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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 Firing Rate Gain Across Conductance Space(A) Firing rate gain for models within subspace A, according to the colorscale at top right. Uncolored cells did not fire under any of the injected currents. Gain sometimes varied nonmonotonically with 								; compare models labeled 1, 2, and 3.							(B) Firing rate versus injected current with fitted gain slopes for Models 1, 2, and 3 shown in (A). Models with low 								 had high spontaneous firing rates but intermediate gain (Model 3, yellow triangles); gain increased for intermediate 								 (Model 2, dark red circles), then decreased for high 								 (Model 1, blue squares).							(C) Sensitivity of firing rate gain to active parameters RCa and 								 (top left and right) and constant density morphologic perturbations D + SA / CD and L + D / CD (bottom left and right) according to the colorscale at top left, for candidate models within subspace A. Arrows indicate the principal direction of global sensitivity trends across the space, which were similar for perturbations of active and morphologic parameters. The sign of sensitivity (marked by “+” and “−”) often changed along this principal direction.
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pcbi-0040011-g007: Sensitivity of Firing Rate Gain Across Conductance Space(A) Firing rate gain for models within subspace A, according to the colorscale at top right. Uncolored cells did not fire under any of the injected currents. Gain sometimes varied nonmonotonically with ; compare models labeled 1, 2, and 3. (B) Firing rate versus injected current with fitted gain slopes for Models 1, 2, and 3 shown in (A). Models with low had high spontaneous firing rates but intermediate gain (Model 3, yellow triangles); gain increased for intermediate (Model 2, dark red circles), then decreased for high (Model 1, blue squares). (C) Sensitivity of firing rate gain to active parameters RCa and (top left and right) and constant density morphologic perturbations D + SA / CD and L + D / CD (bottom left and right) according to the colorscale at top left, for candidate models within subspace A. Arrows indicate the principal direction of global sensitivity trends across the space, which were similar for perturbations of active and morphologic parameters. The sign of sensitivity (marked by “+” and “−”) often changed along this principal direction.

Mentions: The baseline firing rate gain of all active dendrite models within subspace A is illustrated as a colormap in Figure 7A. Representative gains, computed as the slopes of firing rate versus injected current, for the three models labeled (1, 2, and 3) in Figure 7A are shown in Figure 7B. Regions of lowest spontaneous firing rate and lowest gain coincided (Figure 7A and 7B, Model 1); the same was generally true for high spontaneous firing rates and gain (Figure 7A and 7B, Model 2; compare Figures 5A and 7A). The only exceptions to these observations were models with high but low (Figure 7A and 7B, Model 3). Baseline firing rates in these models were high and nearly saturated. Since injecting current had little additional effect, these models had intermediate gain values. In a subset of the candidate models, we compared gains computed from injected somatic current against gains computed from dendritic synaptic excitation. The high correlation between these measures (r2 = 0.992, n = 19; see Materials and Methods) and the linearity of each model's firing rate response to injected current (Figure 7B) demonstrated that the gain was a good measure of the firing activity over a range of inputs.


Neuronal firing sensitivity to morphologic and active membrane parameters.

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

Sensitivity of Firing Rate Gain Across Conductance Space(A) Firing rate gain for models within subspace A, according to the colorscale at top right. Uncolored cells did not fire under any of the injected currents. Gain sometimes varied nonmonotonically with 								; compare models labeled 1, 2, and 3.							(B) Firing rate versus injected current with fitted gain slopes for Models 1, 2, and 3 shown in (A). Models with low 								 had high spontaneous firing rates but intermediate gain (Model 3, yellow triangles); gain increased for intermediate 								 (Model 2, dark red circles), then decreased for high 								 (Model 1, blue squares).							(C) Sensitivity of firing rate gain to active parameters RCa and 								 (top left and right) and constant density morphologic perturbations D + SA / CD and L + D / CD (bottom left and right) according to the colorscale at top left, for candidate models within subspace A. Arrows indicate the principal direction of global sensitivity trends across the space, which were similar for perturbations of active and morphologic parameters. The sign of sensitivity (marked by “+” and “−”) often changed along this principal direction.
© Copyright Policy
Related In: Results  -  Collection

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getmorefigures.php?uid=PMC2211531&req=5

pcbi-0040011-g007: Sensitivity of Firing Rate Gain Across Conductance Space(A) Firing rate gain for models within subspace A, according to the colorscale at top right. Uncolored cells did not fire under any of the injected currents. Gain sometimes varied nonmonotonically with ; compare models labeled 1, 2, and 3. (B) Firing rate versus injected current with fitted gain slopes for Models 1, 2, and 3 shown in (A). Models with low had high spontaneous firing rates but intermediate gain (Model 3, yellow triangles); gain increased for intermediate (Model 2, dark red circles), then decreased for high (Model 1, blue squares). (C) Sensitivity of firing rate gain to active parameters RCa and (top left and right) and constant density morphologic perturbations D + SA / CD and L + D / CD (bottom left and right) according to the colorscale at top left, for candidate models within subspace A. Arrows indicate the principal direction of global sensitivity trends across the space, which were similar for perturbations of active and morphologic parameters. The sign of sensitivity (marked by “+” and “−”) often changed along this principal direction.
Mentions: The baseline firing rate gain of all active dendrite models within subspace A is illustrated as a colormap in Figure 7A. Representative gains, computed as the slopes of firing rate versus injected current, for the three models labeled (1, 2, and 3) in Figure 7A are shown in Figure 7B. Regions of lowest spontaneous firing rate and lowest gain coincided (Figure 7A and 7B, Model 1); the same was generally true for high spontaneous firing rates and gain (Figure 7A and 7B, Model 2; compare Figures 5A and 7A). The only exceptions to these observations were models with high but low (Figure 7A and 7B, Model 3). Baseline firing rates in these models were high and nearly saturated. Since injecting current had little additional effect, these models had intermediate gain values. In a subset of the candidate models, we compared gains computed from injected somatic current against gains computed from dendritic synaptic excitation. The high correlation between these measures (r2 = 0.992, n = 19; see Materials and Methods) and the linearity of each model's firing rate response to injected current (Figure 7B) demonstrated that the gain was a good measure of the firing activity over a range of inputs.

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