Validity of the Cauchy-Born rule applied to discrete cellular-scale models of biological tissues.

The development of new models of biological tissues that consider cells in a discrete manner is becoming increasingly popular as an alternative to continuum methods based on partial differential equations, although formal relationships between the discrete and continuum frameworks remain to be established. For crystal mechanics, the discrete-to-continuum bridge is often made by assuming that local atom displacements can be mapped homogeneously from the mesoscale deformation gradient, an assumption known as the Cauchy-Born rule (CBR). Although the CBR does not hold exactly for noncrystalline materials, it may still be used as a first-order approximation for analytic calculations of effective stresses or strain energies. In this work, our goal is to investigate numerically the applicability of the CBR to two-dimensional cellular-scale models by assessing the mechanical behavior of model biological tissues, including crystalline (honeycomb) and noncrystalline reference states. The numerical procedure involves applying an affine deformation to the boundary cells and computing the quasistatic position of internal cells. The position of internal cells is then compared with the prediction of the CBR and an average deviation is calculated in the strain domain. For center-based cell models, we show that the CBR holds exactly when the deformation gradient is relatively small and the reference stress-free configuration is defined by a honeycomb lattice. We show further that the CBR may be used approximately when the reference state is perturbed from the honeycomb configuration. By contrast, for vertex-based cell models, a similar analysis reveals that the CBR does not provide a good representation of the tissue mechanics, even when the reference configuration is defined by a honeycomb lattice. The paper concludes with a discussion of the implications of these results for concurrent discrete and continuous modeling, adaptation of atom-to-continuum techniques to biological tissues, and model classification

Hierarchical Bayesian inference for ion channel screening dose-response data

Dose-response (or 'concentration-effect') relationships commonly occur in biological and pharmacological systems and are well characterised by Hill curves. These curves are described by an equation with two parameters: the inhibitory concentration 50% (IC50); and the Hill coefficient. Typically just the 'best fit' parameter values are reported in the literature. Here we introduce a Python-based software tool, PyHillFit , and describe the underlying Bayesian inference methods that it uses, to infer probability distributions for these parameters as well as the level of experimental observation noise. The tool also allows for hierarchical fitting, characterising the effect of inter-experiment variability. We demonstrate the use of the tool on a recently published dataset on multiple ion channel inhibition by multiple drug compounds. We compare the maximum likelihood, Bayesian and hierarchical Bayesian approaches. We then show how uncertainty in dose-response inputs can be characterised and propagated into a cardiac action potential simulation to give a probability distribution on model outputs

Problems with the current approach to the dissemination of computational science research and its implications for research integrity

Computational methods are at the heart of all twenty-first century research, but the acceleration of the application of computational approaches to biomedical research is particularly striking. From the simulation of the behaviour of complex systems, through the design and automation of laboratory experiments, to the analysis of both small- and large-scale data, computational approaches, and the well-engineered software that underpins them, have proved to be capable of transforming biomedical research. In parallel, the growth of high-throughput technologies and continual innovation in hardware, imaging, sensing and monitoring, demands unprecedented levels of collaboration between computational and experimental scientists, to continue the transformation of biology and medicine from primarily descriptive to quantitative, predictive disciplines. As a result, biomedical research is dependent as never before on computational science methods and hence also on the instantiation of those methods in research softwar

Identification and attribution of weekly periodic biases in global epidemiological time series data

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

Identification and attribution of weekly periodic biases in epidemiological time series data

COVID-19 data exhibit various biases, not least a significant weekly periodic oscillation observed globally in case and death data. There has been significant debate over whether this may be attributed to weekly socialising and working patterns, or is due to underlying biases in the reporting process. We characterise the weekly biases globally and demonstrate that equivalent biases also occur in the current cholera outbreak in Haiti. By comparing published COVID-19 time series to retrospective datasets from the United Kingdom (UK) that are not subject to the same reporting biases, we demonstrate that this dataset does not contain any weekly periodicity, and hence the weekly trends observed both in the UK and globally 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

Hodgkin–Huxley revisited: reparametrization and identifiability analysis of the classic action potential model with approximate Bayesian methods

As cardiac cell models become increasingly complex, a correspondingly complex ‘genealogy’ of inherited parameter values has also emerged. The result has been the loss of a direct link between model parameters and experimental data, limiting both reproducibility and the ability to re-fit to new data. We examine the ability of approximate Bayesian computation (ABC) to infer parameter distributions in the seminal action potential model of Hodgkin and Huxley, for which an immediate and documented connection to experimental results exists. The ability of ABC to produce tight posteriors around the reported values for the gating rates of sodium and potassium ion channels validates the precision of this early work, while the highly variable posteriors around certain voltage dependency parameters suggests that voltage clamp experiments alone are insufficient to constrain the full model. Despite this, Hodgkin and Huxley's estimates are shown to be competitive with those produced by ABC, and the variable behaviour of posterior parametrized models under complex voltage protocols suggests that with additional data the model could be fully constrained. This work will provide the starting point for a full identifiability analysis of commonly used cardiac models, as well as a template for informative, data-driven parametrization of newly proposed models

Four ways to fit an ion channel model

Mathematical models of ionic currents are used to study the electrophysiology of the heart, brain, gut, and several other organs. Increasingly, these models are being used predictively in the clinic, for example to predict the risks and results of genetic mutations, pharmacological treatments or surgical procedures. These safety-critical applications depend on accurate characterisation of the underlying ionic currents. Four different methods can be found in the literature to fit voltage-sensitive ion channel models to whole-cell current measurements: (Method 1) fitting model equations directly to time constant, steadystate, and I-V summary curves; (Method 2) fitting by comparing simulated versions of these summary curves to their experimental counterparts; (Method 3) fitting to the current traces themselves from a range of protocols; and (Method 4) fitting to a single current trace from a short and rapidly-fluctuating voltage clamp protocol. We compare these methods using a set of experiments in which hERG1a current was measured in nine Chinese Hamster Ovary (CHO) cells. In each cell, the same sequence of fitting protocols was applied, as well as an independent validation protocol. We show that Methods 3 and 4 provide the best predictions on the independent validation set, and that short rapidly-fluctuating protocols like that used in Method 4 can replace much longer conventional protocols without loss of predictive ability. While data for Method 2 is most readily available from the literature, we find it performs poorly compared to Methods 3 and 4 both in accuracy of predictions and computational efficiency. Our results demonstrate how novel experimental and computational approaches can improve the quality of model predictions in safety-critical applications