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Physiological roles of gap junctions and electrical synapses:
Because of the relatively large diameter of their inner pore, gap junctions allow a unique mode of communication between connected cells, by enabling the transfer of ions, metabolites and second messengers having a molecular weight up to 1kDa. Connected cells therefore tend to equilibrate their membrane potentials, and their cytoplasmic composition. These properties combine in different systems to synchronize and homogenize cells’ activity.
For example, the heart expresses a very large number of gap junctions of different isoforms (mostly Cx40, Cx43 and Cx45 – Davis et al., 1994; Davis et al., 1995), and these gap junctions are required for the synchronous contraction of cardiomyocytes. In the vascular system, homogeneous metabolic state between smooth muscles, enabled by gap junctions, ensures a homogeneous resistance of the tissue, ultimately participating in the regulation of blood pressure. Numerous reports indicate changes in connexin regulation and expression in this tissue, in pathological conditions such as diabetes or hypertension (Zhang and Hill, 2005; Hamelin et al., 2009). I would also like to mention the interesting case of gap junctions in the lens, an avascular organ within the eye. In this case, gap junctions between the exterior epithelium and the inner fibers create a syncytium-like tissue, and allow the epithelial cells to literally feed the fibers with nutrients (reviewed in Mathias et al., 2007).
In the next section, I will focus on the physiological roles of electrical synapses, which are gap junctions expressed in neurons.
Physiological role of electrical synapses:
Since electrical synapses allow a passive spread of current between two connected neurons, one of their first attributed physiological role was to mediate synchrony (i.e., correlated spiking) in population of neurons (Beirlein et al., 2000; Landisman et al., 2002; Long et al., 2004), either because of subthreshold membrane potentials equilibration or spikelet transmission. The role of electrical synapses in synchrony was first demonstrated in hippocampal slices in vitro (Draguhn et al., 1998 – Figure I-5), when extracellular recordings in the dentate gyrus, CA1 and CA3, revealed brief bursts of spontaneous high-frequency oscillations (150-200Hz) which were not abolished in presence of gabazine (blocker of GABAA receptors), NBQX (blocker of AMPA receptors), or in absence of extracellular Ca2+ (aiming to block all forms of chemical synaptic transmission). However, the use of gap junction antagonists (either Octanol, halothane or carbenoxolone) was sufficient to reversibly block these correlated discharges.
Passive properties and cable filtering:
Cable filtering can be understood intuitively because of the analogy of the cell membrane with a low-pass filter (i.e., the cell membrane having both channels responsible for its resistivity (R), and lipids arranged in a bilayer fashion acting like capacitors (C), their combination in parallel of each other constitutes an RC filter in electrical terms). As a consequence, a passive membrane is expected to dampen high frequency signals. This means that any electrical current flowing between two points in a neuron will experience a decrease in its peak amplitude, and a slowdown of its kinetics. This phenomenon will be more pronounced for rapid signals (e.g., AMPAergic currents in interneurons), and for signals travelling over long distances in the neuron (e.g., a synaptic event in a remote dendritic compartment spreading to the soma).
This qualitative behaviour has been extensively described in mathematical forms, notably by Wilfrid Rall (tens of articles published between 1953 and 1968), and Guy Major. I also wish to mention two excellent text books (Jack, Noble and Tsien, 1975; Johnston and Wu, 1995), which provide not only an extensive and comprehensive understanding of these phenomena, but also rich repertoires of references for scientific articles related to this topic.
The starting point is usually to consider the analogy of the cell membrane with electrical circuits. In this framework, a single neuron is represented as a « ball » (representing the somatic compartment), onto which are attached « sticks » (representing the dendritic branches). These branches are modelled as cylinders displaying three electrical components:
– an internal resistance (ri), representing how the voltage drops along branches when electrical currents flow.
– a membrane resistance (rm), representing how electrical currents “leak out” of the cell through ion channels opened at rest, without voltage- or ligand-gating mechanisms.
– and a membrane capacitance (cm), representing how charge accumulate on both sides of the cell membrane.
Each of these parameters is expressed in units of impedance, with units of length of dendritic cables (ri in Ω/cm, rm in Ω.cm, and cm in F/cm). These parameters are referred to as « passive », because none of them varies with the voltage drop across the membrane. The general equation describing membrane potential evolution along such cylindrical structures is known as “the cable equation”, generally expressed as follows: 𝜆𝐷𝐶2𝜕2𝑉𝜕𝑥2= 𝜏𝑚𝜕𝑉𝜕𝑡+𝑉 (1).
Hyperpolarisation-activated cation channels:
These channels are quite unique, because they are permeable to both Na+ and K+. Their opening causes a net inward current called Ih (associated to a reversal potential between -20 and 0mV), and this opening is enhanced by hyperpolarization (Yanagihara and Irisawa, 1980). They can therefore cause rebound activity after strong inhibition (Lüthi and McCormick, 1998). They also display a cytoplasmic domain typical of cyclic-nucleotide-bindind domains. Binding of cytoplasmic cAMP to this domain shifts the voltage-dependent activation curve of HCN channels towards more depolarized values, which can ultimately lead to a significant steady-state Ih current in nerve cells when they are at rest (Maccaferri et al., 1993).
Non-linear dendritic integration:
In contrast to cable filtering, dendritic integration can be a non-linear process far more delicate to apprehend. Indeed, if one considers only EPSPs and disregards IPSPs (for the time being), the amplitude and shape of two or more EPSPs occurring within a small time window (compound EPSP), and in proximity of each other (same electrical compartment) may be different from their expected arithmetic sum (Tran-Van-Minh et al., 2015). Dendritic integration can therefore be classified in three groups: linear, supralinear or sublinear, depending on if the compound EPSP is equal to, larger than or smaller than, respectively, the arithmetic sum of the individual EPSPs (Figure I-10, from Tran-Van-Minh et al., 2015). Common dendritic features which endow neurons with non-linear dendritic integration properties are passive cable properties (Abrahamsson et al., 2012) and ligand or voltage-gated ion channel expression (reviewed in Tran-Van-Minh et al., 2015). Non-linear dendritic integration can increase the computational power of neurons (i.e., increase the number of implementable functions which would transform a given number of inputs into different outputs – Cazé et al., 2013), and confer pattern separation properties (Poirazi and Mel, 2001).
Active conductances can counteract electrical filtering:
In a first example (Magee, 2000 – Figure I-12), CA1 pyramidal cells were shown to display two specific features counterbalancing the effects of electrical filtering. While passive properties of dendrites filter high frequency signals out, causing a decrease in amplitude and kinetics of electrical currents as they propagate to the soma, it was shown that, in CA1 pyramidal cells, local EPSPs in dendrites have increasingly higher amplitudes as they are more and more distal, which compensates for the decrease in amplitude they will experience while propagating to the soma. The process of increasing the number of post-synaptic receptors to increase the amplitude of the post-synaptic current seems to serve the purpose (such phrasing has to be written, and therefore read, with high caution: observing a correlation between two parameters A and B is not sufficient to prove any form of causality between them) of normalizing the peak amplitude of synaptic currents arriving in the soma, no matter where they originate from in the dendritic tree. It should be noted, however, that this phenomenon is not, strictly speaking, an active process: the fact that more current is delivered in distal dendritic A schematic pyramidal neurons (y) receives synaptic inputs distributed over n dendritic branches, each of them associated with a non-linear function (s(ni)) and a functional weight over the cell body (ai), itself associated with a threshold function g.
compartments is due to the fact that the synapses of distal compartments display more receptors, and not because a voltage-dependent phenomenon causes these receptors to deliver more current.
Additionally, there exists a gradient of HCN channels along these dendrites, which are opened at rest and deactivated by local changes in membrane potential. The “virtual” outward currents (and local changes in input resistance) produced by their closure leads to a faster repolarization of the cell membrane, which counterbalances temporal widening of distal inputs due to electrical filtering. Ultimately, this phenomenon makes distal input as equal as proximal ones to summate over time.
Active conductances in non-linear dendritic integration:
In this paragraph, I will show one example, among many, where synaptic inputs were shown to summate non-linearly. In layer 2/3 CA3 pyramidal cells of the somatosensory cortex, it was demonstrated that co-activation of clustered synaptic sites in the basal dendrites leads to compound EPSPs having a peak amplitude systematically higher than the peak amplitude of the arithmetic sum of the individual responses (Branco and Haüsser, 2011 – Figure I-12), a phenomenon known as supralinearity. By performing glutamate uncaging experiments in diffraction limited spots onto dendritic spines (an experimental manipulation which aims at mimicking synaptic transmission with high spatial and temporal resolution), the authors recorded synaptic responses when a single synapse was photo-stimulated at a time, or when multiple synapses were co-activated, and found that the non-linearity observed in control conditions was dampened by blocking L-type Voltage-Gated Calcium Channels (VGCCs), and abolished by blocking NMDA receptors with D-AP5. Their results indicate that photo-uncaging onto single synaptic sites mostly triggers the opening of AMPA receptors, and little activation of VGCCs and NMDA receptors; however, co-activation of multiples synaptic sites causes a local depolarization sufficiently strong to remove Mg2+ ions from the interior of NMDA receptors in individual spines, which then become available for opening by photo-released glutamate. Consequently, synaptic currents in the co-activation regime are now a sum of individual AMPA currents already present in single stimulation responses, along with NMDA- and VGCC-mediated currents recruited exclusively in the co-activation regime. The supralinearity observed is then due to the fact that NMDA/VGCC currents and AMPA currents are all inward currents (i.e., if they had an opposite polarity, a sublinearity would be observed instead).
Table of contents :
Preface:
Chapter I – Introduction:
I) Neurons as individual, electrically excitable, nerve cells, communicating through synapses:
Historical overview on the mode of communication between neurons:
II) Electrical synaptic communication:
Historical experiment revealing electrical coupling:
Slow acceptance of electrical coupling by the scientific community:
Electrical synapses as the molecular basis of electrical coupling:
Definition of electrical synapses:
Molecular composition of electrical synapses, and plasticity:
Molecular composition of gap junctions:
Plasticity of electrical synapses:
Structural and functional differences between electrical and chemical synapses:
Physiological roles of gap junctions and electrical synapses:
Physiological roles of gap junctions:
Physiological role of electrical synapses:
III) Dendritic and synaptic integration:
Passive properties and cable filtering:
Active conductances:
Non-linear dendritic integration:
Active conductances can counteract electrical filtering:
Active conductances in non-linear dendritic integration:
Role of neuronal morphology in non-linear dendritic integration:
Integration of excitatory and inhibitory inputs:
Subcellular compartment targeting, and input/output relationship:
Temporal integration of excitatory and inhibitory inputs: example of feed-forward inhibition:
Electrical synapses in the context of dendritic integration:
IV) The cerebellum as a canonical microcircuit:
The cerebellar cortex:
Cell-type diversity and cytoarchitecture:
Differences between stellate cells and basket cells:
Synaptic plasticity in the cerebellar cortex:
Cerebellum-like structures:
Role of the cerebellum in physiology:
Early models of pattern separation in the cerebellar cortex:
Eye-blink conditioning – a classical example of cerebellar temporal learning:
Implication of the cerebellum in sensory motor control:
Implication of the cerebellum in non-motor tasks:
Proposed unifying theories of the role of cerebellum and cerebellar-like structures:
Temporal specific learning:
Multisensory integration:
Multisensory integration and temporal specific learning in cerebellum-like structures:
Long- and short-term plasticity as bases for temporal learning:
Inhibitory interneurons and time processing:
Chapter II – Materials and Methods:
Electrophysiology:
Transmitted light and fluorescence imaging:
Image analysis:
Pharmacological agents:
Parallel fibre-mediated responses:
Detecting electrical and/or chemical synapses in paired recordings:
Data analysis and statistics:
Chapter III: Electrical synapses within a feed-forward electrical circuit generate temporal contrast enhancement:
I) Abstract:
II) Introduction:
III) Results:
PF-evoked and direct recruitment of MLI’s spikelets
Modulation of spikelet polarity by presynaptic membrane potential:
Electrical synapses form the majority of inhibitory connections between BCs in adult animals:
Feed-forward recruitment of spikelets narrows single EPSP time-window, and dampens temporal summation:
Spikelet signalling enables temporal contrast enhancement of temporally coded excitation:
IV) Discussion:
Electrical connectivity of cerebellar cortex is tuned for rapid output synchrony .
Electrical synapses reinforce coincidence detection in electrically connected interneurons
Implications of eFFM in fine-tuning cerebellar-dependent motor behaviours
V) Supplementary figures:
Chapter IV – Integration and modulation of electrical synapses-mediated inputs in cerebellar basket cells:
I) Evidence for transmission of subthreshold EPSCs across electrical synapses:
Discussion:
II) Role of HCN channels in shaping AP waveform, and transmitted spikelets:
Discussion:
III) Frequency-dependent temporal summation of spikelets:
Discussion:
IV) Conclusion:
Chapter V – Evidence for differential dendritic integration properties between SCs and BCs:
I) Differences in dendritic morphology between stellate and basket cells:
BCs have larger dendrites than SCs:
Differences of cable filtering influence between theoretical predications and in vivo data:
II) Impact of cable filtering on PF-mediated EPSCs in BCs and SCs:
Synaptic currents and potentials are unevenly affected by electrical filtering:
Indirect evidence of the passive role of electrical synapses in sharpening EPSP kinetics:
III) Discussion:
Differential dendritic integration behaviour of EPSCs in MLIs:
Passive effect of electrical synapses:
Chapter VI – Discussion, and perspectives
I) Electrical connectivity and spikelet transmission in BCs:
Spikelets can be used to retrieve the resting membrane potential of unperturbed, electrically-connected cells:
Technical considerations on the new method:
Electrical synapses are more frequent than chemical synapses in adult mice:
Spikelet transmission displays characteristic features of FFI:
Narrowing EPSP time window:
Dampening temporal summation:
Frequency-dependent inhibitory action of spikelets:
Spikelets mediate temporal contrast enhancement and coincidence detection:
Transient excitation followed by long-lasting inhibition:
Comparison with previous studies of spikelet transmission in cerebellar basket cells:
Implication for cerebellar processing:
II) Addressing the dendritic integration properties of cerebellar basket cells:
III) Large scale implications:
Implication for cerebellar computation:
Conclusion:
References:
Appendices:
Evidence for indirect coupling in paired recordings:
Simultaneous recruitment of EPSP and spikelets narrows half-width of EPSPs: .
Impact of stimulation intensity of PFs on the temporal summation of EPSPs:
Testing the hypothesis that HCN channels can shape transmitted spikelets: inconclusive but insightful experiments:
Testing the hypothesis that spikelets influence EPSPs’ kinetics – inconclusive but insightful experiments:
Supplementary methods:
Retrieving the resting membrane potential of electrically connected cells
