David Gavaghan’s research while affiliated with University of Oxford and other places

Background L-type calcium channels (LCCs) are macro-molecular complexes that conduct I CaL and are involved in several critical functions in cardiac, skeletal, neuronal, smooth muscle, and endocrine cells. In common with other ionic channels they can be studied by isolating and overexpressing in a cell line, and the current through them can be measured using patch-clamp experiments. However, LCC current recordings are known to be contaminated with attenuation of current, known as ‘rundown’. Previous work has shown that increased accumulation of intracellular calcium is likely associated with increased rundown. Methods We built a mathematical model of I CaL conducted by LCCs overexpressed in CHO cells and systematically investigated the qualitative impact of both user-defined as well as experimental parameters within the typical patch-clamp setup on I CaL rundown. Results Simulations show that calcium-dependent inactivation (CDI) of LCCs modestly contributes towards experimentally observed rundown. The underlying reason for the experimental rundown due to CDI (RCDI) was found to be the non-instantaneous diffusion and reactions of calcium and the calcium-chelating buffer inside the cell. In this study we show that RCDI occurs when the buffer does not have sufficient time to diffuse into the cell; both after patching before the LCCs are activated, and also during the experiment progression. This finding was validated by showing that rundown due to accumulation of Ca ²⁺ can be reduced by increasing the concentration of the calcium-chelating buffer in the intracellular solution. Conclusions To minimise rundown due to CDI, we suggest optimising independent experimental parameters such as buffer concentration and the time scales for diffusion to enable buffer equilibration into the cell. Additionally, we suggest that use of large cells should be avoided since they are more prone to RCDI.

The time-varying reproduction number ($R_t$) gives an indication of the trajectory of an infectious disease outbreak. Commonly used frameworks for inferring $R_t$ from epidemiological time series include those based on compartmental models (such as the SEIR model) and renewal equation models. These inference methods are usually validated using synthetic data generated from a simple model, often from the same class of model as the inference framework. However, in a real outbreak the transmission processes, and thus the infection data collected, are much more complex. The performance of common $R_t$ inference methods on data with similar complexity to real world scenarios has been subject to less comprehensive validation. We therefore propose evaluating these inference methods on outbreak data generated from a sophisticated, geographically accurate agent-based model. We illustrate this proposed method by generating synthetic data for two outbreaks in Northern Ireland: one with minimal spatial heterogeneity, and one with additional heterogeneity. We find that the simple SEIR model struggles with the greater heterogeneity, while the renewal equation model demonstrates greater robustness to spatial heterogeneity, though is sensitive to the accuracy of the generation time distribution used in inference. Our approach represents a principled way to benchmark epidemiological inference tools and is built upon an open-source software platform for reproducible epidemic simulation and inference.

During drug development, candidate compounds are extensively tested for proar-rhythmic risk and in particular risk of Torsade de Pointes (TdP), as indicated by prolongation of the QT interval. Drugs that inhibit the rapid delayed rectifier K ⁺ current (I Kr ) can prolong the action potential duration (APD) and thereby the QT interval, and so are routinely rejected. However, simultaneous inhibition of the L-type Ca ²⁺ current (I CaL ) can mitigate the effect of I Kr inhibition, so that including both effects can improve test specificity. Mathematical models of the action potential (AP) can be used to predict the APD prolongation resulting from a given level of I Kr and I CaL inhibition, but for use in safety-testing their predictive capabilities should first be carefully verified. We present the first systematic comparison between experimental drug-induced APD and predictions by AP models. New experimental data were obtained ex vivo for APD response to I Kr and/or I CaL inhibition by applying 9 compounds at different concentrations to adult human ventricular trabeculae at physiological temperature. Compounds with similar effects on I Kr and I CaL exhibited less APD prolongation compared to selective I Kr inhibitors. We then integrated in vitro IC 50 patch-clamp data for I Kr and I CaL inhibition by the tested compounds into simulations with AP models. Models were assessed against the ex vivo data on their ability to recapitulate drug-induced APD changes observed experimentally. None of the tested AP models reproduced the APD changes observed experimentally across all combinations and degrees of I Kr and/or I CaL inhibition: they matched the data either for selective I Kr inhibitors or for compounds with comparable effects on I Kr and I CaL . This work introduces a new benchmarking framework to assess the predictivity of current and future AP models for APD response to I Kr and/or I CaL inhibition. This is an essential primary step towards an in silico framework that integrates in vitro data for translational clinical cardiac safety. Author summary Before an investigational drug reaches patients, it is tested in vitro to ensure it does not disrupt the heart’s electric activity. This testing often focuses on the drug’s ability to block a specific current called I Kr , which, if inhibited, can prolong the heart cells’ action potential duration (APD), which is associated with an increased risk of irregular heartbeats (proarrhythmia). Our study examines how blocking another current, I CaL , along with I Kr , affects APD. We found that adding I CaL inhibition may mitigate the proarrhythmic effects caused by I Kr inhibition alone. Understanding this balance can improve how we assess the cardiac safety of new drugs, potentially saving promising compounds from being incorrectly discarded. Currently, mathematical models help predict such cardiac responses, but no existing model accurately predicted our findings. Our new data could aid in developing more predictive models in the future. This will contribute to safer drug development and more effective treatments.

Objective COVID-19 data exhibit various biases, not least a significant weekly periodic oscillation observed in case and death data from multiple countries. There has been debate over whether this may be attributed to weekly socialising and working patterns, or is due to underlying biases in the reporting process. We investigate these periodic reporting trends in epidemics of COVID-19 and cholera, and discuss the possible origin of these oscillations. Results We present a systematic, global characterisation of these weekly biases and identify an equivalent bias in the current Haitian cholera outbreak. By comparing published COVID-19 time series to retrospective datasets from the United Kingdom (UK), we demonstrate that the weekly trends observed in the UK may be fully explained by biases in the testing and reporting processes. These conclusions play an important role in forecasting healthcare demand and determining suitable interventions for future infectious disease outbreaks.

Mathematical models of voltammetric experiments commonly contain a singular point value for the reversible potential, whereas experimental data for surface‐confined redox‐active species is often interpreted to contain thermodynamic dispersion, meaning the population of molecules on the electrode possess a distribution of reversible potential values. Large amplitude ramped Fourier Transformed Alternating Current Voltammetry (FTacV), a technique in which a sinusoidal potential‐time oscillation is overlaid onto a linear potential‐time ramp, is known to provide access to higher order harmonic components that are largely devoid of non‐Faradaic current. Initially, a theoretical study reveals that the use of very large amplitude sinusoidal oscillations reduces the apparent effects of thermodynamic dispersion; conversely, frequency can be varied to change the sensitivity of the measurement to kinetic dispersion. Subsequently, FTacV measurements are used to probe a highly thermodynamically dispersed surface‐confined ferrocene derivative attached to a glassy carbon electrode, with amplitudes ranging from 25 to 300 mV and low frequency, which minimises the impact of kinetic dispersion. The results from the experimental study validate the theoretical predictions, demonstrating that we can vary the amplitude in FTacV experiments to tune in and out of thermodynamic dispersion.

The time-dependent reproduction number Rt can be used to track pathogen transmission and to assess the efficacy of interventions. This quantity can be estimated by fitting renewal equation models to time series of infectious disease case counts. These models almost invariably assume a homogeneous population. Individuals are assumed not to differ systematically in the rates at which they come into contact with others. It is also assumed that the typical time that elapses between one case and those it causes (known as the generation time distribution) does not differ across groups. But contact patterns are known to widely differ by age and according to other demographic groupings, and infection risk and transmission rates have been shown to vary across groups for a range of directly transmitted diseases. Here, we derive from first principles a renewal equation framework which accounts for these differences in transmission across groups. We use a generalisation of the classic McKendrick-von Foerster equation to handle populations structured into interacting groups. This system of partial differential equations allows us to derive a simple analytical expression for Rt which involves only group-level contact patterns and infection risks. We show that the same expression emerges from both deterministic and stochastic discrete-time versions of the model and demonstrate via simulations that our Rt expression governs the long-run fate of epidemics. Our renewal equation model provides a basis from which to account for more realistic, diverse populations in epidemiological models and opens the door to inferential approaches which use known group characteristics to estimate Rt.

Background L-type calcium channels (LCCs) are multi-protein macro-molecular ion channel complexes that are involved in several critical functions in cardiac, skeletal, neuronal, smooth muscle, and endocrine cells. Like other ion channels, LCCs can be selectively over-expressed in a host cell line and studied using voltage-clamp patch-clamp experiments. However, L-type calcium current (ICaL) recordings commonly exhibit a reduction in current magnitude over time, commonly termed ‘rundown’. Previous studies have shown the effect of phosphorylation on rundown, here we provide evidence that accumulation of Ca ²⁺ inside the cell also contributes towards ICaL rundown. Methods We generated experimental conditions that should promote the accumulation of sub-membrane Ca ²⁺ in a CHO expression system, by increasing calcium import or decreasing export. These interventions took the form of: a decrease in inter-pulse duration between sweeps, block of the sodium-calcium exchanger, and increased temperature. Results On average, we found that current reduced to 63% of its initial value within 325 seconds. This reduction of current with time was found to follow two main patterns: linear or saturating decay. Additionally, current magnitude in some cells increased before stabilising or decaying. Conclusions This study shows that the rundown of ICaL in patch-clamp experiments can be reduced by modifying the experimental conditions, and implies that reduced accumulation of Ca ²⁺ inside the cell membrane reduces calcium-dependent inactivation of ICaL.

Fourier-transformed alternating current voltammetry (FTacV) is a technique utilizing a combination of a periodic (frequently sinusoidal) oscillation superimposed onto a staircase or linear potential ramp. The advanced utilization of a large amplitude sine wave induces substantial nonlinear current responses. Subsequent filter processing (via Fourier-transformation, band selection, followed by inverse Fourier-transformation) generates a series of harmonics in which rapid electron transfer processes may be separated from non-Faradaic and competing electron transfer processes with slower kinetics. Thus, FTacV enables the isolation of current associated with redox processes under experimental conditions that would not generate meaningful data using direct current voltammetry (dcV). In this study, the enhanced experimental sensitivity and selectivity of FTacV versus dcV are illustrated in measurements that (i) separate the Faradaic current from background current contributions, (ii) use a low (5 μM) concentration of analyte (exemplified with ferrocene), and (iii) enable discrimination of the reversible [Ru(NH3)6]3+/2+ electron-transfer process from the irreversible reduction of oxygen under a standard atmosphere, negating the requirement for inert gas conditions. The simple, homebuilt check-cell described ensures that modern instruments can be checked for their ability to perform valid FTacV experiments. Detailed analysis methods and open-source data sets that accompany this work are intended to facilitate other researchers in the integration of FTacV into their everyday electrochemical methodological toolkit.

Most ordinary differential equation (ODE) models used to describe biological or physical systems must be solved approximately using numerical methods. Perniciously, even those solvers that seem sufficiently accurate for the forward problem, i.e. for obtaining an accurate simulation, might not be sufficiently accurate for the inverse problem, i.e. for inferring the model parameters from data. We show that for both fixed step and adaptive step ODE solvers, solving the forward problem with insufficient accuracy can distort likelihood surfaces, which might become jagged, causing inference algorithms to get stuck in local ‘phantom’ optima. We demonstrate that biases in inference arising from numerical approximation of ODEs are potentially most severe in systems involving low noise and rapid nonlinear dynamics. We reanalyse an ODE change point model previously fit to the COVID-19 outbreak in Germany and show the effect of the step size on simulation and inference results. We then fit a more complicated rainfall run-off model to hydrological data and illustrate the importance of tuning solver tolerances to avoid distorted likelihood surfaces. Our results indicate that, when performing inference for ODE model parameters, adaptive step size solver tolerances must be set cautiously and likelihood surfaces should be inspected for characteristic signs of numerical issues.