Skip to main page content
Access keys NCBI Homepage MyNCBI Homepage Main Content Main Navigation
. 2012 Nov 5;3:421.
doi: 10.3389/fphys.2012.00421. eCollection 2012.

Rapid Genetic Algorithm Optimization of a Mouse Computational Model: Benefits for Anthropomorphization of Neonatal Mouse Cardiomyocytes

Affiliations
Free PMC article

Rapid Genetic Algorithm Optimization of a Mouse Computational Model: Benefits for Anthropomorphization of Neonatal Mouse Cardiomyocytes

Corina T Bot et al. Front Physiol. .
Free PMC article

Abstract

While the mouse presents an invaluable experimental model organism in biology, its usefulness in cardiac arrhythmia research is limited in some aspects due to major electrophysiological differences between murine and human action potentials (APs). As previously described, these species-specific traits can be partly overcome by application of a cell-type transforming clamp (CTC) to anthropomorphize the murine cardiac AP. CTC is a hybrid experimental-computational dynamic clamp technique, in which a computationally calculated time-dependent current is inserted into a cell in real-time, to compensate for the differences between sarcolemmal currents of that cell (e.g., murine) and the desired species (e.g., human). For effective CTC performance, mismatch between the measured cell and a mathematical model used to mimic the measured AP must be minimal. We have developed a genetic algorithm (GA) approach that rapidly tunes a mathematical model to reproduce the AP of the murine cardiac myocyte under study. Compared to a prior implementation that used a template-based model selection approach, we show that GA optimization to a cell-specific model results in a much better recapitulation of the desired AP morphology with CTC. This improvement was more pronounced when anthropomorphizing neonatal mouse cardiomyocytes to human-like APs than to guinea pig APs. CTC may be useful for a wide range of applications, from screening effects of pharmaceutical compounds on ion channel activity, to exploring variations in the mouse or human genome. Rapid GA optimization of a cell-specific mathematical model improves CTC performance and may therefore expand the applicability and usage of the CTC technique.

Keywords: cell-specific model; dynamic clamp; genetic algorithm; neonatal mouse cardiomyocyte.

Figures

Figure 1
Figure 1
Cell-type transforming clamp circuit (adapted from Ahrens-Nicklas and Christini, with permission from Elsevier). A real cell (target myocyte) is simultaneously coupled to a target-canceling computational model (a model of the native isolated cell) and a recipient computational model (a model of the desired cell-type, i.e., human or guinea pig), in a closed-loop circuit. A time-dependent current that compensates for the difference between target cell and recipient model cell currents is inserted into the myocyte at each instance of the measured voltage. The myocyte responds to the injected current such that the membrane voltage is transformed to the recipient model. An offset was added to correct the measured voltage for the liquid junction potential (LJP).
Figure 2
Figure 2
Schematic illustration of the genetic algorithm processes. Each individual is represented by a color and consists of a genotype (here, scaling factors for six conductance parameters), which results in a phenotype (simulated AP). The phenotype is compared to the objective AP (black trace) through an error value (the logarithm of the sum of squared differences). Individuals with lower errors are most likely to be chosen as parents for the subsequent generation. As the first step in generating offspring, two parents each contribute different parts of their genotype in a process known as crossover, to generate two children whose genotypes consist of values inherited from their parents. A second step introduces variation (mutations; gray shading) in these gene values. Finally, the offspring phenotype and associated error value are evaluated. These processes of parent selection, crossover, mutation, and offspring generation and evaluation are repeated to obtain the desired number of individuals in the subsequent generation. In our optimizations, the GA cycles through 15 generations.
Figure 3
Figure 3
Cell-to-cell variability and target to target-canceling model mismatch. (A) Average APs (10 successive beats) from nine neonatal mouse myocytes demonstrating morphological cell-to-cell AP variation. (B) In silico APs obtained using the same neonatal mouse model (the neonatal mouse model with an APD80 of 60 ms; cyan) in both the target and target-canceling positions produce an ideal conversion to the human recipient model (red, dashed line). However, when a small discrepancy is simulated by perturbing the target-canceling model (to neonatal mouse model with an APD80 of 70 ms; blue) there is imperfect anthropomorphization with insufficient AP prolongation (red, solid line).
Figure 4
Figure 4
Genetic algorithm model optimization. Top right panel: population of 40 individuals evolving over 15 generations; color bar denotes value of the error (sum of squared differences; SSD) between model and experiment AP. With GA progression, high-error individuals become less frequent and low-error individuals start to dominate. Left panels: examples of genotypes (scaling factors for conductance parameters as percent change from unperturbed model parameters; insets) and corresponding phenotypes (color-coded as per error heat map) with GA progression. In the first generation (yellow), there is a substantial difference between the phenotype and the optimization objective (black trace). In the sixth generation (green), a very different genotype gives a better fit. In the 15th and final generation (blue), another genotype gives a very strong fit. Bottom right panels: convergence of the average error for the population ensemble (blue) as well as the error of the best individual (red) occurs within a few generations.
Figure 5
Figure 5
Neonatal mouse APs converted to guinea pig AP. (A) Recordings of ten consecutive APs from an isolated neonatal mouse myocyte (cyan traces) are averaged (solid black line). The nominal model (dashed line) is selected from a suite of nine candidate models based solely on the closest match to its APD80 value, but fit the early part of the AP poorly. (B) We then recorded ten successive APs from the same cell (cyan traces) and use their average (solid black line) as the optimization objective. The GA returns a close fit (dashed line). (C) With CTC on, template-based target-canceling model selection resulted in APs (red traces; 20 subsequent APs) morphologically similar to the recipient guinea pig model AP (dashed line), but of much shorter duration. (D) Applying CTC using the GA-optimized model gave guinea pig-like action potentials (red traces; 40 subsequent APs) that mimic the recipient cell model prediction (dashed line).
Figure 6
Figure 6
Statistical analysis of target cell matching and CTC performance with guinea pig recipient model. (A) Average error (SSD) between unperturbed in vitro neonatal mouse myocyte APs and either selected template-based model or GA-fit model showing better fits with GA optimization. (B) Average error for CTC-on APs using the guinea pig recipient model demonstrating higher CTC accuracy with GA-optimized models over template-based model usage. (C) AP duration at different repolarization levels for template-based model CTC vs. GA-fitting CTC. For all three repolarization markers, the GA-fit model CTC reproduces recipient model APD values (diamonds), while template-based model CTC produces waveforms of insufficient duration. Error bars in all panels give standard deviation, n = 10 cells.
Figure 7
Figure 7
Neonatal mouse APs anthropomorphized to human AP. (A) Ten consecutive neonatal mouse myocyte APs (cyan traces) recorded in vitro, their average (solid black line), and the APD80-based nominal model (dashed line). (B) Ten APs from the same murine myocyte (cyan traces), their average (solid black line), and the GA-optimized model (dashed line). (C) With template-based model CTC (red traces), anthropomorphization frequently failed in forming a dome and prolonging the AP to the extent of the recipient model (dashed line). (D) With GA optimization, CTC successfully prolonged the mouse AP, induced a plateau phase, but exaggerated the notch.
Figure 8
Figure 8
Statistical analysis of target cell matching and CTC performance with human recipient model. (A) Decrease in average error between neonatal mouse myocyte APs and GA-fit models compared to nominal models demonstrating better matching with GA optimization. (B) Average error for CTC-on APs using the human recipient model showing better CTC performance with GA-optimized models over template-based model selection. (C) AP duration at different repolarization levels for template-based model CTC vs. GA-fitting CTC. For all three repolarization markers, GA-fit model CTC reproduces recipient model APD values (diamonds), while template-based model CTC resulted in too short waveforms. Error bars in all panels give standard deviation, n = 11 cells.
Figure 9
Figure 9
In silico and in vitro CTC circuit currents. Left panels show APs and related currents in CTC for an experiment using a GA-optimized target-canceling model (solid traces) as well as the corresponding ideal case of simulating that optimized model as both the myocyte and its canceling model (dashed traces). Right panels compare CTC-on APs and currents for an experiment using template-based model selection for the target-canceling model (solid traces) to an in silico case of mismatch between that same template-based target-canceling model and a GA-optimized model to simulate the target myocyte (dashed-dot traces). (A) and (B) target myocyte/model AP; (C) and (D) total current in the target-canceling myocyte/model; (E) and (F) total current in the recipient guinea pig model; (G) and (H) their difference current. With the GA optimization, the currents are close to their ideal behavior and AP transformation is accurate. When template-based selection is used, a lack of repolarizing current in the target-canceling model to counter that in the real myocyte leads to improper repolarization of the target myocyte. Insets show initial peak-current profiles. Same cell as used in Figure 5.

Similar articles

See all similar articles

Cited by 14 articles

See all "Cited by" articles

References

    1. Achard P., De Schutter E. (2006). Complex parameter landscape for a complex neuron model. PLoS Comput. Biol. 2, e94.10.1371/journal.pcbi.0020094 - DOI - PMC - PubMed
    1. Ahrens-Nicklas R. C., Christini D. J. (2009). Anthropomorphizing the mouse cardiac action potential via a novel dynamic clamp method. Biophys. J. 97, 1–1010.1016/j.bpj.2009.09.002 - DOI - PMC - PubMed
    1. Babij P., Askew G. R., Nieuwenhuijsen B., Su C. M., Bridal T. R., Jow B., et al. (1998). Inhibition of cardiac delayed rectifier K+ current by overexpression of the long-QT syndrome HERG G628S mutation in transgenic mice. Circ. Res. 83, 668–67810.1161/01.RES.83.6.668 - DOI - PubMed
    1. Berecki G., Zegers J. G., Bhuiyan Z. A., Verkerk A. O., Wilders R., Van Ginneken A. C. G. (2006). Long-QT syndrome-related sodium channel mutations probed by the dynamic action potential clamp technique. J. Physiol. 570, 237–250 - PMC - PubMed
    1. Berecki G., Zegers J. G., Verkerk O. A., Bhuiyan A. Z., De Jonge B., Veldkamp W. M., et al. (2005). HERG channel (dys)function revealed by dynamic action potential clamp technique. Biophys. J. 88, 566–57810.1529/biophysj.104.047290 - DOI - PMC - PubMed
Feedback