Dynamics of the exponential integrate-and-fire model with slow currents and adaptation

In order to properly capture spike-frequency adaptation with a simplified point-neuron model, we study approximations of Hodgkin-Huxley (HH) models including slow currents by exponential integrate-and-fire (EIF) models that incorporate the same types of currents. We optimize the parameters of the EIF models under the external drive consisting of AMPA-type conductance pulses using the current-voltage curves and the van Rossum metric to best capture the subthreshold membrane potential, firing rate, and jump size of the slow current at the neuron’s spike times. Our numerical simulations demonstrate that, in addition to these quantities, the approximate EIF-type models faithfully reproduce bifurcation properties of the HH neurons with slow currents, which include spike-frequency adaptation, phase-response curves, critical exponents at the transition between a finite and infinite number of spikes with increasing constant external drive, and bifurcation diagrams of interspike intervals in time-periodically forced models. Dynamics of networks of HH neurons with slow currents can also be approximated by corresponding EIF-type networks, with the approximation being at least statistically accurate over a broad range of Poisson rates of the external drive. For the form of external drive resembling realistic, AMPA-like synaptic conductance response to incoming action potentials, the EIF model affords great savings of computation time as compared with the corresponding HH-type model. Our work shows that the EIF model with additional slow currents is well suited for use in large-scale, point-neuron models in which spike-frequency adaptation is important.     

Ca2+-activated K+ currents regulate odor adaptation by modulating spike encoding of olfactory receptor cells

The olfactory system is thought to accomplish odor adaptation through the ciliary transduction machinery in olfactory receptor cells (ORCs). However, ORCs that have lost their cilia can exhibit spike frequency accommodation in which the action potential frequency decreases with time despite a steady depolarizing stimulus. This raises the possibility that somatic ionic channels in ORCs might serve for odor adaptation at the level of spike encoding, because spiking responses in ORCs encode the odor information. Here I investigate the adaptational mechanism at the somatic membrane using conventional and dynamic patch-clamp recording techniques, which enable the ciliary mechanism to be bypassed. A conditioning stimulus with an odorant-induced current markedly shifted the response range of action potentials induced by the same test stimulus to higher concentrations of the odorant, indicating odor adaptation. This effect was inhibited by charybdotoxin and iberiotoxin, Ca2+-activated K+ channel blockers, suggesting that somatic Ca2+-activated K+ currents regulate odor adaptation by modulating spike encoding. I conclude that not only the ciliary machinery but also the somatic membrane currents are crucial to odor adaptation.     

Calcium gradients underlying cell migration

The calcium ion is the simplest and most versatile second messenger in biology. Harboring a myriad of calcium effector proteins, migrating cells display an exquisite multiscaled and multilayered architecture of intracellular calcium dynamics. In motile fibroblasts, for instance, there are transient calcium microdomains ('calcium flickers') of ~5 μm in diameter and 10-2000 ms in duration, a rising flicker activity gradient along the rear-to-front axis, and a shallow background calcium concentration gradient in the opposite direction. When subjected to external gradients of guidance cues, local flicker gradients are created de novo in the leading edge, which steer cells to turn in new directions as defined by the asymmetry of the flicker activity, apparently by a stochastic decision-making mechanism. These recent findings provide a glimpse into how spatiotemporally coordinated calcium gradients orchestrate cellular behavior as complex as directional movement.     

Involvement of apamin-sensitive SK channels in spike frequency adaptation of neurons in nucleus tractus solitarii of the rat

We delineated the role of Ca²⁺-activated K⁺ channels in the phenomenon of spike frequency adaptation (SFA) exhibited by neurons in the caudal region of nucleus tractus solitarius (cNTS) using intracellular recording coupled with the current-clamp technique in rat brain slices. Intracellular injection of a constant depolarizing current evoked a train of action potentials whose discharge frequency declined rapidly to a lower steady-state level of irregular discharges. This manifested phenomenon of SFA was found to be related to extracellular Ca²⁺. Low Ca²⁺ (0.25 mM) or Cd²⁺ (0.5 mM) in the perfusing medium resulted in a significant increase in the adaptation time constant (_adap) and an appreciable reduction in the percentage adaptation of spike frequency (F_adap). In addition, the evoked discharges were converted from an irregular to a regular pattern, accompanied by a profound increase in mean firing rate. Intriguingly, similar alterations in _adap, F_adap, discharge pattern and discharge rate were elicited by apamin (1 µM), a selective blocker for small-conductance Ca²⁺-activated K⁺ (SK) channels. On the other hand, charybdotoxin (0.1 µM), a selective blocker for large-conductance Ca²⁺-activated K⁺ channels, was ineffective. Our results suggest that SK channels of cNTS neurons may subserve the generation of both SFA and irregular discharge patterns displayed by action potentials evoked with a prolonged depolarizing current.     

Small conductance potassium channels cause an activity-dependent spike frequency adaptation and make the transfer function of neurons logarithmic

We made a computational model of a single neuron to study the effect of the small conductance (SK) Ca2+-dependent K+ channel on spike frequency adaptation. The model neuron comprised a Na+ conductance, a Ca2+ conductance, and two Ca2+-independent K+ conductances, as well as a small and a large (BK) Ca2+-activated K+ conductance, a Ca2+ pump, and mechanisms for Ca2+ buffering and diffusion. Sustained current injection that simulated synaptic input resulted in a train of action potentials (APs) which in the absence of the SK conductance showed very little adaptation with time. The transfer function of the neuron was nearly linear, i.e., both asymptotic spike rate as well as the intracellular free Ca2+ concentration ([Ca2+]i) were approximately linear functions of the input current. Adding an SK conductance with a steep nonlinear dependence on [Ca2+]i (. Pflügers Arch. 422:223-232; K?hler, Hirschberg, Bond, Kinzie, Marrion, Maylie, and Adelman. 1996. Science. 273:1709-1714) caused a marked time-dependent spike frequency adaptation and changed the transfer function of the neuron from linear to logarithmic. Moreover, the input range the neuron responded to with regular spiking increased by a factor of 2.2. These results can be explained by a shunt of the cell resistance caused by the activation of the SK conductance. It might turn out that the logarithmic relationships between the stimuli of some modalities (e.g., sound or light) and the perception of the stimulus intensity (Fechner's law) have a cellular basis in the involvement of SK conductances in the processing of these stimuli.     

Robust metabolic adaptation underlying tumor progression

Tumor metabolism represents the end point of many signal cascades recruited by oncogenic activation. Energy metabolism of cancer cells attracted the attention of biochemists over eight decades ago. For example, high consume of glucose and high lactate production under aerobic conditions make up one of the most fundamental characteristics of cancer cells and has been exploited for diagnosis. At the same time, study of the metabolic status of tumor cells during tumor progression reveals characteristic adaptations during carcinogenesis. Although these metabolic adaptations are not the main defects that cause cancer, they may confer advantages to survive. In this review, we discuss the main metabolic hot spots and their relationship with main tumor progression events. An accurate metabolic map of the many tumor phenotypes could offer new options in the treatment of cancer.     

Impact of slow K<Superscript>+</Superscript> currents on spike generation can be described by an adaptive threshold model

A neuron that is stimulated by rectangular current injections initially responds with a high firing rate, followed by a decrease in the firing rate. This phenomenon is called spike-frequency adaptation and is usually mediated by slow K⁺ currents, such as the M-type K⁺ current (I _M ) or the Ca²⁺-activated K⁺ current (I _AHP ). It is not clear how the detailed biophysical mechanisms regulate spike generation in a cortical neuron. In this study, we investigated the impact of slow K⁺ currents on spike generation mechanism by reducing a detailed conductance-based neuron model. We showed that the detailed model can be reduced to a multi-timescale adaptive threshold model, and derived the formulae that describe the relationship between slow K⁺ current parameters and reduced model parameters. Our analysis of the reduced model suggests that slow K⁺ currents have a differential effect on the noise tolerance in neural coding.     

Calcium currents of differentiated mouse neuroblastoma cells

Differentiated mouse neuroblastoma cells (line C 1300, clone N-18-TG₂A₁) were investigated by intracellular dialysis. A slow component was found in the potential-dependent inward current of these cells. The results of investigation of changes in amplitude of this component during variation of the ionic composition of the external and internal solutions showed that this component is due to transport of calcium ions. A calcium current was observed in all cells tested. The region of its activation was between –70 and –65 mV; maximal values of this current were reached when the membrane potential was between –30 and –40 mV. The kinetic characteristics of this current were examined. In its kinetics and potential-dependence, this calcium current of the mouse neuroblastoma cell membrane is analogous to the fast component of the calcium current in normal neurons of rat spinal ganglia.A. A. Bogomolets Institute of Physiology, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Neirofiziologiya, Vol. 16, No. 4, pp. 527–531, July–August, 1984.     

Halothane suppresses slow inward currents in hippocampal slices

Single-electrode voltage-clamp experiments were made on CA1 neurons in the presence of tetrodotoxin and K channel blockers. Applications of halothane (1-3% v/v) for 3-10 min caused a similar marked and reversible depression of slow inward currents (probably Ca currents) evoked by depolarizing pulses from a holding potential near -80 or near -40 mV. The peak amplitudes of the inward currents were much reduced, in a concentration-dependent manner, and they decayed more rapidly (half-decay time was shortened by a quarter). In most cases, leak conductances were diminished by halothane, making it unlikely that the suppression of inward currents was primarily caused by enhancement of outward currents. A similar inactivation of Ca currents in presynaptic terminals would explain why halothane depresses synaptic transmission.     

Transient potassium currents in slow muscle fibers.

Transient changes in potassium conductance in chronically depolarized slow muscle fibers have been studied using a voltage clamp method. The transient behavior included current decays from initial to steady state for hyperpolarizing and depolarizing voltage clamp steps. A two-pulse voltage clamp sequence (conditioning step followed by test step) showed the initial potassium test current to depend sigmoidally on conditioning potential implicating the involvement of a membrane-bound charged group in regulating potassium current.     

Molecular mechanisms underlying thermal adaptation of xeric animals

For many years, we and our collaborators have investigated the adaptive role of heat shock proteins in different animals, including the representatives of homothermic and poikilothermic species that inhabit regions with contrasting thermal conditions. Adaptive evolution of the response to hyperthermia has led to different results depending upon the species. The thermal threshold of induction of heat shock proteins in desert thermophylic species is, as a rule, higher than in the species from less extreme climates. In addition, thermoresistant poikilothermic species often exhibit a certain level of heat shock proteins in cells even at a physiologically normal temperature. Furthermore, there is often a positive correlation between the characteristic temperature of the ecological niche of a given species and the amount of Hsp70-like proteins in the cells at normal temperature. Although in most cases adaptation to hyperthermia occurs without changes in the number of heat shock genes, these genes can be amplified in some xeric species. It was shown that mobile genetic elements may play an important role in the evolution and fine-tuning of the heat shock response system, and can be used for direct introduction of mutations in the promoter regions of these genes.     

Calcium signaling defects underlying salivary gland dysfunction

Salivary glands secrete saliva, a mixture of proteins and fluids, which plays an extremely important role in the maintenance of oral health. Loss of salivary secretion causes a dry mouth condition, xerostomia, which has numerous deleterious consequences including opportunistic infections within the oral cavity, difficulties in eating and swallowing food, and problems with speech. Saliva secretion is regulated by stimulation of specific signaling mechanisms within the acinar cells of the gland. Neurotransmitter-stimulated increase in cytosolic [Ca²⁺] ([Ca²⁺]_i) in acinar cells is the primary trigger for salivary fluid secretion from salivary glands, the loss of which is a critical factor underlying dry mouth conditions in patients. The increase in [Ca²⁺]_i regulates multiple ion channel and transport activities that together generate the osmotic gradient which drives fluid secretion across the apical membrane. Ca²⁺ entry mediated by the Store-Operated Ca²⁺ Entry (SOCE) mechanism provides the essential [Ca²⁺]_i signals to trigger salivary gland fluid secretion. Under physiological conditions depletion of ER-Ca²⁺ stores is caused by activation of IP3R by IP3 and this provides the stimulus for SOCE. Core components of SOCE in salivary gland acinar cells are the plasma membrane Ca²⁺ channels, Orai1 and TRPC1, and STIM1, a Ca²⁺-sensor protein in the ER, which regulates both channels. In addition, STIM2 likely enhances the sensitivity of cells to ER-Ca²⁺ depletion thereby tuning the cellular response to agonist stimulation. Two major, clinically relevant, conditions which cause irreversible salivary gland dysfunction are radiation treatment for head-and-neck cancers and the autoimmune exocrinopathy, Sjögren's syndrome (pSS). However, the exact mechanism(s) that causes the loss of fluid secretion, in either condition, is not clearly understood. A number of recent studies have identified that defects in critical Ca²⁺ signaling mechanisms underlie salivary gland dysfunction caused by radiation treatment or Sjögren's syndrome (pSS). This chapter will discuss these very interesting and important studies.     

Calcium ion currents mediating oocyte maturation events

During maturation, the last phase of oogenesis, the oocyte undergoes several changes which prepare it to be ovulated and fertilized. Immature oocytes are arrested in the first meiotic process prophase, that is morphologically identified by a germinal vesicle. The removal of the first meiotic block marks the initiation of maturation. Although a large number of molecules are involved in complex sequences of events, there is evidence that a calcium increase plays a pivotal role in meiosis re-initiation. It is well established that, during this process, calcium is released from the intracellular stores, whereas less is known on the role of external calcium entering the cell through the plasma membrane ion channels. This review is focused on the functional role of calcium currents during oocyte maturation in all the species, from invertebrates to mammals. The emerging role of specific L-type calcium channels will be discussed.     

Calcium currents in squid giant axon.

Voltage-clamp experiments were carried out on intracellularly perfused squid giant axons in a Na-free solution of 100 mM CaCl2+sucrose. The internal solution was 25 mM CsF+sucrose or 100 mM RbF+50mM tetraethylammonium chloride+sucrose. Depolarizing voltage clamp steps produced small inward currents; at large depolarizations the inward current reversed into an outward current. Tetrodotoxin completely blocked the inward current and part of the outward current. No inward current was seen with 100 mM MgCl2+sucrose as internal solution. It is concluded that the inward current is carried by Ca ions moving through the sodium channel. The reversal potential of the tetrodotoxin-sensitive current was +54mV with 25 mM CsF+sucrose inside and +10 mV with 100 mM RbF+50 mM tetraethylammonium chloride+sucrose inside. From the reversal potentials measured with varying external and internal solutions the relative permeabilities of the sodium channel for Ca, Cs and Na were calculated by means of the constant field equations. The results of the voltage-clamp experiments are compared with measurements of the Ca entry in intact axons.     

The action of spike frequency adaptation in the postural motoneurons of hermit crab abdomen during the first phase of reflex activation

Cuticular strain associated with support of the shell of the hermit crab, Pagurus pollicarus, by its abdomen activates mechanoreceptors that evoke a stereotyped reflex in postural motoneurons. This reflex consists of three phases: a brief high-frequency burst of motoneuron spikes, a pause, and a much longer duration but lower frequency period of spiking. These phases are correlated with a rapid increase in muscle force followed by a slight decline to a level of tone that is greater than that at rest but less than maximal. The present experiments address the mechanisms underlying the transition from the first to second phase of the reflex and their role in force generation. Although centrally generated inhibitory post-synaptic potentials (IPSPS) are present during the pause period of the reflex, intracellular current injection of motoneurons reveals a spike frequency adaptation that rapidly and substantially reduces motoneuron firing frequency and is unchanged in saline that reduces synaptic transmission. The adaptation is voltage sensitive and persists for several hundred milliseconds upon repolarization. Hyperpolarization partially restores the initial response of the motoneuron to depolarizing current. Spike frequency adaptation and synaptic inhibition are important mechanisms in the generation of force that maintains abdominal stiffness at a constant, submaximal level.     

Calcium currents and calcium-activated potassium currents at the frog motor nerve endings

Intracellular recordings were made of evoked electrical response of the nerve endings during experiments on the frog cutaneous pectoral muscle. A delayed inward current was discovered when superfusing the neuromuscular preparation with a calcium-free solution containing tubocurarine in the response evoked at the nerve endings, using CaCl₂-filled electrodes. This was replaced by the opposite (outward) type of current when 4-aminopyridine was added to the external solution. The outward current was dependent on the calcium concentration at the electrode, decreased after local increase on potassium concentration at the electrode, and disappeared under the effects of cobalt. Local iontophoretic application of tetraethylammonium led to the disappearance of the outward current and the appearance of a powerful and protracted inward current. Similar readings of inward and outward currents were obtained when recording electrical signals using electrodes filled with SrCl₂, BaCl₂, and MgCl₂. It was deduced that the late inward current is carried through voltage-dependent calcium channels and outward delayed current through calcium-activated potassium channels at the nerve terminal. The part played by these currents in transmitter secretion from the motor nerve ending is discussed, together with the relationship between them.S. V. Kurashov Medical Institute, Ministry of Health of the RSFSR. V. I. Ul'yanov-Lenin State University, Kazan'. Translated from Neirofiziologiya, Vol. 19, No. 4, 1987, pp. 467–473, July–August, 1987.     

The single-channel basis for the slow kinetics of synaptic currents in vertebrate slow muscle fibers

The time course of synaptic currents is significantly longer in slow than in fast twitch muscle fibers. To examine the underlying basis for these slow synaptic currents, single-channel recordings were made from the synapses of slow muscle fibers. Our analysis indicates that low conductance acetylcholine receptor (AChR) channels predominate in innervated slow fibers. The high level of expression of low conductance channels is in contrast to fast twitch fibers, in which these channels are expressed in significant numbers only in embryonic or denervated muscle. Analysis of the distribution of open durations for the low conductance channel class suggests that the open time of this AChR class is the major determinant in shaping the slow time course of synaptic current decay. The predominant contribution of low conductance channel openings to synaptic currents of slow muscle fibers indicates a well-defined physiological role for this class of AChRs.     

Genomic convergence underlying high-altitude adaptation in alpine plants

Evolutionary convergence is one of the most striking examples of adaptation driven by natural selection.However, genomic evidence for convergent adaptation to extreme environments remains scarce.Here, we assembled reference genomes of two alpine plants, Saussurea obvallata(Asteraceae)and Rheum alexandrae(Polygonaceae), with 37,938 and 61,463 annotated protein-coding genes. By integrating an additional five alpine genomes,we elucidated genomic convergence underlying high-altitude adaptation in al...