Mathematical Model of Bursting in Dissociated Purkinje Neurons

In vitro, Purkinje cell behaviour is sometimes studied in a dissociated soma preparation in which the dendritic projection has been cleaved. A fraction of these dissociated somas spontaneously burst. The mechanism of this bursting is incompletely understood. We have constructed a biophysical Purkinje soma model, guided and constrained by experimental reports in the literature, that can replicate the somatically driven bursting pattern and which hypothesises Persistent Na⁺ current (I_NaP) to be its burst initiator and SK K⁺ current (I_SK) to be its burst terminator.     

Voltage-sensitive Dye Recording from Axons,Dendrites and Dendritic Spines of Individual Neurons in Brain Slices

Understanding the biophysical properties and functional organization of single neurons and how they process information is fundamental for understanding how the brain works. The primary function of any nerve cell is to process electrical signals, usually from multiple sources. Electrical properties of neuronal processes are extraordinarily complex, dynamic, and, in the general case, impossible to predict in the absence of detailed measurements. To obtain such a measurement one would, ideally, like to be able to monitor, at multiple sites, subthreshold events as they travel from the sites of origin on neuronal processes and summate at particular locations to influence action potential initiation. This goal has not been achieved in any neuron due to technical limitations of measurements that employ electrodes. To overcome this drawback, it is highly desirable to complement the patch-electrode approach with imaging techniques that permit extensive parallel recordings from all parts of a neuron. Here, we describe such a technique - optical recording of membrane potential transients with organic voltage-sensitive dyes (V_m-imaging) - characterized by sub-millisecond and sub-micrometer resolution. Our method is based on pioneering work on voltage-sensitive molecular probes ². Many aspects of the initial technology have been continuously improved over several decades ^{3, 5, 11}. Additionally, previous work documented two essential characteristics of V_m-imaging. Firstly, fluorescence signals are linearly proportional to membrane potential over the entire physiological range (-100 mV to +100 mV; ^{10, 14, 16}). Secondly, loading neurons with the voltage-sensitive dye used here (JPW 3028) does not have detectable pharmacological effects. The recorded broadening of the spike during dye loading is completely reversible ^{4, 7}. Additionally, experimental evidence shows that it is possible to obtain a significant number (up to hundreds) of recordings prior to any detectable phototoxic effects ^{4, 6, 12, 13}. At present, we take advantage of the superb brightness and stability of a laser light source at near-optimal wavelength to maximize the sensitivity of the V_m-imaging technique. The current sensitivity permits multiple site optical recordings of V_m transients from all parts of a neuron, including axons and axon collaterals, terminal dendritic branches, and individual dendritic spines. The acquired information on signal interactions can be analyzed quantitatively as well as directly visualized in the form of a movie.     

Noise-Stabilized Long-Distance Synchronization in Populations of Model Neurons

Rhythmic, synchronous firing of groups of neurons is associated with behaviorally relevant states, and it is thus of interest to understand the mechanisms by which synchronization may be achieved. In hippocampal slice preparations, networks of excitatory and inhibitory neurons have been seen to synchronize when strong stimulation is applied at separated sites between which any coupling must be subject to a significant axonal delay. We extend previous work on synchronization in a model system based on the network architecture of these hippocampal slices. Our new analysis addresses the effects of heterogeneous populations and noisy inputs on the stability of synchronous solutions in the system. We find that, with experimentally motivated constraints on the coupling strength, sufficiently large heterogeneity in the input currents renders synchrony unstable. The addition of noise, however, restores stable near-synchrony. We analytically reduce the high-dimensional biophysical equations for the full population to a simple three-dimensional map, and show that the map's stability properties correctly predict both the loss of stability and the restabilizing effect of the noise.     

A Biobased Composite Gel Polymer Electrolyte with Functions of Lithium Dendrites Suppressing and Manganese Ions Trapping

Lithium (Li) dendrites in Li anodes, and dissolution and migration of manganese (Mn) ions in LiMn₂O₄ (LMO) cathodes, have hampered these extraordinary electrode materials from being efficiently applied in high performance Li batteries. Here, a novel, bifunctional, biobased composite gel polymer electrolyte (c‐GPE) is created to simultaneously deal with the two critical issues. The skeleton of c‐GPE is constructed from a sandwich structure composed of porous polydopamine spheres and two layers of the environmentally friendly soy protein isolate‐based nanofiber membranes, and the carbonized polydopamine spheres are coated without any binder on the surface of the membranes. After a facile and innocuous preparation process, the skeleton material displays excellent thermal stability and good affinity to liquid electrolyte, which endows c‐GPE with significant functions of effective mitigation of the dissolution of Mn ions, and chelation of the fleeing Mn ions, as well as the dramatic suppression of Li dendrite growth. Consequently, the LMO/Li batteries involving c‐GPE show a great improvement in the cycling stability and rate performance compared with those of the cells based on commercial Celgard 2400. This work will be quite promising to meet the distinct requirements from Li batteries and provide a high‐efficiency and safe biobased GPE for next generation energy storage systems.     

Summation of Spatiotemporal Input Patterns in Leaky Integrate-and-Fire Neurons: Application to Neurons in the Cochlear Nucleus Receiving Converging Auditory Nerve Fiber Input

The response of leaky integrate-and-fire neurons is analyzed for periodic inputs whose phases vary with their spatial location. The model gives the relationship between the spatial summation distance and the degree of phase locking of the output spikes (i.e., locking to the periodic stochastic inputs, measured by the synchronization index). The synaptic inputs are modeled as an inhomogeneous Poisson process, and the analysis is carried out in the Gaussian approximation. The model has been applied to globular bushy cells of the cochlear nucleus, which receive converging inputs from auditory nerve fibers that originate at neighboring sites in the cochlea. The model elucidates the roles played by spatial summation and coincidence detection, showing how synchronization decreases with an increase in both frequency and spatial spread of inputs. It also shows under what conditions an enhancement of synchronization of the output relative to the input takes place.     

Localization of Glutamate in Trigeminothalamic Projection Neurons: A Combined Retrograde Transport-Immunohistochemical Study

Trigeminothalamic projection neurons are important components of the pathways for conscious perception of pain, temperature, and tactile sensation from the orofacial region. The neurotransmitters utilized by trigeminal neurons projecting to the thalamus are unknown. By use of a monoclonal antibody specific for fixative-modified glutamate and a polyclonal antiserum against glutaminase, we recently identified neurons in the trigeminal sensory complex that cocontain glutamate-like immunoreactivity (Glu-LI) and glutaminase-like immunoreactivity. In the present study, we utilized combined retrograde transport-immunohistochemical techniques to localize putative glutamatergic trigeminothalamic neurons.

Following injection of the retrograde tracer, wheatgerm agglutinin conjugated to horseradish peroxidase (WGA:HRP), into the ventroposterior medial thalamus (VPM), the number of neuronal profiles that were double-labeled with WGA:HRP and Glu-LI was greatest in principal sensory nucleus (Pr5), followed by subnuclei interpolaris (Sp51) and caudalis (Sp5C). The average percentages of projection neurons double-labeled with Glu-LI were approximately 60-70% in Pr5 and Sp51 and 40% in Sp5C. The majority of double-labeled profiles in Sp5C were located in the magnocellular layer, as opposed to the marginal and substantia gelatinosa layers. A large injection site that spread into the intralaminar thalamic nuclei and nucleus submedius—areas implicated in the processing of nociceptive information—resulted in an increase in the ratio of single-labeled to double-labeled projection profiles in Sp5C.

These results suggest that glutamate may be the neurotransmitter for a majority of trigeminothalamic projection neurons located in Sp51 and Pr5. However, on the basis of anatomical association, glutamate does not appear to be the major transmitter for neurons in Sp5C that forward nociceptive information to the thalamus.     

Structure-Dependent Electrical and Concentration Processes in the Dendrites of Pyramidal Neurons of Superficial Neocortical Layers: Model Study

On mathematical models of pyramidal neurons localized in the neocortical layers 2/3, whose reconstructed dendritic arborization possessed passive linear or active nonlinear membrane properties, we studied the effect of morphology of the dendrites on their passive electrical transfer characteristics and also on the formation of patterns of spike discharges at the output of the cell under conditions of tonic activation via uniformly distributed excitatory synapses along the dendrites. For this purpose, we calculated morphometric characteristics of the size, complexity, metric asymmetry, and function of effectiveness of somatopetal transmission of the current (with estimation of the sensitivity of this efficacy to changes in the uniform membrane conductance) for the reconstructed dendritic arborization in general and also for its apical and basal subtrees. Spatial maps of the membrane potential and intracellular calcium concentration, which corresponded to certain temporal patterns of spike discharges generated by the neuron upon different intensities of synaptic activation, were superimposed on the 3D image and dendrograms of the neuron. These maps were considered “spatial autographs” of the above patterns. The main discharge pattern included periodic two-spike bursts (dublets) generated with relatively stable intraburst interspike intervals and interburst intervals decreasing with a rise in the intensity of activation. Under conditions of intense activation, the interburst intervals became close to the intraburst intervals, so the cell began to generate continuous trains of action potentials. Such a repertoire (consisting of two patterns of the activity, periodical dublets and continuous discharges) is considerably scantier than that described earlier in pyramidal neurons of the neocortical layer 5. Under analogous conditions of activation, we observed in the latter cells a variety of patterns of output discharges of different complexities, including stochastic ones. A relatively short length of the apical dendrite subtree of layer 2/3 neurons and, correspondingly, a smaller metric asymmetry (differences between the lengths of the apical and basal dendritic branches and paths), as compared with those in layer 5 pyramidal neurons, are morphological factors responsible for the predominance of periodic spike dublets. As a result, there were two combinations of different electrical states of the sites of dendritic arborization (“spatial autographs”). In the case of dublets, these were high depolarization of the apical dendrites vs. low depolarization of the basal dendrites and a reverse combination; only the latter (reverse) combination corresponded to the case of continuous discharges. The relative simplicity and uniformity of spike patterns in the cells, apparently, promotes the predominance of network interaction in the processes of formation of the activity of pyramidal neurons of layers 2/3 and, thereby, a higher efficiency of the processes of intracortical association.     

Initiation of Sodium Spikelets in Basal Dendrites of Neocortical Pyramidal Neurons

Cortical information processing relies critically on the processing of electrical signals in pyramidal neurons. Electrical transients mainly arise when excitatory synaptic inputs impinge upon distal dendritic regions. To study the dendritic aspect of synaptic integration one must record electrical signals in distal dendrites. Since thin dendritic branches, such as oblique and basal dendrites, do not support routine glass electrode measurements, we turned our effort towards voltage-sensitive dye recordings. Using the optical imaging approach we found and reported previously that basal dendrites of neocortical pyramidal neurons show an elaborate repertoire of electrical signals, including backpropagating action potentials and glutamate-evoked plateau potentials. Here we report a novel form of electrical signal, qualitatively and quantitatively different from backpropagating action potentials and dendritic plateau potentials. Strong glutamatergic stimulation of an individual basal dendrite is capable of triggering a fast spike, which precedes the dendritic plateau potential. The amplitude of the fast initial spikelet was actually smaller that the amplitude of the backpropagating action potential in the same dendritic segment. Therefore, the fast initial spike was dubbed “spikelet”. Both the basal spikelet and plateau potential propagate decrementally towards the cell body, where they are reflected in the somatic whole-cell recordings. The low incidence of basal spikelets in the somatic intracellular recordings and the impact of basal spikelets on soma-axon action potential initiation are discussed.     

Reinforcement Learning Recruits Somata and Apical Dendrites across Layers of Primary Sensory Cortex

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Structure Dependence of the Calcium Dynamics in Purkinje Neuron Dendrites during Generation of Bursting Discharges: a Simulation Study

In the model of a cerebellar Purkinje neuron with reconstructed active dendrites, we investigated the impact of the ratio between volumes of the endoplasmic reticulum (organellar calcium store) and cytosol on the Ca²⁺ dynamics in asymmetrical parts of the dendritic arborization during generation of different structure-dependent patterns of bursting activity. Tonic synaptic excitation homogeneously distributed over the dendrites (a spatially homogeneous stationary input signal) caused spatially heterogeneous variations of the dendritic membrane potential (MP) accompanied by periodical or nonperiodical bursts of action potentials at the cell output. The MP waveforms recorded from the segments of asymmetrical dendrites were then applied to the membrane of selected dendrite segments as command voltages in a dynamic clamp mode. In these segments, the relative size of the stores was varied. This provided equal to each other local calcium currents and influxes into the cytosol of the segment differently filled with the organellar store. Regardless of the impulse pattern, microgeometry of the segment and the store modulated calcium transients exactly in the same way as in previous studies of electrical and concentration responses to local phasic synaptic excitation of the modeled neuron. Peak values of depolarization-induced elevations of the cytosolic Ca²⁺ concentration increased with the portion of the intracellular volume occupied by the store. The most important factor defining this dependence was the ratio of the membrane area vs the organelle-free cytosol volume of the dendritic segment. Concentrations of Са²⁺ deposited in equal-sized segments of asymmetrical parts of the dendritic arborization where asynchronous unequal variations of the MP were observed during generation of nonperiodical bursting at the output demonstrated considerable specificity. A greater amount of calcium was deposited in the segments staying, on average, in a high-depolarization state for a longer time (this intensified activation of calcium channels and amplified the corresponding Ca²⁺ influx into the cytosol). Hence, local dynamics of the Ca²⁺ concentration depend directly on local microgeometry and indirectly on global macrogeometry of the dendrite arborization, as the latter determines spatial asymmetry-related unequal transients in different parts of the dendritic arborization having active membrane properties.     

Patterns of Impulsation Generated by Abducens Motoneurons with Active Reconstructed Dendrites: a Simulation Study

Mathematical models of abducens motoneurons with reconstructed dendritic arborizations were investigated. The two types of models differed from each other in electrical properties of the dendrites, either passive (model group 1) or active and non-linear (model group 2). The relations between morphology of the dendrites, their electrical transfer characteristics, and formation of impulse patterns at the cell output were studied under conditions of tonic activation of glutamatergic (NMDA-type) excitatory synapses homogeneously distributed over the dendrites. For reconstructed dendritic arborizations, their morphometric characteristics (size, complexity, and metrical asymmetry) and electrical ones (somatopetal current transfer effectiveness function and sensitivity of the latter to variations of the homogeneous membrane conductivity) were computed. Changes in the membrane potential were also studied in different parts of the dendritic arborization during generation of various patterns of discharges of action potentials (APs) at the neuronal output under different intensities of synaptic activation; this allowed us to reveal “spatial signatures” of the above-mentioned temporal patterns. The output patterns and their “spatial signatures” changed in a certain manner with increase in the intensity of synaptic activation. A simple periodical discharge of low-frequency APs with constant interspike intervals was replaced by a complex periodical or nonperiodical (stochastic) bursting pattern, which then was replaced again by a simple rhythmic but high-frequency discharge. Simple periodical patterns were associated with generation of synchronous oscillatory dendritic depolarizations phase-shifted in metrically asymmetrical parts of the arborization. In the case of generation of complex periodical or stochastic patterns, depolarization processes in asymmetrical dendritic parts were asynchronous and differed from each other in their amplitude and duration. Such a structure-dependent repertoire of output discharge patterns was quite compatible with that observed earlier in examined simulated neocortical pyramidal and cerebellar Purkinje neurons. This fact is indicative of a possible similarity of the rules governing the formation of specific output patterns in neurons with active membrane properties of the dendrites based on intrinsic mophological/functional features of the dendritic arborization of a given neuron.     

Noise-Induced Coherence and Network Oscillations in a Reduced Bursting Model

The dynamics of the Hindmarsh-Rose (HR) model of bursting thalamic neurons is reduced to a system of two linear differential equations that retains the subthreshold resonance properties of the HR model. Introducing a reset mechanism after a threshold crossing, we turn this system into a resonant integrate-and-fire (RIF) model. Using Monte-Carlo simulations and mathematical analysis, we examine the effects of noise and the subthreshold dynamic properties of the RIF model on the occurrence of coherence resonance (CR). Synchronized burst firing occurs in a network of such model neurons with excitatory pulse-coupling. The coherence level of the network oscillations shows a stochastic resonance-like dependence on the noise level. Stochastic analysis of the equations shows that the slow recovery from the spike-induced inhibition is crucial in determining the frequencies of the CR and the subthreshold resonance in the original HR model. In this particular type of CR, the oscillation frequency strongly depends on the intrinsic time scales but changes little with the noise intensity. We give analytical quantities to describe this CR mechanism and illustrate its influence on the emerging network oscillations. We discuss the profound physiological roles this kind of CR may have in information processing in neurons possessing a subthreshold resonant frequency and in generating synchronized network oscillations with a frequency that is determined by intrinsic properties of the neurons. PACS 05.45.-a, 05.40.Ca, 87.18.Sn, 87.19     

Human Microtubule-Associated Protein-2c Localizes to Dendrites and Axons in Fetal Spinal Motor Neurons

Abstract: Microtubule-associated protein-2 (MAP-2) functions to maintain neuronal morphology by promoting the assembly of microtubules. MAP-2c is an alternately spliced form of MAP-2, containing the first 151 amino acids of high-molecular-weight (HMW) MAP-2 joined to the last 321 amino acids, eliminating 1,352 amino acids specific to HMW MAP-2. A polyclonal antibody generated to the splice site of human MAP-2c was used to determine its cellular localization. The MAP-2c antiserum was depleted of any HMW MAP-2 reactivity by absorption with HMW MAP-2 fusion protein. Western blot analysis of human fetal spinal cord homogenates demonstrated that the antibody is specific for human MAP-2c. MAP-2c immunoreactivity was found in the perinuclear cytoplasm and processes of anterior motor neurons and large processes of the posterior column in sections from 22–24-week human fetal spinal cord. Double-label confocal microscopy was performed using the MAP-2c polyclonal antibody and either a HMW MAP-2 or a neurofilament protein (highly phosphorylated 160- and 200-kDa protein) monoclonal antibody to identify these processes as dendrites or axons, respectively. HMW MAP-2 and MAP-2c colocalized in cell bodies and dendrites of anterior motor neurons, demonstrating for the first time the presence of native MAP-2c within dendrites. In addition, immunoelectron microscopy showed MAP-2c associated with microtubules in dendrites of motor neurons. MAP-2c and the neurofilament proteins were found in axons of the dorsal and ventral roots. The presence of MAP-2c within axons and dendrites suggests that MAP-2c contributes to neuronal plasticity during human fetal development.     

Mesoporous Hybrid Electrolyte for Simultaneously Inhibiting Lithium Dendrites and Polysulfide Shuttle in Li–S Batteries

A bifunctional hybrid electrolyte composed of mesoporous silica nanosheets and liquid electrolyte is achieved for lithium–sulfur (Li–S) batteries. This hybrid electrolyte possesses abundant mesopores (2.8 nm), thin feature (20 µm), and high ionic conductivity (1.17 × 10^?1 mS cm^?1) as well as a low interfacial resistance with electrodes. Such unique features not only enable the efficient inhibition of the growth of lithium dendrites, but also significantly prevents polysulfide shuttling. Consequently, a Li–S battery with this hybrid electrolyte exhibits a relatively high reversible capacity and good capacity retention.     

Spike-Frequency Adaptation of a Generalized Leaky Integrate-and-Fire Model Neuron

Although spike-frequency adaptation is a commonly observed property of neurons, its functional implications are still poorly understood. In this work, using a leaky integrate-and-fire neural model that includes a Ca²⁺-activated K⁺ current (I _AHP), we develop a quantitative theory of adaptation temporal dynamics and compare our results with recent in vivo intracellular recordings from pyramidal cells in the cat visual cortex. Experimentally testable relations between the degree and the time constant of spike-frequency adaptation are predicted. We also contrast the I _AHP model with an alternative adaptation model based on a dynamical firing threshold. Possible roles of adaptation in temporal computation are explored, as a a time-delayed neuronal self-inhibition mechanism. Our results include the following: (1) given the same firing rate, the variability of interspike intervals (ISIs) is either reduced or enhanced by adaptation, depending on whether the I _AHP dynamics is fast or slow compared with the mean ISI in the output spike train; (2) when the inputs are Poisson-distributed (uncorrelated), adaptation generates temporal anticorrelation between ISIs, we suggest that measurement of this negative correlation provides a probe to assess the strength of I _AHP in vivo; (3) the forward masking effect produced by the slow dynamics of I _AHP is nonlinear and effective at selecting the strongest input among competing sources of input signals.