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Neuronal firing sensitivity to morphologic and active membrane parameters.

Weaver CM, Wearne SL - PLoS Comput. Biol. (2007)

Bottom Line: We found domains where different groups of parameters had the highest sensitivities, suggesting that interactions within each group shaped firing behaviors within each specific domain.Significantly, we can predict which active conductances, and how many of them, will compensate for a given age- or development-related structural change, or will offset a morphologic perturbation resulting from trauma or neurodegenerative disorder, to restore normal function.Thus, sensitivity landscapes, and the quantitative predictions they provide, can give new insight into mechanisms of homeostasis in any biological system.

View Article: PubMed Central - PubMed

Affiliation: Laboratory of Biomathematics, Mount Sinai School of Medicine, New York, New York, United States of America. christina.weaver@mssm.edu

ABSTRACT
Both the excitability of a neuron's membrane, driven by active ion channels, and dendritic morphology contribute to neuronal firing dynamics, but the relative importance and interactions between these features remain poorly understood. Recent modeling studies have shown that different combinations of active conductances can evoke similar firing patterns, but have neglected how morphology might contribute to homeostasis. Parameterizing the morphology of a cylindrical dendrite, we introduce a novel application of mathematical sensitivity analysis that quantifies how dendritic length, diameter, and surface area influence neuronal firing, and compares these effects directly against those of active parameters. The method was applied to a model of neurons from goldfish Area II. These neurons exhibit, and likely contribute to, persistent activity in eye velocity storage, a simple model of working memory. We introduce sensitivity landscapes, defined by local sensitivity analyses of firing rate and gain to each parameter, performed globally across the parameter space. Principal directions over which sensitivity to all parameters varied most revealed intrinsic currents that most controlled model output. We found domains where different groups of parameters had the highest sensitivities, suggesting that interactions within each group shaped firing behaviors within each specific domain. Application of our method, and its characterization of which models were sensitive to general morphologic features, will lead to advances in understanding how realistic morphology participates in functional homeostasis. Significantly, we can predict which active conductances, and how many of them, will compensate for a given age- or development-related structural change, or will offset a morphologic perturbation resulting from trauma or neurodegenerative disorder, to restore normal function. Our method can be adapted to analyze any computational model. Thus, sensitivity landscapes, and the quantitative predictions they provide, can give new insight into mechanisms of homeostasis in any biological system.

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Evaluating Sensitivity for Optimized Models Across Parameter Space(A) Location in nine-dimensional parameter space of the 15 optimized passive dendrite models (gray circles and colored triangles), shown in three 3-D subspaces: [								, 								, 								] (top); [Kp, RCa, 								] (middle); and [								, 								, 								] (bottom). Voltage traces and sensitivity coefficients of three models represented as colored triangles (A, B, and C) are compared in (B), (C), and Figure 4.							(B) Comparison of morphologic (D + SA) and active parameter (								) perturbations of the model labeled “B” (blue triangles in [A], above). Solid blue line represents the somatic voltage trace of the unperturbed model. Dashed line shows the response to a 20% decrease in D + SA; solid black line shows the response to a 20% increase in 								. Inset barplot shows the normalized sensitivity coefficients of spontaneous firing rate to D + SA and 								 (Sp. FR Sens.): positive to 								, negative and of greater magnitude to D + SA.							(C) Perturbations of the model labeled “C” (red triangles in [A], above). Shown are perturbations analogous to those in (B) above, except that the solid black line shows the response to a 10% increase in 								. Sensitivity to D + SA is small and negative, while sensitivity to 								 is large and positive. Note the difference in scale between the sensitivity barplot insets in (B) and (C).
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pcbi-0040011-g003: Evaluating Sensitivity for Optimized Models Across Parameter Space(A) Location in nine-dimensional parameter space of the 15 optimized passive dendrite models (gray circles and colored triangles), shown in three 3-D subspaces: [ , , ] (top); [Kp, RCa, ] (middle); and [ , , ] (bottom). Voltage traces and sensitivity coefficients of three models represented as colored triangles (A, B, and C) are compared in (B), (C), and Figure 4. (B) Comparison of morphologic (D + SA) and active parameter ( ) perturbations of the model labeled “B” (blue triangles in [A], above). Solid blue line represents the somatic voltage trace of the unperturbed model. Dashed line shows the response to a 20% decrease in D + SA; solid black line shows the response to a 20% increase in . Inset barplot shows the normalized sensitivity coefficients of spontaneous firing rate to D + SA and (Sp. FR Sens.): positive to , negative and of greater magnitude to D + SA. (C) Perturbations of the model labeled “C” (red triangles in [A], above). Shown are perturbations analogous to those in (B) above, except that the solid black line shows the response to a 10% increase in . Sensitivity to D + SA is small and negative, while sensitivity to is large and positive. Note the difference in scale between the sensitivity barplot insets in (B) and (C).

Mentions: The conductance space locations of 15 optimized models that matched target data are shown in Figure 3A. Nine dimensions of the conductance space (the eight optimized parameters, plus leak conductance ) are illustrated as a set of three 3-D graphs. Optimized models assumed parameter values spanning the full range of conductance parameters, demonstrating that different combinations of parameters can produce similar output [2,6,20]. Interestingly, values of and were correlated across the entire parameter space (r2 = 0.98; Figure S1), suggesting a global compensatory interaction between enhancement ( ) and reduction ( ) of excitability. There was no significant correlation between any other pair of parameters. The spontaneous firing rates of the optimized models, shown in Figure S2A, ranged from 7 to 14 Hz.


Neuronal firing sensitivity to morphologic and active membrane parameters.

Weaver CM, Wearne SL - PLoS Comput. Biol. (2007)

Evaluating Sensitivity for Optimized Models Across Parameter Space(A) Location in nine-dimensional parameter space of the 15 optimized passive dendrite models (gray circles and colored triangles), shown in three 3-D subspaces: [								, 								, 								] (top); [Kp, RCa, 								] (middle); and [								, 								, 								] (bottom). Voltage traces and sensitivity coefficients of three models represented as colored triangles (A, B, and C) are compared in (B), (C), and Figure 4.							(B) Comparison of morphologic (D + SA) and active parameter (								) perturbations of the model labeled “B” (blue triangles in [A], above). Solid blue line represents the somatic voltage trace of the unperturbed model. Dashed line shows the response to a 20% decrease in D + SA; solid black line shows the response to a 20% increase in 								. Inset barplot shows the normalized sensitivity coefficients of spontaneous firing rate to D + SA and 								 (Sp. FR Sens.): positive to 								, negative and of greater magnitude to D + SA.							(C) Perturbations of the model labeled “C” (red triangles in [A], above). Shown are perturbations analogous to those in (B) above, except that the solid black line shows the response to a 10% increase in 								. Sensitivity to D + SA is small and negative, while sensitivity to 								 is large and positive. Note the difference in scale between the sensitivity barplot insets in (B) and (C).
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Related In: Results  -  Collection

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getmorefigures.php?uid=PMC2211531&req=5

pcbi-0040011-g003: Evaluating Sensitivity for Optimized Models Across Parameter Space(A) Location in nine-dimensional parameter space of the 15 optimized passive dendrite models (gray circles and colored triangles), shown in three 3-D subspaces: [ , , ] (top); [Kp, RCa, ] (middle); and [ , , ] (bottom). Voltage traces and sensitivity coefficients of three models represented as colored triangles (A, B, and C) are compared in (B), (C), and Figure 4. (B) Comparison of morphologic (D + SA) and active parameter ( ) perturbations of the model labeled “B” (blue triangles in [A], above). Solid blue line represents the somatic voltage trace of the unperturbed model. Dashed line shows the response to a 20% decrease in D + SA; solid black line shows the response to a 20% increase in . Inset barplot shows the normalized sensitivity coefficients of spontaneous firing rate to D + SA and (Sp. FR Sens.): positive to , negative and of greater magnitude to D + SA. (C) Perturbations of the model labeled “C” (red triangles in [A], above). Shown are perturbations analogous to those in (B) above, except that the solid black line shows the response to a 10% increase in . Sensitivity to D + SA is small and negative, while sensitivity to is large and positive. Note the difference in scale between the sensitivity barplot insets in (B) and (C).
Mentions: The conductance space locations of 15 optimized models that matched target data are shown in Figure 3A. Nine dimensions of the conductance space (the eight optimized parameters, plus leak conductance ) are illustrated as a set of three 3-D graphs. Optimized models assumed parameter values spanning the full range of conductance parameters, demonstrating that different combinations of parameters can produce similar output [2,6,20]. Interestingly, values of and were correlated across the entire parameter space (r2 = 0.98; Figure S1), suggesting a global compensatory interaction between enhancement ( ) and reduction ( ) of excitability. There was no significant correlation between any other pair of parameters. The spontaneous firing rates of the optimized models, shown in Figure S2A, ranged from 7 to 14 Hz.

Bottom Line: We found domains where different groups of parameters had the highest sensitivities, suggesting that interactions within each group shaped firing behaviors within each specific domain.Significantly, we can predict which active conductances, and how many of them, will compensate for a given age- or development-related structural change, or will offset a morphologic perturbation resulting from trauma or neurodegenerative disorder, to restore normal function.Thus, sensitivity landscapes, and the quantitative predictions they provide, can give new insight into mechanisms of homeostasis in any biological system.

View Article: PubMed Central - PubMed

Affiliation: Laboratory of Biomathematics, Mount Sinai School of Medicine, New York, New York, United States of America. christina.weaver@mssm.edu

ABSTRACT
Both the excitability of a neuron's membrane, driven by active ion channels, and dendritic morphology contribute to neuronal firing dynamics, but the relative importance and interactions between these features remain poorly understood. Recent modeling studies have shown that different combinations of active conductances can evoke similar firing patterns, but have neglected how morphology might contribute to homeostasis. Parameterizing the morphology of a cylindrical dendrite, we introduce a novel application of mathematical sensitivity analysis that quantifies how dendritic length, diameter, and surface area influence neuronal firing, and compares these effects directly against those of active parameters. The method was applied to a model of neurons from goldfish Area II. These neurons exhibit, and likely contribute to, persistent activity in eye velocity storage, a simple model of working memory. We introduce sensitivity landscapes, defined by local sensitivity analyses of firing rate and gain to each parameter, performed globally across the parameter space. Principal directions over which sensitivity to all parameters varied most revealed intrinsic currents that most controlled model output. We found domains where different groups of parameters had the highest sensitivities, suggesting that interactions within each group shaped firing behaviors within each specific domain. Application of our method, and its characterization of which models were sensitive to general morphologic features, will lead to advances in understanding how realistic morphology participates in functional homeostasis. Significantly, we can predict which active conductances, and how many of them, will compensate for a given age- or development-related structural change, or will offset a morphologic perturbation resulting from trauma or neurodegenerative disorder, to restore normal function. Our method can be adapted to analyze any computational model. Thus, sensitivity landscapes, and the quantitative predictions they provide, can give new insight into mechanisms of homeostasis in any biological system.

Show MeSH
Related in: MedlinePlus