Structure and Visualization of High-Dimensional Conductance Spaces

Taylor, Adam L.; Hickey, Timothy J.; Prinz, Astrid A.; Marder, Eve

doi:10.1152/jn.00367.2006

Cited by 97 publications

(122 citation statements)

References 36 publications

(18 reference statements)

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“…Our principal firing rate sensitivity directions were consistent with this finding, and also extended to firing rate gain. The silence, regular spiking, and bursting we observed across connected regions of parameter space have also been reported by others [2,20,52]. In our model, bursting was due to the buildup of Ca 2þ and the activation of I K-Ca , either intrinsically at the soma [2,20,53] or in a weakly coupled dendrite that influenced somatic firing [21].…”

Section: Building Upon Previous Approachessupporting

confidence: 83%

“…As in past studies [2,3,6,20,51], we have identified some global tradeoff mechanisms through trends in the parameter space locations of similarly behaving models, including a correlation between g A and g NaP supported by a recent study [50]. Identification of homeostatic mechanisms is an active field of research, with promising techniques beginning to emerge [6,52].…”

Section: Predicting Homeostatic Parameter Compensations In Real Neuronssupporting

confidence: 54%

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Neuronal Firing Sensitivity to Morphologic and Active Membrane Parameters

Weaver¹,

Wearne²

2005

PLoS Comput Biol

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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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Section: Building Upon Previous Approachessupporting

confidence: 83%

Section: Predicting Homeostatic Parameter Compensations In Real Neuronssupporting

confidence: 54%

Neuronal Firing Sensitivity to Morphologic and Active Membrane Parameters

Weaver¹,

Wearne²

2005

PLoS Comput Biol

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“…1A). This illustrates an important general principle, namely, that similar electrophysiological behavior can arise from widely disparate sets of underlying conductances (4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15). Fig.…”

Section: Multiple Solutions and Failure Of Averagingmentioning

confidence: 77%

Variability, compensation, and modulation in neurons and circuits

Marder

2011

Proc. Natl. Acad. Sci. U.S.A.

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334

362

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I summarize recent computational and experimental work that addresses the inherent variability in the synaptic and intrinsic conductances in normal healthy brains and shows that multiple solutions (sets of parameters) can produce similar circuit performance. I then discuss a number of issues raised by this observation, such as which parameter variations arise from compensatory mechanisms and which reflect insensitivity to those particular parameters. I ask whether networks with different sets of underlying parameters can nonetheless respond reliably to neuromodulation and other global perturbations. At the computational level, I describe a paradigm shift in which it is becoming increasingly common to develop families of models that reflect the variance in the biological data that the models are intended to illuminate rather than single, highly tuned models. On the experimental side, I discuss the inherent limitations of overreliance on mean data and suggest that it is important to look for compensations and correlations among as many system parameters as possible, and between each system parameter and circuit performance. This second paradigm shift will require moving away from measurements of each system component in isolation but should reveal important previously undescribed principles in the organization of complex systems such as brains.circuit dynamics | neuronal variability | neuronal homeostasis | dynamic clamp A ll experimental biologists face a daily conundrum: on the one hand, we know that all individual biological organisms, be they lobsters, cats, or humans, are distinct individuals. On the other hand, we must do experiments on multiple individuals to ensure the reliability of our results. As biologists wishing to understand how the function of a cell, a circuit, or a brain depends on the properties of its constituent processes, we confront two issues: (i) all our data come with associated measurement error (often difficult to assess), and (ii) there is considerable natural variability in the populations we study. Consequently, we conventionally rely on statistics calculated from populations to assure ourselves that our measurements are reliable. Most commonly, we report mean data, with the underlying assumption that these means capture something akin to a "platonic ideal" of the individual neurons or animals whose properties were measured. Although this strategy has been enormously useful over the years, it has many limitations, some of which I discuss below. Multiple Solutions and Failure of AveragingDespite the widespread use of means, computational work has shown unambiguously some of the dangers and confounds that can come from exclusive reliance on mean data (1-3). One example of this comes from a study in which several thousand model neurons were generated by randomly picking the maximal conductances of the five different ionic conductances in the model (2). Fig. 1 shows three examples of single-spike bursters chosen from a population of 164 single-spike bursters generated in this study. Alth...

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“…A large body of both experimental and modeling work to address these questions has led to a number of insights about the function of particular current types, including current types that are involved in several different electrical activity types. For example, fast sodium and delayed rectifier potassium currents are known to be the major currents shaping fast action potentials (Hodgkin and Huxley 1952), hyperpolarization-activated cation currents contribute to a cell's postinhibitory rebound properties (McCormick and Pape 1990) and pacemaking activity (Difrancesco 1981), slowly inactivating potassium currents support cellular shortterm memory (Turrigiano et al 1996) and can extend the dynamic range of action potential firing in response to depolarizing current (Kupper et al 2002), transient potassium currents facilitate slow repetitive action potential firing (Connor and Stevens 1971), and depolarizing leak currents determine neuronal excitability (Cymbalyuk et al 2002). Most such studies about the role of particular channel types in neuronal activity seek to be generally applicable to the channel type in question rather than making fine distinctions regarding channel subtypes or the exact voltage dependencies and dynamical properties of a channel.…”

Section: Introductionmentioning

confidence: 99%

Different Roles of Related Currents in Fast and Slow Spiking of Model Neurons From Two Phyla

Hong

Kazanci²,

Prinz³

2008

Journal of Neurophysiology

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Hong E, Gurel Kazanci F, Prinz AA. Different roles of related currents in fast and slow spiking of model neurons from two phyla. J Neurophysiol 100: 2048 -2061, 2008. First published August 20, 2008 doi:10.1152/jn.90567.2008. Neuronal activity arises from the interplay of membrane and synaptic currents. Although many channel proteins conducting these currents are phylogenetically conserved, channels of the same type in different animals can have different voltage dependencies and dynamics. What does this mean for our ability to derive rules about the role of different types of ion channels in neuronal activity? Can results about the role of a particular channel type in a particular type of neuron be generalized to other neuron types? We compare spiking model neurons in two databases constructed by exploring the maximal conductance spaces of two models. The first is a model of crustacean stomatogastric neurons, and the second is a model of rodent thalamocortical neurons, but both models contain similar types of membrane currents. Spiking neurons in both databases show distinct fast and slow subpopulations, but our analysis reveals that related currents play different roles in fast and slow spiking in the stomatogastric versus thalamocortical neurons. This analysis involved conductance-space visualization and comparison of voltage traces, current traces, and frequency-current relationships from all spiker subpopulations. Our results are consistent with previous work indicating that the role a membrane current plays in shaping a neuron's behavior depends on the voltage dependence and dynamics of that current and may be different in different neuron types depending on the properties of other currents it is interacting with. Conclusions about the function of a type of membrane current based on experiments or simulations in one type of neuron may therefore not generalize to other neuron types.

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Structure and Visualization of High-Dimensional Conductance Spaces

Cited by 97 publications

References 36 publications

Neuronal Firing Sensitivity to Morphologic and Active Membrane Parameters

Neuronal Firing Sensitivity to Morphologic and Active Membrane Parameters

Variability, compensation, and modulation in neurons and circuits

Different Roles of Related Currents in Fast and Slow Spiking of Model Neurons From Two Phyla

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