Cyanobacteria are the main autotrophs and N₂-fixing (diazotrophic) organisms in large parts of the oligotrophic global ocean, where generally all heterotrophic production depends on their activity. ...Amino acids (AAs) from cyanobacteria are essential macronutrients for these heterotrophic food webs, yet little is known about the de novo synthesis of AAs during N₂ fixation. Through a combination of bulk and amino acid nitrogen (AAN) specific analyses of field based N₂ fixation experiments, we demonstrate that the de novo synthesis of 13 AAs accounted for the majority of bulk N₂ fixation rates at four stations in the central Baltic Sea in July 2015. Slow AA turnover times of 87 ± 14 d coincided with low phosphate concentrations and high cell-carbon biomasses of unicellular cyanobacteria. Very fast turnover times of 17 ± 3 d coincided with high phosphate concentrations and undecayed Nodularia spumigena cells, but unexpectedly also with phosphate depletion and decayed N. spumigena cells. In a decayed bloom, volumetric N₂ fixation rates into AAN provided a much better estimate of the net incorporation of N₂ into biomass than fixation into bulk nitrogen that rather reflected gross N₂ fixation. In an undecayed bloom, the turnover times of 13 AAs can be predicted from a single bulk N₂ fixation rate. This is the first direct evidence that the very late, decayed stage of a cyanobacteria bloom can be a flashpoint of very fast AA turnover during N₂ fixation with hitherto uncharacterized consequences for heterotrophic food webs and diazotroph N inputs to the global ocean.
Mesophotic reef corals remain largely unexplored in terms of the genetic adaptations and physiological mechanisms to acquire, allocate, and use energy for survival and reproduction. In the Hawaiian ...Archipelago, the Leptoseris species complex form the most spatially extensive mesophotic coral ecosystem known and provide habitat for a unique community. To study how the ecophysiology of Leptoseris species relates to symbiont–host specialization and understand the mechanisms responsible for coral energy acquisition in extreme low light environments, we examined Symbiodinium (endosymbiotic dinoflagellate) photobiological characteristics and the lipids and isotopic signatures from Symbiodinium and coral hosts over a depth-dependent light gradient (55–7 μmol photons m−2 s−1, 60–132 m). Clear performance differences demonstrate different photoadaptation and photoacclimatization across this genus. Our results also show that flexibility in photoacclimatization depends primarily on Symbiodinium type. Colonies harboring Symbiodinium sp. COI-2 showed significant increases in photosynthetic pigment content with increasing depth, whereas colonies harboring Symbiodinium spp. COI-1 and COI-3 showed variability in pigment composition, yield measurements for photosystem II, as well as size and density of Symbiodinium cells. Despite remarkable differences in photosynthetic adaptive strategies, there were no significant differences among lipids of Leptoseris species with depth. Finally, isotopic signatures of both host and Symbiodinium changed with depth, indicating that coral colonies acquired energy from different sources depending on depth. This study highlights the complexity in physiological adaptations within this symbiosis and the different strategies used by closely related mesophotic species to diversify energy acquisition and to successfully establish and compete in extreme light-limited environments.
For any subset
$Z \subseteq {\mathbb {Q}}$
, consider the set
$S_Z$
of subfields
$L\subseteq {\overline {\mathbb {Q}}}$
which contain a co-infinite subset
$C \subseteq L$
that is universally ...definable in L such that
$C \cap {\mathbb {Q}}=Z$
. Placing a natural topology on the set
${\operatorname {Sub}({\overline {\mathbb {Q}}})}$
of subfields of
${\overline {\mathbb {Q}}}$
, we show that if Z is not thin in
${\mathbb {Q}}$
, then
$S_Z$
is meager in
${\operatorname {Sub}({\overline {\mathbb {Q}}})}$
. Here, thin and meager both mean “small”, in terms of arithmetic geometry and topology, respectively. For example, this implies that only a meager set of fields L have the property that the ring of algebraic integers
$\mathcal {O}_L$
is universally definable in L. The main tools are Hilbert’s Irreducibility Theorem and a new normal form theorem for existential definitions. The normal form theorem, which may be of independent interest, says roughly that every
$\exists $
-definable subset of an algebraic extension of
${\mathbb Q}$
is a finite union of single points and projections of hypersurfaces defined by absolutely irreducible polynomials.
Computer models of left ventricular (LV) electro-mechanics (EM) show promise as a tool for assessing the impact of increased afterload upon LV performance. However, the identification of unique ...afterload model parameters and the personalization of EM LV models remains challenging due to significant clinical input uncertainties. Here, we personalized a virtual cohort of N = 17 EM LV models under pressure overload conditions. A global–local optimizer was developed to uniquely identify parameters of a three-element Windkessel (Wk3) afterload model. The sensitivity of Wk3 parameters to input uncertainty and of the EM LV model to Wk3 parameter uncertainty was analysed. The optimizer uniquely identified Wk3 parameters, and outputs of the personalized EM LV models showed close agreement with clinical data in all cases. Sensitivity analysis revealed a strong dependence of Wk3 parameters on input uncertainty. However, this had limited impact on outputs of EM LV models. A unique identification of Wk3 parameters from clinical data appears feasible, but it is sensitive to input uncertainty, thus depending on accurate invasive measurements. By contrast, the EM LV model outputs were less sensitive, with errors of less than 8.14% for input data errors of 10%, which is within the bounds of clinical data uncertainty.
This article is part of the theme issue ‘Uncertainty quantification in cardiac and cardiovascular modelling and simulation’.
Ischaemia, in which inadequate blood supply compromises and eventually kills regions of cardiac tissue, can cause many types of arrhythmia, some life-threatening. A significant component of this is ...the effects of the resulting hypoxia, and concomitant hyperklaemia and acidosis, on the electrophysiological properties of myocytes. Clinical and experimental data have also shown that regions of structural heterogeneity (fibrosis, necrosis, fibro-fatty infiltration) can act as triggers for arrhythmias under acute ischaemic conditions. Mechanistic models have successfully captured these effects in silico. However, the relative significance of these separate facets of the condition, and how sensitive arrhythmic risk is to the extents of each, is far less explored. In this work, we use partitioned Gaussian process emulation and new metrics for source-sink mismatch that rely on simulations of bifurcating cardiac fibresto interrogate a model of heterogeneous ischaemic tissue. Re-entries were most sensitive to the level of hypoxia and the fraction of non-excitable tissue. In addition, our results reveal both protective and pro-arrhythmic effects of hyperklaemia, and present the levels of hyperklaemia, hypoxia and percentage of non-excitable tissue that pose the highest arrhythmic risks.
This article is part of the theme issue ‘Uncertainty quantification in cardiac and cardiovascular modelling and simulation’.
In patients with atrial fibrillation, local activation time (LAT) maps are routinely used for characterizing patient pathophysiology. The gradient of LAT maps can be used to calculate conduction ...velocity (CV), which directly relates to material conductivity and may provide an important measure of atrial substrate properties. Including uncertainty in CV calculations would help with interpreting the reliability of these measurements. Here, we build upon a recent insight into reduced-rank Gaussian processes (GPs) to perform probabilistic interpolation of uncertain LAT directly on human atrial manifolds. Our Gaussian process manifold interpolation (GPMI) method accounts for the topology of the atrium, and allows for calculation of statistics for predicted CV. We demonstrate our method on two clinical cases, and perform validation against a simulated ground truth. CV uncertainty depends on data density, wave propagation direction and CV magnitude. GPMI is suitable for probabilistic interpolation of other uncertain quantities on non-Euclidean manifolds.
This article is part of the theme issue ‘Uncertainty quantification in cardiac and cardiovascular modelling and simulation’.
Mathematical models of ion channels, which constitute indispensable components of action potential models, are commonly constructed by fitting to whole-cell patch-clamp data. In a previous study, we ...fitted cell-specific models to hERG1a (Kv11.1) recordings simultaneously measured using an automated high-throughput system, and studied cell-cell variability by inspecting the resulting model parameters. However, the origin of the observed variability was not identified. Here, we study the source of variability by constructing a model that describes not just ion current dynamics, but the entire voltage-clamp experiment. The experimental artefact components of the model include: series resistance, membrane and pipette capacitance, voltage offsets, imperfect compensations made by the amplifier for these phenomena, and leak current. In this model, variability in the observations can be explained by either cell properties, measurement artefacts, or both. Remarkably, by assuming that variability arises exclusively from measurement artefacts, it is possible to explain a larger amount of the observed variability than when assuming cell-specific ion current kinetics. This assumption also leads to a smaller number of model parameters. This result suggests that most of the observed variability in patch-clamp data measured under the same conditions is caused by experimental artefacts, and hence can be compensated for in post-processing by using our model for the patch-clamp experiment. This study has implications for the question of the extent to which cell-cell variability in ion channel kinetics exists, and opens up routes for better correction of artefacts in patch-clamp data.
This article is part of the theme issue ‘Uncertainty quantification in cardiac and cardiovascular modelling and simulation’.
Uncertainty quantification (UQ) is a vital step in using mathematical models and simulations to take decisions. The field of cardiac simulation has begun to explore and adopt UQ methods to ...characterize uncertainty in model inputs and how that propagates through to outputs or predictions; examples of this can be seen in the papers of this issue. In this review and perspective piece, we draw attention to an important and under-addressed source of uncertainty in our predictions—that of uncertainty in the model structure or the equations themselves. The difference between imperfect models and reality is termed model discrepancy, and we are often uncertain as to the size and consequences of this discrepancy. Here, we provide two examples of the consequences of discrepancy when calibrating models at the ion channel and action potential scales. Furthermore, we attempt to account for this discrepancy when calibrating and validating an ion channel model using different methods, based on modelling the discrepancy using Gaussian processes and autoregressive-moving-average models, then highlight the advantages and shortcomings of each approach. Finally, suggestions and lines of enquiry for future work are provided.
This article is part of the theme issue ‘Uncertainty quantification in cardiac and cardiovascular modelling and simulation’.
Delayed afterdepolarizations (DADs) and spontaneous depolarizations (SDs) are typically triggered by spontaneous diastolic Ca2+ release from the sarcoplasmic reticulum (SR) which is caused by an ...elevated SR Ca2+-ATPase (SERCA) uptake and dysfunctional ryanodine receptors. However, recent studies on the T-box transcription factor gene (TBX5) demonstrated that abnormal depolarizations could occur despite a reduced SERCA uptake. Similar findings have also been reported in experimental or clinical studies of diabetes and heart failure. To investigate the sensitivity of SERCA in the genesis of DADs/SDs as well as its dependence on other Ca2+ handling channels, we performed systematic analyses using the Maleckar et al. model. Results showed that the modulation of SERCA alone cannot trigger abnormal depolarizations, but can instead affect the interdependency of other Ca2+ handling channels in triggering DADs/SDs. Furthermore, we discovered the existence of a threshold value for the intracellular concentration of Ca2+ (Ca2+i) for abnormal depolarizations, which is modulated by the maximum SERCA uptake and the concentration of Ca2+ in the uptake and release compartments in the SR (Ca2+up and Ca2+rel). For the first time, our modelling study reconciles different mechanisms of abnormal depolarizations in the setting of ‘lone’ AF, reduced TBX5, diabetes and heart failure, and may lead to more targeted treatment for these patients.
This article is part of the theme issue ‘Uncertainty quantification in cardiac and cardiovascular modelling and simulation’.
Mathematical models of a cellular action potential (AP) in cardiac modelling have become increasingly complex, particularly in gating kinetics, which control the opening and closing of individual ion ...channel currents. As cardiac models advance towards use in personalized medicine to inform clinical decision-making, it is critical to understand the uncertainty hidden in parameter estimates from their calibration to experimental data. This study applies approximate Bayesian computation to re-calibrate the gating kinetics of four ion channels in two existing human atrial cell models to their original datasets, providing a measure of uncertainty and indication of potential issues with selecting a single unique value given the available experimental data. Two approaches are investigated to reduce the uncertainty present: re-calibrating the models to a more complete dataset and using a less complex formulation with fewer parameters to constrain. The re-calibrated models are inserted back into the full cell model to study the overall effect on the AP. The use of more complete datasets does not eliminate uncertainty present in parameter estimates. The less complex model, particularly for the fast sodium current, gave a better fit to experimental data alongside lower parameter uncertainty and improved computational speed.
This article is part of the theme issue ‘Uncertainty quantification in cardiac and cardiovascular modelling and simulation’.
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