowledge of how these architectures determine the QS response in realistic spatiotemporally varying flow conditions. Here we develop and apply a general theory that identifies and quantifies the conditions required for QS activation in fluid flow by systematically linking cell- and population-level genetic and physical processes. We predict that when a subset of the population meets these conditions, cell-level positive feedback promotes a robust collective response by overcoming flow-induced autoinducer concentration gradients. By accounting for a dynamic flow in our theory, we predict that positive feedback in cells acts as a low-pass filter at the population level in oscillatory flow, allowing a population to respond only to changes in flow that occur over slow enough timescales. Our theory is readily extendable and provides a framework for assessing the functional roles of diverse QS network architectures in realistic flow conditions.

Using singular perturbation theory to determine kinetic parameters in a non-standard coupled enzyme assay.

We investigate how to characterize the kinetic parameters of an aminotransaminase using a non-standard coupled (or auxiliary) enzyme assay, where the peculiarity arises for two reasons. First, one of the products of the auxiliary enzyme is a substrate for the primary enzyme and, second, we explicitly account for the reversibility of the auxiliary enzyme reaction. Using singular perturbation theory, we characterize the two distinguished asymptotic limits in terms of the strength of the reverse reaction, which allows us to determine how to deduce the kinetic parameters of the primary enzyme for a characterized auxiliary enzyme. This establishes a parameter-estimation algorithm that is applicable more generally to similar reaction networks. We demonstrate the applicability of our theory by performing enzyme assays to characterize a novel putative aminotransaminase enzyme, CnAptA (UniProtKB Q0KEZ8) from Cupriavidus necator H16, for two different omega-amino acid substrates.

An Asymptotic Analysis of the Malonyl-CoA Route to 3-Hydroxypropionic Acid in Genetically Engineered Microbes.

There has been recent interest in creating an efficient microbial production route for 3-hydroxypropionic acid, an important platform chemical. We develop and solve a mathematical model for the time-dependent metabolite concentrations in the malonyl-CoA pathway for 3-hydroxypropionic acid production in microbes, using a combination of numerical and asymptotic methods. This allows us to identify the most important targets for enzyme regulation therein under conditions of plentiful and sparse pyruvate, and to quantify their relative importance. In our model, we account for sinks of acetyl-CoA and malonyl-CoA to, for example, the citric acid cycle and fatty acid biosynthesis, respectively. Notably, in the plentiful pyruvate case we determine that there is a bifurcation in the asymptotic structure of the system, the crossing of which corresponds to a significant increase in 3-hydroxypropionic acid production. Moreover, we deduce that the most significant increases to 3-hydroxypropionic acid production can be obtained by up-regulating two specific enzymes in tandem, as the inherent nonlinearity of the system means that a solo up-regulation of either does not result in large increases in production. The types of issue arising here are prevalent in synthetic biology applications, and it is hoped that the system considered provides an instructive exemplar for broader applications.

Multi-timescale analysis of a metabolic network in synthetic biology: a kinetic model for 3-hydroxypropionic acid production via beta-alanine.

A biosustainable production route for 3-hydroxypropionic acid (3HP), an important platform chemical, would allow 3HP to be produced without using fossil fuels. We are interested in investigating a potential biochemical route to 3HP from pyruvate through [Formula: see text]-alanine and, in this paper, we develop and solve a mathematical model for the reaction kinetics of the metabolites involved in this pathway. We consider two limiting cases, one where the levels of pyruvate are never replenished, the other where the levels of pyruvate are continuously replenished and thus kept constant. We exploit the natural separation of both the time scales and the metabolite concentrations to make significant asymptotic progress in understanding the system without resorting to computationally expensive parameter sweeps. Using our asymptotic results, we are able to predict the most important reactions to maximize the production of 3HP in this system while reducing the maximum amount of the toxic intermediate compound malonic semi-aldehyde present at any one time, and thus we are able to recommend which enzymes experimentalists should focus on manipulating.

Applying asymptotic methods to synthetic biology: Modelling the reaction kinetics of the mevalonate pathway.

The mevalonate pathway is normally found in eukaryotes, and allows for the production of isoprenoids, a useful class of organic compounds. This pathway has been successfully introduced to Escherichia coli, enabling a biosynthetic production route for many isoprenoids. In this paper, we develop and solve a mathematical model for the concentration of metabolites in the mevalonate pathway over time, accounting for the loss of acetyl-CoA to other metabolic pathways. Additionally, we successfully test our theoretical predictions experimentally by introducing part of the pathway into Cupriavidus necator. In our model, we exploit the natural separation of time scales as well as of metabolite concentrations to make significant asymptotic progress in understanding the system. We confirm that our asymptotic results agree well with numerical simulations, the former enabling us to predict the most important reactions to increase isopentenyl diphosphate production whilst minimizing the levels of HMG-CoA, which inhibits cell growth. Thus, our mathematical model allows us to recommend the upregulation of certain combinations of enzymes to improve production through the mevalonate pathway.