A model of on/off transitions in neurons of the deep cerebellar nuclei: deciphering the underlying ionic mechanisms

The neurons of the deep cerebellar nuclei (DCNn) represent the main functional link between the cerebellar cortex and the rest of the central nervous system. Therefore, understanding the electrophysiological properties of DCNn is of fundamental importance to understand the overall functioning of the cerebellum. Experimental data suggest that DCNn can reversibly switch between two states: the firing of spikes (F state) and a stable depolarized state (SD state). We introduce a new biophysical model of the DCNn membrane electro-responsiveness to investigate how the interplay between the documented conductances identified in DCNn give rise to these states. In the model, the F state emerges as an isola of limit cycles, i.e. a closed loop of periodic solutions disconnected from the branch of SD fixed points. This bifurcation structure endows the model with the ability to reproduce the [Formula: see text] transition triggered by hyperpolarizing current pulses. The model also reproduces the [Formula: see text] transition induced by blocking Ca currents and ascribes this transition to the blocking of the high-threshold Ca current. The model suggests that intracellular current injections can trigger fully reversible [Formula: see text] transitions. Investigation of low-dimension reduced models suggests that the voltage-dependent Na current is prominent for these dynamical features. Finally, simulations of the model suggest that physiological synaptic inputs may trigger [Formula: see text] transitions. These transitions could explain the puzzling observation of positively correlated activities of connected Purkinje cells and DCNn despite the former inhibit the latter.

Endocannabinoids mediate bidirectional striatal spike-timing-dependent plasticity

KEY POINTS

Although learning can arise from few or even a single trial, synaptic plasticity is commonly assessed under prolonged activation. Here, we explored the existence of rapid responsiveness of synaptic plasticity at corticostriatal synapses in a major synaptic learning rule, spike-timing-dependent plasticity (STDP). We found that spike-timing-dependent depression (tLTD) progressively disappears when the number of paired stimulations (below 50 pairings) is decreased whereas spike-timing-dependent potentiation (tLTP) displays a biphasic profile: tLTP is observed for 75-100 pairings, is absent for 25-50 pairings and re-emerges for 5-10 pairings. This tLTP induced by low numbers of pairings (5-10) depends on activation of the endocannabinoid system, type-1 cannabinoid receptor and the transient receptor potential vanilloid type-1. Endocannabinoid-tLTP may represent a physiological mechanism operating during the rapid learning of new associative memories and behavioural rules characterizing the flexible behaviour of mammals or during the initial stages of habit learning.

ABSTRACT

Synaptic plasticity, a main substrate for learning and memory, is commonly assessed with prolonged stimulations. Since learning can arise from few or even a single trial, synaptic strength is expected to adapt rapidly. However, whether synaptic plasticity occurs in response to limited event occurrences remains elusive. To answer this question, we investigated whether a low number of paired stimulations can induce plasticity in a major synaptic learning rule, spike-timing-dependent plasticity (STDP). It is known that 100 pairings induce bidirectional STDP, i.e. spike-timing-dependent potentiation (tLTP) and depression (tLTD) at most central synapses. In rodent striatum, we found that tLTD progressively disappears when the number of paired stimulations is decreased (below 50 pairings) whereas tLTP displays a biphasic profile: tLTP is observed for 75-100 pairings, absent for 25-50 pairings and re-emerges for 5-10 pairings. This tLTP, induced by very few pairings (∼5-10) depends on the endocannabinoid (eCB) system. This eCB-dependent tLTP (eCB-tLTP) involves postsynaptic endocannabinoid synthesis, requires paired activity (post- and presynaptic) and the activation of type-1 cannabinoid receptor (CB1R) and transient receptor potential vanilloid type-1 (TRPV1). eCB-tLTP occurs in both striatopallidal and striatonigral medium-sized spiny neurons (MSNs) and is dopamine dependent. Lastly, we show that eCB-LTP and eCB-LTD can be induced sequentially in the same neuron, depending on the cellular conditioning protocol. Thus, while endocannabinoids are usually thought simply to depress synaptic function, they also constitute a versatile system underlying bidirectional plasticity. Our results reveal a novel form of synaptic plasticity, eCB-tLTP, which may underlie rapid learning capabilities characterizing behavioural flexibility.

Dendritic signals command firing dynamics in a mathematical model of cerebellar Purkinje cells

Dendrites of cerebellar Purkinje cells (PCs) respond to brief excitations from parallel fibers with lasting plateau depolarizations. It is unknown whether these plateaus are local events that boost the synaptic signals or they propagate to the soma and directly take part in setting the cell firing dynamics. To address this issue, we analyzed a likely mechanism underlying plateaus in three representations of a reconstructed PC with increasing complexity. Analysis in an infinite cable suggests that Ca plateaus triggered by direct excitatory inputs from parallel fibers and their mirror signals, valleys (putatively triggered by the local feed forward inhibitory network), cannot propagate. However, simulations of the model in electrotonic equivalent cables prove that Ca plateaus (resp. valleys) are conducted over the entire cell with velocities typical of passive events once they are triggered by threshold synaptic inputs that turn the membrane current inward (resp. outward) over the whole cell surface. Bifurcation analysis of the model in equivalent cables, and simulations in a fully reconstructed PC both indicate that dendritic Ca plateaus and valleys, respectively, command epochs of firing and silencing of PCs.

Multiple forms of activity-dependent intrinsic plasticity in layer V cortical neurones in vivo

Synaptic plasticity is classically considered as the neuronal substrate for learning and memory. However, activity-dependent changes in neuronal intrinsic excitability have been reported in several learning-related brain regions, suggesting that intrinsic plasticity could also participate to information storage. Compared to synaptic plasticity, there has been little exploration of the properties of induction and expression of intrinsic plasticity in an intact brain. Here, by the means of in vivo intracellular recordings in the rat we have examined how the intrinsic excitability of layer V motor cortex pyramidal neurones is altered following brief periods of repeated firing. Changes in membrane excitability were assessed by modifications in the discharge frequency versus injected current (F-I) curves. Most (approximately 64%) conditioned neurones exhibited a long-lasting intrinsic plasticity, which was expressed either by selective changes in the current threshold or in the slope of the F-I curve, or by concomitant changes in both parameters. These modifications in the neuronal input-output relationship led to a global increase or decrease in intrinsic excitability. Passive electrical membrane properties were unaffected by the intracellular conditioning, indicating that intrinsic plasticity resulted from modifications of voltage-gated ion channels. These results demonstrate that neocortical pyramidal neurones can express in vivo a bidirectional use-dependent intrinsic plasticity, modifying their sensitivity to weak inputs and/or the gain of their input-output function. These multiple forms of experience-dependent intrinsic changes, which expand the computational abilities of individual neurones, could shape new network dynamics and thus might participate in the formation of mnemonic motor engrams.

A new principle for information storage in an enzymatic pathway model

Strong experimental evidence indicates that protein kinase and phosphatase (KP) cycles are critical to both the induction and maintenance of activity-dependent modifications in neurons. However, their contribution to information storage remains controversial, despite impressive modeling efforts. For instance, plasticity models based on KP cycles do not account for the maintenance of plastic modifications. Moreover, bistable KP cycle models that display memory fail to capture essential features of information storage: rapid onset, bidirectional control, graded amplitude, and finite lifetimes. Here, we show in a biophysical model that upstream activation of KP cycles, a ubiquitous mechanism, is sufficient to provide information storage with realistic induction and maintenance properties: plastic modifications are rapid, bidirectional, and graded, with finite lifetimes that are compatible with animal and human memory. The maintenance of plastic modifications relies on negligible reaction rates in basal conditions and thus depends on enzyme nonlinearity and activation properties of the activity-dependent KP cycle. Moreover, we show that information coding and memory maintenance are robust to stochastic fluctuations inherent to the molecular nature of activity-dependent KP cycle operation. This model provides a new principle for information storage where plasticity and memory emerge from a single dynamic process whose rate is controlled by neuronal activity. This principle strongly departs from the long-standing view that memory reflects stable steady states in biological systems, and offers a new perspective on memory in animals and humans.

How reliable is the allopurinol load in detecting carriers for ornithine transcarbamylase deficiency?

The allopurinol test aims to distinguish carriers and noncarriers for ornithine transcarbamylase (OTC) deficiency. We have evaluated the reliability of the test in at-risk females of known genotype. Results based on urine orotidine and/or orotic acid measurement were compared in terms of sensitivity and specificity. Retrospectively, we analysed the results of allopurinol tests in 42 women (22 confirmed heterozygotes and 20 noncarriers) from 23 pedigrees at risk of being carriers for OTC deficiency. Using a cut-off of 2 standard deviations above the mean of controls, the highest sensitivity (91%) was given by orotidine alone or in combination with orotic acid, but specificity was only 70% and 65%, respectively. We conclude that the value of the allopurinol test for detecting OTC carriers in at-risk females is limited. This needs to be recognized when counselling families. The test still has a role as a safe, quick, noninvasive screen of individuals at risk, but test results in possible carriers should be interpreted with caution. In the absence of other supportive evidence, confirmation by mutation analysis is required.

A biophysical model of nonlinear dynamics underlying plateau potentials and calcium spikes in purkinje cell dendrites

Computational capabilities of Purkinje cells (PCs) are central to the cerebellum function. Information originating from the whole nervous system converges on their dendrites, and their axon is the sole output of the cerebellar cortex. PC dendrites respond to weak synaptic activation with long-lasting, low-amplitude plateau potentials, but stronger synaptic activation can generate fast, large amplitude calcium spikes. Pharmacological data have suggested the involvement of only the P-type of Ca channels in both of these electric responses. However, the mechanism allowing this Ca current to underlie responses with such different dynamics is still unclear. This mechanism was explored by constraining a biophysical model with electrophysiological, Ca-imaging, and single ion channel data. A model is presented here incorporating a simplified description of [Ca](i) regulation and three ionic currents: 1) the P-type Ca current, 2) a delayed-rectifier K current, and 3) a generic class of K channels activating sharply in the sub-threshold voltage range. This model sustains fast spikes and long-lasting plateaus terminating spontaneously with recovery of the resting potential. Small depolarizing, tonic inputs turn plateaus into a stable membrane state and endow the dendrite with bistability properties. With larger tonic inputs, the plateau remains the unique equilibrium state, showing long traces of transient inhibitory inputs that are called "valley potentials" because their dynamics mirrors that of inverted, finite-duration plateaus. Analyzing the slow subsystem obtained by assuming instantaneous activation of the delayed-rectifier reveals that the time course of plateaus and valleys is controlled by the slow [Ca](i) dynamics, which arises from the high Ca-buffering capacity of PCs. A bifurcation analysis shows that tonic currents modulate sub-threshold dynamics by displacing the resting state along a hysteresis region edged by two saddle-node bifurcations; these bifurcations mark transitions from finite-duration plateaus to bistability and from bistability to valley potentials, respectively. This low-dimensionality model may be introduced into large-scale models to explore the role of PC dendrite computations in the functional capabilities of the cerebellum.

The influence of plasma membrane electrostatic properties on the stability of cell ionic composition

An electro-osmotic model is developed to examine the influence of plasma membrane superficial charges on the regulation of cell ionic composition. Assuming membrane osmotic equilibrium, the ion distribution predicted by Gouy-Chapman-Grahame (GCG) theory is introduced into ion transport equations, which include a kinetic model of the Na/K-ATPase based on the stimulation of this ion pump by internal Na(+) ions. The algebro-differential equation system describing dynamics of the cell model has a unique resting state, stable with respect to finite-sized perturbations of various types. Negative charges on the membrane are found to greatly enhance relaxation toward steady state following these perturbations. We show that this heightened stability stems from electrostatic interactions at the inner membrane side that shift resting state coordinates along the sigmoidal activation curve of the sodium pump, thereby increasing the pump sensitivity to internal Na(+) fluctuations. The accuracy of electrostatic potential description with GCG theory is proved using an alternate formalism, based on irreversible thermodynamics, which shows that pressure contribution to ion potential energy is negligible in electrostatic double layers formed at the surfaces of biological membranes. We discuss implications of the results regarding a reliable operation of ionic process coupled to the transmembrane electrochemical gradient of Na(+) ions.

A common 2 bp deletion mutation in the glucose-6-phosphatase gene in Indian patients with glycogen storage disease type Ia

This study reports a novel mutation which may be prevalent in Indian patients with glycogen storage disease type Ia.

Mutational analysis in X-linked spondyloepiphyseal dysplasia tarda

Spondyloepiphyseal dysplasia tarda (SEDT) is an X-linked recessive disorder characterized by short stature due to defective growth of the vertebral bodies. In addition, deformities of the femoral heads result in early onset secondary osteoarthritis of the hips. The disorder affects males only with heterozygous female carriers showing no consistent abnormalities. The gene causing SEDT, which is located on Xp22.12-p22.31, consists of 6 exons of which only exons 3, 4, 5, and 6 are translated to yield an 140 amino acid protein, referred to as SEDLIN. SEDLIN mutations have been observed in SEDT patients, and we have undertaken studies to characterize such mutations in four unrelated SEDT kindreds by DNA sequence analysis. We identified two nonsense and two intragenic deletional frameshift mutations. The nonsense mutations occurred in exons 4 (TGG-->TGA, Trp70Stop) and 6 (CGA-->TGA, Arg122Stop). Both of the intragenic deletions, which were approximately 750 bp and 1300-1445 bp in size, involved intron 5 and part of exon 6 and resulted in frameshifts that lead to premature termination (Stop) signals. Thus, all four mutations are predicted to result in truncated proteins. The results of our study expand the spectrum of SEDLIN mutations associated with SEDT, and this will help to elucidate further the role of this novel protein in the etiology of this form of osteochondrodysplasia.

A few comments on electrostatic interactions in cell physiology

The role of fixed charges present at the surface of biological membranes is usually described by the Gouy-Chapman-Grahame theory of the electric double-layer where the Grahame equation is applied independently on each side of the membrane and where the capacitive charges (linked to the transmembrane ionic currents) are disregarded. In this article, we generalize the Gouy-Chapman-Grahame theory by taking into account both intrinsic charges (resulting from the dissociation of membrane constituents) and capacitive charges, in the density value of the membrane surface charges. In the first part, we show that capacitive charges couple electrostatic potentials present on both sides of the membrane. The intensity of this coupling depends both on the value of the membrane specific capacitance and the transmembrane electric potential difference. In the second part, we suggest some physiological implications of membrane electric double-layers.

Mutation detection in 65 families with a possible diagnosis of ornithine carbamoyltransferase deficiency including 14 novel mutations

The high new mutation rate and the wide spectrum of mutations found in patients with ornithine carbamoyltransferase (OCT) deficiency means that direct mutation analysis is essential for providing accurate carrier detection and prenatal diagnosis in affected families. We present our strategy for mutation detection in the OCT gene and summarize the results from 31 families with a confirmed diagnosis and 34 families with a suspected diagnosis of OCT deficiency, and describe 14 previously unreported mutations.

Effects of free radicals on cytosolic creatine kinase activities and protection by antioxidant enzymes and sulfhydryl compounds

The main purpose of this study was to investigate the effect of free radicals and experimental diabetes on cytosolic creatine kinase activity in rat heart, muscle and brain. Hydrogen peroxide decreased creatine kinase activity in a dose dependent manner which was reversed by catalase. Xanthine/xanthine oxidase, which produces superoxide anion, lowered the creatine kinase activity in the same manner whose effect was protected by superoxide dismutase. N-acetylcysteine and dithiothreitol also significantly ameliorated the effect of Xanthine/xanthine oxidase and hydrogen peroxide. Experimental diabetes of twenty-one days (induced by alloxan), also caused a similar decrease in the activity of creatine kinase. This led us to the conclusion that the decrease in creatine kinase activity during diabetes could be due to the production of reactive oxygen species. The free radical effect could be on the sulfhydryl groups of the enzyme at the active sites, since addition of sulfhydryl groups like N-acetylcysteine and dithiothreitol showed a significant reversal effect.

Effects of vanadate, insulin and fenugreek (Trigonella foenum graecum) on creatine kinase levels in tissues of diabetic rat

The in vivo effects of insulin, and other insulino mimetic agents like vanadate and fenugreek (T. foenum graecum) were followed on the changes in the activities of creatine kinase in heart, skeletal muscle and liver of experimental diabetic rats. As compared to control rats, creatine kinase activities were found to decrease significantly in the tissues during experimental diabetes. All the antidiabetic compounds used namely, insulin, vanadate and Fenugreek seed powder normalised the decreased activities to almost control values. The effects of insulin and vanadate were comparable in restoring normoglycemia and the creatine kinase activities.

Hyperpolarizing current of the Na/K ATPase contributes to the membrane polarization of the Purkinje cell in rat cerebellum

The contribution of the Na/K ATPase (pump) current to the polarization of the Purkinje cell has been studied using slices of the rat cerebellum by blocking the pump with dihydro-ouabain (DHO) while recording the membrane potential with microelectrodes in the somata. From our recordings, it appeared that blocking the pump depolarized the Purkinje cells more rapidly than might be expected from shifts in Na+ and K+ concentrations, suggesting the removal of a hyperpolarizing current. Application of DHO, in the presence of tetrodotoxin (TTX), led to calcium spike firing and plateau-like discharges suggesting activation of voltage-dependent calcium channels in the dendrites. Adding 2 mM CO2+ to the medium did not prevent the depolarizations. Removing calcium from the bathing medium containing 2 mM CO2+ blocked the spiking activity but DHO application still produced a depolarization. Experiments to measure the current inhibited by DHO indicated that the Na/K pump supplies a constant current of 240 pA. Substitution of the sodium with choline produced a hyperpolarization, during which DHO had no effect on the membrane potential. Substitution of the sodium with lithium produced only a slowly developing depolarization. It is concluded that in the cerebellar Purkinje cell, a continuous sodium ion influx activates the pumps which produce a current that directly contributes to the membrane polarization. Possible pathways for this sodium influx are discussed.

B-cell-negative severe combined immunodeficiency associated with a common gamma chain mutation

Severe combined immunodeficiency (SCID) is caused by a variety of underlying defects. Approximately 40% of cases are thought to be of the X-linked type (SCIDX1), which is phenotypically characterised by the absence, or very low numbers, of T cells, but normal or even high B cell numbers. The gene responsible for SCIDX1 is that coding for the common gamma chain (gamma c), a component of multiple cytokine receptors. Mutations in this gene have been demonstrated in a large number of boys affected by typical SCIDX1. We describe a sporadic case of a boy who had SCID with absent B cells and absent T cells, but in whom a mutation in the gamma c gene has been demonstrated. In the absence of a typical X-linked pedigree, the phenotype in this boy suggested an autosomal recessive form of SCID and the family would usually have been counselled accordingly. This family raises the question of the true frequency of SCIDX1 amongst sporadic male cases of SCID and highlights the need to screen these boys for gamma chain mutations.

The cation distribution set by surface charges explains a paradoxical membrane excitability behavior

It is widely accepted that divalent cations can affect membrane excitability by interacting with negative charges on the membrane surface. This effect is generally supposed to arise from a modulation of the surface charge electrostatic field within the membrane. As an alternative mechanism, we propose that this effect may also be due to a generalized coupling between ion currents mediated by ionic composition changes at the membrane surface. To test this hypothesis we have computed the transmembrane potential using ionic current relations in which bulk external Ca2+ and K+ activities are substituted with superficial activities deduced from a Grahame-Langmuir isotherm. The model behavior agrees well with published results on Paramecium electrophysiology and furthermore explains 2 paradoxical observations on the cell membrane excitability upon changes of external Ca2+ and K+.

Screening for mutations causing X-linked severe combined immunodeficiency in the IL-2R gamma chain gene by single-strand conformation polymorphism analysis

Mutations in the common gamma chain (gamma c or IL2RG) of the interleukin-2, -4, -7, -9 and -15 receptors have been found to cause X-linked severe combined immunodeficiency (SCIDX1). We report here on the mutations identified in a further ten families. Two of the mutations identified have occurred twice in unrelated families, indicating two possible mutational hotspots. Seven of the mutations, which were identified by single-strand conformational polymorphism (SSCP) analysis, are point mutations, and the eighth is a small deletion. We also report on the first use of assays based on these mutations within IL2RG for unambiguous carrier determination. The consequences for the gamma c proteins produced as a result of these mutations are discussed.

Carrier determination for X-linked agammaglobulinemia using X inactivation analysis of purified B cells

We report the development of a relatively quick and simple method for the assessment of X inactivation status for carrier determination in families affected by X-linked agammaglobulinemia (XLA). This method utilises an immunomagnetic separation technique for B cell purification and a polymerase chain reaction (PCR) based assay for the determination of methylation status at the androgen receptor (AR) gene locus to assess whether X inactivation is random or non-random at this locus. We report the results we have obtained using this assay to investigate females known to be carriers of various X-linked immunodeficiency disorders. In addition, we investigated four females from different families affected by XLA, two of whom were of unknown carrier status, and we discuss the results obtained with this and other X-inactivation assays. A similar assay has recently been described by Allen et al. (1992) and applied to members of one family affected by XLA.

Female twin with Hunter disease due to nonrandom inactivation of the X-chromosome: a consequence of twinning

We report the occurrence of Hunter disease (mucopolysaccharidosis type II) in a karyotypically normal girl who was one of identical twins. Molecular studies showed nonrandom X-inactivation in both her fibroblasts and lymphocytes, while her normal twin showed equal usage of both X chromosomes. In view of previous reports of 7 pairs of identical female twins in which one had Duchenne muscular dystrophy, it seems that twinning may be strongly associated with nonrandom X-inactivation, and is not specific to the properties of the disease causing gene.

Carrier detection for X-linked agammaglobulinaemia (Bruton type) in an Irish family using linked DNA probes

Being an X-linked condition, the sisters of men with X-linked agammaglobulinaemia have a 50% risk of being carriers of the disease gene (provided the disease has not developed as a results of a new mutation). We demonstrate how this risk can be modified very significantly by DNA analysis using linked DNA probes. The value of such tests for genetic purposes is discussed.

Pitfalls in counselling: the craniosynostoses

We describe three families to highlight the variability of expression and penetrance that can occur in the craniosynostoses. In two of the families, gene carriers were only identified in retrospect by looking at photographs of other family members. In the third family, identical twins were initially thought to be discordant for sagittal craniosynostosis until early skull x rays were examined and both were found to be affected. The dilemmas faced when counselling these families are discussed.