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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 Across Parameter Space(A) Colored symbols show 136 Area II–like candidate models identified during the systematic search of conductance space. Values of 								, 								, and 								(top graph) and 								 (middle graph, z-axis) were the same for all candidate models; locations along Kp and RCa dimensions (middle graph) and 								, 								 and 								 dimensions (bottom graph) varied. Some models have been shifted slightly along the 								 axis to aid in visualization. Red dots indicate candidate models within subspace A (Figure 5A); the blue triangle (“M”) marks the active parameter values used in the systematic search of morphologic space.							(B) Sensitivity of spontaneous firing rate to parameter perturbations of the subspace A candidate models as a function of their location in the lower [								, 								, 								] subspace. Color indicates sensitivity magnitude and sign according to the colorscale shown at top left. Shown are sensitivities to active parameters RCa and 								 (top left and right, respectively) and to morphologic parameters D + SA and L + D with constant channel densities (“CD”; bottom left and right). Arrows indicate the principal sensitivity direction across the space.
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pcbi-0040011-g006: Sensitivity of Spontaneous Firing Rate Across Parameter Space(A) Colored symbols show 136 Area II–like candidate models identified during the systematic search of conductance space. Values of , , and (top graph) and (middle graph, z-axis) were the same for all candidate models; locations along Kp and RCa dimensions (middle graph) and , and dimensions (bottom graph) varied. Some models have been shifted slightly along the axis to aid in visualization. Red dots indicate candidate models within subspace A (Figure 5A); the blue triangle (“M”) marks the active parameter values used in the systematic search of morphologic space. (B) Sensitivity of spontaneous firing rate to parameter perturbations of the subspace A candidate models as a function of their location in the lower [ , , ] subspace. Color indicates sensitivity magnitude and sign according to the colorscale shown at top left. Shown are sensitivities to active parameters RCa and (top left and right, respectively) and to morphologic parameters D + SA and L + D with constant channel densities (“CD”; bottom left and right). Arrows indicate the principal sensitivity direction across the space.

Mentions: The shape of the sensitivity landscape depended both upon location in parameter space and baseline firing rate. To analyze sensitivity trends independent of baseline firing rate effects, we focused on Area II–like “candidate models” firing spontaneously from 7–13 Hz; the gain of these models was unconstrained (see Materials and Methods). Figure 6A shows 136 candidate models identified during the systematic search. With four dimensions [ , , , and ] held fixed, these candidate models were connected across the remaining five-dimensional search space, forming a wedge in the [ , , ] subspace (Figure 6A).


Neuronal firing sensitivity to morphologic and active membrane parameters.

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

Sensitivity of Spontaneous Firing Rate Across Parameter Space(A) Colored symbols show 136 Area II–like candidate models identified during the systematic search of conductance space. Values of 								, 								, and 								(top graph) and 								 (middle graph, z-axis) were the same for all candidate models; locations along Kp and RCa dimensions (middle graph) and 								, 								 and 								 dimensions (bottom graph) varied. Some models have been shifted slightly along the 								 axis to aid in visualization. Red dots indicate candidate models within subspace A (Figure 5A); the blue triangle (“M”) marks the active parameter values used in the systematic search of morphologic space.							(B) Sensitivity of spontaneous firing rate to parameter perturbations of the subspace A candidate models as a function of their location in the lower [								, 								, 								] subspace. Color indicates sensitivity magnitude and sign according to the colorscale shown at top left. Shown are sensitivities to active parameters RCa and 								 (top left and right, respectively) and to morphologic parameters D + SA and L + D with constant channel densities (“CD”; bottom left and right). Arrows indicate the principal sensitivity direction across the space.
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Related In: Results  -  Collection

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getmorefigures.php?uid=PMC2211531&req=5

pcbi-0040011-g006: Sensitivity of Spontaneous Firing Rate Across Parameter Space(A) Colored symbols show 136 Area II–like candidate models identified during the systematic search of conductance space. Values of , , and (top graph) and (middle graph, z-axis) were the same for all candidate models; locations along Kp and RCa dimensions (middle graph) and , and dimensions (bottom graph) varied. Some models have been shifted slightly along the axis to aid in visualization. Red dots indicate candidate models within subspace A (Figure 5A); the blue triangle (“M”) marks the active parameter values used in the systematic search of morphologic space. (B) Sensitivity of spontaneous firing rate to parameter perturbations of the subspace A candidate models as a function of their location in the lower [ , , ] subspace. Color indicates sensitivity magnitude and sign according to the colorscale shown at top left. Shown are sensitivities to active parameters RCa and (top left and right, respectively) and to morphologic parameters D + SA and L + D with constant channel densities (“CD”; bottom left and right). Arrows indicate the principal sensitivity direction across the space.
Mentions: The shape of the sensitivity landscape depended both upon location in parameter space and baseline firing rate. To analyze sensitivity trends independent of baseline firing rate effects, we focused on Area II–like “candidate models” firing spontaneously from 7–13 Hz; the gain of these models was unconstrained (see Materials and Methods). Figure 6A shows 136 candidate models identified during the systematic search. With four dimensions [ , , , and ] held fixed, these candidate models were connected across the remaining five-dimensional search space, forming a wedge in the [ , , ] subspace (Figure 6A).

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