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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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Sensitivity of Spontaneous Firing Rate to Model Parameters Varied Across Parameter Space(A–C) Somatic voltage traces and normalized sensitivity coefficients to perturbations of active (								, 								, 								, Kp, RCa, 								, 								, 								) and morphologic (L + D, L + SA, D + SA) parameters, for the models labeled A, B, and C in Figures 3A and (D) (colored triangles). For some regions of parameter space (points A and B), the pattern of parameter sensitivities was similar. In other regions (C), the sensitivity to several parameters changed dramatically (compare colored bars in [A] and [B] versus [C]), so that the relative influence of different parameters on spontaneous firing rate was changed.							(D) Firing rate sensitivity to D + SA of all optimized models, as a function of their location in the [								, 								, 								] subspace. The points shown in (A–C) above are labeled (A, B, and C), with color indicating the magnitude and sign of firing rate sensitivity to D + SA according to the colorscale shown on the right. Arrows show the directions along which sensitivity to D + SA was relatively constant (thin arrow), and along which it changed substantially (thick arrow). Along this principal direction, even the sensitivity sign reversed (yellow circle, marked with “+”). In the 11 models shown as filled circles, firing rate sensitivity was largest to the morphologic parameter D + SA than to any active parameter. Open squares show the four models for which firing rate sensitivity was greater to at least one active parameter than to D + SA.
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pcbi-0040011-g004: Sensitivity of Spontaneous Firing Rate to Model Parameters Varied Across Parameter Space(A–C) Somatic voltage traces and normalized sensitivity coefficients to perturbations of active ( , , , Kp, RCa, , , ) and morphologic (L + D, L + SA, D + SA) parameters, for the models labeled A, B, and C in Figures 3A and (D) (colored triangles). For some regions of parameter space (points A and B), the pattern of parameter sensitivities was similar. In other regions (C), the sensitivity to several parameters changed dramatically (compare colored bars in [A] and [B] versus [C]), so that the relative influence of different parameters on spontaneous firing rate was changed. (D) Firing rate sensitivity to D + SA of all optimized models, as a function of their location in the [ , , ] subspace. The points shown in (A–C) above are labeled (A, B, and C), with color indicating the magnitude and sign of firing rate sensitivity to D + SA according to the colorscale shown on the right. Arrows show the directions along which sensitivity to D + SA was relatively constant (thin arrow), and along which it changed substantially (thick arrow). Along this principal direction, even the sensitivity sign reversed (yellow circle, marked with “+”). In the 11 models shown as filled circles, firing rate sensitivity was largest to the morphologic parameter D + SA than to any active parameter. Open squares show the four models for which firing rate sensitivity was greater to at least one active parameter than to D + SA.

Mentions: (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.


Neuronal firing sensitivity to morphologic and active membrane parameters.

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

Sensitivity of Spontaneous Firing Rate to Model Parameters Varied Across Parameter Space(A–C) Somatic voltage traces and normalized sensitivity coefficients to perturbations of active (								, 								, 								, Kp, RCa, 								, 								, 								) and morphologic (L + D, L + SA, D + SA) parameters, for the models labeled A, B, and C in Figures 3A and (D) (colored triangles). For some regions of parameter space (points A and B), the pattern of parameter sensitivities was similar. In other regions (C), the sensitivity to several parameters changed dramatically (compare colored bars in [A] and [B] versus [C]), so that the relative influence of different parameters on spontaneous firing rate was changed.							(D) Firing rate sensitivity to D + SA of all optimized models, as a function of their location in the [								, 								, 								] subspace. The points shown in (A–C) above are labeled (A, B, and C), with color indicating the magnitude and sign of firing rate sensitivity to D + SA according to the colorscale shown on the right. Arrows show the directions along which sensitivity to D + SA was relatively constant (thin arrow), and along which it changed substantially (thick arrow). Along this principal direction, even the sensitivity sign reversed (yellow circle, marked with “+”). In the 11 models shown as filled circles, firing rate sensitivity was largest to the morphologic parameter D + SA than to any active parameter. Open squares show the four models for which firing rate sensitivity was greater to at least one active parameter than to D + SA.
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC2211531&req=5

pcbi-0040011-g004: Sensitivity of Spontaneous Firing Rate to Model Parameters Varied Across Parameter Space(A–C) Somatic voltage traces and normalized sensitivity coefficients to perturbations of active ( , , , Kp, RCa, , , ) and morphologic (L + D, L + SA, D + SA) parameters, for the models labeled A, B, and C in Figures 3A and (D) (colored triangles). For some regions of parameter space (points A and B), the pattern of parameter sensitivities was similar. In other regions (C), the sensitivity to several parameters changed dramatically (compare colored bars in [A] and [B] versus [C]), so that the relative influence of different parameters on spontaneous firing rate was changed. (D) Firing rate sensitivity to D + SA of all optimized models, as a function of their location in the [ , , ] subspace. The points shown in (A–C) above are labeled (A, B, and C), with color indicating the magnitude and sign of firing rate sensitivity to D + SA according to the colorscale shown on the right. Arrows show the directions along which sensitivity to D + SA was relatively constant (thin arrow), and along which it changed substantially (thick arrow). Along this principal direction, even the sensitivity sign reversed (yellow circle, marked with “+”). In the 11 models shown as filled circles, firing rate sensitivity was largest to the morphologic parameter D + SA than to any active parameter. Open squares show the four models for which firing rate sensitivity was greater to at least one active parameter than to D + SA.
Mentions: (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.

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