Neuronal Firing Sensitivity to Morphologic and Active Membrane Parameters

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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. Homeostasis is a process that allows a system to maintain a certain level of output over a long time, even though the inputs controlling the output are changing. Recently, studies of neurons and neuronal networks have shown that the “active” parameters that describe the movement of ions across the cell membrane contribute to homeostasis, since these parameters can be combined in different ways to maintain a specific output. There is also evidence that the physical shape (“morphology”) of the neuron may play a role in homeostasis, but this possibility has not been explored in computational models. We have developed a method that uses sensitivity analysis to evaluate how different kinds of parameters, like active and morphologic ones, affect model output. Across a multi-dimensional parameter space, we identified both local and global trends in parameter sensitivities that indicate regions where different parameters, even morphologic ones, contribute strongly to homeostasis. Significantly, the authors used sensitivities to predict which parameters should change, and by how much, to compensate for changes in another parameter to restore normal function. These predictions may prove important to neuronal aging, disease, and trauma research, but the method can be used to analyze any computational model.