Limits...
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.

Show MeSH

Related in: MedlinePlus

Constructing the Morphologic Model(A) Morphology of an Area II neuron traced in 3-D. The reduced morphology in (B) conserved the surface area of the soma (shown in green) and the length and surface area of the dendritic tree. The axon (truncated thick process extending from the left of the soma) was omitted.(B) Channel distributions in active and passive dendrite models. Red compartments included active channels; gray compartments included only passive ones.(C) Morphologic perturbations. Top left: unperturbed model morphology. Top right, L + SA: dendritic length L and surface area SA perturbed with dendritic diameter D held constant. Bottom left, D + SA: D and SA perturbed with L held constant. Bottom right, L + D: L increased and D decreased such that SA remained constant.(D) When dendritic morphology of the active dendrite was perturbed (e.g., L + SA), either the original dendritic channel density of each ion species was conserved (constant density; middle) or the number of dendritic channels was conserved (constant numbers; bottom).(E) Top, spatial distribution of active channels in the active dendrite. Dendritic channel density (as a proportion of its somatic density) either increased (						, thick dashed line), decreased (						, solid black line; 						, 						, 						, red solid line), or remained constant (						, thin dashed line). See Materials and Methods. Bottom, decremental AP backpropagation as a function of distance from the soma, for the conductance distributions shown at top. Somatic AP shown in red.
© Copyright Policy
Related In: Results  -  Collection


getmorefigures.php?uid=PMC2211531&req=5

pcbi-0040011-g001: Constructing the Morphologic Model(A) Morphology of an Area II neuron traced in 3-D. The reduced morphology in (B) conserved the surface area of the soma (shown in green) and the length and surface area of the dendritic tree. The axon (truncated thick process extending from the left of the soma) was omitted.(B) Channel distributions in active and passive dendrite models. Red compartments included active channels; gray compartments included only passive ones.(C) Morphologic perturbations. Top left: unperturbed model morphology. Top right, L + SA: dendritic length L and surface area SA perturbed with dendritic diameter D held constant. Bottom left, D + SA: D and SA perturbed with L held constant. Bottom right, L + D: L increased and D decreased such that SA remained constant.(D) When dendritic morphology of the active dendrite was perturbed (e.g., L + SA), either the original dendritic channel density of each ion species was conserved (constant density; middle) or the number of dendritic channels was conserved (constant numbers; bottom).(E) Top, spatial distribution of active channels in the active dendrite. Dendritic channel density (as a proportion of its somatic density) either increased ( , thick dashed line), decreased ( , solid black line; , , , red solid line), or remained constant ( , thin dashed line). See Materials and Methods. Bottom, decremental AP backpropagation as a function of distance from the soma, for the conductance distributions shown at top. Somatic AP shown in red.

Mentions: A reduced model neuron was constructed to conserve the maximal dendritic length and surface area of an Area II neuron electrophysiologically characterized in vivo [30] and reconstructed in three dimensions (3-D; Figure 1A; see Materials and Methods). The model included seven conductances, fired regular action potentials (APs) without external excitation, and exhibited a biphasic afterhyperpolarization (AHP) following the AP. The model morphology, a cylindrical soma with a constant diameter dendrite (14 compartments overall; Figure 1B), was parameterized by length (L), diameter (D), and total surface area (SA); somatic dimensions were held constant.


Neuronal firing sensitivity to morphologic and active membrane parameters.

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

Constructing the Morphologic Model(A) Morphology of an Area II neuron traced in 3-D. The reduced morphology in (B) conserved the surface area of the soma (shown in green) and the length and surface area of the dendritic tree. The axon (truncated thick process extending from the left of the soma) was omitted.(B) Channel distributions in active and passive dendrite models. Red compartments included active channels; gray compartments included only passive ones.(C) Morphologic perturbations. Top left: unperturbed model morphology. Top right, L + SA: dendritic length L and surface area SA perturbed with dendritic diameter D held constant. Bottom left, D + SA: D and SA perturbed with L held constant. Bottom right, L + D: L increased and D decreased such that SA remained constant.(D) When dendritic morphology of the active dendrite was perturbed (e.g., L + SA), either the original dendritic channel density of each ion species was conserved (constant density; middle) or the number of dendritic channels was conserved (constant numbers; bottom).(E) Top, spatial distribution of active channels in the active dendrite. Dendritic channel density (as a proportion of its somatic density) either increased (						, thick dashed line), decreased (						, solid black line; 						, 						, 						, red solid line), or remained constant (						, thin dashed line). See Materials and Methods. Bottom, decremental AP backpropagation as a function of distance from the soma, for the conductance distributions shown at top. Somatic AP shown in red.
© Copyright Policy
Related In: Results  -  Collection

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

pcbi-0040011-g001: Constructing the Morphologic Model(A) Morphology of an Area II neuron traced in 3-D. The reduced morphology in (B) conserved the surface area of the soma (shown in green) and the length and surface area of the dendritic tree. The axon (truncated thick process extending from the left of the soma) was omitted.(B) Channel distributions in active and passive dendrite models. Red compartments included active channels; gray compartments included only passive ones.(C) Morphologic perturbations. Top left: unperturbed model morphology. Top right, L + SA: dendritic length L and surface area SA perturbed with dendritic diameter D held constant. Bottom left, D + SA: D and SA perturbed with L held constant. Bottom right, L + D: L increased and D decreased such that SA remained constant.(D) When dendritic morphology of the active dendrite was perturbed (e.g., L + SA), either the original dendritic channel density of each ion species was conserved (constant density; middle) or the number of dendritic channels was conserved (constant numbers; bottom).(E) Top, spatial distribution of active channels in the active dendrite. Dendritic channel density (as a proportion of its somatic density) either increased ( , thick dashed line), decreased ( , solid black line; , , , red solid line), or remained constant ( , thin dashed line). See Materials and Methods. Bottom, decremental AP backpropagation as a function of distance from the soma, for the conductance distributions shown at top. Somatic AP shown in red.
Mentions: A reduced model neuron was constructed to conserve the maximal dendritic length and surface area of an Area II neuron electrophysiologically characterized in vivo [30] and reconstructed in three dimensions (3-D; Figure 1A; see Materials and Methods). The model included seven conductances, fired regular action potentials (APs) without external excitation, and exhibited a biphasic afterhyperpolarization (AHP) following the AP. The model morphology, a cylindrical soma with a constant diameter dendrite (14 compartments overall; Figure 1B), was parameterized by length (L), diameter (D), and total surface area (SA); somatic dimensions were held constant.

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