Mathematical reconstruction of the metabolic network in an in-vitro multiple myeloma model.

It is increasingly apparent that cancer cells, in addition to remodelling their metabolism to survive and proliferate, adapt and manipulate the metabolism of other cells. This property may be a telling sign that pre-clinical tumour metabolism studies exclusively utilising in-vitro mono-culture models could prove to be limited for uncovering novel metabolic targets able to translate into clinical therapies. Although this is increasingly recognised, and work towards addressing the issue is becoming routinary much remains poorly understood. For instance, knowledge regarding the biochemical mechanisms through which cancer cells manipulate non-cancerous cell metabolism, and the subsequent impact on their survival and proliferation remains limited. Additionally, the variations in these processes across different cancer types and progression stages, and their implications for therapy, also remain largely unexplored. This study employs an interdisciplinary approach that leverages the predictive power of mathematical modelling to enrich experimental findings. We develop a functional multicellular in-silico model that facilitates the qualitative and quantitative analysis of the metabolic network spawned by an in-vitro co-culture model of bone marrow mesenchymal stem- and myeloma cell lines. To procure this model, we devised a bespoke human genome constraint-based reconstruction workflow that combines aspects from the legacy mCADRE & Metabotools algorithms, the novel redHuman algorithm, along with 13C-metabolic flux analysis. Our workflow transforms the latest human metabolic network matrix (Recon3D) into two cell-specific models coupled with a metabolic network spanning a shared growth medium. When cross-validating our in-silico model against the in-vitro model, we found that the in-silico model successfully reproduces vital metabolic behaviours of its in-vitro counterpart; results include cell growth predictions, respiration rates, as well as support for observations which suggest cross-shuttling of redox-active metabolites between cells.

Interplay of p53 and XIAP protein dynamics orchestrates cell fate in response to chemotherapy.

Chemotherapeutic drugs are used to treat almost all types of cancer, but the intended response, i.e., elimination, is often incomplete, with a subset of cancer cells resisting treatment. Two critical factors play a role in chemoresistance: the p53 tumour suppressor gene and the X-linked inhibitor of apoptosis (XIAP). These proteins have been shown to act synergistically to elicit cellular responses upon DNA damage induced by chemotherapy, yet, the mechanism is poorly understood. This study introduces a mathematical model characterising the apoptosis pathway activation by p53 before and after mitochondrial outer membrane permeabilisation upon treatment with the chemotherapy Doxorubicin (Dox). "In-silico" simulations show that the p53 dynamics change dose-dependently. Under medium to high doses of Dox, p53 concentration ultimately stabilises to a high level regardless of XIAP concentrations. However, caspase-3 activation may be triggered or not depending on the XIAP induction rate, ultimately determining whether the cell will perish or resist. Consequently, the model predicts that failure to activate apoptosis in some cancer cells expressing wild-type p53 might be due to heterogeneity between cells in upregulating the XIAP protein, rather than due to the p53 protein concentration. Our model suggests that the interplay of the p53 dynamics and the XIAP induction rate is critical to determine the cancer cells' therapeutic response.

Proline synthesis through PYCR1 is required to support cancer cell proliferation and survival in oxygen-limiting conditions.

The demands of cancer cell proliferation alongside an inadequate angiogenic response lead to insufficient oxygen availability in the tumor microenvironment. Within the mitochondria, oxygen is the major electron acceptor for NADH, with the result that the reducing potential produced through tricarboxylic acid (TCA) cycle activity and mitochondrial respiration are functionally linked. As the oxidizing activity of the TCA cycle is required for efficient synthesis of anabolic precursors, tumoral hypoxia could lead to a cessation of proliferation without another means of correcting the redox imbalance. We show that in hypoxic conditions, mitochondrial pyrroline 5-carboxylate reductase 1 (PYCR1) activity is increased, oxidizing NADH with the synthesis of proline as a by-product. We further show that PYCR1 activity is required for the successful maintenance of hypoxic regions by permitting continued TCA cycle activity, and that its loss leads to significantly increased hypoxia in vivo and in 3D culture, resulting in widespread cell death.

Calcium Dynamics and Water Transport in Salivary Acinar Cells.

Saliva is secreted from the acinar cells of the salivary glands, using mechanisms that are similar to other types of water-transporting epithelial cells. Using a combination of theoretical and experimental techniques, over the past 20 years we have continually developed and modified a quantitative model of saliva secretion, and how it is controlled by the dynamics of intracellular calcium. However, over approximately the past 5 years there have been significant developments both in our understanding of the underlying mechanisms and in the way these mechanisms should best be modelled. Here, we review the traditional understanding of how saliva is secreted, and describe how our work has suggested important modifications to this traditional view. We end with a brief description of the most recent data from living animals and discuss how this is now contributing to yet another iteration of model construction and experimental investigation.

A Multicellular Model of Primary Saliva Secretion in the Parotid Gland.

We construct a three-dimensional anatomically accurate multicellular model of a parotid gland acinus to investigate the influence that the topology of its lumen has on primary fluid secretion. Our model consists of seven individual cells, coupled via a common lumen and intercellular signalling. Each cell is equipped with the intracellular calcium ([Formula: see text])-signalling model developed by Pages et al, Bull Math Biol 81: 1394-1426, 2019. https://doi.org/10.1007/s11538-018-00563-z and the secretion model constructed by Vera-Sigüenza et al., Bull Math Biol 81: 699-721, 2019. https://doi.org/10.1007/s11538-018-0534-z. The work presented here is a continuation of these studies. While previous mathematical research has proven invaluable, to the best of our knowledge, a multicellular modelling approach has never been implemented. Studies have hypothesised the need for a multiscale model to understand the primary secretion process, as acinar cells do not operate on an individual basis. Instead, they form racemous clusters that form intricate water and protein delivery networks that join the acini with the gland's ducts-questions regarding the extent to which the acinus topology influences the efficiency of primary fluid secretion to persist. We found that (1) The topology of the acinus has almost no effect on fluid secretion. (2) A multicellular spatial model of secretion is not necessary when modelling fluid flow. Although the inclusion of intercellular signalling introduces vastly more complex dynamics, the total secretory rate remains fundamentally unchanged. (3) To obtain an acinus, or better yet a gland flow rate estimate, one can multiply the output of a well-stirred single-cell model by the total number of cells required.

A Model of [Formula: see text] Dynamics in an Accurate Reconstruction of Parotid Acinar Cells.

We have constructed a spatiotemporal model of [Formula: see text] dynamics in parotid acinar cells, based on new data about the distribution of inositol trisphophate receptors (IPR). The model is solved numerically on a mesh reconstructed from images of a cluster of parotid acinar cells. In contrast to our earlier model (Sneyd et al. in J Theor Biol 419:383-393. https://doi.org/10.1016/j.jtbi.2016.04.030 , 2017b), which cannot generate realistic [Formula: see text] oscillations with the new data on IPR distribution, our new model reproduces the [Formula: see text] dynamics observed in parotid acinar cells. This model is then coupled with a fluid secretion model described in detail in a companion paper: A mathematical model of fluid transport in an accurate reconstruction of a parotid acinar cell (Vera-Sigüenza et al. in Bull Math Biol. https://doi.org/10.1007/s11538-018-0534-z , 2018b). Based on the new measurements of IPR distribution, we show that Class I models (where [Formula: see text] oscillations can occur at constant [[Formula: see text]]) can produce [Formula: see text] oscillations in parotid acinar cells, whereas Class II models (where [[Formula: see text]] needs to oscillate in order to produce [Formula: see text] oscillations) are unlikely to do so. In addition, we demonstrate that coupling fluid flow secretion with the [Formula: see text] signalling model changes the dynamics of the [Formula: see text] oscillations significantly, which indicates that [Formula: see text] dynamics and fluid flow cannot be accurately modelled independently. Further, we determine that an active propagation mechanism based on calcium-induced calcium release channels is needed to propagate the [Formula: see text] wave from the apical region to the basal region of the acinar cell.

A Mathematical Model of Fluid Transport in an Accurate Reconstruction of Parotid Acinar Cells.

Salivary gland acinar cells use the calcium ([Formula: see text]) ion as a signalling messenger to regulate a diverse range of intracellular processes, including the secretion of primary saliva. Although the underlying mechanisms responsible for saliva secretion are reasonably well understood, the precise role played by spatially heterogeneous intracellular [Formula: see text] signalling in these cells remains uncertain. In this study, we use a mathematical model, based on new and unpublished experimental data from parotid acinar cells (measured in excised lobules of mouse parotid gland), to investigate how the structure of the cell and the spatio-temporal properties of [Formula: see text] signalling influence the production of primary saliva. We combine a new [Formula: see text] signalling model [described in detail in a companion paper: Pages et al. in Bull Math Biol 2018, submitted] with an existing secretion model (Vera-Sigüenza et al. in Bull Math Biol 80:255-282, 2018. https://doi.org/10.1007/s11538-017-0370-6 ) and solve the resultant model in an anatomically accurate three-dimensional cell. Our study yields three principal results. Firstly, we show that spatial heterogeneities of [Formula: see text] concentration in either the apical or basal regions of the cell have no significant effect on the rate of primary saliva secretion. Secondly, in agreement with previous work (Palk et al., in J Theor Biol 305:45-53, 2012. https://doi.org/10.1016/j.jtbi.2012.04.009 ) we show that the frequency of [Formula: see text] oscillation has no significant effect on the rate of primary saliva secretion, which is determined almost entirely by the mean (over time) of the apical and basal [Formula: see text]. Thirdly, it is possible to model the rate of primary saliva secretion as a quasi-steady-state function of the cytosolic [Formula: see text] averaged over the entire cell when modelling the flow rate is the only interest, thus ignoring all the dynamic complexity not only of the fluid secretion mechanism but also of the intracellular heterogeneity of [Formula: see text]. Taken together, our results demonstrate that an accurate multiscale model of primary saliva secretion from a single acinar cell can be constructed by ignoring the vast majority of the spatial and temporal complexity of the underlying mechanisms.

A Mathematical Model Supports a Key Role for Ae4 (Slc4a9) in Salivary Gland Secretion.

We develop a mathematical model of a salivary gland acinar cell with the objective of investigating the role of two [Formula: see text] exchangers from the solute carrier family 4 (Slc4), Ae2 (Slc4a2) and Ae4 (Slc4a9), in fluid secretion. Water transport in this type of cell is predominantly driven by [Formula: see text] movement. Here, a basolateral [Formula: see text] adenosine triphosphatase pump (NaK-ATPase) and a [Formula: see text]-[Formula: see text]-[Formula: see text] cotransporter (Nkcc1) are primarily responsible for concentrating the intracellular space with [Formula: see text] well above its equilibrium potential. Gustatory and olfactory stimuli induce the release of [Formula: see text] ions from the internal stores of acinar cells, which triggers saliva secretion. [Formula: see text]-dependent [Formula: see text] and [Formula: see text] channels promote ion secretion into the luminal space, thus creating an osmotic gradient that promotes water movement in the secretory direction. The current model for saliva secretion proposes that [Formula: see text] anion exchangers (Ae), coupled with a basolateral [Formula: see text] ([Formula: see text]) (Nhe1) antiporter, regulate intracellular pH and act as a secondary [Formula: see text] uptake mechanism (Nauntofte in Am J Physiol Gastrointest Liver Physiol 263(6):G823-G837, 1992; Melvin et al. in Annu Rev Physiol 67:445-469, 2005. https://doi.org/10.1146/annurev.physiol.67.041703.084745 ). Recent studies demonstrated that Ae4 deficient mice exhibit an approximate [Formula: see text] decrease in gland salivation (Peña-Münzenmayer et al. in J Biol Chem 290(17):10677-10688, 2015). Surprisingly, the same study revealed that absence of Ae2 does not impair salivation, as previously suggested. These results seem to indicate that the Ae4 may be responsible for the majority of the secondary [Formula: see text] uptake and thus a key mechanism for saliva secretion. Here, by using 'in-silico' Ae2 and Ae4 knockout simulations, we produced mathematical support for such controversial findings. Our results suggest that the exchanger's cotransport of monovalent cations is likely to be important in establishing the osmotic gradient necessary for optimal transepithelial fluid movement.