. The action potential of the unmyelinated nerve is metabolically expensive. Using the energetic cost per unit length for the biophysically modeled action potential of the squid giant axon, we analyze this cost and identify one possible optimization. The energetic cost arising from an action potential is divided into three separate components: 1) the depolarization of the rising phase; 2) the hyperpolarization of the falling phase; and 3) the largest component, the overlapping of positive and negative currents, which has no electrical effect. Using both the Hodgkin-Huxley (HH) model and an improved version of the HH model (HHSFL), we investigate the variation of these three components as a function of easily evolvable parameters, axon diameter and ion channel densities. Assuming conduction velocity is well designed for each organism, the energy component associated with the rising phase attains a minimum near the biological values of the diameter and channel densities. This optimization is explained by the membrane capacitance per unit length. The functional capacitance is the sum of the intrinsic membrane capacitance and the gating capacitance associated with the sodium channel, and this capacitance minimizes at nearly the same values of diameter and channel density. Because capacitance is temperature independent and because this result is independent of the assumed velocity, the result generalizes to unmyelinated mammalian axons. That is, channel density is arguably an evolved property that goes hand-in-hand with the evolutionary stability of the sodium channel. I N T R O D U C T I O NIn the nervous system, the action potential is used for long-distance information transmission. Delivery of such information in a timely fashion requires an action potential of sufficient velocity. On the other hand, sufficient velocity has its costs. In what follows, we assume that across species and across the life span of the organism the velocity of any axon is appropriate to its role in information processing.In the neuropil of neocortex, where axons must be unmyelinated if each one is to make several thousand sequential or neighboring synapses, the metabolic costs are surprisingly large. Attwell and Laughlin (2001) estimated that 75% of the adenosine triphosphate (ATP) consumed by neurons in the rat brain is used for communication and computation. Of this, half is used by the unmyelinated axons.This metabolic perspective contrasts with and, as we will see, ultimately complements Hodgkin's conjectured constraint on action potential velocity. Both Hodgkin (1975) and Adrian (1975) proposed that the gating charge movement that inevitably accompanies rapid activation of a voltage-dependent channel leads to an optimal density of fast Na ϩ channels. This optimization occurs because the movement of charge specifically restricted to the transmembrane voltage field contributes, albeit transiently, to membrane capacitance. Because increasing capacitance slows action potential propagation, Hodgkin proposed that the Na ϩ channel dens...

Alcohol-induced alterations of cerebellar function cause motor coordination impairments that are responsible for millions of injuries and deaths worldwide. Cognitive deficits associated with alcoholism are also a consequence of cerebellar dysfunction. The mechanisms responsible for these effects of ethanol are poorly understood. Recent studies have identified neurons in the input layer of the cerebellar cortex as important ethanol targets. In this layer, granule cells receive the majority of sensory inputs to the cerebellum via the mossy fibers. Information flow at these neurons is gated by a specialized pacemaker interneuron known as the Golgi cell, which provides divergent GABAergic input to thousands of granule cells. In vivo electrophysiological experiments have previously demonstrated that acute ethanol exposure abolishes granule cell responsiveness to sensory inputs carried by mossy fibers. Slice electrophysiological studies suggest that ethanol causes this effect by potentiating GABAergic transmission at Golgi cell-to-granule cell synapses via an increase in Golgi cell excitability. Using patch-clamp electrophysiological techniques in cerebellar slices and computer modeling, we demonstrate here that ethanol excites Golgi cells by inhibiting the Na+/K+ ATPase. Voltage-clamp recordings of Na+/K+ ATPase currents indicated that ethanol partially inhibits this pump and this effect could be mimicked by low concentrations of ouabain. Partial inhibition of Na+/K+ ATPase function in a computer model of the Golgi cell reproduced these experimental findings. These results establish a novel mechanism of action of ethanol on neuronal excitability, which likely plays a role in ethanol-induced cerebellar dysfunction and may also contribute to neuronal functional alterations in other brain regions.

Deep cerebellar nucleus (DCN) neurons show pronounced post-hyperpolarization rebound burst behavior, which may contribute significantly to responses to strong inhibitory inputs from cerebellar cortical Purkinje cells. Thus, rebound behavior could importantly shape the output from the cerebellum. We used whole cell recordings in brain slices to characterize DCN rebound properties and their dependence on hyperpolarization duration and depth. We found that DCN rebounds showed distinct fast and prolonged components, with different stimulus dependence and different underlying currents. The initial depolarization leading into rebound spiking was carried by HCN current, and variable expression of this current could lead to a control of rebound latency. The ensuing fast rebound burst was due to T-type calcium current, as previously described. It was highly variable between cells in strength, and could be expressed fully after short periods of hyperpolarization. In contrast, a subsequent prolonged rebound component required longer and deeper periods of hyperpolarization before it was fully established. We found using voltage-clamp and dynamic clamp analyses that a slowly inactivating persistent sodium current fit the conductance underlying this prolonged rebound component resulting in spike rate increases over several seconds. Overall, our results demonstrate that multiphasic DCN rebound properties could be elicited differentially by different levels of Purkinje cell activation, and thus create a rich repertoire of potential rebound dynamics in the cerebellar control of motor timing.

Analysis of the optimal channel density of the squid giant axon using a reparameterized Hodgkin-Huxley model. J Neurophysiol 91: 2541-2550, 2004; 10.1152/jn.00646.2003. A reparameterized HodgkinHuxley-type model is developed that improves the 1952 model's fit to the biological action potential. In addition to altering Na ϩ inactivation and K ϩ activation kinetics, a voltage-dependent gating-current mechanism has been added to the model. The resulting improved model fits the experimental trace nearly exactly over the rising phase, and it has a propagation velocity that is within 3% of the experimentally measured value of 21.2 m/s (at 18.5°C). Having eliminated most inaccuracies associated with the velocity-dependent rising phase of the action potential, the model is used to test Hodgkin's maximum velocity hypothesis, which asserts that channel density has evolved to maximize conduction velocity. In fact the predicted optimal channel density is more than twice as high as the actual squid channel density. When the available capacitance is reduced to approximate more modern serial Na ϩ -channel models, the optimal channel density is 4 times the actual value. We suggest that, although Hodgkin's maximum velocity hypothesis is acceptable as a first approximation, the microscopic optimization perspective of natural selection will not explain the channel density of the squid unless other constraints are taken into account, for example, the metabolic costs of velocity. I N T R O D U C T I O NA theoretical estimation of the channel density of the squid giant axon based on evolutionary arguments was first made by Hodgkin (1975). Hodgkin's velocity optimization perspective seeks to explain how the squid giant axon evolved its present channel density. Before proceeding on a renewed analysis of Hodgkin's ideas, we describe the known inaccuracies of the 1952 squid action potential model, particularly those inaccuracies relevant to a careful examination of the velocity optimization hypothesis. Hodgkin's maximum velocity hypothesisA useful strategy for studying biology is to step into the role of nature, asking what selective changes could produce an organism that is more efficient or more likely to survive. Using a biological model that is sufficiently accurate, one can selectively tune parameters to optimize a specific quantified function of an organism according to a hypothesized design specification. A seminal and apparently successful example in neuroscience that uses this strategy is Barlow's (1952) prediction for the optimal size of ommatidia versus insect eye diameter. Here we reconsider Hodgkin's proposal (1975) concerning action potential velocity and Na ϩ channel density. Hodgkin (1975) proposes that the squid, which uses its giant axon to control escape jetting, has evolved to maximize the action potential's propagation velocity by optimizing the Na ϩ channel density. He points out that, on the one hand, an increased channel density produces greater current per unit length, leading to more rapid depolarization of the...

Neuronal recordings and computer simulations produce ever growing amounts of data, impeding conventional analysis methods from keeping pace. Such large datasets can be automatically analyzed by taking advantage of the well-established relational database paradigm. Raw electrophysiology data can be entered into a database by extracting its interesting characteristics (e.g., firing rate). Compared to storing the raw data directly, this database representation is several orders of magnitude higher efficient in storage space and processing time. Using two large electrophysiology recording and simulation datasets, we demonstrate that the database can be queried, transformed and analyzed. This process is relatively simple and easy to learn because it takes place entirely in Matlab, using our database analysis toolbox, PANDORA. It is capable of acquiring data from common recording and simulation platforms and exchanging data with external database engines and other analysis toolboxes, which make analysis simpler and highly interoperable. PANDORA is available to be freely used and modified because it is open-source (http://software.incf.org/software/pandora/home).