Towards systematic, data-driven validation of a collaborative, multi-scale model of Caenorhabditis elegans.

ADVERTISEMENT RETURN TO ISSUEPREVReviewNEXTModeling and Simulation of Ion ChannelsChristopher Maffeo, Swati Bhattacharya, Jejoong Yoo, David Wells, and Aleksei Aksimentiev*View Author Information Department of Physics, University of Illinois, 1110 W. Green Street, Urbana, Illinois 61801, United States*E-mail: [email protected]Cite this: Chem. Rev. 2012, 112, 12, 6250–6284Publication Date (Web):October 4, 2012Publication History Received29 June 2012Published online4 October 2012Published inissue 12 December 2012https://pubs.acs.org/doi/10.1021/cr3002609https://doi.org/10.1021/cr3002609review-articleACS PublicationsCopyright © 2012 American Chemical SocietyRequest reuse permissionsArticle Views10617Altmetric-Citations188LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InRedditEmail Other access optionsGet e-Alertsclose SUBJECTS:Electrical conductivity,Genetics,Ions,Membranes,Potassium Get e-Alerts

In this paper, an improved Poisson-Nernst-Planck ion channel (PNPic) model is presented, along with its effective finite element solver and software package for an ion channel protein in a solution of multiple ionic species. Numerical studies are then done on the effects of boundary value conditions, membrane charges, and bulk concentrations on electrostatics and ionic concentrations for an ion channel protein, a gramicidin A (gA), and five different ionic solvents with up to four species. Numerical results indicate that the cation selectivity property of gA occurs within a central portion of ion channel pore, insensitively to any change of boundary value condition, membrane charge, or bulk concentration. Moreover, a numerical scheme for computing the electric currents induced by ion transports across membrane via an ion channel pore is presented and implemented as a part of the PNPic finite element package. It is then applied to the calculation of current-voltage curves, well validating the PNPic model and finite element package by electric current experimental data.

Modeling of biological ion channels has a long history, going back more then 100 yr ([Hille 1984][1]). In the old, premolecular biology era, interpretation of these simple models provided the primary source of information about channel structure. As molecular biology and, now, x-ray diffraction have

A Poisson-Nernst-Planck single ion channel model and its effective finite element solver

Piezo1 ion channels are voltage-modulated, stretch-activated ion channels involved in a variety of important physiological and pathophysiological processes, as, for example, cardiovascular development and homeostasis. Since their discovery, it has been known that this type of ion channel desensitizes when exposed to stretch. However recent experiments on Piezo1 ion channels have uncovered that their stretch response is qualitatively different when exposed to positive electrochemical driving forces, where the desensitization is reset. In this work we propose a novel voltage-modulated mathematical model of Piezo1 based on a continuous-time Markov chain. We show that our Piezo1 model is able to quantitatively reproduce a wide range of experimental observations. Furthermore we integrate our new ion channel model into the Mahajan-Shiferaw ventricular cardiomyocyte model to study the effect of electromechanical pacing at the cellular scale. This integrated cell model is able to qualitatively reproduce some aspects of the experimental observations regarding the rate-dependence of electromechanical pacing protocols. Our studies suggest that the Piezo1 ion channel is an important component that significantly contributes to the electromechanical coupled response ofcardiomyocytes. KEY POINTS: PIEZO ion channels are voltage-modulated, mechanically gated ion channels involved in a large variety of mechanically regulated physiological processes and diseases. Recent experiments on Langendorff-perfused rabbit hearts by A. Quinn and P. Kohl [2016] suggest a non-trivial relation between the number of captured mechanical stimuli and the electromechanical pacing protocol. We present a novel thermodynamically consistent in silico model of the Piezo1 ion channel with electromechanical gating that can reproduce a large variety of experimental observations during combined exposure to electrical and mechanical stimuli. The new ion channel model is integrated into the well-established Mahajan-Shiferaw rabbit ventricular cardiomyocyte model to study its role during normal heart beat and during electromechanical pacing protocols. Our in silico studies suggest that the Piezo1 ion channel alone may not be sufficient to explain the experimental observations made by A. Quinn and P. Kohl.

A lipid bilayer membrane as a model cell membrane is used in a variety of biophysical studies including activities of ion channel/membrane proteins and lipid-lipid/lipid-protein interactions. In addition, ion channel integrated membranes provide versatile platforms for biosensing at the single molecular level. In this study, we have established two model membrane platforms. A planar lipid bilayer allows us to measure ion current across the membrane in a very quantitative manner. Furthermore, we are able to study ion transport across the membrane in a low salt condition. To elucidate molecular interactions of ion channels and the membranes, we used gramicidin A as a model ion channel, which create cation selective channels when they are dimerized. Each monomers freely diffuses laterally along the membrane. Perturbation of the membrane due to small molecules may change the free energy of gA dimerization, which can be measured by electrical current, as well as ion transport across the membrane. We will show how the small molecules are interfering with membranes and ion channels.

Some contemporary theorists such as Mazzocchi, Theise and Kafatos are convinced that the reformed complementarity may redefine how we might exploit the complexity theory in 21st-century life sciences research. However, the motives behind the profound re-invention of "biological complementarity" need to be substantiated with concrete shreds of evidence about this principle's applicability in real-life science experimentation, which we found missing in the literature. This paper discusses such pieces of evidence by confronting Bohr's complementarity and ion channel modeling practice. We examine whether and to what extent this principle might assist in developing ion channel models incorporating both deterministic and stochastic solutions. According to the "mutual exclusiveness of experimental setups" version of Bohr's complementarity, this principle is needed when two mutually exclusive perspectives or approaches are right, necessary in a particular context, and are not contradictory as they arise in mutually exclusive conditions (mutually exclusive experimental or modeling setups).A detailed examination of the modeling practice reveals that both solutions are often used simultaneously in a single ion channel model, suggesting that the opposite conceptual frameworks can coexist in the same modeling setup. We concluded that Bohr's complementarity might find applications in these complex modeling setups but only through its realistic phenomenological interpretation that allows applying different modes of description regardless of the nature of the underlying ion channel opening process. Also, we propose the combined use of complementarity and Complex thinking in building the multifaceted ion channel models. Overall, this paper's results support the efforts to establish a more general form of complementarity to meet today's complexity theory-inspired life sciences modeling demands.

One of the most fundamental challenges in biochemistry and biophysics is describing the function of ion channels, proteins that control ion transport across cell membranes. One approach to this problem is the application of Poisson–Nernst–Planck (PNP) theory. In practice, applying PNP theory involves creating a computational model of the ion channel and generating a numerical solution of differential equations that describes ion transport and electrostatic interactions. The PNP Cyclic Peptide Ion Channel Model is a simulation tool designed to offer an integrated approach to this important problem in bionanotechnology by demonstrating and explaining the application of PNP theory in a way that is accessible to students at an upper undergraduate level. The program interface was made using the free Rapid Application Infrastructure (Rappture) software made available by the Network for Computational Nanotechnology (NCN). Rappture is designed specifically for Web-based applications. Here we introduce a free version of the PNP Cyclic Peptide Ion Channel Model for use in the simulation of ion transport properties for a model ion channel structure that has been the subject of recent experiments.

In this paper, we present a novel method of simulating KcsA ion channels using a TCAD solid-state device simulator [1]. The ion transport in these channels has interesting similarities with the flow of carriers in electronic nanodevices. With this perspective, we have modeled ion channels as solid-state nanodevices and obtained self-consistent solutions of the axial potential and ion fluxes. Models of cylindrical and KcsA channels are built with the TCAD simulation tools and their steady-state characteristics are studied. The simulation results are compared with the reported experimental results in the literature to verify the efficacy of our method. The ability to simulate realistic ion channel models with such computational ease and reasonable accuracy provides a powerful tool for studying the biological functions of these channels with deeper insight. Ion channels are the ultimate in natural nanotubes that regulate the ion flux across a cell membrane, and thereby play an integral role in cellular signaling mechanisms (Figure 1) [2]. Among the approaches for ion channel modeling, molecular dynamics are the most accurate but presently limited by long simulation times [3]. Continuum electrostatics provides an alternative approach, which involves solving the PoissonNernst-Planck (PNP) equations for the charge distribution in the channel. This technique has proven suitable in predicting the behavior of KcsA and Ca 2+ voltage-gated channels [4]. We have simulated a cylindrical channel and a KcsA channel made of two materials: silicon to mimic the conducting water continuum and SiO2 to mimic the nonconducting protein walls. The carrier concentration, degree of ionization, and diffusion coefficients are adjusted in each conducting region to emulate the realistic motion of K + ions in the channel’s vestibule. Two electrodes are placed at either ends of the reservoirs. The simulations are performed by solving the discretized PNP equations with a computation time ~5sec. Figure 2 shows our TCAD cylindrical channel model (35A long and and 6A wide). Figure 3 shows a decreased carrier concentration in the channel’s vestibule, as also predicted by Brownian dynamics simulations [3]. We also considered the effect of protein surface charges in manipulating the energy profile of an ion traversing a channel. These surface charges are known to influence the gating, conductance, and toxinbinding effects of ion channels. As shown in Figure 4, an energy barrier inside the channel is transformed into a potential well by the inclusion of surface charges, thus increasing the chances of ion permeation through the channel [3]. Based on the KcsA ion channel structure revealed by x-ray crystallography [2], we have built a TCAD KcsA channel model as shown in Figure 5. The KcsA channel is 40A long, with a narrow selectivity filter (12A long and 3A wide). Figure 6 shows the axial potential variation under different electrode voltages. Most of the transmembrane potential drop incurs in the selectivity filter, crucial for the selectivity and permeation of various ions. In Figure 7, we compare the current-voltage (IV) results from our simulations with those from experiments [5]. With accuracy within 3% over 200mV, this degree of agreement with the experimental data is better than those reported elsewhere [6].

This chapter focuses on homology modeling and molecular dynamics (MD) simulations studies of ion channels for the range of single cell organisms from prokaryotes to eukaryotes. The glutamate receptor channels (GluRs) share some distant homology in their transmembrane (TM) domains with K channels but possess distinct extracellular ligand-binding domains for which several structures, of both bacterial and mammalian homologs, are known. It can be seen that molecular modeling and simulations can contribute to studies of ion channels in two respects. Modeling studies enable extrapolation from experimental structures of prokaryotic ion channels to molecular models of eukaryotic homologs, thus aiding design and interpretation of, for example, mutation experiments for dissecting structure-function relationships. Ion channel structures and ion channel models may also be used as the basis of multinanosecond MD simulations. Finally, it will become increasingly important to run multiple simulations on multiple channels to allow comparative analysis of simulation results, which in turn will enable the formulation of more general hypotheses concerning the relationship between the conformational dynamics of channel proteins and their physiological functions.

Ion channel models present many challenging optimisation problems. These include unidentifiable parameters, noisy data, unobserved states, and a combination of both fast and slow timescales. This can make it difficult to choose a suitable optimisation routine a priori. Nevertheless, many attempts have been made to design optimisation routines specifically for ion channel models, however, little work has been done to compare these optimisation approaches. We have developed ionBench, an open-source optimisation benchmarking framework, to evaluate and compare these approaches against a standard set of ion channel optimisation problems. We included implementations of thirty-four unique optimisation approaches that have been previously applied to ion channel models and evaluated them against the ionBench test suite, consisting of five parameter optimisation problems derived from the cardiac ion channel literature. Each optimisation approach was initiated from multiple starting parameters and tasked with reproducing a problem-specific simulated dataset. Through ionBench, we tracked and evaluated the performance of these optimisations, identifying the expected run time until a successful optimisation for each approach, which was used for comparisons. Finally, we used these results, in addition to other literature results, to identify a new efficient approach. Its use could reduce computation time by multiple orders of magnitude, while also improving the reliability of ion channel parameter optimisation.

Mathematical models of voltage-gated ion channels are used in basic research, industrial and clinical settings. These models range in complexity, but typically contain numerous variables representing the proportion of channels in a given state, and parameters describing the voltage-dependent rates of transition between states. An open problem is selecting the appropriate degree of complexity and structure for an ion channel model given data availability. Here, we simplify a model of the cardiac human Ether-à-go-go related gene (hERG) potassium ion channel, which carries cardiac IKr, using the manifold boundary approximation method (MBAM). The MBAM approximates high-dimensional model-output manifolds by reduced models describing their boundaries, resulting in models with fewer parameters (and often variables). We produced a series of models of reducing complexity starting from an established five-state hERG model with 15 parameters. Models with up to three fewer states and eight fewer parameters were shown to retain much of the predictive capability of the full model and were validated using experimental hERG1a data collected in HEK293 cells at 37°C. The method provides a way to simplify complex models of ion channels that improves parameter identifiability and will aid in future model development.

Recent experiments have demonstrated that the timescale of adaptation of single neurons and ion channel populations to stimuli slows down as the length of stimulation increases; in fact, no upper bound on temporal timescales seems to exist in such systems. Furthermore, patch clamp experiments on single ion channels have hinted at the existence of large, mostly unobservable, inactivation state spaces within a single ion channel. This raises the question of the relation between this multitude of inactivation states and the observed behavior. In this work we propose a minimal model for ion channel dynamics which does not assume any specific structure of the inactivation state space. The model is simple enough to render an analytical study possible. This leads to a clear and concise explanation of the experimentally observed exponential history-dependent relaxation in sodium channels in a voltage clamp setting, and shows that their recovery rate from slow inactivation must be voltage dependent. Furthermore, we predict that history-dependent relaxation cannot be created by overly sparse spiking activity. While the model was created with ion channel populations in mind, its simplicity and genericalness render it a good starting point for modeling similar effects in other systems, and for scaling up to higher levels such as single neurons which are also known to exhibit multiple time scales.

Calcium Channels Exhibit Electric Field Dependent Valve-Like Behavior

Context. Manual unit test creation is a cognitively intensive and time-consuming activity, prompting researchers and practitioners to increasingly adopt automated testing tools. Recent advancements in language models have expanded automation possibilities, including unit test generation, yet these models raise substantial sustainability concerns due to their energy consumption compared to conventional, specialized tools. Goal. Our research investigates whether the energy overhead associated with employing a small language model (SLM) for unit test generation is justified compared to a conventional, lightweight testing tool. We compare and analyze the energy consumption incurred during test suite generation, as well as the fault-finding effectiveness of the resulting test suites, for an SLM (Phi-3.1 Mini 128k) and Pynguin, a purpose-built tool for unit test generation. Method.We posed two research questions: (i) What is the difference in energy usage between Phi and Pynguin during the generation of unit test suites for Python programs?; and (ii) To what extent do unit test suites generated by Phi and Pynguin differ in their fault-finding effectiveness? To rigorously address the first research question, we employed Bayesian Data Analysis (BDA). For the second research question, we conducted a complementary empirical analysis using descriptive statistics. Results. Our Bayesian analysis provides robust evidence indicating that Phi consistently consumes significantly more energy than Pynguin during test suite generation. Conclusions. These findings underscore significant sustainability concerns associated with employing even SLMs for routine Software Engineering tasks such as unit test generation. The results challenge the assumption of universal energy efficiency benefits from smaller-scale models and emphasize the necessity for careful energy consumption evaluations in the adoption of automated software testing approaches.