Four Ways to Fit an Ion Channel Model

© 2019 Biophysical Society 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 characterization 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, steady-state, 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 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. Although data for method 2 are 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

Models of the cardiac L-type calcium current: a quantitative comparison

The L-type calcium current (ICaL) plays a critical role in cardiac electrophysiology, and models of ICaL are vital tools to predict arrhythmogenicity of drugs and mutations. Five decades of measuring and modelling ICaL have resulted in several competing theories (encoded in mathematical equations). However, the introduction of new models has not typically been accompanied by a data-driven critical comparison with previous work, so that it is unclear where predictions overlap or conflict, or which model is best suited for any particular application. We gathered 71 mammalian ICaL models, compared their structure, and reproduced simulated experiments to show that there is a large variability in their predictions, which was not substantially diminished when grouping by species or other categories. By highlighting the differences in these competing theories, listing major data sources, and providing simulation code, we have laid strong foundations for the development of a consensus model of ICaL

Tecnologias digitais no processo de alfabetização: analisando o uso do laboratório de informática nos anos iniciais

Este artigo discute tecnologias digitais na alfabetização, onde os estudantes as utilizam para desenvolver seus conhecimentos. Iniciamos com breves considerações sobre o uso das tecnologias na educação e as implicações na alfabetização. Em seguida, apresentamos resultados de uma pesquisa qualitativa, realizada com 15 professores que atuam nas salas de aula de alfabetização de 1º e 2º anos do Ensino Fundamental e professores de laboratório de informática de seis escolas no Município de Curitiba – PR. O propósito deste estudo foi analisar e investigar o impacto do uso do laboratório de informática no processo de alfabetização dos educandos nos anos iniciais. Este trabalho de pesquisa junto aos professores alfabetizadores permitiu que se elencassem duas categorias de análise preliminar: Uso e Planejamento para o Laboratório de Informática; Contribuições para Aprendizagem e Alfabetização no Laboratório de Informática. As reflexões baseiam-se nos estudos de Almeida (2005; 1998); Kenski (2012), Leite, Colello e Arantes (2010), Lucena (2002), Masetto(2000), Moran (2007), Nóvoa (2010), Pretto (2000), Sancho e Hernandez (2006), Soares (2004; 1998), Valente (1999; 1998). O resultado apontou que os professores alfabetizadores utilizam o laboratório de informática nas práticas educativas e que há saberes e habilidades que os alfabetizandos adquirem fazendo uso deste ambiente como melhora na leitura e na oralidade,reconhecimento de letras, registro de letras, palavras e textos, coordenação motora, atenção, raciocínio e nas suas produções

Immediate and Delayed Response of Simulated Human Atrial Myocytes to Clinically-Relevant Hypokalemia

Although plasma electrolyte levels are quickly and precisely regulated in the mammalian cardiovascular system, even small transient changes in K+, Na+, Ca2+, and/or Mg2+ can significantly alter physiological responses in the heart, blood vessels, and intrinsic (intracardiac) autonomic nervous system. We have used mathematical models of the human atrial action potential (AP) to explore the electrophysiological mechanisms that underlie changes in resting potential (Vr) and the AP following decreases in plasma K+, [K+]o, that were selected to mimic clinical hypokalemia. Such changes may be associated with arrhythmias and are commonly encountered in patients (i) in therapy for hypertension and heart failure; (ii) undergoing renal dialysis; (iii) with any disease with acid-base imbalance; or (iv) post-operatively. Our study emphasizes clinically-relevant hypokalemic conditions, corresponding to [K+]o reductions of approximately 1.5 mM from the normal value of 4 to 4.5 mM. We show how the resulting electrophysiological responses in human atrial myocytes progress within two distinct time frames: (i) Immediately after [K+]o is reduced, the K+-sensing mechanism of the background inward rectifier current (IK1) responds. Specifically, its highly non-linear current-voltage relationship changes significantly as judged by the voltage dependence of its region of outward current. This rapidly alters, and sometimes even depolarizes, Vr and can also markedly prolong the final repolarization phase of the AP, thus modulating excitability and refractoriness. (ii) A second much slower electrophysiological response (developing 5–10 minutes after [K+]o is reduced) results from alterations in the intracellular electrolyte balance. A progressive shift in intracellular [Na+]i causes a change in the outward electrogenic current generated by the Na+/K+ pump, thereby modifying Vr and AP repolarization and changing the human atrial electrophysiological substrate. In this study, these two effects were investigated quantitatively, using seven published models of the human atrial AP. This highlighted the important role of IK1 rectification when analyzing both the mechanisms by which [K+]o regulates Vr and how the AP waveform may contribute to “trigger” mechanisms within the proarrhythmic substrate. Our simulations complement and extend previous studies aimed at understanding key factors by which decreases in [K+]o can produce effects that are known to promote atrial arrhythmias in human hearts

chaste codegen: automatic CellML to C++ code generation with fixes for singularities and automatically generated Jacobians

Hundreds of different mathematical models have been proposed for describing electrophysiology of various cell types. These models are quite complex (nonlinear systems of typically tens of ODEs and sometimes hundreds of parameters) and software packages such as the Cancer, Heart and Soft Tissue Environment (Chaste) C++ library have been designed to run simulations with these models in isolation or coupled to form a tissue simulation. The complexity of many of these models makes sharing and translating them to new simulation environments difficult. CellML is an XML format that offers a solution to this problem and has been widely-adopted. This paper specifically describes the capabilities of chaste_codegen, a Python-based CellML to C++ converter based on the new cellmlmanip Python library for reading and manipulating CellML models. While chaste_codegen is a Python 3 redevelopment of a previous Python 2 tool (called PyCML) it has some additional new features that this paper describes. Most notably, chaste_codegen has the ability to generate analytic Jacobians without the use of proprietary software, and also to find singularities occurring in equations and automatically generate and apply linear approximations to prevent numerical problems at these points

cellmlmanip and chaste_codegen: automatic CellML to C++ code generation with fixes for singularities and automatically generated Jacobians

Hundreds of different mathematical models have been proposed for describing electrophysiology of various cell types. These models are quite complex (nonlinear systems of typically tens of ODEs and sometimes hundreds of parameters) and software packages such as the Cancer, Heart and Soft Tissue Environment (Chaste) C++ library have been designed to run simulations with these models in isolation or coupled to form a tissue simulation. The complexity of many of these models makes sharing and translating them to new simulation environments difficult. CellML is an XML format that offers a widely-adopted solution to this problem. This paper specifically describes the capabilities of two new Python tools: the cellmlmanip library for reading and manipulating CellML models; and chaste_codegen, a CellML to C++ converter. These tools provide a Python 3 replacement for a previous Python 2 tool (called PyCML) and they also provide additional new features that this paper describes. Most notably, they can generate analytic Jacobians without the use of proprietary software, and also find singularities occurring in equations and automatically generate and apply linear approximations to prevent numerical problems at these points

Robust automated detection of microstructural white matter degeneration in Alzheimer’s disease using machine learning classification of multicenter DTI data

Diffusion tensor imaging (DTI) based assessment of white matter fiber tract integrity can support the diagnosis of Alzheimer’s disease (AD). The use of DTI as a biomarker, however, depends on its applicability in a multicenter setting accounting for effects of different MRI scanners. We applied multivariate machine learning (ML) to a large multicenter sample from the recently created framework of the European DTI study on Dementia (EDSD). We hypothesized that ML approaches may amend effects of multicenter acquisition. We included a sample of 137 patients with clinically probable AD (MMSE 20.6±5.3) and 143 healthy elderly controls, scanned in nine different scanners. For diagnostic classification we used the DTI indices fractional anisotropy (FA) and mean diffusivity (MD) and, for comparison, gray matter and white matter density maps from anatomical MRI. Data were classified using a Support Vector Machine (SVM) and a Naïve Bayes (NB) classifier. We used two cross-validation approaches, (i) test and training samples randomly drawn from the entire data set (pooled cross-validation) and (ii) data from each scanner as test set, and the data from the remaining scanners as training set (scanner-specific cross-validation). In the pooled cross-validation, SVM achieved an accuracy of 80% for FA and 83% for MD. Accuracies for NB were significantly lower, ranging between 68% and 75%. Removing variance components arising from scanners using principal component analysis did not significantly change the classification results for both classifiers. For the scanner-specific cross-validation, the classification accuracy was reduced for both SVM and NB. After mean correction, classification accuracy reached a level comparable to the results obtained from the pooled cross-validation. Our findings support the notion that machine learning classification allows robust classification of DTI data sets arising from multiple scanners, even if a new data set comes from a scanner that was not part of the training sample

Multi-site genetic analysis of diffusion images and voxelwise heritability analysis : a pilot project of the ENIGMA–DTI working group

The ENIGMA (Enhancing NeuroImaging Genetics through Meta-Analysis) Consortium was set up to analyze brain measures and genotypes from multiple sites across the world to improve the power to detect genetic variants that influence the brain. Diffusion tensor imaging (DTI) yields quantitative measures sensitive to brain development and degeneration, and some common genetic variants may be associated with white matter integrity or connectivity. DTI measures, such as the fractional anisotropy (FA) of water diffusion, may be useful for identifying genetic variants that influence brain microstructure. However, genome-wide association studies (GWAS) require large populations to obtain sufficient power to detect and replicate significant effects, motivating a multi-site consortium effort. As part of an ENIGMA–DTI working group, we analyzed high-resolution FA images from multiple imaging sites across North America, Australia, and Europe, to address the challenge of harmonizing imaging data collected at multiple sites. Four hundred images of healthy adults aged 18–85 from four sites were used to create a template and corresponding skeletonized FA image as a common reference space. Using twin and pedigree samples of different ethnicities, we used our common template to evaluate the heritability of tract-derived FA measures. We show that our template is reliable for integrating multiple datasets by combining results through meta-analysis and unifying the data through exploratory mega-analyses. Our results may help prioritize regions of the FA map that are consistently influenced by additive genetic factors for future genetic discovery studies. Protocols and templates are publicly available at (http://enigma.loni.ucla.edu/ongoing/dti-working-group/)

A Parameter Representing Missing Charge Should Be Considered when Calibrating Action Potential Models

Computational models of the electrical potential across a cell membrane are longstanding and vital tools in electrophysiology research and applications. These models describe how ionic currents, internal fluxes, and buffering interact to determine membrane voltage and form action potentials (APs). Although this relationship is usually expressed as a differential equation, previous studies have shown it can be rewritten in an algebraic form, allowing direct calculation of membrane voltage. Rewriting in this form requires the introduction of a new parameter, called Γ 0 in this manuscript, which represents the net concentration of all charges that influence membrane voltage but are not considered in the model. Although several studies have examined the impact of Γ 0 on long-term stability and drift in model predictions, there has been little examination of its effects on model predictions, particularly when a model is refit to new data. In this study, we illustrate how Γ 0 affects important physiological properties such as action potential duration restitution, and examine the effects of (in)correctly specifying Γ 0 during model calibration. We show that, although physiologically plausible, the range of concentrations used in popular models leads to orders of magnitude differences in Γ 0 , which can lead to very different model predictions. In model calibration, we find that using an incorrect value of Γ 0 can lead to biased estimates of the inferred parameters, but that the predictive power of these models can be restored by fitting Γ 0 as a separate parameter. These results show the value of making Γ 0 explicit in model formulations, as it forces modellers and experimenters to consider the effects of uncertainty and potential discrepancy in initial concentrations upon model predictions

The influence of semantic and phonological factors on syntactic decisions: An event-related brain potential study

During language production and comprehension, information about a word's syntactic properties is sometimes needed. While the decision about the grammatical gender of a word requires access to syntactic knowledge, it has also been hypothesized that semantic (i.e., biological gender) or phonological information (i.e., sound regularities) may influence this decision. Event-related potentials (ERPs) were measured while native speakers of German processed written words that were or were not semantically and/or phonologically marked for gender. Behavioral and ERP results showed that participants were faster in making a gender decision when words were semantically and/or phonologically gender marked than when this was not the case, although the phonological effects were less clear. In conclusion, our data provide evidence that even though participants performed a grammatical gender decision, this task can be influenced by semantic and phonological factors