Oscillations in three-reaction quadratic mass-action systems.

It is known that rank-two bimolecular mass-action systems do not admit limit cycles. With a view to understanding which small mass-action systems admit oscillation, in this paper we study rank-two networks with bimolecular source complexes but allow target complexes with higher molecularities. As our goal is to find oscillatory networks of minimal size, we focus on networks with three reactions, the minimum number that is required for oscillation. However, some of our intermediate results are valid in greater generality. One key finding is that an isolated periodic orbit cannot occur in a three-reaction, trimolecular, mass-action system with bimolecular sources. In fact, we characterize all networks in this class that admit a periodic orbit; in every case, all nearby orbits are periodic too. Apart from the well-known Lotka and Ivanova reactions, we identify another network in this class that admits a center. This new network exhibits a vertical Andronov-Hopf bifurcation. Furthermore, we characterize all two-species, three-reaction, bimolecular-sourced networks that admit an Andronov-Hopf bifurcation with mass-action kinetics. These include two families of networks that admit a supercritical Andronov-Hopf bifurcation and hence a stable limit cycle. These networks necessarily have a target complex with a molecularity of at least four, and it turns out that there are exactly four such networks that are tetramolecular.

Estimates of pandemic excess mortality in India based on civil registration data.

The population health impacts of the COVID-19 pandemic are less well understood in low and middle-income countries, where mortality surveillance before the pandemic was patchy. Interpreting the limited all-cause mortality data available in India is challenging. We use existing data on all-cause mortality from civil registration systems of twelve Indian states comprising around 60% of the national population to understand the scale and timing of excess deaths in India during the COVID-19 pandemic. We carefully characterize the reasons why registration is incomplete and estimate the extent of coverage in the data. Comparing the pandemic period to 2019, we estimate excess mortality in twelve Indian states, and extrapolate our estimates to the rest of India. We explore sensitivity of the estimates to various assumptions. For the 12 states with available all-cause mortality data, we document an increase of 28% in deaths during April 2020-May 2021 relative to expectations from 2019. This level of increase in mortality, if it applies nationally, would imply 2.8-2.9 million excess deaths. More limited data from June 2021 increases national estimates of excess deaths during April 2020-June 2021 to 3.8 million. With more optimistic or pessimistic assumptions, excess deaths during this period could credibly lie between 2.8 million and 5.2 million. The scale of estimated excess deaths is broadly consistent with expectations based on seroprevalence and COVID-19 fatality rates observed internationally. Moreover, the timing of excess deaths and recorded COVID-19 deaths is similar-they rise and fall at the same time. The surveillance of pandemic mortality in India has been extremely poor, with 8-10 times as many excess deaths as officially recorded COVID-19 deaths. India is among the countries most severely impacted by the pandemic. Our approach highlights the utility of all-cause mortality data, as well as the significant challenges in interpreting it.

CoNtRol: an open source framework for the analysis of chemical reaction networks.

UNLABELLED: We introduce CoNtRol, a web-based framework for analysis of chemical reaction networks (CRNs). It is designed to be both extensible and simple to use, complementing existing CRN-related tools. CoNtRol currently implements a number of necessary and/or sufficient structural tests for multiple equilibria, stable periodic orbits, convergence to equilibria and persistence, with the potential for incorporation of further tests. AVAILABILITY AND IMPLEMENTATION: Reference implementation: reaction-networks.net/control/. Source code and binaries, released under the GPLv3: reaction-networks.net/control/download/. Documentation: reaction-networks.net/wiki/CoNtRol.

Modelling cerebrovascular reactivity: a novel near-infrared biomarker of cerebral autoregulation?

Understanding changes in cerebral oxygenation, haemodynamics and metabolism holds the key to individualised, optimised therapy after acute brain injury. Near-infrared spectroscopy (NIRS) offers the potential for non-invasive, continuous bedside measurement of surrogates for these processes. Interest has grown in applying this technique to interpret cerebrovascular pressure reactivity (CVPR), a surrogate of the brain's ability to autoregulate blood flow. We describe a physiological model-based approach to NIRS interpretation which predicts autoregulatory efficiency from a model parameter k_aut. Data from three critically brain-injured patients exhibiting a change in CVPR were investigated. An optimal value for k_aut was determined to minimise the difference between measured and simulated outputs. Optimal values for k_aut appropriately tracked changes in CVPR under most circumstances. Further development of this technique could be used to track CVPR providing targets for individualised management of patients with altered vascular reactivity, minimising secondary neurological insults.

Can mitochondrial cytochrome oxidase mediate hypoxic vasodilation via nitric oxide metabolism?

The brain responds to hypoxia with an increase in cerebral blood flow (CBF). Many mechanisms have been proposed for this hypoxic vasodilation, but none has gained universal acceptance. Although there is some disagreement about the shape of the relationship between arterial oxygen partial pressure (PaO(2)) and CBF, it is generally agreed that CBF does not increase until the PaO(2) reaches a threshold value. We used a previously published computational model of brain oxygen transport and metabolism (BRAINSIGNALS) to test possible molecular mechanisms for such a threshold phenomenon. One suggestion has been that a decrease in the metabolism of nitric oxide by mitochondrial cytochrome c oxidase (CCO) at low PaO(2) could be responsible for raising NO levels and the consequent triggering of the hypoxic blood flow increase. We tested the plausibility of this mechanism using the known rate constants for NO interactions with CCO. We showed that the shape of the CBF-PaO(2) curve could indeed by reproduced, but only if NO production by the enzyme nitric oxide synthase had a very low Michaelis constant K (m) for oxygen. Even then, in the current version of BRAINSIGNALS the NO-induced CBF rise occurs at much lower PaO(2) than is consistent with the in vivo data.

Modelling noninvasively measured cerebral signals during a hypoxemia challenge: steps towards individualised modelling.

Noninvasive approaches to measuring cerebral circulation and metabolism are crucial to furthering our understanding of brain function. These approaches also have considerable potential for clinical use "at the bedside". However, a highly nontrivial task and precondition if such methods are to be used routinely is the robust physiological interpretation of the data. In this paper, we explore the ability of a previously developed model of brain circulation and metabolism to explain and predict quantitatively the responses of physiological signals. The five signals all noninvasively-measured during hypoxemia in healthy volunteers include four signals measured using near-infrared spectroscopy along with middle cerebral artery blood flow measured using transcranial Doppler flowmetry. We show that optimising the model using partial data from an individual can increase its predictive power thus aiding the interpretation of NIRS signals in individuals. At the same time such optimisation can also help refine model parametrisation and provide confidence intervals on model parameters. Discrepancies between model and data which persist despite model optimisation are used to flag up important questions concerning the underlying physiology, and the reliability and physiological meaning of the signals.

Computational modelling of the piglet brain to simulate near-infrared spectroscopy and magnetic resonance spectroscopy data collected during oxygen deprivation.

We describe a computational model to simulate measurements from near-infrared spectroscopy (NIRS) and magnetic resonance spectroscopy (MRS) in the piglet brain. Piglets are often subjected to anoxic, hypoxic and ischaemic insults, as experimental models for human neonates. The model aims to help interpret measurements and increase understanding of physiological processes occurring during such insults. It is an extension of a previous model of circulation and mitochondrial metabolism. This was developed to predict NIRS measurements in the brains of healthy adults i.e. concentration changes of oxyhaemoglobin and deoxyhaemoglobin and redox state changes of cytochrome c oxidase (CCO). We altered and enhanced the model to apply to the anaesthetized piglet brain. It now includes metabolites measured by (31)P-MRS, namely phosphocreatine, inorganic phosphate and adenosine triphosphate (ATP). It also includes simple descriptions of glycolysis, lactate dynamics and the tricarboxylic acid (TCA) cycle. The model is described, and its simulations compared with existing measurements from piglets during anoxia. The NIRS and MRS measurements are predicted well, although this requires a reduction in blood pressure autoregulation. Predictions of the cerebral metabolic rate of oxygen consumption (CMRO(2)) and lactate concentration, which were not measured, are given. Finally, the model is used to investigate hypotheses regarding changes in CCO redox state during anoxia.

Modelling of mitochondrial oxygen consumption and NIRS detection of cytochrome oxidase redox state.

In recent years there has been widespread use of near infrared spectroscopy (NIRS) to monitor the brain. The signals of interest include changes in the levels of oxygenated and deoxygenated haemoglobin and tissue oxygen saturation. In addition to oxy- and deoxy-haemoglobin, the Cu(A) centre in cytochrome-c-oxidase (CCO) is a significant NIR absorber, giving rise to another signal termed the DeltaoxCCO signal. This signal has great potential as a marker of cellular oxygen metabolism, but is also the hardest to interpret. Here we use a recently constructed model to predict NIRS signal changes, and compare the model output to data from an in vivo hypoxia study in healthy adults. Our findings indicate strongly that the DeltaoxCCO signal contains useful information despite the noise, and has responses consistent with the known physiology.

Graph-theoretic criteria for injectivity and unique equilibria in general chemical reaction systems.

In this paper we discuss the question of how to decide when a general chemical reaction system is incapable of admitting multiple equilibria, regardless of parameter values such as reaction rate constants, and regardless of the type of chemical kinetics, such as mass-action kinetics, Michaelis-Menten kinetics, etc. Our results relate previously described linear algebraic and graph-theoretic conditions for injectivity of chemical reaction systems. After developing a translation between the two formalisms, we show that a graph-theoretic test developed earlier in the context of systems with mass action kinetics, can be applied to reaction systems with arbitrary kinetics. The test, which is easy to implement algorithmically, and can often be decided without the need for any computation, rules out the possibility of multiple equilibria for the systems in question.

Monotone dynamics of two cells dynamically coupled by a voltage-dependent gap junction.

We introduce and analyse a simple model for two non-excitable cells that are dynamically coupled by a gap junction, a plaque of aqueous channels that electrically couple the cells. The gap junction channels have a low and high conductance state, and the transition rates between these states are voltage-dependent. We show that the number and stability of steady states of the system has a simple relationship with the determinant of the Jacobian matrix. For the case that channel opening rates decrease with increasing trans-junctional voltage, and closing rates increase with increasing trans-junctional voltage, we show that the system is monotone, with tridiagonal Jacobian matrix, and hence every initial condition evolves to a steady state, but that there may be multiple steady states.

A model of brain circulation and metabolism: NIRS signal changes during physiological challenges.

We construct a model of brain circulation and energy metabolism. The model is designed to explain experimental data and predict the response of the circulation and metabolism to a variety of stimuli, in particular, changes in arterial blood pressure, CO(2) levels, O(2) levels, and functional activation. Significant model outputs are predictions about blood flow, metabolic rate, and quantities measurable noninvasively using near-infrared spectroscopy (NIRS), including cerebral blood volume and oxygenation and the redox state of the Cu(A) centre in cytochrome c oxidase. These quantities are now frequently measured in clinical settings; however the relationship between the measurements and the underlying physiological events is in general complex. We anticipate that the model will play an important role in helping to understand the NIRS signals, in particular, the cytochrome signal, which has been hard to interpret. A range of model simulations are presented, and model outputs are compared to published data obtained from both in vivo and in vitro settings. The comparisons are encouraging, showing that the model is able to reproduce observed behaviour in response to various stimuli.

Relationship between activation of the sympathetic nervous system and renal blood flow autoregulation in cirrhosis.

BACKGROUND & AIMS: It has been proposed that activation of the sympathetic nervous system causes a rightward shift in the renal autoregulatory curve such that renal blood flow is critically dependent on renal perfusion pressure and that this contributes to the development of the hepatorenal syndrome. The aims of the study were to determine the relationship of renal blood flow and renal perfusion pressure in patients with liver cirrhosis and the effect on renal hemodynamics following insertion of a transjugular intrahepatic portosystemic shunt (TIPS). METHODS: Fifty-six patients were recruited into groups (1) with no ascites, (2) with diuretic-responsive ascites, (3) with intractable ascites, (4) with type II hepatorenal syndrome, and (5) requiring a TIPSs for refractory ascites. We measured cardiac hemodynamics, renal blood flow, renal perfusion pressure, and portal pressure and norepinephrine levels and mathematically modeled the renal autoregulatory curve. RESULTS: Renal blood flow correlated with renal perfusion pressure (r(2) = 0.78; P < .001) and inversely with the hepatic venous pressure gradient (r(2) = 0.61; P < .0001) and plasma norepinephrine levels (r(2) = 0.78; P < .0001). Norepinephrine levels increased with increasing disease severity, and this was associated with a rightward and downward shift of the renal blood flow/renal perfusion pressure autoregulatory curve. TIPS insertion reduced portal pressure and plasma norepinephrine levels (P < .001), and the renal blood flow/renal perfusion pressure curve was shifted upward. CONCLUSIONS: The relationship between renal blood flow and renal perfusion pressure involves a critical interplay between the sympathetic nervous system and the kidney. TIPS insertion decreases sympathetic activation and improves renal function through positive effects on renal blood flow autoregulation.

A generic model of electron transport in mitochondria.

In this paper, a simplified, generic model of mitochondrial metabolism is explored. In particular the following question is addressed: To what extent are phenomena observed in experiments and simulations of mitochondrial metabolism generic, in the sense that they must occur in all models with this basic structure? Of particular interest are the electron transport chain and oxidative phosphorylation, and how flux through the system and the redox states of intermediates respond to physiologically important stimuli. These stimuli include changes in substrate supply (NADH/FADH(2)), in oxygenation, and in membrane proton gradient/ATP demand. Analytical techniques are used to show that certain experimentally observed effects must occur in the generic model. These include the responses of both flux and redox states to changed substrate and oxygen concentrations. At the same time other effects, such as the responses of redox states to changes in proton gradient, are dependent on the details of the model, and are not common to every model with the same basic structure. The phenomenon of saturation in response to large inputs is also discussed.

A physiological model of cerebral blood flow control.

The construction of a computational model of the human brain circulation is described. We combine an existing model of the biophysics of the circulatory system, a basic model of brain metabolic biochemistry, and a model of the functioning of vascular smooth muscle (VSM) into a single model. This represents a first attempt to understand how the numerous different feedback pathways by which cerebral blood flow is controlled interact with each other. The present work comprises the following: Descriptions of the physiology underlying the model; general comments on the processes by which this physiology is translated into mathematics; comments on parameter setting; and some simulation results. The simulations presented are preliminary, but show qualitative agreement between model behaviour and experimental results.

Strongly asymmetric clustering in systems of phase oscillators.

In this paper, we look at clustering in systems of globally coupled identical phase oscillators. In particular, we extend and apply techniques developed earlier to study stable clustering behavior involving clusters of greatly differing size. We discuss the bifurcations in which these asymmetric cluster states are created, and how these relate to bifurcations of the synchronized state. Because of the simplicity of systems of phase oscillators, it is possible to say a significant amount about asymmetric clustering analytically. We apply some of the theory developed to one particular system, and illustrate how the techniques can be used to find behavior which might otherwise be missed.