Effect of neuritic cables on conductance estimates for remote electrical synapses

Modulation of Murine Olivary Connexin 36 Gap Junctions by PKA and CaMKII

The inferior olive (IO) is a nucleus located in the brainstem and it is part of the olivo-cerebellar loop. This circuit plays a fundamental role in generation and acquisition of coherent motor patterns and it relies on synchronous activation of groups of Purkinje cells (PC) in the cerebellar cortex. IO neurons integrate their intrinsic oscillatory activity with excitatory inputs coming from the somatosensory system and inhibitory feedback coming from the cerebellar nuclei. Alongside these chemical synaptic inputs, IO neurons are coupled to one another via connexin 36 (Cx36) containing gap junctions (GJs) that create a functional syncytium between neurons. Communication between olivary neurons is regulated by these GJs and their correct functioning contributes to coherent oscillations in the IO and proper motor learning. Here, we explore the cellular pathways that can regulate the coupling between olivary neurons. We combined in vitro electrophysiology and immunohistochemistry (IHC) on mouse acute brain slices to unravel the pathways that regulate olivary coupling. We found that enhancing the activity of the protein kinase A (PKA) pathway and blocking the Ca²⁺/calmodulin-dependent protein kinase II (CaMKII) pathway can both down-regulate the size of the coupled network. However, these two kinases follow different mechanisms of action. Our results suggest that activation of the PKA pathway reduces the opening probability of the Cx36 GJs, whereas inhibition of the CaMKII pathway reduces the number of Cx36 GJs. The low densities of Cx36 proteins and electrical synapses in βCaMKII knock-out mice point towards an essential role for this protein kinase in regulating the density of GJs in the IO. Thus, the level of olivary coupling is a dynamic process and regulated by a variety of enzymes modulating GJs expression, docking and activity.

From Neuron Biophysics to Orientation Selectivity in Electrically Coupled Networks of Neocortical L2/3 Large Basket Cells

In the neocortex, inhibitory interneurons of the same subtype are electrically coupled with each other via dendritic gap junctions (GJs). The impact of multiple GJs on the biophysical properties of interneurons and thus on their input processing is unclear. The present experimentally based theoretical study examined GJs in L2/3 large basket cells (L2/3 LBCs) with 3 goals in mind: (1) To evaluate the errors due to GJs in estimating the cable properties of individual L2/3 LBCs and suggest ways to correct these errors when modeling these cells and the networks they form; (2) to bracket the GJ conductance value (0.05-0.25 nS) and membrane resistivity (10 000-40 000 Ω cm(2)) of L2/3 LBCs; these estimates are tightly constrained by in vitro input resistance (131 ± 18.5 MΩ) and the coupling coefficient (1-3.5%) of these cells; and (3) to explore the functional implications of GJs, and show that GJs: (i) dynamically modulate the effective time window for synaptic integration; (ii) improve the axon's capability to encode rapid changes in synaptic inputs; and (iii) reduce the orientation selectivity, linearity index, and phase difference of L2/3 LBCs. Our study provides new insights into the role of GJs and calls for caution when using in vitro measurements for modeling electrically coupled neuronal networks.

The robustness of phase-locking in neurons with dendro-dendritic electrical coupling

We examine the effects of dendritic filtering on the existence, stability, and robustness of phase-locked states to heterogeneity and noise in a pair of electrically coupled ball-and-stick neurons with passive dendrites. We use the theory of weakly coupled oscillators and analytically derived filtering properties of the dendritic coupling to systematically explore how the electrotonic length and diameter of dendrites can alter phase-locking. In the case of a fixed value of the coupling conductance (gc) taken from the literature, we find that repeated exchanges in stability between the synchronous and anti-phase states can occur as the electrical coupling becomes more distally located on the dendrites. However, the robustness of the phase-locked states in this case decreases rapidly towards zero as the distance between the electrical coupling and the somata increases. Published estimates of gc are calculated from the experimentally measured coupling coefficient (CC) based on a single-compartment description of a neuron, and therefore may be severe underestimates of gc. With this in mind, we re-examine the stability and robustness of phase-locking using a fixed value of CC, which imposes a limit on the maximum distance the electrical coupling can be located away from the somata. In this case, although the phase-locked states remain robust over the entire range of possible coupling locations, no exchanges in stability with changing coupling position are observed except for a single exchange that occurs in the case of a high somatic firing frequency and a large dendritic radius. Thus, our analysis suggests that multiple exchanges in stability with changing coupling location are unlikely to be observed in real neural systems.

Measuring action potential-evoked transmission at individual synaptic contacts

In the neuronal culture experimental system, the total synaptic connection between two neurons can consist of large numbers of synaptic sites, each behaving probabilistically. Studies of synaptic function with paired recordings typically consider the summed response across all of these sites and from this infer the average response. Understanding of synaptic transmission and plasticity could be improved by examination of activity at as few synaptic sites as possible. To this end, we develop a system for recording responses from individual contacts. It relies on a precisely regulated pneumatic/hydrostatic pressure system to create a microenvironment within which individual synapses are active, and an acoustic signature method to monitor the stability of this microenvironment noninvasively. With this method we are able to record action potential-evoked postsynaptic currents consistent with individual quanta. The approach does not distort synaptic current waveforms and permits stable recording for several hours. The method is applied to address mechanisms of short-term plasticity, the variability of latency at individual synaptic sites and, in a preliminary experiment, the independence of nearby synapses on the same axon.

The passive cable properties of hair cell stereocilia and their contribution to somatic capacitance measurements

Somatic measurements of whole-cell capacitance are routinely used to understand physiologic events occurring in remote portions of cells. These studies often assume the intracellular space is voltage-clamped. We questioned this assumption in auditory and vestibular hair cells with respect to their stereocilia based on earlier studies showing that neurons, with radial dimensions similar to stereocilia, are not always isopotential under voltage-clamp. To explore this, we modeled the stereocilia as passive cables with transduction channels located at their tips. We found that the input capacitance measured at the soma changes when the transduction channels at the tips of the stereocilia are open compared to when the channels are closed. The maximum capacitance is felt with the transducer closed but will decrease as the transducer opens due to a length-dependent voltage drop along the stereocilium length. This potential drop is proportional to the intracellular resistance and stereocilium tip conductance and can produce a maximum capacitance error on the order of fF for single stereocilia and pF for the bundle.

Membrane capacitance measurements revisited: dependence of capacitance value on measurement method in nonisopotential neurons

During growth or degeneration neuronal surface area can change dramatically. Measurements of membrane protein concentration, as in ion channel or ionic conductance density, are often normalized by membrane capacitance, which is proportional to the surface area, to express changes independently from cell surface variations. Several electrophysiological protocols are used to measure cell capacitance, all based on the assumption of membrane isopotentiality. Yet, most neurons violate this assumption because of their complex anatomical structure, raising the question of which protocol yields measurements that are closest to the actual total membrane capacitance. We measured the capacitance of identified neurons from crab stomatogastric ganglia using three different protocols: the current-clamp step, the voltage-clamp step, and the voltage-clamp ramp protocols. We observed that the current-clamp protocol produced significantly higher capacitance values than those of either voltage-clamp protocol. Computational models of various anatomical complexities suggest that the current-clamp protocol can yield accurate capacitance estimates. In contrast, the voltage-clamp protocol estimates rapidly deteriorate as isopotentiality is reduced. We provide a mathematical description of these results by analyzing a simple two-compartment model neuron to facilitate an intuitive understanding of these methods. Together, the experiments, modeling, and mathematical analysis indicate that accurate total membrane capacitance measurements cannot be obtained with voltage-clamp protocols in nonisopotential neurons. Furthermore, although current-clamp steps can theoretically yield accurate measurements, experimentalists should be aware of limitations imposed by step duration and numerical errors during fitting procedures to obtain the membrane time constant.

Inferring connection proximity in networks of electrically coupled cells by subthreshold frequency response analysis

Electrical synapses continuously transfer signals bi-directionally from one cell to another, directly or indirectly via intermediate cells. Electrical synapses are common in many brain structures such as the inferior olive, the subcoeruleus nucleus and the neocortex, between neurons and between glial cells. In the cortex, interneurons have been shown to be electrically coupled and proposed to participate in large, continuous cortical syncytia, as opposed to smaller spatial domains of electrically coupled cells. However, to explore the significance of these findings it is imperative to map the electrical synaptic microcircuits, in analogy with in vitro studies on monosynaptic and disynaptic chemical coupling. Since "walking" from cell to cell over large distances with a glass pipette is challenging, microinjection of (fluorescent) dyes diffusing through gap-junctions remains so far the only method available to decipher such microcircuits even though technical limitations exist. Based on circuit theory, we derive analytical descriptions of the AC electrical coupling in networks of isopotential cells. We then suggest an operative electrophysiological protocol to distinguish between direct electrical connections and connections involving one or more intermediate cells. This method allows inferring the number of intermediate cells, generalizing the conventional coupling coefficient, which provides limited information. We validate our method through computer simulations, theoretical and numerical methods and electrophysiological paired recordings.

Electrical synapses in basal ganglia

The basal ganglia (BG) provide a major integrative system of the forebrain involved in the organization of goal-directed behaviour. Pathological alteration of BG function leads to major motor and cognitive impairments such as observed in Parkinson's disease. Recent advances in BG research stress the role of neural oscillations and synchronization in the normal and pathological function of BG. As demonstrated in several brain structures, these patterns of neural activity can emerge from electrically coupled neuronal networks. This review aims at addressing the presence, functionality and putative role of electrical synapses in BG, with a particular emphasis on the striatum and the substantia nigra pars compacta (SNc), two main BG nuclei in which the existence and functional properties of neuronal coupling are best documented.

Magnetic stimulation of curved nerves

Magnetic stimulation of nerves is attracting increased attention recently, as it has been found to be useful in therapy of neural disorders in humans. In an effort to explain the mechanisms of magnetic stimulation, we focus in this paper on the dependence of magnetic stimulation on neuronal morphology and in particular on the importance of curvature of axonal bundles. Using the theory of passive membrane dynamics, we predict the threshold power (the minimum stimulation power required to initiate an action potential) of specific axonal morphologies. In the experimental section, we show that magnetic stimulation of the frog sciatic nerve follows our theoretical predictions. Furthermore, the voltage length constant of the nerve can be measured based on these results alone.