Axonal excitability revisited

On mathematical modeling of the propagation of a wave ensemble within an individual axon

The long history of studying the propagation of an action potential has revealed that an electrical signal is accompanied by mechanical and thermal effects. All these effects together generate an ensemble of waves. The consistent models of such a complex phenomenon can be derived by using properly the fundamental physical principles. In this paper, attention is paid to the analysis of concepts of continuum physics that constitute a basis for deriving the mathematical models which describe the emergence and propagation of a wave ensemble in an axon. Such studies are interdisciplinary and based on biology, physics, mathematics, and chemistry. The governing equations for the action potential together with mechanical and thermal effects are derived starting from basics: Maxwell equations, conservation of momentum, Fourier's law, etc., but modified following experimental studies in electrophysiology. Several ideas from continuum physics like external forces and internal variables can also be used in deriving the corresponding models. Some mathematical concepts used in modeling are also briefly described. A brief overview of several mathematical models is presented that allows us to analyze the present ideas of modeling. Most mathematical models deal with the propagation of signals in a healthy axon. Further analysis is needed for better modeling the pathological situations and the explanation of the influence of the structural details like the myelin sheath or the cytoskeleton in the axoplasm. The future possible trends in improving the models are envisaged.

The influence of hydrogen peroxide concentration on the chemical kinetics of photo-accelerated tooth whitening

BACKGROUND

The bleaching procedure consists of chemical principles of free radical release that react with chromophores, which results in an amount of energy released in this process. However, the evaluation of the electrical potential generated in these protocols has not yet been thoroughly investigated in the literature. Thus, this study aimed to examine variations in pH, mV, and temperature of different concentrations of hydrogen peroxide in the presence or absence of an intermittent LED/LASER photo acceleration system.

METHODS

The study was divided into six groups (n = 9) according to the concentration of hydrogen peroxide (6%, 15%, and 35%), associated or not with the photo acceleration system LED/LASER. We followed the variation of pH, mV, and temperature at 1, 5, 10, 15, and 30 min after gel manipulation. Data were evaluated by two-way ANOVA of repeated measures (α =0.05).

RESULTS

pH, mV, and temperature of the groups showed statistical differences both in the light and bleach and in the interaction between the two factors (p < 0.0001), where pH and mV were more influenced by the bleach and light factor, while the temperature was influenced by the bleach factor associated with light. HP15 presented the most significant change in pH, mV, and temperature.

CONCLUSION

The use of LED/laser increased the temperature of the gels and altered the pH and mV kinetics of HP6 and HP15, which did not occur in HP35, possibly due to the high ionic potential linked to the concentration.

Modulating RhoA effectors induces transitions to oscillatory and more wavelike RhoA dynamics in C. elegans zygotes

Pulsatile RhoA dynamics underlie a wide range of cell and tissue behaviors. The circuits that produce these dynamics in different cells share common architectures based on fast positive and delayed negative feedback through F-actin, but they can produce very different spatiotemporal patterns of RhoA activity. However, the underlying causes of this variation remain poorly understood. Here we asked how this variation could arise through modulation of actin network dynamics downstream of active RhoA in early C. elegans embryos. We find that perturbing two RhoA effectors - formin and anillin - induce transitions from non-recurrent focal pulses to either large noisy oscillatory pulses (formin depletion) or noisy oscillatory waves (anillin depletion). In both cases these transitions could be explained by changes in local F-actin levels and depletion dynamics, leading to changes in spatial and temporal patterns of RhoA inhibition. However, the underlying mechanisms for F-actin depletion are distinct, with different dependencies on myosin II activity. Thus, modulating actomyosin network dynamics could shape the spatiotemporal dynamics of RhoA activity for different physiological or morphogenetic functions. [Media: see text] [Media: see text] [Media: see text] [Media: see text] [Media: see text] [Media: see text] [Media: see text] [Media: see text] [Media: see text].

Assessment of the temporal variation of electrical potential and pH of different bleaching agents

INTRODUCTION

Tooth whitening procedures are under continuous investigation to improve esthetic outcomes and reduce bleaching sensitivity (BS) precipitating from treatments. During the dental bleaching process it is known that the release of free radicals degrades the organic pigment molecules of the tooth and with this an amount of energy is released. Nonetheless, previous studies have never investigated the temporal correlation between of pH and electric potential (EP) generated in this treatment.

OBJECTIVES

Therefore, the objective of the present study was to investigate temporal variations of pH and EP associated with three different commercially available bleaching gels and the correlation levels between parameters of interest to provide relevant information regarding the kinetics of oxidation reactions in dental bleaching procedures.

METHODS

The study was divided into 3 groups (n = 9) in function of hydrogen peroxide concentration (either 6%, 15% and 35%). The temporal evolution of pH and EP values were determined using a highly-accurate and previously calibrated pH meter at specific time-points (5, 10, 15 and 30 min).

RESULTS

Data obtained were submitted to one-way ANOVA of repeated measures with Bonferroni post-test (α = 0.05). The results of the study showed difference in the factor gel concentration (p < 0,0001), time (p < 0,0001) and interaction (gel/time) (p = 0.002) while throughout the intervals evaluated the groups remained relatively stable and without significant difference in the intragroup variation of pH (p < 0.05) and in EDP only with significant difference in the 5 min interval of the 35% concentration. A 2nd order polynomial relationship test showed high correlation levels.

CONCLUSION

It can thus be concluded that there is a negative relationship between EP and pH variation in the different gel concentrations.

CLINICAL SIGNIFICANCE

The findings of the present study suggest that bleaching gels of higher concentration may provoke BS that are more intense and durable due to significant electric depolarization of neuronal extensions of pulpal tissues.

The effects of vesicle toxin from the sea anemone Bunodosoma cangicum on the behavior of a freshwater shrimp, Palaemon argentinus, and shore crab, Neohelice granulata

Sea anemones of the genus Bunodosoma possess along their body column, longitudinally arranged brown-colored vesicles. We have shown that in B. cangicum, these warty structures contain a mixture of potent toxins. This work highlights the neuro-inhibitory effects exhibited by two decapod crustacean species exposed to the extracts from these vesicles. For this, we use the unrefined toxin in doses, exposure times, and different exposure pathways. The findings show that at least one neuro-inhibitory compound is present and remains active regardless of the exposure method or dose tested. This toxin affects neuro-motor pathways but not neuro-sensory pathways. Shrimp exposed to toxin could continue to perceive and track food pellets but could not secure and consume their ration. Of six anatomical reflexes tested under the toxin's influence, voluntary movements of the mouthparts were impacted most commonly. Interestingly, all subject animals recovered from the toxin exposure within 2 h. Finally, we propose Reflexive Action Analysis (RAMP) as a tool to evaluate the potency of other neurotoxic or neuro-inhibitory compounds in crustacea. This work is the first to show the neuro-inhibitory activity of extracts from these sea anemone columnar vesicle structures and the first to evaluate these effects using RAMP reflex analysis.

Diffusion tensor imaging and electrophysiology as robust assays to evaluate the severity of acute spinal cord injury in rats

Background

Diffusion tensor imaging (DTI) is an effective method to identify subtle changes to normal-appearing white matter (WM). Here we analyzed the DTI data with other examinations, including motor evoked potentials (MEPs), histopathological images, and behavioral results, to reflect the lesion development in different degrees of spinal cord injury (SCI) in acute and subacute stages.

Method

Except for 2 Sprague -Dawley rats which died from the anesthesia accident, the rest 42 female rats were randomized into 3 groups: control group (n = 6), moderate group (n = 18), and severe group (n = 18). Moderate (a 50-g aneurysm clip with 0.4-mm thickness spacer) or severe (a 50-g aneurysm clip with no spacer) contusion SCI at T8 vertebrae was induced. Then the electrophysiological assessments via MEPs, behavioral deterioration via the Basso, Beattie, and Bresnaha (BBB) scores, DTI data, and histopathology examination were analyzed.

Results

In this study, we found that the damage of WM myelin, MEPs amplitude, BBB scores and the decreases in the values of fractional anisotropy (FA) and axial diffusivity (AD) were more obvious in the severe injury group than those of the moderate group. Additionally, the FA and AD values could identify the extent of SCI in subacute and early acute SCI respectively, which was reflected in a robust correlations with MEPs and BBB scores. While the values of radial diffusivity (RD) showed no significant changes.

Conclusions

Our data confirmed that DTI was a valuable in ex vivo imaging tool to identify damaged white matter tracts after graded SCI in rat, which may provide useful information for the early identification of the severity of SCI.

Modelling of processes in nerve fibres at the interface of physiology and mathematics

The in silico simulations are widely used in contemporary systems biology including the analysis of nerve pulse propagation. As known from numerous experiments, the propagation of an action potential is accompanied by mechanical and thermal effects. This calls for an analysis at the interface of physics, physiology and mathematics. In this paper, the background of the model equations governing the effects in nerve fibres is analysed from a physical viewpoint and then discussed how to unite them into a system by using the coupling forces. The leading hypothesis associates the coupling to the changes of variables, not to their values or amplitudes. This hypothesis models actually the physiological mechanisms of energy transductions in a fibre. The general assumptions in modelling the processes and the properties of the coupled system of equations are described. The dimensionless mathematical model which couples the action potential with mechanical waves together with temperature effects is presented in "Appendix". This model generates an ensemble of waves including the electrical signal and mechanical and thermal effects.

Modeling of complex signals in nerve fibers

Experiments have demonstrated that signals in nerve fibers are composed by electrical and mechanical components. In this paper a coupled mathematical model is described which unites the governing equations for the action potential, the pressure wave in the axoplasm and the longitudinal and the transverse waves in the surrounding biomembrane into one system of equations. As a solution of this system, an ensemble of waves is generated. The main hypotheses of such a model are related to the nature of coupling forces between the single waves in the ensemble. These coupling forces are assumed to have bi-polar shapes leading to energetically stable solutions. The in silico modeling demonstrates the qualitative resemblance of computed wave profiles to experimental ones. The ideas of possible experimental validation of the model are briefly described.

The Space-Clamped Hodgkin-Huxley System with Random Synaptic Input: Inhibition of Spiking by Weak Noise and Analysis with Moment Equations

We consider a classical space-clamped Hodgkin-Huxley model neuron stimulated by synaptic excitation and inhibition with conductances represented by Ornstein-Uhlenbeck processes. Using numerical solutions of the stochastic model system obtained by an Euler method, it is found that with excitation only, there is a critical value of the steady-state excitatory conductance for repetitive spiking without noise, and for values of the conductance near the critical value, small noise has a powerfully inhibitory effect. For a given level of inhibition, there is also a critical value of the steady-state excitatory conductance for repetitive firing, and it is demonstrated that noise in either the excitatory or inhibitory processes or both can powerfully inhibit spiking. Furthermore, near the critical value, inverse stochastic resonance was observed when noise was present only in the inhibitory input process. The system of deterministic differential equations for the approximate first- and second-order moments of the model is derived. They are solved using Runge-Kutta methods, and the solutions are compared with the results obtained by simulation for various sets of parameters, including some with conductances obtained by experiment on pyramidal cells of rat prefrontal cortex. The mean and variance obtained from simulation are in good agreement when there is spiking induced by strong stimulation and relatively small noise or when the voltage is fluctuating at subthreshold levels. In the occasional spike mode sometimes exhibited by spinal motoneurons and cortical pyramidal cells, the assumptions underlying the moment equation approach are not satisfied. The simulation results show that noisy synaptic input of either an excitatory or inhibitory character or both may lead to the suppression of firing in neurons operating near a critical point and this has possible implications for cortical networks. Although suppression of firing is corroborated for the system of moment equations, there seem to be substantial differences between the dynamical properties of the original system of stochastic differential equations and the much larger system of moment equations.

Identifying a kinase network regulating FGF14:Nav1.6 complex assembly using split-luciferase complementation

Kinases play fundamental roles in the brain. Through complex signaling pathways, kinases regulate the strength of protein:protein interactions (PPI) influencing cell cycle, signal transduction, and electrical activity of neurons. Changes induced by kinases on neuronal excitability, synaptic plasticity and brain connectivity are linked to complex brain disorders, but the molecular mechanisms underlying these cellular events remain for the most part elusive. To further our understanding of brain disease, new methods for rapidly surveying kinase pathways in the cellular context are needed. The bioluminescence-based luciferase complementation assay (LCA) is a powerful, versatile toolkit for the exploration of PPI. LCA relies on the complementation of two firefly luciferase protein fragments that are functionally reconstituted into the full luciferase enzyme by two interacting binding partners. Here, we applied LCA in live cells to assay 12 kinase pathways as regulators of the PPI complex formed by the voltage-gated sodium channel, Nav1.6, a transmembrane ion channel that elicits the action potential in neurons and mediates synaptic transmission, and its multivalent accessory protein, the fibroblast growth factor 14 (FGF14). Through extensive dose-dependent validations of structurally-diverse kinase inhibitors and hierarchical clustering, we identified the PI3K/Akt pathway, the cell-cycle regulator Wee1 kinase, and protein kinase C (PKC) as prospective regulatory nodes of neuronal excitability through modulation of the FGF14:Nav1.6 complex. Ingenuity Pathway Analysis shows convergence of these pathways on glycogen synthase kinase 3 (GSK3) and functional assays demonstrate that inhibition of GSK3 impairs excitability of hippocampal neurons. This combined approach provides a versatile toolkit for rapidly surveying PPI signaling, allowing the discovery of new modular pathways centered on GSK3 that might be the basis for functional alterations between the normal and diseased brain.

The what and where of adding channel noise to the Hodgkin-Huxley equations

Conductance-based equations for electrically active cells form one of the most widely studied mathematical frameworks in computational biology. This framework, as expressed through a set of differential equations by Hodgkin and Huxley, synthesizes the impact of ionic currents on a cell's voltage--and the highly nonlinear impact of that voltage back on the currents themselves--into the rapid push and pull of the action potential. Later studies confirmed that these cellular dynamics are orchestrated by individual ion channels, whose conformational changes regulate the conductance of each ionic current. Thus, kinetic equations familiar from physical chemistry are the natural setting for describing conductances; for small-to-moderate numbers of channels, these will predict fluctuations in conductances and stochasticity in the resulting action potentials. At first glance, the kinetic equations provide a far more complex (and higher-dimensional) description than the original Hodgkin-Huxley equations or their counterparts. This has prompted more than a decade of efforts to capture channel fluctuations with noise terms added to the equations of Hodgkin-Huxley type. Many of these approaches, while intuitively appealing, produce quantitative errors when compared to kinetic equations; others, as only very recently demonstrated, are both accurate and relatively simple. We review what works, what doesn't, and why, seeking to build a bridge to well-established results for the deterministic equations of Hodgkin-Huxley type as well as to more modern models of ion channel dynamics. As such, we hope that this review will speed emerging studies of how channel noise modulates electrophysiological dynamics and function. We supply user-friendly MATLAB simulation code of these stochastic versions of the Hodgkin-Huxley equations on the ModelDB website (accession number 138950) and http://www.amath.washington.edu/~etsb/tutorials.html.

The impact of the glial spatial buffering on the K(+) Nernst potential

Astrocytes play a critical role in CNS metabolism, regulation of volume and ion homeostasis of the interstitial space. Of special relevance is their clearance of K(+) that is released by active neurons into the extracellular space. Mathematical analysis of a modified Nernst equation for the electrochemical equilibrium of neuronal plasma membranes, suggests that K(+) uptake by glial cells is not only relevant during neuronal activity but also has a non-neglectable impact on the basic electrical membrane properties, specifically the resting membrane potential, of neurons and might be clinically valuable as a factor in the genetics and epigenetics of the epilepsy and tuberous sclerosis complex.

Action potentials in primary osteoblasts and in the MG-63 osteoblast-like cell line

Whole-cell patch-clamp analysis revealed a resting membrane potential of -60 mV in primary osteoblasts and in the MG-63 osteoblast-like cells. Depolarization-induced action potentials were characterized by duration of 60 ms, a minimal peak-to-peak distance of 180 ms, a threshold value of -20 mV and a repolarization between the spikes to -45 mV. Expressed channels were characterized by application of voltage pulses between -150 mV and 90 mV in 10 mV steps, from a holding potential of -40 mV. Voltages below -60 mV induced an inward current. Depolarizing voltages above -30 mV evoked two currents: (a) a fast activated and inactivated inward current at voltages between -30 and 30 mV, and (b) a delayed-activated outward current that was induced by voltages above -30 mV. Electrophysiological and pharmacological parameters indicated that hyperpolarization activated strongly rectifying K(+) (K(ir)) channels, whereas depolarization activated tetrodotoxin sensitive voltage gated Na(+) (Na(v)) channels as well as delayed, slowly activated, non-inactivating, and tetraethylammonium sensitive voltage gated K(+) (K(v)) channels. In addition, RT-PCR showed expression of Na(v)1.3, Na(v)1.4, Na(v)1.5, Na(v)1.6, Na(v)1.7, and K(ir)2.1, K(ir)2.3, and K(ir)2.4 as well as K(v)2.1. We conclude that osteoblasts express channels that allow firing of action potentials.

Evolution and comparative genomics of subcellular specializations: EST sequencing of Torpedo electric organ

Uncharacterized open reading frames (ORFs) in human genomic sequence often show a high degree of evolutionary conservation, yet have little or no tissue EST or protein data suggestive of protein product function. The encoded proteins may have highly restricted expression in specialized cells, subcellular specializations, and/or narrow windows during development. One such highly specialized and minute subcellular compartment is the neuromuscular junction (NMJ), where motorneurons contact muscle fibers. The electric Torpedo ray has evolved to expand the NMJ structure to the size of a large organ (electroplax organ), and we hypothesized that Torpedo electroplax proteins would be candidates for human ESTs expressed at the human NMJ. A total of 9719 primary electroplax cDNA clones were sequenced. We identified 44 human ORFs showing high (>63%) amino acid identity to Torpedo electroplax transcripts with enrichment for mRNA splicing motifs (SH2 and pre-mRNA splicing domains), an observation potentially important for the strict nuclear domains maintained by myonuclei underlying the NMJ. We generated antibodies against two uncharacterized human genes (C19orf29 [Drosophila cactin] and C15orf24) and showed that these were indeed expressed at the murine NMJ. Cactin, a member of the Rel transcription factor family in Drosophila, localized to the postsynaptic cytosol of the NMJ and nuclear membrane. C15orf24 protein localized to the murine postsynaptic sarcolemma. We show a novel approach towards identifying proteins expressed at a subcellular specialization using evolutionary diversity of organ function and cross-species mapping.

Frequency-dependent interaction of ultrashort E-fields with nociceptor membranes and proteins

We examined the influence of ultrashort pulses (USP) on sensory neurons. Single and high frequency bursts of 12 ns E-fields were presented to rat skin nociceptors that expressed distinct combinations of voltage-sensitive proteins. A single E-field pulse produced action potentials in all nociceptor subtypes at a critical threshold (E(c) ) of 403 V/cm. When configured into high frequency bursts, USP charge integrated to reduce the action potential threshold in a frequency and burst duration-dependent manner with E(c) as low as 16 V/cm (4000 Hz, 25 ms burst). There was no evidence of electroporation at field intensities near the E(c) for nociceptor activation. USP bursts activated a late, persistent Ca(++) flux that was identified as a dantrolene-sensitive Ca(++) -induced Ca(++) release (CICR). Influx of Ca(++) into the cell was required for the CICR and resulted in a reduction of the single pulse E(c) by about 50%.

Windows to cell function and dysfunction: signatures written in the boundary layers

The medium surrounding cells either in culture or in tissues contains a chemical mix varying with cell state. As solutes move in and out of the cytoplasmic compartment they set up characteristic signatures in the cellular boundary layers. These layers are complex physical and chemical environments the profiles of which reflect cell physiology and provide conduits for intercellular messaging. Here we review some of the most relevant characteristics of the extracellular/intercellular space. Our initial focus is primarily on cultured cells but we extend our consideration to the far more complex environment of tissues, and discuss how chemical signatures in the boundary layer can or may affect cell function. Critical to the entire essay are the methods used, or being developed, to monitor chemical profiles in the boundary layers. We review recent developments in ultramicro electrochemical sensors and tailored optical reporters suitable for the task in hand.

Optimization of the leak conductance in the squid giant axon

We report on a theoretical study showing that the leak conductance density, G{L} , in the squid giant axon appears to be optimal for the action potential firing frequency. More precisely, the standard assumption that the leak current is composed of chloride ions leads to the result that the experimental value for G{L} is very close to the optimal value in the Hodgkin-Huxley model, which minimizes the absolute refractory period of the action potential, thereby maximizing the maximum firing frequency under stimulation by sharp, brief input current spikes to one end of the axon. The measured value of G{L} also appears to be close to optimal for the frequency of repetitive firing caused by a constant current input to one end of the axon, especially when temperature variations are taken into account. If, by contrast, the leak current is assumed to be composed of separate voltage-independent sodium and potassium currents, then these optimizations are not observed.

Josephson junction simulation of neurons

With the goal of understanding the intricate behavior and dynamics of collections of neurons, we present superconducting circuits containing Josephson junctions that model biologically realistic neurons. These "Josephson junction neurons" reproduce many characteristic behaviors of biological neurons such as action potentials, refractory periods, and firing thresholds. They can be coupled together in ways that mimic electrical and chemical synapses. Using existing fabrication technologies, large interconnected networks of Josephson junction neurons would operate fully in parallel. They would be orders of magnitude faster than both traditional computer simulations and biological neural networks. Josephson junction neurons provide a new tool for exploring long-term large-scale dynamics for networks of neurons.

Response of a Hodgkin-Huxley neuron to a high-frequency input

We study the response of a Hodgkin-Huxley neuron stimulated by a periodic sequence of conductance pulses arriving through the synapse in the high-frequency regime. In addition to the usual excitation threshold there is a smooth crossover from the firing to the silent regime for increasing pulse amplitude gsyn. The amplitude of the voltage spikes decreases approximately linearly with gsyn. In some regions of parameter space the response is irregular, probably chaotic. In the chaotic regime between the mode-locked regions 3:1 and 2:1 near the lower excitation threshold, the output interspike interval histogram (ISIH) undergoes a sharp transition. If the driving period is below the critical value, T<T*, the output histogram contains only odd multiples of Ti. For Ti>T* even multiples of Ti also appear in the histogram, starting from the largest values. Near T* the ISIH scales logarithmically on both sides of the transition. The coefficient of variation of ISIH has a cusp singularity at T*. The average response period has a maximum slightly above T*. Near the excitation threshold in the chaotic regime the average firing rate rises sublinearly from frequencies of order 1 Hz.

Simulation of the electrically stimulated cochlear neuron: modeling adaptation to trains of electric pulses

The Hodgkin-Huxley (HH) model does not simulate the significant changes in auditory nerve fiber (ANF) responses to sustained stimulation that are associated with neural adaptation. Given that the electric stimuli used by cochlear prostheses can result in adapted responses, a computational model incorporating an adaptation process is warranted if such models are to remain relevant and contribute to related research efforts. In this paper, we describe the development of a modified HH single-node model that includes potassium ion ( K(+)) concentration changes in response to each action potential. This activity-related change results in an altered resting potential, and hence, excitability. Our implementation of K(+)-related changes uses a phenomenological approach based upon K(+) accumulation and dissipation time constants. Modeled spike times were computed using repeated presentations of modeled pulse-train stimuli. Spike-rate adaptation was characterized by rate decrements and time constants and compared against ANF data from animal experiments. Responses to relatively low (250 pulse/s) and high rate (5000 pulse/s) trains were evaluated and the novel adaptation model results were compared against model results obtained without the adaptation mechanism. In addition to spike-rate changes, jitter and spike intervals were evaluated and found to change with the addition of modeled adaptation. These results provide one means of incorporating a heretofore neglected (although important) aspect of ANF responses to electric stimuli. Future studies could include evaluation of alternative versions of the adaptation model elements and broadening the model to simulate a complete axon, and eventually, a spatially realistic model of the electrically stimulated nerve within extracochlear tissues.

Forcing function diagnostics for nonlinear dynamics

This article investigates the problem of model diagnostics for systems described by nonlinear ordinary differential equations (ODEs). I propose modeling lack of fit as a time-varying correction to the right-hand side of a proposed differential equation. This correction can be described as being a set of additive forcing functions, estimated from data. Representing lack of fit in this manner allows us to graphically investigate model inadequacies and to suggest model improvements. I derive lack-of-fit tests based on estimated forcing functions. Model building in partially observed systems of ODEs is particularly difficult and I consider the problem of identification of forcing functions in these systems. The methods are illustrated with examples from computational neuroscience.

A simple modification of the Hodgkin and Huxley equations explains type 3 excitability in squid giant axons

The Hodgkin and Huxley (HH) model predicts sustained repetitive firing of nerve action potentials for a suprathreshold depolarizing current pulse for as long as the pulse is applied (type 2 excitability). Squid giant axons, the preparation for which the model was intended, fire only once at the beginning of the pulse (type 3 behaviour). This discrepancy between the theory and experiments can be removed by modifying a single parameter in the HH equations for the K+ current as determined from the analysis in this paper. K+ currents in general have been described by IK=gK(V-EK), where gK is the membrane's K+ current conductance and EK is the K+ Nernst potential. However, IK has a nonlinear dependence on (V-EK) well described by the Goldman-Hodgkin-Katz equation that determines the voltage dependence of gK. This experimental finding is the basis for the modification in the HH equations describing type 3 behaviour. Our analysis may have broad significance given the use of IK=gK(V-EK) to describe K+ currents in a wide variety of biological preparations.

Probing peptide libraries from Conus achatinus using mass spectrometry and cDNA sequencing: identification of delta and omega-conotoxins

The peptide library present in the venom of the piscivorous marine snail Conus achatinus has been probed using a combination of mass spectrometry and cDNA sequencing methods. Matrix assisted laser desorption ionization mass spectrometry (MALDI-MS) analysis, before and following global reduction/alkylation of peptide mixtures, permits the rapid classification of individual components on the basis of the number of disulfide bonds. Mass fingerprinting and the reverse phase HPLC retention times permit a further deconvolution of the library in terms of peptide size and hydrophobicity. Sequencing of cDNA derived using O-superfamily specific primers yielded five complete conotoxin precursor sequences, ranging in polypeptide length from 75-87 residues containing six Cys residues at the C-terminus. Sequence analysis permits classification of the five putative mature peptides (Ac 6.1 to Ac 6.5) as delta, omega, and omega-like conotoxins. The presence of these predicted peptides in crude venom was established by direct matrix assisted laser desorption ionization tandem mass spectrometry (MALDI-MS/MS) sequencing following trypsin digestion of the peptide mixture after global reduction/alkylation. The determination of partial peptide sequences and comparison with the predicted sequences resulted in the identification of four of the five predicted conotoxins. The characterization of posttranslationally modified analogs, which are hydroxylated at proline or amidated at the C-terminus is also demonstrated. Crude venom analysis should prove powerful in studying both inter- and intra-species variation in peptide libraries.

Developmental changes in potassium currents at the rat calyx of Held presynaptic terminal

During early postnatal development, the calyx of Held synapse in the auditory brainstem of rodents undergoes a variety of morphological and functional changes. Among ionic channels expressed in the calyx, voltage-dependent K+ channels regulate transmitter release by repolarizing the nerve terminal. Here we asked whether voltage-dependent K+ channels in calyceal terminals undergo developmental changes, and whether they contribute to functional maturation of this auditory synapse. From postnatal day (P) 7 to P14, K+ currents became larger and faster in activation kinetics, but did not change any further to P21. Likewise, presynaptic action potentials became shorter in duration from P7 to P14 and remained stable thereafter. The density of presynaptic K+ currents, assessed from excised patch recording and whole-cell recordings with reduced [K+]i, increased by 2-3-fold during the second postnatal week. Pharmacological isolation of K+ current subtypes using tetraethylammonium (1 mM) and margatoxin (10 nM) revealed that the density of Kv3 and Kv1 currents underwent a parallel increase, and their activation kinetics became accelerated by 2-3-fold. In contrast, BK currents, isolated using iberiotoxin (100 nM), showed no significant change during the second postnatal week. Pharmacological block of Kv3 or Kv1 channels at P7 and P14 calyceal terminals indicated that the developmental changes of Kv3 channels contribute to the establishment of reliable action potential generation at high frequency, whereas those of Kv1 channels contribute to stabilizing the nerve terminal. We conclude that developmental changes in K+ currents in the nerve terminal contribute to maturation of high-fidelity fast synaptic transmission at this auditory relay synapse.

Noisy inputs and the induction of on-off switching behavior in a neuronal pacemaker

Neuronal oscillators can function as bistable toggle switches, flipping between quiescence and rhythmic firing in response to an input stimulus. In theory, such switching should be sensitive to small noisy inputs if the bistable states are in close proximity, which we test here using a perfused squid axon preparation. We find that small noisy stimulus currents induce a multitude of paths between two nearby stable states: repetitive firing and quiescence. The pattern of on-off switching of the pacemaker depends on the intensity, spectral properties, and phase angle of stimulus current fluctuations. Analysis by spike-triggered averaging of the stimulus currents near the transitions reveals that sinusoidal stimuli timed antiphase or in phase with repetitive firing correlates with switching of the pacemaker off or on, respectively. Our results reveal a distinct form of bistability in which noise can either silence pacemaker activity, trigger repetitive firing, or induce sporadic burst patterns similar to those recorded in a variety of normal and pathological neurons.

Hodgkin–Huxley type ion channel characterization: An improved method of voltage clamp experiment parameter estimation

The Hodgkin-Huxley formalism for quantitative characterization of ionic channels is widely used in cellular electrophysiological models. Model parameters for these individual channels are determined from voltage clamp experiments and usually involve the assumption that inactivation process occurs on a time scale which is infinitely slow compared to the activation process. This work shows that such an assumption may lead to appreciable errors under certain physiological conditions and proposes a new numerical approach to interpret voltage clamp experiment results. In simulated experimental protocols the new method was shown to exhibit superior accuracy compared to the traditional least squares fitting methods. With noiseless input data the error in gating variables and time constants was less than 1%, whereas the traditional methods generated upwards of 10% error and predicted incorrect gating kinetics. A sensitivity analysis showed that the new method could tolerate up to approximately 15% perturbation in the input data without unstably amplifying error in the solution. This method could also assist in designing more efficient experimental protocols, since all channel parameters (gating variables, time constants and maximum conductance) could be determined from a single voltage step.

Potassium channel blockers in multiple sclerosis: Neuronal Kv channels and effects of symptomatic treatment

Multiple sclerosis (MS) is an inflammatory disease of the central nervous system (CNS) characterized by demyelination, with a relative sparing of axons. In MS patients, many neurologic signs and symptoms have been attributed to the underlying conduction deficits. The idea that neurologic function might be improved if conduction could be restored in CNS demyelinated axons led to the testing of potassium (K(+)) channel blockers as a symptomatic treatment. To date, only 2 broad-spectrum K(+) channel blockers, 4-aminopyridine (4-AP) and 3,4-diaminopyridine (3,4-DAP), have been tested in MS patients. Although both 4-AP and 3,4-DAP produce clear neurologic benefits, their use has been limited by toxicity. Here we review the current status of basic science and clinical research related to the therapeutic targeting of voltage-gated K(+) channels (K(v)) in MS. By bringing together 3 distinct but interrelated disciplines, we aim to provide perspective on a vast body of work highlighting the lengthy and ongoing process entailed in translating fundamental K(v) channel knowledge into new clinical treatments for patients with MS and other demyelinating diseases. Covered are (1) K(v) channel nomenclature, structure, function, and pharmacology; (2) classic and current experimental morphology and neurophysiology studies of demyelination and conduction deficits; and (3) a comprehensive overview of clinical trials utilizing 4-AP and 3,4-DAP in MS patients.

Metabolic energy cost of action potential velocity

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.