Modeling variability.

<p>(A) Types of variation and their relative impacts on measured properties. Significant linkages are shown with solid lines while weak effects are shown with dashed lines. Types of variation marked with an asterisk are not described in depth but are included for completeness (B) In order to model both cell-to-cell and inter-monolayer conductance variability, a mean monolayer conductance (black dashed line) is selected from a random normal distribution (blue distribution). The conductance of each node within the monolayer is then selected from a random normal distribution around the mean monolayer conductance (red distribution)</p

Modeling an Excitable Biosynthetic Tissue with Inherent Variability for Paired Computational-Experimental Studies

<div><p>To understand how excitable tissues give rise to arrhythmias, it is crucially necessary to understand the electrical dynamics of cells in the context of their environment. Multicellular monolayer cultures have proven useful for investigating arrhythmias and other conduction anomalies, and because of their relatively simple structure, these constructs lend themselves to paired computational studies that often help elucidate mechanisms of the observed behavior. However, tissue cultures of cardiomyocyte monolayers currently require the use of neonatal cells with ionic properties that change rapidly during development and have thus been poorly characterized and modeled to date. Recently, Kirkton and Bursac demonstrated the ability to create biosynthetic excitable tissues from genetically engineered and immortalized HEK293 cells with well-characterized electrical properties and the ability to propagate action potentials. In this study, we developed and validated a computational model of these excitable HEK293 cells (called “Ex293” cells) using existing electrophysiological data and a genetic search algorithm. In order to reproduce not only the mean but also the variability of experimental observations, we examined what sources of variation were required in the computational model. Random cell-to-cell and inter-monolayer variation in both ionic conductances and tissue conductivity was necessary to explain the experimentally observed variability in action potential shape and macroscopic conduction, and the spatial organization of cell-to-cell conductance variation was found to not impact macroscopic behavior; the resulting model accurately reproduces both normal and drug-modified conduction behavior. The development of a computational Ex293 cell and tissue model provides a novel framework to perform paired computational-experimental studies to study normal and abnormal conduction in multidimensional excitable tissue, and the methodology of modeling variation can be applied to models of any excitable cell.</p></div

Model action potential replicates experimental action potential.

<p>(A) Model fitting was performed by simulating conduction in a 2-D monolayer and recording an action potential 6 mm from the stimulus site (asterisk). Dashed lines are isochrones of activation at intervals of 5 ms. (B) The action potential generated by the fitted Ex293 membrane model (solid black line) replicates the morphology of the experimentally-recorded Ex293 action potential from [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005342#pcbi.1005342.ref007" target="_blank">7</a>] (dashed gray line).</p

Comparison of simulated channel blockade with experimental findings.

<p>Simulated blockade of the sodium currents via TTX (B) and of IK₁ current via barium chloride (D) qualitatively replicates the effects of experimental blockade (A: experimental TTX; C: experimental BaCl₂). Note that there is a sigmoidal relationship between drug dose and degree of block, and that the x-axis of panels B and D has been inverse-sigmoidally transformed to allow for direct comparison of simulated response and experimental results. Panels A and C from [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005342#pcbi.1005342.ref007" target="_blank">7</a>], used with permission.</p

Conduction slowing due to increased extracellular potassium.

<p>An increase in extracellular potassium concentration in experimental Ex293 monolayers leads to conduction slowing, and conduction failure for concentrations greater than 7.4 mM (closed circles). The model shows similar behavior, but conduction failure occurs at a lower concentration (open diamonds). When the model is modified to reflect non-Nernstian changes in potassium reversal potential, conduction slowing more closely replicates experimental observations (open squares).</p

Ex293 restitution behavior.

<p>The base model (solid line) is able to closely mimic the experimentally observed (open circles) conduction velocity (A) and action potential duration (B) restitution profiles (R² = 0.97 and 0.82, respectively). Model variability (dashed lines represent +/- 1 SD) approximates the degree of experimental variability. Note that experimental data from [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005342#pcbi.1005342.ref009" target="_blank">9</a>] is plotted as mean ± s.d.</p

Model recapitulates experimental current properties.

<p>(A,C) The Ex293 membrane model replicates (dotted line) the experimentally observed peak current-voltage relationships (closed circles) of the transfected potassium and sodium channels at 23°C. An increase in current density and shift in voltage dependence is seen in the model at physiological temperature (dashed line) (B,D) The model (left panel) also replicates the dynamics of channel activity (right panel). Note that the model conductances in panels B and D were selected to match the experimental traces; these are not the same as the mean model conductances.</p

Spatial organization of ionic variation does not affect macroscopic conduction.

<p>The introduction of a central region with reduced variance and prolonged APD (A, red) into a tissue model with and without non-conductive fibrosis-like obstacles (A. yellow) does not cause additional conduction slowing and APD shortening at 1 Hz pacing beyond the effect of fibrosis alone (B). A fibrosis induced exaggeration of CV slowing (D), but not APD shortening (C), at short diastolic (S1-S2) intervals (plotted as mean +/- standard error) is also unaffected by the spatial organization of variation. In addition, spatial organization maintains but does not enhance premature failure, as characterized by minimum S1-S2 intervals able to fully conduct across the domain (E). (* p < 0.05 main effect of fibrosis)</p

Model optimization via genetic search algorithm (n = 9 runs).

<p>Model optimization via genetic search algorithm (n = 9 runs).</p

Modeling variability.

<p>(A) Types of variation and their relative impacts on measured properties. Significant linkages are shown with solid lines while weak effects are shown with dashed lines. Types of variation marked with an asterisk are not described in depth but are included for completeness (B) In order to model both cell-to-cell and inter-monolayer conductance variability, a mean monolayer conductance (black dashed line) is selected from a random normal distribution (blue distribution). The conductance of each node within the monolayer is then selected from a random normal distribution around the mean monolayer conductance (red distribution)</p