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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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Spontaneous Firing Rate Sensitivity across Constant Density and Constant Numbers Morphologic Spaces(A) Baseline spontaneous firing rate represented as a colormap across CD morphologic space (colorscale 0–25 Hz; top right). Black dot marks the original morphology used for the conductance space searches. Thick black curve indicates all models matching the original SA.(B) Spontaneous firing rate sensitivities to perturbations of active parameters RCa and 								 (top row), and morphologic parameters D + SA / CD and L + D / CD (bottom row) of candidate models across the space. Arrows indicate the principal sensitivity trend to each parameter. In the bottom left of (B), filled circles indicate models for which sensitivity to D + SA / CD was greater than sensitivity to all active parameters except 								. In the model shown as an open square, sensitivity to two or more active parameters was greater than sensitivity to D + SA / CD. In the bottom right of (B), filled circles and open squares likewise compare the sensitivity to L + D / CD and sensitivities to active parameters. Analogous colormaps across CN morphologic space are shown for (C) baseline spontaneous firing rate and (D) spontaneous firing rate sensitivity to parameter perturbations among candidate models. The black curve in (C) indicates all models matching the original axial resistance (see Materials and Methods). In the bottom row of (D), filled circles show models for which sensitivity to either D + SA / CN or L + D / CN was greater than sensitivities to all active parameters except 								 and 								. In models shown as open squares, sensitivity to three or more active parameters was greater than sensitivity to either D + SA / CN or L + D / CN.
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pcbi-0040011-g008: Spontaneous Firing Rate Sensitivity across Constant Density and Constant Numbers Morphologic Spaces(A) Baseline spontaneous firing rate represented as a colormap across CD morphologic space (colorscale 0–25 Hz; top right). Black dot marks the original morphology used for the conductance space searches. Thick black curve indicates all models matching the original SA.(B) Spontaneous firing rate sensitivities to perturbations of active parameters RCa and (top row), and morphologic parameters D + SA / CD and L + D / CD (bottom row) of candidate models across the space. Arrows indicate the principal sensitivity trend to each parameter. In the bottom left of (B), filled circles indicate models for which sensitivity to D + SA / CD was greater than sensitivity to all active parameters except . In the model shown as an open square, sensitivity to two or more active parameters was greater than sensitivity to D + SA / CD. In the bottom right of (B), filled circles and open squares likewise compare the sensitivity to L + D / CD and sensitivities to active parameters. Analogous colormaps across CN morphologic space are shown for (C) baseline spontaneous firing rate and (D) spontaneous firing rate sensitivity to parameter perturbations among candidate models. The black curve in (C) indicates all models matching the original axial resistance (see Materials and Methods). In the bottom row of (D), filled circles show models for which sensitivity to either D + SA / CN or L + D / CN was greater than sensitivities to all active parameters except and . In models shown as open squares, sensitivity to three or more active parameters was greater than sensitivity to either D + SA / CN or L + D / CN.

Mentions: Figure 8A shows the spontaneous firing rate of models across CD morphologic space. A small, connected set of models did not fire spontaneously (uncolored cells); the others fired regularly at rates up to 25 Hz. Firing rate varied less across this morphologic space than across conductance space because active parameter values in the soma, the site of AP initiation, were held fixed along each dimension of the space. Firing rates varied continuously over the sampled points, and inversely with D. Models with similar firing rates lay in colored bands of vertical stripes over the lower half of the D range, and in approximately hyperbolic shaped bands over the upper half of the D range (Figure 8A). These observations revealed an interaction between L and D, largely driven by D over the lower half of the D range, and by SA as a whole (Figure 8A; black curve indicates constant SA ∝ L × D matching the original morphology). Increasing SA increased both the electrical load on the soma and also the number of active channels (dominated by inhibitory ), resulting in lower firing rates. Of the 225 models analyzed across this region of morphologic space, 47 Area II–like candidate models were identified, shown as colored symbols in the subpanels of Figure 8B.


Neuronal firing sensitivity to morphologic and active membrane parameters.

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

Spontaneous Firing Rate Sensitivity across Constant Density and Constant Numbers Morphologic Spaces(A) Baseline spontaneous firing rate represented as a colormap across CD morphologic space (colorscale 0–25 Hz; top right). Black dot marks the original morphology used for the conductance space searches. Thick black curve indicates all models matching the original SA.(B) Spontaneous firing rate sensitivities to perturbations of active parameters RCa and 								 (top row), and morphologic parameters D + SA / CD and L + D / CD (bottom row) of candidate models across the space. Arrows indicate the principal sensitivity trend to each parameter. In the bottom left of (B), filled circles indicate models for which sensitivity to D + SA / CD was greater than sensitivity to all active parameters except 								. In the model shown as an open square, sensitivity to two or more active parameters was greater than sensitivity to D + SA / CD. In the bottom right of (B), filled circles and open squares likewise compare the sensitivity to L + D / CD and sensitivities to active parameters. Analogous colormaps across CN morphologic space are shown for (C) baseline spontaneous firing rate and (D) spontaneous firing rate sensitivity to parameter perturbations among candidate models. The black curve in (C) indicates all models matching the original axial resistance (see Materials and Methods). In the bottom row of (D), filled circles show models for which sensitivity to either D + SA / CN or L + D / CN was greater than sensitivities to all active parameters except 								 and 								. In models shown as open squares, sensitivity to three or more active parameters was greater than sensitivity to either D + SA / CN or L + D / CN.
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Related In: Results  -  Collection

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getmorefigures.php?uid=PMC2211531&req=5

pcbi-0040011-g008: Spontaneous Firing Rate Sensitivity across Constant Density and Constant Numbers Morphologic Spaces(A) Baseline spontaneous firing rate represented as a colormap across CD morphologic space (colorscale 0–25 Hz; top right). Black dot marks the original morphology used for the conductance space searches. Thick black curve indicates all models matching the original SA.(B) Spontaneous firing rate sensitivities to perturbations of active parameters RCa and (top row), and morphologic parameters D + SA / CD and L + D / CD (bottom row) of candidate models across the space. Arrows indicate the principal sensitivity trend to each parameter. In the bottom left of (B), filled circles indicate models for which sensitivity to D + SA / CD was greater than sensitivity to all active parameters except . In the model shown as an open square, sensitivity to two or more active parameters was greater than sensitivity to D + SA / CD. In the bottom right of (B), filled circles and open squares likewise compare the sensitivity to L + D / CD and sensitivities to active parameters. Analogous colormaps across CN morphologic space are shown for (C) baseline spontaneous firing rate and (D) spontaneous firing rate sensitivity to parameter perturbations among candidate models. The black curve in (C) indicates all models matching the original axial resistance (see Materials and Methods). In the bottom row of (D), filled circles show models for which sensitivity to either D + SA / CN or L + D / CN was greater than sensitivities to all active parameters except and . In models shown as open squares, sensitivity to three or more active parameters was greater than sensitivity to either D + SA / CN or L + D / CN.
Mentions: Figure 8A shows the spontaneous firing rate of models across CD morphologic space. A small, connected set of models did not fire spontaneously (uncolored cells); the others fired regularly at rates up to 25 Hz. Firing rate varied less across this morphologic space than across conductance space because active parameter values in the soma, the site of AP initiation, were held fixed along each dimension of the space. Firing rates varied continuously over the sampled points, and inversely with D. Models with similar firing rates lay in colored bands of vertical stripes over the lower half of the D range, and in approximately hyperbolic shaped bands over the upper half of the D range (Figure 8A). These observations revealed an interaction between L and D, largely driven by D over the lower half of the D range, and by SA as a whole (Figure 8A; black curve indicates constant SA ∝ L × D matching the original morphology). Increasing SA increased both the electrical load on the soma and also the number of active channels (dominated by inhibitory ), resulting in lower firing rates. Of the 225 models analyzed across this region of morphologic space, 47 Area II–like candidate models were identified, shown as colored symbols in the subpanels of Figure 8B.

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