Creating Computational Models of Ion Channel Dynamics.

Markov models are widely used to represent ion channel protein configurations as different states in the model's topology. Such models allow for dynamic simulation of ion channel kinetics through the simulated application of voltage potentials across a cell membrane. In this chapter, we present a general method for creating Markov models of ion channel kinetics using computational optimization alongside a fully featured example model of a cardiac potassium channel. Our methods cover designing training protocols, iteratively testing potential model topologies for structure identification, creation of algorithms for model simulation, as well as methods for assessing the quality of fit for a finalized model.

Using automated patch clamp electrophysiology platforms in ion channel drug discovery: an industry perspective.

INTRODUCTION: Automated patch clamp (APC) is now well established as a mature technology for ion channel drug discovery in academia, biotech and pharma companies, and in contract research organizations (CRO), for a variety of applications including channelopathy research, compound screening, target validation and cardiac safety testing. AREAS COVERED: Ion channels are an important class of drugged and approved drug targets. The authors present a review of the current state of ion channel drug discovery along with new and exciting developments in ion channel research involving APC. This includes topics such as native and iPSC-derived cells in ion channel drug discovery, channelopathy research, organellar and biologics in ion channel drug discovery. EXPERT OPINION: It is our belief that APC will continue to play a critical role in ion channel drug discovery, not only in 'classical' hit screening, target validation and cardiac safety testing, but extending these applications to include high throughput organellar recordings and optogenetics. In this way, with advancements in APC capabilities and applications, together with high resolution cryo-EM structures, ion channel drug discovery will be re-invigorated, leading to a growing list of ion channel ligands in clinical development.

Analysis of pressure-activated Piezo1 open and subconductance states at a single channel level.

Mechanically activated Piezo1 channels undergo transitions from closed to open-state in response to pressure and other mechanical stimuli. However, the molecular details of these mechanosensitive gating transitions are unknown. Here, we used cell-attached pressure-clamp recordings to acquire single channel data at steady-state conditions (where inactivation has settled down), at various pressures and voltages. Importantly, we identify and analyze subconductance states of the channel which were not reported before. Pressure-dependent activation of Piezo1 increases the occupancy of open and subconductance state at the expense of decreased occupancy of shut-states. No significant change in the mean open time of subconductance states was observed with increasing negative pipette pressure or with varying voltages (ranging from -40 to -100 mV). Using Markov-chain modeling, we identified a minimal four-states kinetic scheme, which recapitulates essential characteristics of the single channel data, including that of the subconductance level. This study advances our understanding of Piezo1-gating mechanism in response to discrete stimuli (such as pressure and voltage) and paves the path to develop cellular and tissue level models to predict Piezo1 function in various cell types.

Exploration of the Parameter Space of an Ion Channel Kinetic Model by a Markov-Chain-Based Methodology.

In this work, we propose a methodology based on Monte Carlo Markov chains to explore the parameter space of kinetic models for ion channels. The methodology allows the detection of potential parameter sets of a model that are compatible with experimentally obtained whole-cell currents, which could remain hidden when methods focus on obtaining the parameters that provide the best fit. To show its implementation and utility, we considered a four-state kinetic model proposed in the literature to describe the activation of the voltage-gated proton channel (Hv1), Biophysical Journal, 2014, 107, 1564. In that work, a set of values for the rate transitions that describe the channel kinetics at different intracellular H+ concentration (pHi) were obtained by the Simplex method. With our approach, we find that, in fact, there is more than one parameter set for each pHi, which renders the same open probability temporal course within the experimental error margin for all of the considered voltages. The large differences that we obtained for the values of some rate constants among the different solutions show that there is more than one possible interpretation of this channel behavior as a function of pHi. We also simulated a proposed new experimental condition where it is possible to observe that different sets of parameters yield different results. Our study highlights the importance of a comprehensive analysis of parameter space in kinetic models and the utility of the proposed methodology for finding potential solutions.

Uncertainty assessment of proarrhythmia predictions derived from multi-level in silico models.

In silico methods can be used for an early assessment of arrhythmogenic properties of drug candidates. However, their use for decision-making is conditioned by the possibility to estimate the predictions' uncertainty. This work describes our efforts to develop uncertainty quantification methods for the predictions produced by multi-level proarrhythmia models. In silico models used in this field usually start with experimental or predicted IC50 values that describe drug-induced ion channel blockade. Using such inputs, an electrophysiological model computes how the ion channel inhibition, exerted by a drug in a certain concentration, translates to an altered shape and duration of the action potential in cardiac cells, which can be represented as arrhythmogenic risk biomarkers such as the APD90. Using this framework, we identify the main sources of aleatory and epistemic uncertainties and propose a method based on probabilistic simulations that replaces single-point estimates predicted using multiple input values, including the IC50s and the electrophysiological parameters, by distributions of values. Two selected variability types associated with these inputs are then propagated through the multi-level model to estimate their impact on the uncertainty levels in the output, expressed by means of intervals. The proposed approach yields single predictions of arrhythmogenic risk biomarkers together with value intervals, providing a more comprehensive and realistic description of drug effects on a human population. The methodology was tested by predicting arrhythmogenic biomarkers on a series of twelve well-characterised marketed drugs, belonging to different arrhythmogenic risk classes.

High-throughput assessment identifying major platelet Ca2+ entry pathways via tyrosine kinase-linked and G protein-coupled receptors.

In platelets, elevated cytosolic Ca2+ is a crucial second messenger, involved in most functional responses, including shape change, secretion, aggregation and procoagulant activity. The platelet Ca2+ response consists of Ca2+ mobilization from endoplasmic reticulum stores, complemented with store-operated or receptor-operated Ca2+ entry pathways. Several channels can contribute to the Ca2+ entry, but their relative contribution is unclear upon stimulation of ITAM-linked receptors such as glycoprotein VI (GPVI) and G-protein coupled receptors such as the protease-activated receptors (PAR) for thrombin. We employed a 96-well plate high-throughput assay with Fura-2-loaded human platelets to perform parallel [Ca2+]i measurements in the presence of EGTA or CaCl2. Per agonist condition, this resulted in sets of EGTA, CaCl2 and Ca2+ entry ratio curves, defined by six parameters, reflecting different Ca2+ ion fluxes. We report that threshold stimulation of GPVI or PAR, with a variable contribution of secondary mediators, induces a maximal Ca2+ entry ratio of 3-7. Strikingly, in combination with Ca2+-ATPase inhibition by thapsigargin, the maximal Ca2+ entry ratio increased to 400 (GPVI) or 40 (PAR), pointing to a strong receptor-dependent enhancement of store-operated Ca2+ entry. By pharmacological blockage of specific Ca2+ channels in platelets, we found that, regardless of GPVI or PAR stimulation, the Ca2+ entry ratio was strongest affected by inhibition of ORAI1 (2-APB, Synta66) > Na+/Ca2+ exchange (NCE) > P2×1 (only initial). In contrast, inhibition of TRPC6, Piezo1/2 or STIM1 was without effect. Together, these data reveal ORAI1 and NCE as dominating Ca2+ carriers regulating GPVI- and PAR-induced Ca2+ entry in human platelets.

2D-dwell-time analysis with simulations of ion-channel gating using high-performance computing.

Single-channel patch-clamp recordings allow observing the action of a single protein complex in real time and hence the deduction of the underlying conformational changes in the ion-channel protein. Commonly, recordings are modeled using hidden Markov chains, connecting open and closed states in the experimental data with protein conformations. The rates between states denote transition probabilities that could be modified by membrane voltage or ligand binding. Modeling algorithms have to deal with limited recording bandwidth and a very noisy background. It was previously shown that the fit of two-dimensional (2D)-dwell-time histograms with simulations is very robust in that regard. Errors introduced by the low-pass filter or noise cancel out to a certain degree when comparing experimental and simulated data. In addition, the topology of models (that is, the chain of open and closed states) could be inferred from 2D-histograms. However, the 2D-fit was never applied to its full potential. A major reason may be the extremely time-consuming and often unreliable fitting process, due to the stochastic variability in the simulations. We have now solved these issues by introducing a message-passing interface (MPI) allowing massive parallel computing on a high-performance computing (HPC) cluster and obtaining ensemble solutions. With ensembles, we have demonstrated how important ranked solutions are for difficult tasks related to a noisy background, fast gating events beyond the corner frequency of the low-pass filter, and topology estimation of the underlying Markov model. Finally, we have shown that, by combining the objective function of the 2D-fit with the deviation of the current amplitude distributions, automatic determination of the current level of the conducting state is possible, even with an apparent current reduction due to low-pass filtering. Making use of an HPC cluster, the power of 2D-dwell-time analysis can be used to its fullest with minor input of the experimenter.

An ion-channel-gene-based prediction model for head and neck squamous cell carcinoma: Prognostic assessment and treatment guidance.

Purpose: Head and neck squamous cell carcinoma (HNSCC) is a very diverse malignancy with a poor prognosis. The purpose of this study was to develop a new signature based on 12 ion channel genes to predict the outcome and immune status of HNSCC patients. Methods: Clinicopathological information and gene sequencing data of HNSCC patients were generated from the Cancer Genome Atlas and Gene Expression Omnibus databases. A set of 323 ion channel genes was obtained from the HUGO Gene Nomenclature Committee database and literature review. Using univariate Cox regression analysis, the ion channel genes related to HNSCC prognosis were identified. A prognostic signature and nomogram were then created using machine learning methods. Kaplan-Meier analysis was used to explore the relevance of the risk scores and overall survival (OS). We also investigated the association between risk scores, tumor immune infiltration, and gene mutational status. Finally, we detected the expression levels of the signature genes by quantitative real-time polymerase chain reaction, western blotting, and immunohistochemistry. Results: We separated the patients into high- and low-risk groups according to the risk scores computed based on these 12 ion channel genes, and the OS of the low-risk group was significantly longer (p<0.001). The area under the curve for predicting 3-year survival was 0.729. Univariate and multivariate analyses showed that the 12-ion-channel-gene risk model was an independent prognostic factor. We also developed a nomogram model based on risk scores and clinicopathological variables to forecast outcomes. Furthermore, immune cell infiltration, gene mutation status, immunotherapy response, and chemotherapeutic treatment sensitivity were all linked to risk scores. Moreover, high expression levels of ANO1, AQP9, and BEST2 were detected in HNSCC tissues, whereas AQP5, SCNN1G, and SCN4A expression was low in HNSCC tissues, as determined by experiments. Conclusion: The 12-ion-channel-gene prognostic signatures have been demonstrated to be highly efficient in predicting the prognosis, immune microenvironment, gene mutation status, immunotherapy response, and chemotherapeutic sensitivity of HNSCC patients.

Safety pharmacology in 2022: Taking one small step for cardiovascular safety assay development but one giant leap for regulatory drug safety assessment.

The 2021 Annual Safety Pharmacology (SP) Society (SPS) meeting was held virtually October 4-8, 2021 due to the continuing COVID-19 global pandemic. This themed issue of J Pharmacol Toxicol Methods comprises articles arising from the meeting. As in previous years the manuscripts reflect various areas of innovation in SP including a perspective on aging and its impact on drug attrition during safety assessments, an integrated assessment of respiratory, cardiovascular and animal activity of in vivo nonclinical studies, development of a dynamic QT-rate correction method in primates, evaluation of the "comprehensive in vitro proarrhythmia assay" (CiPA) ion channel protocol to the automated patch clamp, and best practices regarding the conduct of hERG electrophysiology studies and an analysis of secondary pharmacology assays by the FDA. The meeting also generated 85 abstracts (reproduced in the current volume of J Pharmacol Toxicol Methods). It appears that the validation of methods remains a challenge in SP. Nevertheless, the continued efforts to mine approaches to detection of proarrhythmia liability remains a baffling obsession given the ability of Industry to completely prevent drugs entering into clinical study only to be found to have proarrhythmic properties, with no reports of such for at least ten years. Perhaps it is time to move on from CiPA and find genuine problems to solve?

Pareto optimality, economy-effectiveness trade-offs and ion channel degeneracy: improving population modelling for single neurons.

Neurons encounter unavoidable evolutionary trade-offs between multiple tasks. They must consume as little energy as possible while effectively fulfilling their functions. Cells displaying the best performance for such multi-task trade-offs are said to be Pareto optimal, with their ion channel configurations underpinning their functionality. Ion channel degeneracy, however, implies that multiple ion channel configurations can lead to functionally similar behaviour. Therefore, instead of a single model, neuroscientists often use populations of models with distinct combinations of ionic conductances. This approach is called population (database or ensemble) modelling. It remains unclear, which ion channel parameters in the vast population of functional models are more likely to be found in the brain. Here we argue that Pareto optimality can serve as a guiding principle for addressing this issue by helping to identify the subpopulations of conductance-based models that perform best for the trade-off between economy and functionality. In this way, the high-dimensional parameter space of neuronal models might be reduced to geometrically simple low-dimensional manifolds, potentially explaining experimentally observed ion channel correlations. Conversely, Pareto inference might also help deduce neuronal functions from high-dimensional Patch-seq data. In summary, Pareto optimality is a promising framework for improving population modelling of neurons and their circuits.

Use of automated patch clamp in cardiac safety assessment: Past, present & future perspectives.

There is no doubt that automated patch clamp (APC) technology has revolutionized research in biomedical science. High throughput ion channel screening is now an integral part of the development and safety profiling of the majority of new chemical entities currently developed to address unmet medical needs. The increased throughput it provides has significantly improved the ability to overcome the time-consuming, low throughput bottlenecks resulting from the more conventional manual patch clamp method, considered the 'gold standard', for studying ion channel function and pharmacology. While systems offering the luxury of automation have only been commercially available for two decades, the road leading to this new technology is long and rich in seminal, hands-on, studies dating back as far as the 18th century. So where does this technology currently stand, and what will it look like in the future? In the current article, we review the scientific history leading to the development of APC systems, examine key drivers in the rapid development of this technology (such as failed ion channel programmes and the issue of drug-induced hERG inhibition and QT interval prolongation), highlight key capabilities and finally provide some perspective on the current and future impact of the technology on cardiac safety assessment and biomedical science.

Identification of structures for ion channel kinetic models.

Markov models of ion channel dynamics have evolved as experimental advances have improved our understanding of channel function. Past studies have examined limited sets of various topologies for Markov models of channel dynamics. We present a systematic method for identification of all possible Markov model topologies using experimental data for two types of native voltage-gated ion channel currents: mouse atrial sodium currents and human left ventricular fast transient outward potassium currents. Successful models identified with this approach have certain characteristics in common, suggesting that aspects of the model topology are determined by the experimental data. Incorporating these channel models into cell and tissue simulations to assess model performance within protocols that were not used for training provided validation and further narrowing of the number of acceptable models. The success of this approach suggests a channel model creation pipeline may be feasible where the structure of the model is not specified a priori.

A549 in-silico 1.0: A first computational model to simulate cell cycle dependent ion current modulation in the human lung adenocarcinoma.

Lung cancer is still a leading cause of death worldwide. In recent years, knowledge has been obtained of the mechanisms modulating ion channel kinetics and thus of cell bioelectric properties, which is promising for oncological biomarkers and targets. The complex interplay of channel expression and its consequences on malignant processes, however, is still insufficiently understood. We here introduce the first approach of an in-silico whole-cell ion current model of a cancer cell, in particular of the A549 human lung adenocarcinoma, including the main functionally expressed ion channels in the plasma membrane as so far known. This hidden Markov-based model represents the electrophysiology behind proliferation of the A549 cell, describing its rhythmic oscillation of the membrane potential able to trigger the transition between cell cycle phases, and it predicts membrane potential changes over the cell cycle provoked by targeted ion channel modulation. This first A549 in-silico cell model opens up a deeper insight and understanding of possible ion channel interactions in tumor development and progression, and is a valuable tool for simulating altered ion channel function in lung cancer electrophysiology.

Memory in Ion Channel Kinetics.

Ion channels are transport proteins present in the lipid bilayers of biological membranes. They are involved in many physiological processes, such as the generation of nerve impulses, hormonal secretion, and heartbeat. Conformational changes in the ion channel-forming protein allow the opening or closing of pores to control the ionic flux through the cell membranes. The opening and closing of the ion channel have been classically treated as a random kinetic process, known as a Markov process. Here the time the channel remains in a given state is assumed to be independent of the condition it had in the previous state. More recently, however, several studies have shown that this process is not random but a deterministic one, where both the open and closed dwell-times and the ionic current flowing through the channel are history-dependent. This property is called long memory or long-range correlation. However, there is still much controversy regarding how this memory originates, which region of the channel is responsible for this property, and which models could best reproduce the memory effect. In this article, we provide a review of what is, where it is, its possible origin, and the mathematical methods used to analyze the long-term memory present in the kinetic process of ion channels.

Resolving molecular contributions of ion channel noise to interspike interval variability through stochastic shielding.

Molecular fluctuations can lead to macroscopically observable effects. The random gating of ion channels in the membrane of a nerve cell provides an important example. The contributions of independent noise sources to the variability of action potential timing have not previously been studied at the level of molecular transitions within a conductance-based model ion-state graph. Here we study a stochastic Langevin model for the Hodgkin-Huxley (HH) system based on a detailed representation of the underlying channel state Markov process, the "[Formula: see text]D model" introduced in (Pu and Thomas in Neural Computation 32(10):1775-1835, 2020). We show how to resolve the individual contributions that each transition in the ion channel graph makes to the variance of the interspike interval (ISI). We extend the mean return time (MRT) phase reduction developed in (Cao et al. in SIAM J Appl Math 80(1):422-447, 2020) to the second moment of the return time from an MRT isochron to itself. Because fixed-voltage spike detection triggers do not correspond to MRT isochrons, the inter-phase interval (IPI) variance only approximates the ISI variance. We find the IPI variance and ISI variance agree to within a few percent when both can be computed. Moreover, we prove rigorously, and show numerically, that our expression for the IPI variance is accurate in the small noise (large system size) regime; our theory is exact in the limit of small noise. By selectively including the noise associated with only those few transitions responsible for most of the ISI variance, our analysis extends the stochastic shielding (SS) paradigm (Schmandt and Galán in Phys Rev Lett 109(11):118101, 2012) from the stationary voltage clamp case to the current clamp case. We show numerically that the SS approximation has a high degree of accuracy even for larger, physiologically relevant noise levels. Finally, we demonstrate that the ISI variance is not an unambiguously defined quantity, but depends on the choice of voltage level set as the spike detection threshold. We find a small but significant increase in ISI variance, the higher the spike detection voltage, both for simulated stochastic HH data and for voltage traces recorded in in vitro experiments. In contrast, the IPI variance is invariant with respect to the choice of isochron used as a trigger for counting "spikes."

Use of automated patch clamp in cardiac safety assessment: past, present and future perspectives.

There is no doubt that automated patch clamp (APC) technology has revolutionized research in biomedical science. High throughput ion channel screening is now an integral part of the development and safety profiling of the majority of new chemical entities currently developed to address unmet medical needs. The increased throughput it provides has significantly improved the ability to overcome the time-consuming, low throughput bottlenecks resulting from the more conventional manual patch clamp method, considered the 'gold standard', for studying ion channel function and pharmacology. While systems offering the luxury of automation have only been commercially available for two decades, the road leading to this new technology is long and rich in seminal, hands-on, studies dating back as far as the 18th century. So where does this technology currently stand, and what will it look like in the future? In the current article, we review the scientific history leading to the development of APC systems, examine key drivers in the rapid development of this technology (such as failed ion channel programmes and the issue of drug-induced hERG inhibition and QT interval prolongation), highlight key capabilities and finally provide some perspective on the current and future impact of the technology on cardiac safety assessment and biomedical science.

Analysis of patchclamp recordings: model-free multiscale methods and software.

Analysis of patchclamp recordings is often a challenging issue. We give practical guidance how such recordings can be analyzed using the model-free multiscale idealization methodology JSMURF, JULES, and HILDE. We provide an operational manual how to use the accompanying software available as an R-package and as a graphical user interface. This includes selection of the right approach and tuning of parameters. We also discuss advantages and disadvantages of model-free approaches in comparison to hidden Markov model approaches and explain how they complement each other.

Computationally going where experiments cannot: a dynamical assessment of dendritic ion channel currents during in vivo-like states.

Background: Despite technological advances, how specific cell types are involved in brain function remains shrouded in mystery. Further, little is known about the contribution of different ion channel currents to cell excitability across different neuronal subtypes and their dendritic compartments in vivo. The picture that we do have is largely based on somatic recordings performed in vitro. Uncovering dendritic ion channel current contributions in neuron subtypes that represent a minority of the neuronal population is not currently a feasible task using purely experimental means. Methods: We employ two morphologically-detailed multi-compartment models of a specific type of inhibitory interneuron, the oriens lacunosum moleculare (OLM) cell. The OLM cell is a well-studied cell type in CA1 hippocampus that is important in gating sensory and contextual information. We create in vivo-like states for these cellular models by including levels of synaptic bombardment that would occur in vivo. Using visualization tools and analyses we assess the ion channel current contribution profile across the different somatic and dendritic compartments of the models. Results: We identify changes in dendritic excitability, ion channel current contributions and co-activation patterns between in vitro and in vivo-like states. Primarily, we find that the relative timing between ion channel currents are mostly invariant between states, but exhibit changes in magnitudes and decreased propagation across dendritic compartments. We also find enhanced dendritic hyperpolarization-activated cyclic nucleotide-gated channel (h-channel) activation during in vivo-like states, which suggests that dendritically located h-channels are functionally important in altering signal propagation in the behaving animal. Conclusions: Overall, we have demonstrated, using computational modelling, the dynamical changes that can occur to ion channel mechanisms governing neuronal spiking in vitro and in vivo. In particular, we have shown that the magnitudes of some ion channel current contributions are differentially altered during in vivo-like states relative to in vitro.

Calibration of ionic and cellular cardiac electrophysiology models.

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.

Prediction and Dissipation in Nonequilibrium Molecular Sensors: Conditionally Markovian Channels Driven by Memoryful Environments.

Biological sensors must often predict their input while operating under metabolic constraints. However, determining whether or not a particular sensor is evolved or designed to be accurate and efficient is challenging. This arises partly from the functional constraints being at cross purposes and partly since quantifying the prediction performance of even in silico sensors can require prohibitively long simulations, especially when highly complex environments drive sensors out of equilibrium. To circumvent these difficulties, we develop new expressions for the prediction accuracy and thermodynamic costs of the broad class of conditionally Markovian sensors subject to complex, correlated (unifilar hidden semi-Markov) environmental inputs in nonequilibrium steady state. Predictive metrics include the instantaneous memory and the total predictable information (the mutual information between present sensor state and input future), while dissipation metrics include power extracted from the environment and the nonpredictive information rate. Success in deriving these formulae relies on identifying the environment's causal states, the input's minimal sufficient statistics for prediction. Using these formulae, we study large random channels and the simplest nontrivial biological sensor model-that of a Hill molecule, characterized by the number of ligands that bind simultaneously-the sensor's cooperativity. We find that the seemingly impoverished Hill molecule can capture an order of magnitude more predictable information than large random channels.