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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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Using Sensitivities To Predict Parameter Compensations for Firing Rate Homeostasis in the Reduced and Realistic Morphologies(A–B) Parameter perturbations of Model 1 from subspace E (Figure S5, and inset of [E] below).(A) A 15% reduction of D + SA increased firing rate to 14.2 Hz (thick green line) relative to the unperturbed model (12.1 Hz; thin black line); a 14.8% reduction is needed to return to the unperturbed firing rate.(B) As predicted from its firing rate sensitivity (inset barplot), a 10.5% decrease in 							 compensated almost exactly for the effect of the D + SA perturbation on firing rate in (A) (see Discussion for details). The red trace, shifted up slightly along the vertical axis for visualization, overlays the unperturbed voltage trace very closely.						(C–F) Homeostatic parameter compensations can also be predicted in models with realistic morphology.(C) When Model 1 from subspace E was simulated in the realistic AII morphology, a 15% reduction of D + SA increased firing rate by 20.3% relative to the unperturbed value.(D) The compensatory perturbations for Model 1 of two different active parameters (							 in red, shifted vertically up; 							 in blue, shifted down) were predicted from their firing rate sensitivities (inset barplots). The blue and red compensated traces overlie the unperturbed (black) trace very closely, demonstrating excellent compensation.						(E–F) Compensatory perturbations predicted from sensitivities computed at a different point in parameter space: Model 3 of subspace E, implemented in the realistic morphology with an analogous 15% reduction of D + SA. Inset in E shows the location of Models 1, 2, and 3 in the [							, 							, 							] subspace (also see Figure S5A). For Model 3, firing rate sensitivities to 							 and 							 were about twice as large as for Model 1. Accordingly, the predicted magnitudes for Model 3 were about half of those for Model 1; compare (D) and (F). For both models, the close match of red (shifted up), blue (shifted down), and black traces demonstrate that the predicted perturbations of either active parameter compensated almost exactly for the effect of the D + SA reduction ([C] and [E]), even for large predicted increases of 							. See Discussion for details.
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pcbi-0040011-g011: Using Sensitivities To Predict Parameter Compensations for Firing Rate Homeostasis in the Reduced and Realistic Morphologies(A–B) Parameter perturbations of Model 1 from subspace E (Figure S5, and inset of [E] below).(A) A 15% reduction of D + SA increased firing rate to 14.2 Hz (thick green line) relative to the unperturbed model (12.1 Hz; thin black line); a 14.8% reduction is needed to return to the unperturbed firing rate.(B) As predicted from its firing rate sensitivity (inset barplot), a 10.5% decrease in compensated almost exactly for the effect of the D + SA perturbation on firing rate in (A) (see Discussion for details). The red trace, shifted up slightly along the vertical axis for visualization, overlays the unperturbed voltage trace very closely. (C–F) Homeostatic parameter compensations can also be predicted in models with realistic morphology.(C) When Model 1 from subspace E was simulated in the realistic AII morphology, a 15% reduction of D + SA increased firing rate by 20.3% relative to the unperturbed value.(D) The compensatory perturbations for Model 1 of two different active parameters ( in red, shifted vertically up; in blue, shifted down) were predicted from their firing rate sensitivities (inset barplots). The blue and red compensated traces overlie the unperturbed (black) trace very closely, demonstrating excellent compensation. (E–F) Compensatory perturbations predicted from sensitivities computed at a different point in parameter space: Model 3 of subspace E, implemented in the realistic morphology with an analogous 15% reduction of D + SA. Inset in E shows the location of Models 1, 2, and 3 in the [ , , ] subspace (also see Figure S5A). For Model 3, firing rate sensitivities to and were about twice as large as for Model 1. Accordingly, the predicted magnitudes for Model 3 were about half of those for Model 1; compare (D) and (F). For both models, the close match of red (shifted up), blue (shifted down), and black traces demonstrate that the predicted perturbations of either active parameter compensated almost exactly for the effect of the D + SA reduction ([C] and [E]), even for large predicted increases of . See Discussion for details.

Mentions: In the present study, our morphologic model comprised a soma and cylindrical dendrite. We chose a simply parameterized morphology to illustrate a comparison between sensitivities to morphologic and active parameters. While it clarified essential morphologic mechanisms that influence somatic firing patterns, this simple model cannot reproduce all the subtle interactions that shape neuronal function in realistic morphologies. Fortunately, the model reduction is not a necessary step in our analysis. As demonstrated below (Figure 11), our method can be applied to models with more realistic morphologies. The trends identified here may change when analyzing sensitivity to more complex morphologic features of dendrites, such as tapering, branching, and varied dendritic lengths. Nonetheless, supported by findings that dendritic current flow can significantly affect gain control and excitability [54–56], our results indicate that morphology can play a key role in functional homeostasis.


Neuronal firing sensitivity to morphologic and active membrane parameters.

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

Using Sensitivities To Predict Parameter Compensations for Firing Rate Homeostasis in the Reduced and Realistic Morphologies(A–B) Parameter perturbations of Model 1 from subspace E (Figure S5, and inset of [E] below).(A) A 15% reduction of D + SA increased firing rate to 14.2 Hz (thick green line) relative to the unperturbed model (12.1 Hz; thin black line); a 14.8% reduction is needed to return to the unperturbed firing rate.(B) As predicted from its firing rate sensitivity (inset barplot), a 10.5% decrease in 							 compensated almost exactly for the effect of the D + SA perturbation on firing rate in (A) (see Discussion for details). The red trace, shifted up slightly along the vertical axis for visualization, overlays the unperturbed voltage trace very closely.						(C–F) Homeostatic parameter compensations can also be predicted in models with realistic morphology.(C) When Model 1 from subspace E was simulated in the realistic AII morphology, a 15% reduction of D + SA increased firing rate by 20.3% relative to the unperturbed value.(D) The compensatory perturbations for Model 1 of two different active parameters (							 in red, shifted vertically up; 							 in blue, shifted down) were predicted from their firing rate sensitivities (inset barplots). The blue and red compensated traces overlie the unperturbed (black) trace very closely, demonstrating excellent compensation.						(E–F) Compensatory perturbations predicted from sensitivities computed at a different point in parameter space: Model 3 of subspace E, implemented in the realistic morphology with an analogous 15% reduction of D + SA. Inset in E shows the location of Models 1, 2, and 3 in the [							, 							, 							] subspace (also see Figure S5A). For Model 3, firing rate sensitivities to 							 and 							 were about twice as large as for Model 1. Accordingly, the predicted magnitudes for Model 3 were about half of those for Model 1; compare (D) and (F). For both models, the close match of red (shifted up), blue (shifted down), and black traces demonstrate that the predicted perturbations of either active parameter compensated almost exactly for the effect of the D + SA reduction ([C] and [E]), even for large predicted increases of 							. See Discussion for details.
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Related In: Results  -  Collection

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getmorefigures.php?uid=PMC2211531&req=5

pcbi-0040011-g011: Using Sensitivities To Predict Parameter Compensations for Firing Rate Homeostasis in the Reduced and Realistic Morphologies(A–B) Parameter perturbations of Model 1 from subspace E (Figure S5, and inset of [E] below).(A) A 15% reduction of D + SA increased firing rate to 14.2 Hz (thick green line) relative to the unperturbed model (12.1 Hz; thin black line); a 14.8% reduction is needed to return to the unperturbed firing rate.(B) As predicted from its firing rate sensitivity (inset barplot), a 10.5% decrease in compensated almost exactly for the effect of the D + SA perturbation on firing rate in (A) (see Discussion for details). The red trace, shifted up slightly along the vertical axis for visualization, overlays the unperturbed voltage trace very closely. (C–F) Homeostatic parameter compensations can also be predicted in models with realistic morphology.(C) When Model 1 from subspace E was simulated in the realistic AII morphology, a 15% reduction of D + SA increased firing rate by 20.3% relative to the unperturbed value.(D) The compensatory perturbations for Model 1 of two different active parameters ( in red, shifted vertically up; in blue, shifted down) were predicted from their firing rate sensitivities (inset barplots). The blue and red compensated traces overlie the unperturbed (black) trace very closely, demonstrating excellent compensation. (E–F) Compensatory perturbations predicted from sensitivities computed at a different point in parameter space: Model 3 of subspace E, implemented in the realistic morphology with an analogous 15% reduction of D + SA. Inset in E shows the location of Models 1, 2, and 3 in the [ , , ] subspace (also see Figure S5A). For Model 3, firing rate sensitivities to and were about twice as large as for Model 1. Accordingly, the predicted magnitudes for Model 3 were about half of those for Model 1; compare (D) and (F). For both models, the close match of red (shifted up), blue (shifted down), and black traces demonstrate that the predicted perturbations of either active parameter compensated almost exactly for the effect of the D + SA reduction ([C] and [E]), even for large predicted increases of . See Discussion for details.
Mentions: In the present study, our morphologic model comprised a soma and cylindrical dendrite. We chose a simply parameterized morphology to illustrate a comparison between sensitivities to morphologic and active parameters. While it clarified essential morphologic mechanisms that influence somatic firing patterns, this simple model cannot reproduce all the subtle interactions that shape neuronal function in realistic morphologies. Fortunately, the model reduction is not a necessary step in our analysis. As demonstrated below (Figure 11), our method can be applied to models with more realistic morphologies. The trends identified here may change when analyzing sensitivity to more complex morphologic features of dendrites, such as tapering, branching, and varied dendritic lengths. Nonetheless, supported by findings that dendritic current flow can significantly affect gain control and excitability [54–56], our results indicate that morphology can play a key role in functional homeostasis.

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