Biological mechanism and identifiability of a class of stationary conductance model for Voltage-gated Ion channels

The physiology of voltage gated ion channels is complex and insights into their gating mechanism is incomplete. Their function is best represented by Markov models with relatively large number of distinct states that are connected by thermodynamically feasible transitions. On the other hand, popular models such as the one of Hodgkin and Huxley have empirical assumptions that are generally unrealistic. Experimental protocols often dictate the number of states in proposed Markov models, thus creating disagreements between various observations on the same channel. Here we aim to propose a limit to the minimum number of states required to model ion channels by employing a paradigm to define stationary conductance in a class of ion-channels. A simple expression is generated using concepts in elementary thermodynamics applied to protein conformational transitions. Further, it matches well many published channel current-voltage characteristics and parameters of the model are found to be identifiable and easily determined from usual experimental protocols

Calibration of ionic and cellular cardiac electrophysiology models

© 2020 The Authors. WIREs Systems Biology and Medicine published by Wiley Periodicals, Inc. Cardiac electrophysiology models are among the most mature and well-studied mathematical models of biological systems. This maturity is bringing new challenges as models are being used increasingly to make quantitative rather than qualitative predictions. As such, calibrating the parameters within ion current and action potential (AP) models to experimental data sets is a crucial step in constructing a predictive model. This review highlights some of the fundamental concepts in cardiac model calibration and is intended to be readily understood by computational and mathematical modelers working in other fields of biology. We discuss the classic and latest approaches to calibration in the electrophysiology field, at both the ion channel and cellular AP scales. We end with a discussion of the many challenges that work to date has raised and the need for reproducible descriptions of the calibration process to enable models to be recalibrated to new data sets and built upon for new studies. This article is categorized under: Analytical and Computational Methods > Computational Methods Physiology > Mammalian Physiology in Health and Disease Models of Systems Properties and Processes > Cellular Models

Cardiac cell modelling: Observations from the heart of the cardiac physiome project

In this manuscript we review the state of cardiac cell modelling in the context of international initiatives such as the IUPS Physiome and Virtual Physiological Human Projects, which aim to integrate computational models across scales and physics. In particular we focus on the relationship between experimental data and model parameterisation across a range of model types and cellular physiological systems. Finally, in the context of parameter identification and model reuse within the Cardiac Physiome, we suggest some future priority areas for this field

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

Parameter Estimation of Ion Current Formulations Requires Hybrid Optimization Approach to Be Both Accurate and Reliable

Computational models of cardiac electrophysiology provided insights into arrhythmogenesis and paved the way toward tailored therapies in the last years. To fully leverage in silico models in future research, these models need to be adapted to reflect pathologies, genetic alterations, or pharmacological effects, however. A common approach is to leave the structure of established models unaltered and estimate the values of a set of parameters. Today’s high-throughput patch clamp data acquisition methods require robust, unsupervised algorithms that estimate parameters both accurately and reliably. In this work, two classes of optimization approaches are evaluated: gradient-based trust-region-reflective and derivative-free particle swarm algorithms. Using synthetic input data and different ion current formulations from the Courtemanche et al. electrophysiological model of human atrial myocytes, we show that neither of the two schemes alone succeeds to meet all requirements. Sequential combination of the two algorithms did improve the performance to some extent but not satisfactorily. Thus, we propose a novel hybrid approach coupling the two algorithms in each iteration. This hybrid approach yielded very accurate estimates with minimal dependency on the initial guess using synthetic input data for which a ground truth parameter set exists. When applied to measured data, the hybrid approach yielded the best fit, again with minimal variation. Using the proposed algorithm, a single run is sufficient to estimate the parameters. The degree of superiority over the other investigated algorithms in terms of accuracy and robustness depended on the type of current. In contrast to the non-hybrid approaches, the proposed method proved to be optimal for data of arbitrary signal to noise ratio. The hybrid algorithm proposed in this work provides an important tool to integrate experimental data into computational models both accurately and robustly allowing to assess the often non-intuitive consequences of ion channel-level changes on higher levels of integration

Reproducible model development in the Cardiac Electrophysiology Web Lab

The modelling of the electrophysiology of cardiac cells is one of the most mature areas of systems biology. This extended concentration of research effort brings with it new challenges, foremost among which is that of choosing which of these models is most suitable for addressing a particular scientific question. In a previous paper, we presented our initial work in developing an online resource for the characterisation and comparison of electrophysiological cell models in a wide range of experimental scenarios. In that work, we described how we had developed a novel protocol language that allowed us to separate the details of the mathematical model (the majority of cardiac cell models take the form of ordinary differential equations) from the experimental protocol being simulated. We developed a fully-open online repository (which we termed the Cardiac Electrophysiology Web Lab) which allows users to store and compare the results of applying the same experimental protocol to competing models. In the current paper we describe the most recent and planned extensions of this work, focused on supporting the process of model building from experimental data. We outline the necessary work to develop a machine-readable language to describe the process of inferring parameters from wet lab datasets, and illustrate our approach through a detailed example of fitting a model of the hERG channel using experimental data. We conclude by discussing the future challenges in making further progress in this domain towards our goal of facilitating a fully reproducible approach to the development of cardiac cell models

Data assimilation for conductance-based neuronal models

This dissertation illustrates the use of data assimilation algorithms to estimate unobserved variables and unknown parameters of conductance-based neuronal models. Modern data assimilation (DA) techniques are widely used in climate science and weather prediction, but have only recently begun to be applied in neuroscience. The two main classes of DA techniques are sequential methods and variational methods. Throughout this work, twin experiments, where the data is synthetically generated from output of the model, are used to validate use of these techniques for conductance-based models observing only the voltage trace. In Chapter 1, these techniques are described in detail and the estimation problem for conductance-based neuron models is derived. In Chapter 2, these techniques are applied to a minimal conductance-based model, the Morris-Lecar model. This model exhibits qualitatively different types of neuronal excitability due to changes in the underlying bifurcation structure and it is shown that the DA methods can identify parameter sets that produce the correct bifurcation structure even with initial parameter guesses that correspond to a different excitability regime. This demonstrates the ability of DA techniques to perform nonlinear state and parameter estimation, and introduces the geometric structure of inferred models as a novel qualitative measure of estimation success. Chapter 3 extends the ideas of variational data assimilation to include a control term to relax the problem further in a process that is referred to as nudging from the geoscience community. The nudged 4D-Var is applied to twin experiments from a more complex, Hodgkin-Huxley-type two-compartment model for various time-sampling strategies. This controlled 4D-Var with nonuniform time-samplings is then applied to voltage traces from current-clamp recordings of suprachiasmatic nucleus neurons in diurnal rodents to improve upon our understanding of the driving forces in circadian (~24) rhythms of electrical activity. In Chapter 4 the complementary strengths of 4D-Var and UKF are leveraged to create a two-stage algorithm that uses 4D-Var to estimate fast timescale parameters and UKF for slow timescale parameters. This coupled approach is applied to data from a conductance-based model of neuronal bursting with distinctive slow and fast time-scales present in the dynamics. In Chapter 5, the ideas of identifiability and sensitivity are introduced. The Morris-Lecar model and a subset of its parameters are shown to be identifiable through the use of numerical techniques. Chapter 6 frames the selection of stimulus waveforms to inject into neurons during patch-clamp recordings as an optimal experimental design problem. Results on the optimal stimulus waveforms for improving the identifiability of parameters for a Hodgkin-Huxley-type model are presented. Chapter 7 shows the preliminary application of data assimilation for voltage-clamp, rather than current-clamp, data and expands on voltage-clamp principles to formulate a reduced assimilation problem driven by the observed voltage. Concluding thoughts are given in Chapter 8