Identifiability of enzyme kinetic parameters in substrate competition: a case study of CD39/NTPDase1.

CD39 (NTPDase1-nucleoside triphosphate diphosphohydrolase 1) is a membrane-tethered ectonucleotidase that hydrolyzes extracellular ATP to ADP and ADP to AMP. This enzyme is expressed in a variety of cell types and tissues and has broadly been recognized within vascular tissue to have a protective role in converting "danger" ligands (ATP) into neutral ligands (AMP). In this study, we investigate the enzyme kinetics of CD39 using a Michaelis-Menten modeling framework. We show how the unique situation of having a reaction product also serving as a substrate (ADP) complicates the determination of the governing kinetic parameters. Model simulations using values for the kinetic parameters reported in the literature do not align with corresponding time-series data. This dissonance is explained by CD39 kinetic parameters previously being determined by graphical/linearization methods, which have been shown to distort the underlying error structure and lead to inaccurate parameter estimates. Modern methods of estimating these kinetic parameters using nonlinear least squares are still challenging due to unidentifiable parameter interactions. We propose a workflow to accurately determine these parameters by isolating the ADPase and ATPase reactions and estimating the respective ADPase parameters and ATPase parameters with independent data sets. Theoretically, this ensures all kinetic parameters are identifiable and reliable for future prospective model simulations involving CD39. These kinds of mathematical models can be used to understand how circulating purinergic nucleotides affect disease etiology and potentially inform the development of corresponding therapies.

Hypoxic pulmonary vasoconstriction as a regulator of alveolar-capillary oxygen flux: A computational model of ventilation-perfusion matching.

The relationship between regional variabilities in airflow (ventilation) and blood flow (perfusion) is a critical determinant of gas exchange efficiency in the lungs. Hypoxic pulmonary vasoconstriction is understood to be the primary active regulator of ventilation-perfusion matching, where upstream arterioles constrict to direct blood flow away from areas that have low oxygen supply. However, it is not understood how the integrated action of hypoxic pulmonary vasoconstriction affects oxygen transport at the system level. In this study we develop, and make functional predictions with a multi-scale multi-physics model of ventilation-perfusion matching governed by the mechanism of hypoxic pulmonary vasoconstriction. Our model consists of (a) morphometrically realistic 2D pulmonary vascular networks to the level of large arterioles and venules; (b) a tileable lumped-parameter model of vascular fluid and wall mechanics that accounts for the influence of alveolar pressure; (c) oxygen transport accounting for oxygen bound to hemoglobin and dissolved in plasma; and (d) a novel empirical model of hypoxic pulmonary vasoconstriction. Our model simulations predict that under the artificial test condition of a uniform ventilation distribution (1) hypoxic pulmonary vasoconstriction matches perfusion to ventilation; (2) hypoxic pulmonary vasoconstriction homogenizes regional alveolar-capillary oxygen flux; and (3) hypoxic pulmonary vasoconstriction increases whole-lobe oxygen uptake by improving ventilation-perfusion matching.

Neuroprotective role of hydralazine in rat spinal cord injury-attenuation of acrolein-mediated damage.

Acrolein, an α,ß-unsaturated aldehyde and a reactive product of lipid peroxidation, has been suggested as a key factor in neural post-traumatic secondary injury in spinal cord injury (SCI), mainly based on in vitro and ex vivo evidence. Here, we demonstrate an increase of acrolein up to 300%; the elevation lasted at least 2 weeks in a rat SCI model. More importantly, hydralazine, a known acrolein scavenger can provide neuroprotection when applied systemically. Besides effectively reducing acrolein, hydralazine treatment also resulted in significant amelioration of tissue damage, motor deficits, and neuropathic pain. This effect was further supported by demonstrating the ability of hydralazine to reach spinal cord tissue at a therapeutic level following intraperitoneal application. This suggests that hydralazine is an effective neuroprotective agent not only in vitro, but in a live animal model of SCI as well. Finally, the role of acrolein in SCI was further validated by the fact that acrolein injection into the spinal cord caused significant SCI-like tissue damage and motor deficits. Taken together, available evidence strongly suggests a critical causal role of acrolein in the pathogenesis of spinal cord trauma. Since acrolein has been linked to a variety of illness and conditions, we believe that acrolein-scavenging measures have the potential to be expanded significantly ensuring a broad impact on human health.

What happens inside a fuel cell? Developing an experimental functional map of fuel cell performance.

Fuel cell performance is determined by the complex interplay of mass transport, energy transfer and electrochemical processes. The convolution of these processes leads to spatial heterogeneity in the way that fuel cells perform, particularly due to reactant consumption, water management and the design of fluid-flow plates. It is therefore unlikely that any bulk measurement made on a fuel cell will accurately represent performance at all parts of the cell. The ability to make spatially resolved measurements in a fuel cell provides one of the most useful ways in which to monitor and optimise performance. This Minireview explores a range of in situ techniques being used to study fuel cells and describes the use of novel experimental techniques that the authors have used to develop an 'experimental functional map' of fuel cell performance. These techniques include the mapping of current density, electrochemical impedance, electrolyte conductivity, contact resistance and CO poisoning distribution within working PEFCs, as well as mapping the flow of reactant in gas channels using laser Doppler anemometry (LDA). For the high-temperature solid oxide fuel cell (SOFC), temperature mapping, reference electrode placement and the use of Raman spectroscopy are described along with methods to map the microstructural features of electrodes. The combination of these techniques, applied across a range of fuel cell operating conditions, allows a unique picture of the internal workings of fuel cells to be obtained and have been used to validate both numerical and analytical models.

Practical identifiability and uncertainty quantification of a pulsatile cardiovascular model.

Mathematical models are essential tools to study how the cardiovascular system maintains homeostasis. The utility of such models is limited by the accuracy of their predictions, which can be determined by uncertainty quantification (UQ). A challenge associated with the use of UQ is that many published methods assume that the underlying model is identifiable (e.g. that a one-to-one mapping exists from the parameter space to the model output). In this study we present a novel workflow to calibrate a lumped-parameter model to left ventricular pressure and volume time series data. Key steps include using (1) literature and available data to determine nominal parameter values; (2) sensitivity analysis and subset selection to determine a set of identifiable parameters; (3) optimization to find a point estimate for identifiable parameters; and (4) frequentist and Bayesian UQ calculations to assess the predictive capability of the model. Our results show that it is possible to determine 5 identifiable model parameters that can be estimated to our experimental data from three rats, and that computed UQ intervals capture the measurement and model error.

Increase in oxidative stress biomarkers in dogs with ascending-descending myelomalacia following spinal cord injury.

Multiple biochemical and immunohistochemical tests were performed to elucidate the role of oxidative stress during ascending-descending (A-D) myelomalacia by comparing dogs with this progressive terminal condition to dogs with chronic, focal spinal cord injuries (SCIs) and controls without SCI. Dogs with A-D myelomalacia exhibited increased biochemical markers for oxidative stress, including 8-isoprostane F2α and acrolein, as well as decreased endogenous glutathione with greatest changes occurring at the lesion center. Inflammation, as evident by the concentration of CD18+ phagocytes and hemorrhagic necrosis, was also exacerbated in the lesion of A-D myelomalacic spinal cord compared to focal SCI. The greatest differences in oxidative stress occurred at the lesion center and diminished distally in both spinal cords with A-D myelomalacia and focal SCIs. The spatial progression and time course of A-D myelomalacia are consistent with the development of secondary injury post-SCI. Ascending-descending myelomalacia is proposed as a clinical model that may further the understanding of the role of oxidative stress during secondary injury. Our results indicate that the pathology of A-D myelomalacia is also similar to subacute progressive ascending myelopathy in humans, which is characterized by recurrent neurodegeneration of spinal cord post-injury.