Excitability constraints on voltage-gated sodium channels

Changes of the biophysical properties of voltage-gated Na+ currents during maturation of the sodium-taste cells in rat fungiform papillae

Taste cells are a heterogeneous population of sensory receptors that undergo continuous turnover. Different chemo-sensitive cell lines rely on action potentials to release the neurotransmitter onto nerve endings. The electrical excitability is due to the presence of a tetrodotoxin-sensitive, voltage-gated sodium current (I_Na ) similar to that found in neurons. Since the biophysical properties of neuronal I_Na change during development, we wondered whether the same also occurred in taste cells. Here, we used the patch-clamp recording technique to study I_Na in salt-sensing cells (sodium cells) of rat fungiform papillae. We identified these cells by exploiting the known blocking effect of amiloride on ENaC, the sodium (salt) receptor. Based on the amplitude of I_Na , which is known to increase during development, we subdivided sodium cells into two groups: cells with small sodium current (SSC cells; I_Na  < 1 nA) and cells with large sodium current (LSC cells; I_Na  > 1 nA). We found that: the voltage dependence of activation and inactivation significantly differed between these subsets; a slowly inactivating sodium current was more prominent in LSC cells; membrane capacitance in SSC cells was larger than in LSC cells. mRNA expression analysis of the α-subunits of voltage-gated sodium channels in fungiform taste buds supported the functional data. Lucifer Yellow labelling of recorded cells revealed that our electrophysiological criterion for distinguishing two broad groups of taste cells was in good agreement with morphological observations for cell maturity. Thus, all these findings are consistent with developmental changes in the voltage-dependent properties of sodium-taste cells. KEY POINTS: Taste cells are sensory receptors that undergo continuous turnover while they detect food chemicals and communicate with afferent nerve fibres. The voltage-gated sodium current (I_Na ) is a key ion current for generating action potentials in fully differentiated and chemo-sensitive taste cells, which use electrical signalling to release neurotransmitters. Here we show that, during the maturation of rat taste cells involved in salt detection (sodium cells), the biophysical properties of I_Na , such as voltage dependence of activation and inactivation, change significantly. Our results help reveal how taste cells gain electrical excitability during turnover, a property critical to their operation as chemical detectors that relay sensory information to nerve fibres.

Electrical match between initial segment and somatodendritic compartment for action potential backpropagation in retinal ganglion cells

The action potential of most vertebrate neurons initiates in the axon initial segment (AIS) and is then transmitted to the soma where it is regenerated by somatodendritic sodium channels. For successful transmission, the AIS must produce a strong axial current, so as to depolarize the soma to the threshold for somatic regeneration. Theoretically, this axial current depends on AIS geometry and Na⁺ conductance density. We measured the axial current of mouse retinal ganglion cells using whole cell recordings with post hoc AIS labeling. We found that this current is large, implying high Na⁺ conductance density, and carries a charge that covaries with capacitance so as to depolarize the soma by ∼30 mV. Additionally, we observed that the axial current attenuates strongly with depolarization, consistent with sodium channel inactivation, but temporally broadens so as to preserve the transmitted charge. Thus, the AIS appears to be organized so as to reliably backpropagate the axonal action potential.NEW & NOTEWORTHY We measured the axial current produced at spike initiation by the axon initial segment of mouse retinal ganglion cells. We found that it is a large current, requiring high sodium channel conductance density, which covaries with cell capacitance so as to ensure a ∼30 mV depolarization. During sustained depolarization the current attenuated, but it broadened to preserve somatic depolarization. Thus, properties of the initial segment are adjusted to ensure backpropagation of the axonal action potential.

Theoretical relation between axon initial segment geometry and excitability

In most vertebrate neurons, action potentials are triggered at the distal end of the axon initial segment (AIS). Both position and length of the AIS vary across and within neuron types, with activity, development and pathology. What is the impact of AIS geometry on excitability? Direct empirical assessment has proven difficult because of the many potential confounding factors. Here, we carried a principled theoretical analysis to answer this question. We provide a simple formula relating AIS geometry and sodium conductance density to the somatic voltage threshold. A distal shift of the AIS normally produces a (modest) increase in excitability, but we explain how this pattern can reverse if a hyperpolarizing current is present at the AIS, due to resistive coupling with the soma. This work provides a theoretical tool to assess the significance of structural AIS plasticity for electrical function.

Spike-Conducting Integrate-and-Fire Model

Modeling is a useful tool for investigating various biophysical characteristics of neurons. Recent simulation studies of propagating action potentials (spike conduction) along axons include the investigation of neuronal activity evoked by electrical stimulation from implantable prosthetic devices. In contrast to point-neuron simulations, where a large variety of models are readily available, Hodgkin–Huxley-type conductance-based models have been almost the only option for simulating axonal spike conduction, as simpler models cannot faithfully replicate the waveforms of propagating spikes. Since the amount of available physiological data, especially in humans, is usually limited, calibration, and justification of the large number of parameters of a complex model is generally difficult. In addition, not all simulation studies of axons require detailed descriptions of nonlinear ionic dynamics. In this study, we construct a simple model of spike generation and conduction based on the exponential integrate-and-fire model, which can simulate the rapid growth of the membrane potential at spike initiation. In terms of the number of parameters and equations, this model is much more compact than conventional models, but can still reliably simulate spike conduction along myelinated and unmyelinated axons that are stimulated intracellularly or extracellularly. Our simulations of auditory nerve fibers with this new model suggest that, because of the difference in intrinsic membrane properties, the axonal spike conduction of high-frequency nerve fibers is faster than that of low-frequency fibers. The simple model developed in this study can serve as a computationally efficient alternative to more complex models for future studies, including simulations of neuroprosthetic devices.

Human Cortical Pyramidal Neurons: From Spines to Spikes via Models

We present detailed models of pyramidal cells from human neocortex, including models on their excitatory synapses, dendritic spines, dendritic NMDA- and somatic/axonal Na⁺ spikes that provided new insights into signal processing and computational capabilities of these principal cells. Six human layer 2 and layer 3 pyramidal cells (HL2/L3 PCs) were modeled, integrating detailed anatomical and physiological data from both fresh and postmortem tissues from human temporal cortex. The models predicted particularly large AMPA- and NMDA-conductances per synaptic contact (0.88 and 1.31 nS, respectively) and a steep dependence of the NMDA-conductance on voltage. These estimates were based on intracellular recordings from synaptically-connected HL2/L3 pairs, combined with extra-cellular current injections and use of synaptic blockers, and the assumption of five contacts per synaptic connection. A large dataset of high-resolution reconstructed HL2/L3 dendritic spines provided estimates for the EPSPs at the spine head (12.7 ± 4.6 mV), spine base (9.7 ± 5.0 mV), and soma (0.3 ± 0.1 mV), and for the spine neck resistance (50–80 MΩ). Matching the shape and firing pattern of experimental somatic Na⁺-spikes provided estimates for the density of the somatic/axonal excitable membrane ion channels, predicting that 134 ± 28 simultaneously activated HL2/L3-HL2/L3 synapses are required for generating (with 50% probability) a somatic Na⁺ spike. Dendritic NMDA spikes were triggered in the model when 20 ± 10 excitatory spinous synapses were simultaneously activated on individual dendritic branches. The particularly large number of basal dendrites in HL2/L3 PCs and the distinctive cable elongation of their terminals imply that ~25 NMDA-spikes could be generated independently and simultaneously in these cells, as compared to ~14 in L2/3 PCs from the rat somatosensory cortex. These multi-sites non-linear signals, together with the large (~30,000) excitatory synapses/cell, equip human L2/L3 PCs with enhanced computational capabilities. Our study provides the most comprehensive model of any human neuron to-date demonstrating the biophysical and computational distinctiveness of human cortical neurons.

Gain Modulation of Cholinergic Neurons in the Medial Septum-Diagonal Band of Broca Through Hyperpolarization

Hippocampal network oscillations are important for learning and memory. Theta rhythms are involved in attention, navigation, and memory encoding, whereas sharp wave-ripple complexes are involved in memory consolidation. Cholinergic neurons in the medial septum-diagonal band of Broca (MS-DB) influence both types of hippocampal oscillations, promoting theta rhythms and suppressing sharp wave-ripples. They also receive frequency-dependent hyperpolarizing feedback from hippocamposeptal connections, potentially affecting their role as neuromodulators in the septohippocampal circuit. However, little is known about how the integration properties of cholinergic MS-DB neurons change with hyperpolarization. By potentially altering firing behavior in cholinergic neurons, hyperpolarizing feedback from the hippocampal neurons may, in turn, change hippocampal network activity. To study changes in membrane integration properties in cholinergic neurons in response to hyperpolarizing inputs, we used whole-cell patch-clamp recordings targeting genetically labeled, choline acetyltransferase-positive neurons in mouse brain slices. Hyperpolarization of cholinergic MS-DB neurons resulted in a long-lasting decrease in spike firing rate and input-output gain. Additionally, voltage-clamp measures implicated a slowly inactivating, 4-AP-insensitive, outward K⁺ conductance. Using a conductance-based model of cholinergic MS-DB neurons, we show that the ability of this conductance to modulate firing rate and gain depends on the expression of an experimentally verified shallow intrinsic spike frequency-voltage relationship. Together, these findings point to a means through which negative feedback from hippocampal neurons can influence the role of cholinergic MS-DB neurons. © 2016 Wiley Periodicals, Inc.

What is the most realistic single-compartment model of spike initiation?

A large variety of neuron models are used in theoretical and computational neuroscience, and among these, single-compartment models are a popular kind. These models do not explicitly include the dendrites or the axon, and range from the Hodgkin-Huxley (HH) model to various flavors of integrate-and-fire (IF) models. The main classes of models differ in the way spikes are initiated. Which one is the most realistic? Starting with some general epistemological considerations, I show that the notion of realism comes in two dimensions: empirical content (the sort of predictions that a model can produce) and empirical accuracy (whether these predictions are correct). I then examine the realism of the main classes of single-compartment models along these two dimensions, in light of recent experimental evidence.

Uncertainty quantification of fast sodium current steady-state inactivation for multi-scale models of cardiac electrophysiology

Perhaps the most mature area of multi-scale systems biology is the modelling of the heart. Current models are grounded in over fifty years of research in the development of biophysically detailed models of the electrophysiology (EP) of cardiac cells, but one aspect which is inadequately addressed is the incorporation of uncertainty and physiological variability. Uncertainty quantification (UQ) is the identification and characterisation of the uncertainty in model parameters derived from experimental data, and the computation of the resultant uncertainty in model outputs. It is a necessary tool for establishing the credibility of computational models, and will likely be expected of EP models for future safety-critical clinical applications. The focus of this paper is formal UQ of one major sub-component of cardiac EP models, the steady-state inactivation of the fast sodium current, INa. To better capture average behaviour and quantify variability across cells, we have applied for the first time an 'individual-based' statistical methodology to assess voltage clamp data. Advantages of this approach over a more traditional 'population-averaged' approach are highlighted. The method was used to characterise variability amongst cells isolated from canine epi and endocardium, and this variability was then 'propagated forward' through a canine model to determine the resultant uncertainty in model predictions at different scales, such as of upstroke velocity and spiral wave dynamics. Statistically significant differences between epi and endocardial cells (greater half-inactivation and less steep slope of steady state inactivation curve for endo) was observed, and the forward propagation revealed a lack of robustness of the model to underlying variability, but also surprising robustness to variability at the tissue scale. Overall, the methodology can be used to: (i) better analyse voltage clamp data; (ii) characterise underlying population variability; (iii) investigate consequences of variability; and (iv) improve the ability to validate a model. To our knowledge this article is the first to quantify population variability in membrane dynamics in this manner, and the first to perform formal UQ for a component of a cardiac model. The approach is likely to find much wider applicability across systems biology as current application domains reach greater levels of maturity.

Spike-threshold adaptation predicted by membrane potential dynamics in vivo

Neurons encode information in sequences of spikes, which are triggered when their membrane potential crosses a threshold. In vivo, the spiking threshold displays large variability suggesting that threshold dynamics have a profound influence on how the combined input of a neuron is encoded in the spiking. Threshold variability could be explained by adaptation to the membrane potential. However, it could also be the case that most threshold variability reflects noise and processes other than threshold adaptation. Here, we investigated threshold variation in auditory neurons responses recorded in vivo in barn owls. We found that spike threshold is quantitatively predicted by a model in which the threshold adapts, tracking the membrane potential at a short timescale. As a result, in these neurons, slow voltage fluctuations do not contribute to spiking because they are filtered by threshold adaptation. More importantly, these neurons can only respond to input spikes arriving together on a millisecond timescale. These results demonstrate that fast adaptation to the membrane potential captures spike threshold variability in vivo.

Neurons spike when their membrane potential exceeds a threshold value, but this value has been shown to be variable in the same neuron recorded in vivo. This variability could reflect noise, or deterministic processes that make the threshold vary with the membrane potential. The second alternative would have important functional consequences. Here, we show that threshold variability is a genuine feature of neurons, which reflects adaptation to the membrane potential at a short timescale, with little contribution from noise. This demonstrates that a deterministic model can predict spikes based only on the membrane potential.

Sharpness of spike initiation in neurons explained by compartmentalization

In cortical neurons, spikes are initiated in the axon initial segment. Seen at the soma, they appear surprisingly sharp. A standard explanation is that the current coming from the axon becomes sharp as the spike is actively backpropagated to the soma. However, sharp initiation of spikes is also seen in the input–output properties of neurons, and not only in the somatic shape of spikes; for example, cortical neurons can transmit high frequency signals. An alternative hypothesis is that Na channels cooperate, but it is not currently supported by direct experimental evidence. I propose a simple explanation based on the compartmentalization of spike initiation. When Na channels are placed in the axon, the soma acts as a current sink for the Na current. I show that there is a critical distance to the soma above which an instability occurs, so that Na channels open abruptly rather than gradually as a function of somatic voltage.

Spike initiation determines how the combined inputs to a neuron are converted to an output. Since the pioneering work of Hodgkin and Huxley, it is known that spikes are generated by the opening of sodium channels with depolarization. According to this standard theory, these channels should open gradually when the membrane potential increases, but spikes measured at the soma appear to suddenly rise from rest. This apparent contradiction has triggered a controversy about the origin of spike “sharpness.” This study shows with biophysical modelling that if sodium channels are placed in the axon rather than in the soma, they open all at once when the somatic membrane potential exceeds a critical value. This work explains the sharpness of spike initiation and provides another demonstration that morphology plays a critical role in neural function.

Spiking models for level-invariant encoding

Levels of ecological sounds vary over several orders of magnitude, but the firing rate and membrane potential of a neuron are much more limited in range. In binaural neurons of the barn owl, tuning to interaural delays is independent of level differences. Yet a monaural neuron with a fixed threshold should fire earlier in response to louder sounds, which would disrupt the tuning of these neurons. How could spike timing be independent of input level? Here I derive theoretical conditions for a spiking model to be insensitive to input level. The key property is a dynamic change in spike threshold. I then show how level invariance can be physiologically implemented, with specific ionic channel properties. It appears that these ingredients are indeed present in monaural neurons of the sound localization pathway of birds and mammals.

Ion channels and schizophrenia: a gene set-based analytic approach to GWAS data for biological hypothesis testing

Schizophrenia is a complex genetic disorder. Gene set-based analytic (GSA) methods have been widely applied for exploratory analyses of large, high-throughput datasets, but less commonly employed for biological hypothesis testing. Our primary hypothesis is that variation in ion channel genes contribute to the genetic susceptibility to schizophrenia. We applied Exploratory Visual Analysis (EVA), one GSA application, to analyze European-American (EA) and African-American (AA) schizophrenia genome-wide association study datasets for statistical enrichment of ion channel gene sets, comparing GSA results derived under three SNP-to-gene mapping strategies: (1) GENIC; (2) 500-Kb; (3) 2.5-Mb and three complimentary SNP-to-gene statistical reduction methods: (1) minimum p value (pMIN); (2) a novel method, proportion of SNPs per Gene with p values below a pre-defined α-threshold (PROP); and (3) the truncated product method (TPM). In the EA analyses, ion channel gene set(s) were enriched under all mapping and statistical approaches. In the AA analysis, ion channel gene set(s) were significantly enriched under pMIN for all mapping strategies and under PROP for broader mapping strategies. Less extensive enrichment in the AA sample may reflect true ethnic differences in susceptibility, sampling or case ascertainment differences, or higher dimensionality relative to sample size of the AA data. More consistent findings under broader mapping strategies may reflect enhanced power due to increased SNP inclusion, enhanced capture of effects over extended haplotypes or significant contributions from regulatory regions. While extensive pMIN findings may reflect gene size bias, the extent and significance of PROP and TPM findings suggest that common variation at ion channel genes may capture some of the heritability of schizophrenia.

Impact of fast sodium channel inactivation on spike threshold dynamics and synaptic integration

Neurons spike when their membrane potential exceeds a threshold value. In central neurons, the spike threshold is not constant but depends on the stimulation. Thus, input-output properties of neurons depend both on the effect of presynaptic spikes on the membrane potential and on the dynamics of the spike threshold. Among the possible mechanisms that may modulate the threshold, one strong candidate is Na channel inactivation, because it specifically impacts spike initiation without affecting the membrane potential. We collected voltage-clamp data from the literature and we found, based on a theoretical criterion, that the properties of Na inactivation could indeed cause substantial threshold variability by itself. By analyzing simple neuron models with fast Na inactivation (one channel subtype), we found that the spike threshold is correlated with the mean membrane potential and negatively correlated with the preceding depolarization slope, consistent with experiments. We then analyzed the impact of threshold dynamics on synaptic integration. The difference between the postsynaptic potential (PSP) and the dynamic threshold in response to a presynaptic spike defines an effective PSP. When the neuron is sufficiently depolarized, this effective PSP is briefer than the PSP. This mechanism regulates the temporal window of synaptic integration in an adaptive way. Finally, we discuss the role of other potential mechanisms. Distal spike initiation, channel noise and Na activation dynamics cannot account for the observed negative slope-threshold relationship, while adaptive conductances (e.g. K+) and Na inactivation can. We conclude that Na inactivation is a metabolically efficient mechanism to control the temporal resolution of synaptic integration.

Neurons spike when their combined inputs exceed a threshold value, but recent experimental findings have shown that this value also depends on the inputs. Thus, to understand how neurons respond to input spikes, it is important to know how inputs modify the spike threshold. Spikes are generated by sodium channels, which inactivate when the neuron is depolarized, raising the threshold for spike initiation. We found that inactivation properties of sodium channels could indeed cause substantial threshold variability in central neurons. We then analyzed in models the implications of this form of threshold modulation on neuronal function. We found that this mechanism makes neurons more sensitive to coincident spikes and provides them with an energetically efficient form of gain control.

A general mathematical model of transduction events in mechano-sensory stretch receptors

Crayfish (Astacus astacus) muscle stretch receptors show strong homology to mammalian muscle spindles and bipolar neurons in D. melanogaster. All are typical, non-ciliated, stretch-sensitive, afferent neurons. Such receptors are observed in many species and perform an important sensory role. However, they are poorly characterised. A previous study reported a bio-mechanical and behavioural model of A. astacus stretch receptors, which used the principles of elasticity and tension in a spring to describe the adaptation of a mechano-sensory ending. This model described the changing mechano-sensory currents in the receptor when subjected to a stretch protocol. Here, we re-implement and extend this model. Notably, we introduce additional descriptions of voltage-gated channels that are suggested to contribute to stretch receptor mechano-transduction. Our model presents a more complete picture of the initiation of the mechano-receptor potential in response to a stretching stimulus. The inclusion of voltage-dependent sodium and potassium currents in addition to the initial mechano-sensitive sodium current allowed the model to account for most of the initial stretch response of the receptor. This preliminary model has potential for extension to describe fully the behaviour of non-ciliated mechano-sensors across species and predict the molecular mediators of mechano-transduction.

Expansion of voltage-dependent Na+ channel gene family in early tetrapods coincided with the emergence of terrestriality and increased brain complexity

Mammals have ten voltage-dependent sodium (Nav) channel genes. Nav channels are expressed in different cell types with different subcellular distributions and are critical for many aspects of neuronal processing. The last common ancestor of teleosts and tetrapods had four Nav channel genes, presumably on four different chromosomes. In the lineage leading to mammals, a series of tandem duplications on two of these chromosomes more than doubled the number of Nav channel genes. It is unknown when these duplications occurred and whether they occurred against a backdrop of duplication of flanking genes on their chromosomes or as an expansion of ion channel genes in general. We estimated key dates of the Nav channel gene family expansion by phylogenetic analysis using teleost, elasmobranch, lungfish, amphibian, avian, lizard, and mammalian Nav channel sequences, as well as chromosomal synteny for tetrapod genes. We tested, and exclude, the null hypothesis that Nav channel genes reside in regions of chromosomes prone to duplication by demonstrating the lack of duplication or duplicate retention of surrounding genes. We also find no comparable expansion in other voltage-dependent ion channel gene families of tetrapods following the teleost-tetrapod divergence. We posit a specific expansion of the Nav channel gene family in the Devonian and Carboniferous periods when tetrapods evolved, diversified, and invaded the terrestrial habitat. During this time, the amniote forebrain evolved greater anatomical complexity and novel tactile sensory receptors appeared. The duplication of Nav channel genes allowed for greater regional specialization in Nav channel expression, variation in subcellular localization, and enhanced processing of somatosensory input.

A threshold equation for action potential initiation

In central neurons, the threshold for spike initiation can depend on the stimulus and varies between cells and between recording sites in a given cell, but it is unclear what mechanisms underlie this variability. Properties of ionic channels are likely to play a role in threshold modulation. We examined in models the influence of Na channel activation, inactivation, slow voltage-gated channels and synaptic conductances on spike threshold. We propose a threshold equation which quantifies the contribution of all these mechanisms. It provides an instantaneous time-varying value of the threshold, which applies to neurons with fluctuating inputs. We deduce a differential equation for the threshold, similar to the equations of gating variables in the Hodgkin-Huxley formalism, which describes how the spike threshold varies with the membrane potential, depending on channel properties. We find that spike threshold depends logarithmically on Na channel density, and that Na channel inactivation and K channels can dynamically modulate it in an adaptive way: the threshold increases with membrane potential and after every action potential. Our equation was validated with simulations of a previously published multicompartemental model of spike initiation. Finally, we observed that threshold variability in models depends crucially on the shape of the Na activation function near spike initiation (about −55 mV), while its parameters are adjusted near half-activation voltage (about −30 mV), which might explain why many models exhibit little threshold variability, contrary to experimental observations. We conclude that ionic channels can account for large variations in spike threshold.

Neurons communicate primarily with stereotypical electrical impulses, action potentials, which are fired when a threshold level of excitation is reached. This threshold varies between cells and over time as a function of previous stimulations, which has major functional implications on the integrative properties of neurons. Ionic channels are thought to play a central role in this modulation but the precise relationship between their properties and the threshold is unclear. We examined this relationship in biophysical models and derived a formula which quantifies the contribution of various mechanisms. The originality of our approach is that it provides an instantaneous time-varying value for the threshold, which applies to the highly fluctuating regimes characterizing neurons in vivo. In particular, two known ionic mechanisms were found to make the threshold adapt to the membrane potential, thus providing the cell with a form of gain control.

Action potential energy efficiency varies among neuron types in vertebrates and invertebrates

The initiation and propagation of action potentials (APs) places high demands on the energetic resources of neural tissue. Each AP forces ATP-driven ion pumps to work harder to restore the ionic concentration gradients, thus consuming more energy. Here, we ask whether the ionic currents underlying the AP can be predicted theoretically from the principle of minimum energy consumption. A long-held supposition that APs are energetically wasteful, based on theoretical analysis of the squid giant axon AP, has recently been overturned by studies that measured the currents contributing to the AP in several mammalian neurons. In the single compartment models studied here, AP energy consumption varies greatly among vertebrate and invertebrate neurons, with several mammalian neuron models using close to the capacitive minimum of energy needed. Strikingly, energy consumption can increase by more than ten-fold simply by changing the overlap of the Na(+) and K(+) currents during the AP without changing the APs shape. As a consequence, the height and width of the AP are poor predictors of energy consumption. In the Hodgkin-Huxley model of the squid axon, optimizing the kinetics or number of Na(+) and K(+) channels can whittle down the number of ATP molecules needed for each AP by a factor of four. In contrast to the squid AP, the temporal profile of the currents underlying APs of some mammalian neurons are nearly perfectly matched to the optimized properties of ionic conductances so as to minimize the ATP cost.

Structural and regulatory evolution of cellular electrophysiological systems

Cellular electrophysiological systems, like developmental systems, appear to evolve primarily by means of regulatory evolution. It is suggested that electrophysiological systems share two key features with developmental systems that account for this dependence on regulatory evolution. For both systems, structural evolution has the potential to create significant problems of pleiotropy and both systems are predominantly computational in nature. It is concluded that the relative balance of physical and computational tasks that a biological system has to perform, combined with the probability that these tasks may have to change significantly during the course of evolution, will be major factors in determining the relative mix of regulatory and structural evolution that is observed for a given system. Physiological systems that directly interface with the environment will almost always perform some low-level physical task. In the majority of cases this will require evolution of protein function in order for the tasks themselves to evolve. For complex physiological systems a large fraction of their function will be devoted to high-level control functions that are predominantly computational in nature. In most cases regulatory evolution will be sufficient in order for these computational tasks to evolve.

Dynamics and bifurcations of the adaptive exponential integrate-and-fire model

Recently, several two-dimensional spiking neuron models have been introduced, with the aim of reproducing the diversity of electrophysiological features displayed by real neurons while keeping a simple model, for simulation and analysis purposes. Among these models, the adaptive integrate-and-fire model is physiologically relevant in that its parameters can be easily related to physiological quantities. The interaction of the differential equations with the reset results in a rich and complex dynamical structure. We relate the subthreshold features of the model to the dynamical properties of the differential system and the spike patterns to the properties of a Poincaré map defined by the sequence of spikes. We find a complex bifurcation structure which has a direct interpretation in terms of spike trains. For some parameter values, spike patterns are chaotic.

More gating charges are needed to open a Shaker K+ channel than are needed to open an rBIIA Na+ channel

This study presents what is, to our knowledge, a novel technique by means of which the ratio of the single gating charges of voltage-gated rat brain IIA (rBIIA) sodium and Shaker potassium ion channels was estimated. In the experiment, multiple tandems of enhanced green fluorescent protein were constructed and inserted into the C-terminals of Na(+) and K(+) ion channels. cRNA of Na(+) and K(+) ion channels was injected and expressed in Xenopus laevis oocytes. The two electrode voltage-clamp technique allowed us to determine the total gating charge of sodium and potassium ion channels, while a relative measure of the amount of expressed channels could be established on the basis of the quantification of the fluorescence intensity of membrane-bound channels marked by enhanced green fluorescent proteins. As a result, gating charge and fluorescence intensity were found to be positively correlated. A relative comparison of the single gating charges of voltage-gated sodium and potassium ion channels could thus be established: the ratio of the single gating charges of the Shaker potassium channel and the rBIIA sodium channel was found to be 2.5 +/- 0.4. Assuming the single channel gating charge of the Shaker K(+) channel to be approximately 13 elementary charges (well supported by other studies), this leads to approximately six elementary charges for the rBIIA sodium channel, which includes a fraction of gating charge that is missed during inactivation.