Limits...
Sensitivity of rabbit ventricular action potential and Ca²⁺ dynamics to small variations in membrane currents and ion diffusion coefficients.

Lo YH, Peachey T, Abramson D, McCulloch A, Michailova A - Biomed Res Int (2013)

Bottom Line: We applied sensitivity analysis to quantify the sensitivity of Shannon et al. model (Biophys.Our studies highlight the need for more precise measurements and further extending and testing of the Shannon et al. model.Our results demonstrate usefulness of sensitivity analysis to identify specific knowledge gaps and controversies related to ventricular cell electrophysiology and Ca²⁺ signaling.

View Article: PubMed Central - PubMed

Affiliation: Department of Bioengineering, PFBH 241, University of California San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0412, USA.

ABSTRACT
Little is known about how small variations in ionic currents and Ca²⁺ and Na⁺ diffusion coefficients impact action potential and Ca²⁺ dynamics in rabbit ventricular myocytes. We applied sensitivity analysis to quantify the sensitivity of Shannon et al. model (Biophys. J., 2004) to 5%-10% changes in currents conductance, channels distribution, and ion diffusion in rabbit ventricular cells. We found that action potential duration and Ca²⁺ peaks are highly sensitive to 10% increase in L-type Ca²⁺ current; moderately influenced by 10% increase in Na⁺-Ca²⁺ exchanger, Na⁺-K⁺ pump, rapid delayed and slow transient outward K⁺ currents, and Cl⁻ background current; insensitive to 10% increases in all other ionic currents and sarcoplasmic reticulum Ca²⁺ fluxes. Cell electrical activity is strongly affected by 5% shift of L-type Ca²⁺ channels and Na⁺-Ca²⁺ exchanger in between junctional and submembrane spaces while Ca²⁺-activated Cl⁻-channel redistribution has the modest effect. Small changes in submembrane and cytosolic diffusion coefficients for Ca²⁺, but not in Na⁺ transfer, may alter notably myocyte contraction. Our studies highlight the need for more precise measurements and further extending and testing of the Shannon et al. model. Our results demonstrate usefulness of sensitivity analysis to identify specific knowledge gaps and controversies related to ventricular cell electrophysiology and Ca²⁺ signaling.

Show MeSH

Related in: MedlinePlus

Parameter sensitivity analysis of APD60, Δ[Ca]i, Δ[Ca]SL, and Δ[Ca]jct sensitivities toward 10% increases in maximal transporters' conductance and permeability. Positive value indicates direct relationship between parameter and output (e.g., enhanced L-type Ca2+ permeability prolongs APD60), and negative value indicates indirect relationship between parameter and output. Nimrod/E-Lenth plots (left column), PLS-bar plots (right column). Nimrod/E analysis produced similar qualitative results as PLS analysis.
© Copyright Policy
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC3814049&req=5

fig2: Parameter sensitivity analysis of APD60, Δ[Ca]i, Δ[Ca]SL, and Δ[Ca]jct sensitivities toward 10% increases in maximal transporters' conductance and permeability. Positive value indicates direct relationship between parameter and output (e.g., enhanced L-type Ca2+ permeability prolongs APD60), and negative value indicates indirect relationship between parameter and output. Nimrod/E-Lenth plots (left column), PLS-bar plots (right column). Nimrod/E analysis produced similar qualitative results as PLS analysis.

Mentions: To perform sensitivity analysis, the Shannon et al. MatLab code was modified to extract the desired model outputs. Under basal conditions or by varying one parameter at a time AP and Ca2+ transients appeared stable (after 6–8 s until 8 min) at stimulus frequency of 1 Hz. For this reason we recorded and analyzed AP and Ca2+ signals ([Ca]i, [Ca]SL, [Ca]jct) at 9-10 s of every simulation. In all numerical experiments (0 ≤ t ≤ 8 min) [K]i remained unchanged while the variations in [Na]i were small (ranging from 20 μM to 100 μM) with insignificant effects on calculated AP and Ca2+ traces at 6–8 s. The APD60 and delta [Ca]j (Δ[Ca]j, j = i, SL,  jct) quantities were used to analyze the model sensitivity. Δ[Ca]j is defined as the difference between peak Ca2+ concentration in the particular compartment and the diastolic Ca2+ concentration of 0.1 μM. The modified code was uploaded onto Nimrod/E toolset and was executed repeatedly using permutations of parameter sets that were ±10% or ±5% of default values (see the appendix, Tables 1–3). Then Nimrod/E fractional-factorial analysis and PLS were used to analyze the effects of single parameter changes. In addition, Nimrod/E allowed examining the two-level parameter interactions on model outputs. In the Results section the sensitivities of selected biomarkers to variations of parameters are displayed graphically as either “Lenth plots” in Nimrod/E, or as “bar plots” in PLS. Before performing PLS regression analysis to obtain sensitivity values, z-scores of input and output matrices were calculated using MatLab's z-score function; that is, z = (x − mean(x))/std(x). Each z-score value was computed using the mean and standard deviations along each column of the matrices. The columns of matrices have mean zero and standard deviation one. The PLS regression coefficients, or sensitivity values (see Figures 2, 4, and 6), indicate how changes in input parameters lead to changes in outputs. Examining these numbers allows for an assessment of the relative contributions of the various parameters. The sensitivity values in the “bar plots” could be interpreted quantitatively as follows. Because input and output matrices are mean-centered and normalized to standard deviations computed column by column, each sensitivity value is defined relatively to the relevant deviations. For instance, if the regression coefficient for the input PCaL and the output APD60 is 0.5, then when PCaL is one standard deviation greater than the mean, APD60 will increase by half a standard deviation. Conversely, if the value is −0.5, then when PCaL is one standard deviation greater than the mean, APD60 will decrease by half a standard deviation, and vice versa. The estimate values in the “Lenth plots” (y-axis) provide a qualitative overview of the inputs' relative effects on outputs and offer a comparison to the PLS-bar graphs. Changing the number of parameters studied slightly varied the magnitude of “regression coefficients” of bar plot and “estimate” of Lenth plot, but the relative effects and overall parameter-to-output relationships remained constant. The effects of sample sizes on model predictive efficacy by randomly picking subsets from sample pool, ranging from 15, 20, 50, 100, 200, and 500 to 1000 trials was examined. The adjusted R2 values (coefficient of determination, quantifying the explanatory capacity of the regression analysis) were calculated and averaged. At the low end of 15 samples, the regression model explained 90.8 ± 2.4% of the variance. At the high end of 1000 samples, the model explained 96.4 ± 0.3% of the variance. This relatively low decrease in prediction efficacy suggests that sample sizes do not significantly change the qualitative information obtained from the experiments. Considering this statistical analysis, the results were not included.


Sensitivity of rabbit ventricular action potential and Ca²⁺ dynamics to small variations in membrane currents and ion diffusion coefficients.

Lo YH, Peachey T, Abramson D, McCulloch A, Michailova A - Biomed Res Int (2013)

Parameter sensitivity analysis of APD60, Δ[Ca]i, Δ[Ca]SL, and Δ[Ca]jct sensitivities toward 10% increases in maximal transporters' conductance and permeability. Positive value indicates direct relationship between parameter and output (e.g., enhanced L-type Ca2+ permeability prolongs APD60), and negative value indicates indirect relationship between parameter and output. Nimrod/E-Lenth plots (left column), PLS-bar plots (right column). Nimrod/E analysis produced similar qualitative results as PLS analysis.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3814049&req=5

fig2: Parameter sensitivity analysis of APD60, Δ[Ca]i, Δ[Ca]SL, and Δ[Ca]jct sensitivities toward 10% increases in maximal transporters' conductance and permeability. Positive value indicates direct relationship between parameter and output (e.g., enhanced L-type Ca2+ permeability prolongs APD60), and negative value indicates indirect relationship between parameter and output. Nimrod/E-Lenth plots (left column), PLS-bar plots (right column). Nimrod/E analysis produced similar qualitative results as PLS analysis.
Mentions: To perform sensitivity analysis, the Shannon et al. MatLab code was modified to extract the desired model outputs. Under basal conditions or by varying one parameter at a time AP and Ca2+ transients appeared stable (after 6–8 s until 8 min) at stimulus frequency of 1 Hz. For this reason we recorded and analyzed AP and Ca2+ signals ([Ca]i, [Ca]SL, [Ca]jct) at 9-10 s of every simulation. In all numerical experiments (0 ≤ t ≤ 8 min) [K]i remained unchanged while the variations in [Na]i were small (ranging from 20 μM to 100 μM) with insignificant effects on calculated AP and Ca2+ traces at 6–8 s. The APD60 and delta [Ca]j (Δ[Ca]j, j = i, SL,  jct) quantities were used to analyze the model sensitivity. Δ[Ca]j is defined as the difference between peak Ca2+ concentration in the particular compartment and the diastolic Ca2+ concentration of 0.1 μM. The modified code was uploaded onto Nimrod/E toolset and was executed repeatedly using permutations of parameter sets that were ±10% or ±5% of default values (see the appendix, Tables 1–3). Then Nimrod/E fractional-factorial analysis and PLS were used to analyze the effects of single parameter changes. In addition, Nimrod/E allowed examining the two-level parameter interactions on model outputs. In the Results section the sensitivities of selected biomarkers to variations of parameters are displayed graphically as either “Lenth plots” in Nimrod/E, or as “bar plots” in PLS. Before performing PLS regression analysis to obtain sensitivity values, z-scores of input and output matrices were calculated using MatLab's z-score function; that is, z = (x − mean(x))/std(x). Each z-score value was computed using the mean and standard deviations along each column of the matrices. The columns of matrices have mean zero and standard deviation one. The PLS regression coefficients, or sensitivity values (see Figures 2, 4, and 6), indicate how changes in input parameters lead to changes in outputs. Examining these numbers allows for an assessment of the relative contributions of the various parameters. The sensitivity values in the “bar plots” could be interpreted quantitatively as follows. Because input and output matrices are mean-centered and normalized to standard deviations computed column by column, each sensitivity value is defined relatively to the relevant deviations. For instance, if the regression coefficient for the input PCaL and the output APD60 is 0.5, then when PCaL is one standard deviation greater than the mean, APD60 will increase by half a standard deviation. Conversely, if the value is −0.5, then when PCaL is one standard deviation greater than the mean, APD60 will decrease by half a standard deviation, and vice versa. The estimate values in the “Lenth plots” (y-axis) provide a qualitative overview of the inputs' relative effects on outputs and offer a comparison to the PLS-bar graphs. Changing the number of parameters studied slightly varied the magnitude of “regression coefficients” of bar plot and “estimate” of Lenth plot, but the relative effects and overall parameter-to-output relationships remained constant. The effects of sample sizes on model predictive efficacy by randomly picking subsets from sample pool, ranging from 15, 20, 50, 100, 200, and 500 to 1000 trials was examined. The adjusted R2 values (coefficient of determination, quantifying the explanatory capacity of the regression analysis) were calculated and averaged. At the low end of 15 samples, the regression model explained 90.8 ± 2.4% of the variance. At the high end of 1000 samples, the model explained 96.4 ± 0.3% of the variance. This relatively low decrease in prediction efficacy suggests that sample sizes do not significantly change the qualitative information obtained from the experiments. Considering this statistical analysis, the results were not included.

Bottom Line: We applied sensitivity analysis to quantify the sensitivity of Shannon et al. model (Biophys.Our studies highlight the need for more precise measurements and further extending and testing of the Shannon et al. model.Our results demonstrate usefulness of sensitivity analysis to identify specific knowledge gaps and controversies related to ventricular cell electrophysiology and Ca²⁺ signaling.

View Article: PubMed Central - PubMed

Affiliation: Department of Bioengineering, PFBH 241, University of California San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0412, USA.

ABSTRACT
Little is known about how small variations in ionic currents and Ca²⁺ and Na⁺ diffusion coefficients impact action potential and Ca²⁺ dynamics in rabbit ventricular myocytes. We applied sensitivity analysis to quantify the sensitivity of Shannon et al. model (Biophys. J., 2004) to 5%-10% changes in currents conductance, channels distribution, and ion diffusion in rabbit ventricular cells. We found that action potential duration and Ca²⁺ peaks are highly sensitive to 10% increase in L-type Ca²⁺ current; moderately influenced by 10% increase in Na⁺-Ca²⁺ exchanger, Na⁺-K⁺ pump, rapid delayed and slow transient outward K⁺ currents, and Cl⁻ background current; insensitive to 10% increases in all other ionic currents and sarcoplasmic reticulum Ca²⁺ fluxes. Cell electrical activity is strongly affected by 5% shift of L-type Ca²⁺ channels and Na⁺-Ca²⁺ exchanger in between junctional and submembrane spaces while Ca²⁺-activated Cl⁻-channel redistribution has the modest effect. Small changes in submembrane and cytosolic diffusion coefficients for Ca²⁺, but not in Na⁺ transfer, may alter notably myocyte contraction. Our studies highlight the need for more precise measurements and further extending and testing of the Shannon et al. model. Our results demonstrate usefulness of sensitivity analysis to identify specific knowledge gaps and controversies related to ventricular cell electrophysiology and Ca²⁺ signaling.

Show MeSH
Related in: MedlinePlus