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

Quantifying Model Output(A) Computing firing rate gain. Black circles and solid line show firing rates and the associated fit for a model with a gain of 331.1 Hz/nA. A model with a gain of 640.0 Hz/nA is also shown (blue open triangles and dashed line).(B) Typical match of optimized model (red) against target data (black dashed line), for 0 and 100 pA injected current (top and bottom, respectively). Models were constrained to match the general AP shape, and approximate firing rates, of the synthetic target data.
© Copyright Policy
Related In: Results  -  Collection


getmorefigures.php?uid=PMC2211531&req=5

pcbi-0040011-g002: Quantifying Model Output(A) Computing firing rate gain. Black circles and solid line show firing rates and the associated fit for a model with a gain of 331.1 Hz/nA. A model with a gain of 640.0 Hz/nA is also shown (blue open triangles and dashed line).(B) Typical match of optimized model (red) against target data (black dashed line), for 0 and 100 pA injected current (top and bottom, respectively). Models were constrained to match the general AP shape, and approximate firing rates, of the synthetic target data.

Mentions: Model output was quantified by two variables: spontaneous firing rate, and firing rate gain (Materials and Methods). Firing rate gain, a best-fit line to the firing rate versus current curve, provided a general measure of neuronal excitability: models with low gain were less excitable than those with high gain (compare solid black and dashed blue lines in Figure 2A). Normalized sensitivity coefficients were calculated for each model, estimating the change in each output measure to a small perturbation in each parameter (Equation 7, Materials and Methods). We explored sensitivity landscapes by evaluating normalized sensitivity coefficients across the parameter space. To demonstrate the method, we describe trends in the sensitivity landscapes of the two output variables to active and morphologic parameters for both the optimized and candidate model types. We describe trends over two generalized parameter spaces: one defined by active and passive parameters (“conductance space”), the other defined by morphologic parameters (“morphologic space”).


Neuronal firing sensitivity to morphologic and active membrane parameters.

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

Quantifying Model Output(A) Computing firing rate gain. Black circles and solid line show firing rates and the associated fit for a model with a gain of 331.1 Hz/nA. A model with a gain of 640.0 Hz/nA is also shown (blue open triangles and dashed line).(B) Typical match of optimized model (red) against target data (black dashed line), for 0 and 100 pA injected current (top and bottom, respectively). Models were constrained to match the general AP shape, and approximate firing rates, of the synthetic target data.
© Copyright Policy
Related In: Results  -  Collection

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

pcbi-0040011-g002: Quantifying Model Output(A) Computing firing rate gain. Black circles and solid line show firing rates and the associated fit for a model with a gain of 331.1 Hz/nA. A model with a gain of 640.0 Hz/nA is also shown (blue open triangles and dashed line).(B) Typical match of optimized model (red) against target data (black dashed line), for 0 and 100 pA injected current (top and bottom, respectively). Models were constrained to match the general AP shape, and approximate firing rates, of the synthetic target data.
Mentions: Model output was quantified by two variables: spontaneous firing rate, and firing rate gain (Materials and Methods). Firing rate gain, a best-fit line to the firing rate versus current curve, provided a general measure of neuronal excitability: models with low gain were less excitable than those with high gain (compare solid black and dashed blue lines in Figure 2A). Normalized sensitivity coefficients were calculated for each model, estimating the change in each output measure to a small perturbation in each parameter (Equation 7, Materials and Methods). We explored sensitivity landscapes by evaluating normalized sensitivity coefficients across the parameter space. To demonstrate the method, we describe trends in the sensitivity landscapes of the two output variables to active and morphologic parameters for both the optimized and candidate model types. We describe trends over two generalized parameter spaces: one defined by active and passive parameters (“conductance space”), the other defined by morphologic parameters (“morphologic space”).

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