The exponential tracking and disturbance rejection of the propagated membrane action potential with conductance coefficient feedforward controllers

In the early 1950's, using their experimental data, Hodgkin and Huxley constructed the sodium and potassium conductance feedback controllers for their mathematical model of the flow of electric current through the surface membrane of a giant nerve fibre. In this paper, we re-formulate the construction as a problem of exponential tracking and disturbance rejection and then re-construct new conductance feedforward controllers in the more complicated case of a propagated action potential. The dynamics of the potential is governed by the Hodgkin-Huxley's partial differential equation (PDE) model. The problem is solved for any current disturbances and potential references and conductance coefficient feedforward controllers are designed by using the method of variable transform. It is proved that, under the designed feedforward controllers, the potential tracks exponentially a desired potential reference uniformly on an interval of one unit and the reference satisfies the controlled PDE model except an initial condition. A numerical example shows that the simulated action potential and sodium and potassium conductances are close to the experimental observations.

The exponential tracking and disturbance rejection of the propagated membrane action potential with conductance coefficient feedforward controllers

In the early 1950's, using their experimental data, Hodgkin and Huxley constructed the sodium and potassium conductance feedback controllers for their mathematical model of the flow of electric current through the surface membrane of a giant nerve fibre. In this paper, we re-formulate the construction as a problem of exponential tracking and disturbance rejection and then re-construct new conductance feedforward controllers in the more complicated case of a propagated action potential. The dynamics of the potential is governed by the Hodgkin-Huxley's partial differential equation (PDE) model. The problem is solved for any current disturbances and potential references and conductance coefficient feedforward controllers are designed by using the method of variable transform. It is proved that, under the designed feedforward controllers, the potential tracks exponentially a desired potential reference uniformly on an interval of one unit and the reference satisfies the controlled PDE model except an initial condition. A numerical example shows that the simulated action potential and sodium and potassium conductances are close to the experimental observations.

Human sperm ion channel (dys)function: implications for fertilization

BACKGROUND Intensive research on sperm ion channels has identified members of several ion channel families in both mouse and human sperm. Gene knock-out studies have unequivocally demonstrated the importance of the calcium and potassium conductances in sperm for fertility. In both species, the calcium current is carried by the highly complex cation channel of sperm (CatSper). In mouse sperm, the potassium current has been conclusively shown to be carried by a channel consisting of the pore forming subunit SLO3 and auxiliary subunit leucine-rich repeat-containing 52 (LRRC52). However, in human sperm it is controversial whether the pore forming subunit of the channel is composed of SLO3 and/or SLO1. Deciphering the role of the proton-specific Hv1 channel is more challenging as it is only expressed in human sperm. However, definitive evidence for a role in, and importance for, human fertility can only be determined through studies using clinical samples. OBJECTIVE AND RATIONALE This review aims to provide insight into the role of sperm ion channels in human fertilization as evidenced from recent studies of sperm from infertile men. We also summarize the key discoveries from mouse ion channel knock-out models and contrast the properties of mouse and human CatSper and potassium currents. We detail the evidence for, and consequences of, defective ion channels in human sperm and discuss hypotheses to explain how defects arise and why affected sperm have impaired fertilization potential. SEARCH METHODS Relevant studies were identified using PubMed and were limited to ion channels that have been characterized in mouse and human sperm. Additional notable examples from other species are included as appropriate. OUTCOMES There are now well-documented fundamental differences between the properties of CatSper and potassium channel currents in mouse and human sperm. However, in both species, sperm lacking either channel cannot fertilize in vivo and CatSper-null sperm also fail to fertilize at IVF. Sperm-lacking potassium currents are capable of fertilizing at IVF, albeit at a much lower rate. However, additional complex and heterogeneous ion channel dysfunction has been reported in sperm from infertile men, the causes of which are unknown. Similarly, the nature of the functional impairment of affected patient sperm remains elusive. There are no reports of studies of Hv1 in human sperm from infertile men. WIDER IMPLICATIONS Recent studies using sperm from infertile men have given new insight and critical evidence supporting the supposition that calcium and potassium conductances are essential for human fertility. However, it should be highlighted that many fundamental questions remain regarding the nature of molecular and functional defects in sperm with dysfunctional ion channels. The development and application of advanced technologies remains a necessity to progress basic and clinical research in this area, with the aim of providing effective screening methodologies to identify and develop treatments for affected men in order to help prevent failed ART cycles. Conversely, development of drugs that block calcium and/or potassium conductances in sperm is a plausible strategy for producing sperm-specific contraceptives.

Visual ecology and potassium conductances of insect photoreceptors

Voltage-activated potassium channels (Kv channels) in the microvillar photoreceptors of arthropods are responsible for repolarization and regulation of photoreceptor signaling bandwidth. On the basis of analyzing Kv channels in dipteran flies, it was suggested that diurnal, rapidly flying insects predominantly express sustained K+ conductances, whereas crepuscular and nocturnally active animals exhibit strongly inactivating Kv conductances. The latter was suggested to function for minimizing cellular energy consumption. In this study we further explore the evolutionary adaptations of the photoreceptor channelome to visual ecology and behavior by comparing K+ conductances in 15 phylogenetically diverse insects, using patch-clamp recordings from dissociated ommatidia. We show that rapid diurnal flyers such as the blowfly ( Calliphora vicina) and the honeybee ( Apis mellifera) express relatively large noninactivating Kv conductances, conforming to the earlier hypothesis in Diptera. Nocturnal and/or slow-moving species do not in general exhibit stronger Kv conductance inactivation in the physiological membrane voltage range, but the photoreceptors in species that are known to rely more on vision behaviorally had higher densities of sustained Kv conductances than photoreceptors of less visually guided species. No statistically significant trends related to visual performance could be identified for the rapidly inactivating Kv conductances. Counterintuitively, strong negative correlations were observed between photoreceptor capacitance and specific membrane conductance for both sustained and inactivating fractions of Kv conductance, suggesting insignificant evolutionary pressure to offset negative effects of high capacitance on membrane filtering with increased conductance.

Postnatal development attunes olfactory bulb mitral cells to high-frequency signaling

Mitral cells (MCs) are a major class of principal neurons in the vertebrate olfactory bulb, conveying odor-evoked activity from the peripheral sensory neurons to olfactory cortex. Previous work has described the development of MC morphology and connectivity during the first few weeks of postnatal development. However, little is known about the postnatal development of MC intrinsic biophysical properties. To understand stimulus encoding in the developing olfactory bulb, we have therefore examined the development of MC intrinsic biophysical properties in acute slices from postnatal day (P)7–P35 mice. Across development, we observed systematic changes in passive membrane properties and action potential waveforms consistent with a developmental increase in sodium and potassium conductances. We further observed developmental decreases in hyperpolarization-evoked membrane potential sag and firing regularity, extending recent links between MC sag heterogeneity and firing patterns. We then applied a novel combination of statistical analyses to examine how the evolution of these intrinsic biophysical properties specifically influenced the representation of fluctuating stimuli by MCs. We found that immature MCs responded to frozen fluctuating stimuli with lower firing rates, lower spike-time reliability, and lower between-cell spike-time correlations than more mature MCs. Analysis of spike-triggered averages revealed that these changes in spike timing were driven by a developmental shift from broad integration of inputs to more selective detection of coincident inputs. Consistent with this shift, generalized linear model fits to MC firing responses demonstrated an enhanced encoding of high-frequency stimulus features by mature MCs.

Thalamic mechanisms underlying alpha-delta sleep with implications for fibromyalgia

Alpha-delta sleep is the abnormal intrusion of alpha activity (8- to 13-Hz oscillations) into the delta activity (1- to 4-Hz oscillations) that defines slow-wave sleep. Alpha-delta sleep is especially prevalent in fibromyalgia patients, and there is evidence suggesting that the irregularities in the sleep of these patients may cause the muscle and tissue pain that characterizes the disorder. We constructed a biophysically realistic mathematical model of alpha-delta sleep. Imaging studies in fibromyalgia patients suggesting altered levels of activity in the thalamus motivated a thalamic model as the source of alpha activity. Since sodium oxybate helps to alleviate the symptoms of fibromyalgia and reduces the amount of alpha-delta sleep in fibromyalgia patients, we examined how changes in the molecular targets of sodium oxybate affected alpha-delta activity in our circuit. Our model shows how alterations in GABAB currents and two thalamic currents, Ih (a hyperpolarization-activated current) and a potassium leak current, transform a circuit that normally produces delta oscillations into one that produces alpha-delta activity. Our findings suggest that drugs that reduce Ih conductances and/or increase potassium conductances, without necessarily increasing GABAB conductances, might be sufficient to restore delta sleep. Furthermore, they suggest that delta sleep might be restored by drugs that preferentially target these currents in the thalamus; such drugs might have fewer side effects than drugs that act systemically.

Control of the Firing Patterns of Vibrissa Motoneurons by Modulatory and Phasic Synaptic Inputs: A Modeling Study

Vibrissa motoneurons (vMNs) generate rhythmic firing that controls whisker movements, even without cortical, cerebellar, or sensory inputs. vMNs receive serotonergic modulation from brain stem areas, which mainly increases their persistent sodium conductance ( gNaP) and, possibly, phasic input from a putative central pattern generator (CPG). In response to serotonergic modulation or just-suprathreshold current steps, vMNs fire at low rates, below the firing frequency of exploratory whisking. In response to periodic inputs, vMNs exhibit nonlinear suprathreshold resonance in frequency ranges of exploratory whisking. To determine how firing patterns of vMNs are determined by their 1) intrinsic ionic conductances and 2) responses to periodic input from a putative CPG and to serotonergic modulation, we construct and analyze a single-compartment, conductance-based model of vMNs. Low firing rates are supported in extended regimes by adaptation currents and the minimal firing rate decreases with gNaP and increases with M-potassium and h-cation conductances. Suprathreshold resonance results from the locking properties of vMN firing to stimuli and from reduction of firing rates at low frequencies by slow M and afterhyperpolarization potassium conductances. h conductance only slightly affects the suprathreshold resonance. When a vMN is subjected to a small periodic CPG input, serotonergically induced gNaP elevation may transfer the system from quiescence to a firing state that is highly locked to the CPG input. Thus we conclude that for vMNs, the CPG controls firing frequency and phase and enables bursting, whereas serotonergic modulation controls transitions from quiescence to firing unless the CPG input is sufficiently strong.