Local Climatological Data : Urbana, 1889-1970

Urbana has a temperate continental climate with characteristics reflecting its geographical position in Illinois. Urbana's climate is representative of the conditions found in East Central Illinois, which is primarily an area of climatic transition between the northern and southern sectors of the state.published or submitted for publicationis peer reviewedOpenOpe

Early afterdepolarisation tendency as a simulated pro-arrhythmic risk indicator

Drug-induced Torsades de Pointes (TdP) arrhythmia is of major interest in predictive toxicology. Drugs which cause TdP block the hERG cardiac potassium channel. However, not all drugs that block hERG cause TdP. As such, further understanding of the mechanistic route to TdP is needed. Early afterdepolarisations (EADs) are a cell-level phenomenon in which the membrane of a cardiac cell depolarises a second time before repolarisation, and EADs are seen in hearts during TdP. Therefore, we propose a method of predicting TdP using induced EADs combined with multiple ion channel block in simulations using biophysically-based mathematical models of human ventricular cell electrophysiology. EADs were induced in cardiac action potential models using interventions based on diseases that are known to cause EADs, including: increasing the conduction of the L-type calcium channel, decreasing the conduction of the hERG channel, and shifting the inactivation curve of the fast sodium channel. The threshold of intervention that was required to cause an EAD was used to classify drugs into clinical risk categories. The metric that used L-type calcium induced EADs was the most accurate of the EAD metrics at classifying drugs into the correct risk categories, and increased in accuracy when combined with action potential duration measurements. The EAD metrics were all more accurate than hERG block alone, but not as predictive as simpler measures such as simulated action potential duration. This may be because different routes to EADs represent risk well for different patient subgroups, something that is difficult to assess at present

Subcellular phenomena in colorectal cancer

The Wnt signalling pathway is involved in stem cell maintenance, differentiation and tissue development, and in so doing plays a key role in controlling the homeostasis of colorectal crypts. In response to an external Wnt stimulus, the intracellular levels of the protein beta-catenin are regulated by the proteins which make up the Wnt signalling pathway. Abnormalities in the Wnt signalling pathway have been implicated in the initiation of colorectal and other cancers. In this thesis we analyse and simplify existing models of the Wnt signalling pathway, formulate models for Wnt's control of the cell cycle in a single cell, and incorporate these into a multiscale model to describe how Wnt may control the patterns of proliferation in a colorectal crypt. A systematic asymptotic analysis of an existing ODE-based model of the Wnt signalling pathway is undertaken, highlighting the operation of different pathway components over three different timescales. Guided by this analysis we derive a simplified model which is shown to retain the essential behaviour of the Wnt pathway, recreating the accumulation and degradation of beta-catenin. We utilise our simple model by coupling it to a model of the cell cycle. Our findings agree well with the observed patterns of proliferation in healthy colon crypts. Furthermore, the model clarifies a mechanism by which common colorectal cancer mutations may cause elevated beta-catenin and Cyclin~D levels, leading to uncontrolled cell proliferation and thereby initiating colorectal cancer. A second model for the influence of the Wnt pathway on the cell cycle is constructed to incorporate the results of a recent set of knockout experiments. This model reproduces the healthy proliferation observed in crypts and additionally recreates the results of knockout experiments by additionally including the influence of Myc and CDK4 on the cell cycle. Analysis of this model leads us to suggest novel drug targets that may reverse the effects of an early mutation in the Wnt pathway. We have helped to build a flexible software environment for cell-based simulations of healthy and cancerous tissues. We discuss the software engineering approach that we have used to develop this environment, and its suitability for scientific computing. We then use this software to perform multiscale simulations with subcellular Wnt signalling models inside individual cells, the cells forming an epithelial crypt tissue. We have used the multiscale model to compare the effect of different subcellular models on crypt dynamics and predicting the distribution of beta-catenin throughout the crypt. We assess the extent to which a common experiment reveals the actual dynamics of a crypt and finally explain some recent mitochondrial-DNA experiments in terms of cell dynamics

Sequential forward and reverse transport of the Na+ Ca2+ exchanger generates Ca2+ oscillations within mitochondria

Mitochondrial Ca2+ homoeostasis regulates aerobic metabolism and cell survival. Ca2+ flux into mitochondria is mediated by the mitochondrial calcium uniporter (MCU) channel whereas Ca2+ export is often through an electrogenic Na+–Ca2+ exchanger. Here, we report remarkable functional versatility in mitochondrial Na+–Ca2+ exchange under conditions where mitochondria are depolarised. Following physiological stimulation of cell-surface receptors, mitochondrial Na+–Ca2+ exchange initially operates in reverse mode, transporting cytosolic Ca2+ into the matrix. As matrix Ca2+ rises, the exchanger reverts to its forward mode state, extruding Ca2+. Transitions between reverse and forward modes generate repetitive oscillations in matrix Ca2+. We further show that reverse mode Na+–Ca2+ activity is regulated by the mitochondrial fusion protein mitofusin 2. Our results demonstrate that reversible switching between transport modes of an ion exchanger molecule generates functionally relevant oscillations in the levels of the universal Ca2+ messenger within an organelle

Gaussian process emulation for discontinuous response surfaces with applications for cardiac electrophysiology models

Mathematical models of biological systems are beginning to be used for safety-critical applications, where large numbers of repeated model evaluations are required to perform uncertainty quantification and sensitivity analysis. Most of these models are nonlinear both in variables and parameters/inputs which has two consequences. First, analytic solutions are rarely available so repeated evaluation of these models by numerically solving differential equations incurs a significant computational burden. Second, many models undergo bifurcations in behaviour as parameters are varied. As a result, simulation outputs often contain discontinuities as we change parameter values and move through parameter/input space. Statistical emulators such as Gaussian processes are frequently used to reduce the computational cost of uncertainty quantification, but discontinuities render a standard Gaussian process emulation approach unsuitable as these emulators assume a smooth and continuous response to changes in parameter values. In this article, we propose a novel two-step method for building a Gaussian Process emulator for models with discontinuous response surfaces. We first use a Gaussian Process classifier to detect boundaries of discontinuities and then constrain the Gaussian Process emulation of the response surface within these boundaries. We introduce a novel `certainty metric' to guide active learning for a multi-class probabilistic classifier. We apply the new classifier to simulations of drug action on a cardiac electrophysiology model, to propagate our uncertainty in a drug's action through to predictions of changes to the cardiac action potential. The proposed two-step active learning method significantly reduces the computational cost of emulating models that undergo multiple bifurcations

Neural Network Differential Equations For Ion Channel Modelling

Mathematical models of cardiac ion channels have been widely used to study and predict the behaviour of ion currents. Typically models are built using biophysically-based mechanistic principles such as Hodgkin-Huxley or Markov state transitions. These models provide an abstract description of the underlying conformational changes of the ion channels. However, due to the abstracted conformation states and assumptions for the rates of transition between them, there are differences between the models and reality—termed model discrepancy or misspecification. In this paper, we demonstrate the feasibility of using a mechanistically-inspired neural network differential equation model, a hybrid non-parametric model, to model ion channel kinetics. We apply it to the hERG potassium ion channel as an example, with the aim of providing an alternative modelling approach that could alleviate certain limitations of the traditional approach. We compare and discuss multiple ways of using a neural network to approximate extra hidden states or alternative transition rates. In particular we assess their ability to learn the missing dynamics, and ask whether we can use these models to handle model discrepancy. Finally, we discuss the practicality and limitations of using neural networks and their potential applications

Control of NFAT Isoform Activation and NFAT-Dependent Gene Expression through Two Coincident and Spatially Segregated Intracellular Ca 2+ Signals

© 2016 The Author(s) Excitation-transcription coupling, linking stimulation at the cell surface to changes in nuclear gene expression, is conserved throughout eukaryotes. How closely related coexpressed transcription factors are differentially activated remains unclear. Here, we show that two Ca2+-dependent transcription factor isoforms, NFAT1 and NFAT4, require distinct sub-cellular InsP3 and Ca2+ signals for physiologically sustained activation. NFAT1 is stimulated by sub-plasmalemmal Ca2+ microdomains, whereas NFAT4 additionally requires Ca2+ mobilization from the inner nuclear envelope by nuclear InsP3 receptors. NFAT1 is rephosphorylated (deactivated) more slowly than NFAT4 in both cytoplasm and nucleus, enabling a more prolonged activation phase. Oscillations in cytoplasmic Ca2+, long considered the physiological form of Ca2+ signaling, play no role in activating either NFAT protein. Instead, effective sustained physiological activation of NFAT4 is tightly linked to oscillations in nuclear Ca2+. Our results show how gene expression can be controlled by coincident yet geographically distinct Ca2+ signals, generated by a freely diffusible InsP3 message

mRNA Expression Levels in Failing Human Hearts Predict Cellular Electrophysiological Remodeling: A Population-Based Simulation Study

Differences in mRNA expression levels have been observed in failing versus non-failing human hearts for several membrane channel proteins and accessory subunits. These differences may play a causal role in electrophysiological changes observed in human heart failure and atrial fibrillation, such as action potential (AP) prolongation, increased AP triangulation, decreased intracellular calcium transient (CaT) magnitude and decreased CaT triangulation. Our goal is to investigate whether the information contained in mRNA measurements can be used to predict cardiac electrophysiological remodeling in heart failure using computational modeling. Using mRNA data recently obtained from failing and non-failing human hearts, we construct failing and non-failing cell populations incorporating natural variability and up/down regulation of channel conductivities. Six biomarkers are calculated for each cell in each population, at cycle lengths between 1500 ms and 300 ms. Regression analysis is performed to determine which ion channels drive biomarker variability in failing versus non-failing cardiomyocytes. Our models suggest that reported mRNA expression changes are consistent with AP prolongation, increased AP triangulation, increased CaT duration, decreased CaT triangulation and amplitude, and increased delay between AP and CaT upstrokes in the failing population. Regression analysis reveals that changes in AP biomarkers are driven primarily by reduction in IKr, and changes in CaT biomarkers are driven predominantly by reduction in ICaL and SERCA. In particular, the role of IICaL is pacing rate dependent. Additionally, alternans developed at fast pacing rates for both failing and non-failing cardiomyocytes, but the underlying mechanisms are different in control and heart failure. © 2013 Walmsley et al

Rapid Characterization of hERG Channel Kinetics I: Using an Automated High-Throughput System

Predicting how pharmaceuticals may affect heart rhythm is a crucial step in drug-development, and requires a deep understanding of a compound’s action on ion channels. In vitro hERG-channel current recordings are an important step in evaluating the pro-arrhythmic potential of small molecules, and are now routinely performed using automated high-throughput patch clamp platforms. These machines can execute traditional voltage clamp protocols aimed at specific gating processes, but the array of protocols needed to fully characterise a current is typically too long to be applied in a single cell. Shorter high-information protocols have recently been introduced which have this capability, but they are not typically compatible with high-throughput platforms. We present a new 15 second protocol to characterise hERG (Kv11.1) kinetics, suitable for both manual and high-throughput systems. We demonstrate its use on the Nanion SyncroPatch 384PE, a 384 well automated patch clamp platform, by applying it to CHO cells stably expressing hERG1a. From these recordings we construct 124 cell-specific variants/parameterisations of a hERG model at 25C. A further 8 independent protocols are run in each cell, and are used to validate the model predictions. We then combine the experimental recordings using a hierarchical Bayesian model, which we use to quantify the uncertainty in the model parameters, and their variability from cell to cell, which we use to suggest reasons for the variability. This study demonstrates a robust method to measure and quantify uncertainty, and shows that it is possible and practical to use high-throughput systems to capture full hERG channel kinetics quantitatively and rapidly