Basket to Purkinje Cell Inhibitory Ephaptic Coupling Is Abolished in Episodic Ataxia Type 1

Dominantly inherited missense mutations of the KCNA1 gene, which encodes the KV1.1 potassium channel subunit, cause Episodic Ataxia type 1 (EA1). Although the cerebellar incoordination is thought to arise from abnormal Purkinje cell output, the underlying functional deficit remains unclear. Here we examine synaptic and non-synaptic inhibition of Purkinje cells by cerebellar basket cells in an adult mouse model of EA1. The synaptic function of basket cell terminals was unaffected, despite their intense enrichment for KV1.1-containing channels. In turn, the phase response curve quantifying the influence of basket cell input on Purkine cell output was maintained. However, ultra-fast non-synaptic ephaptic coupling, which occurs in the cerebellar ‘pinceau’ formation surrounding the axon initial segment of Purkinje cells, was profoundly reduced in EA1 mice in comparison with their wild type littermates. The altered temporal profile of basket cell inhibition of Purkinje cells underlines the importance of Kv1.1 channels for this form of signalling, and may contribute to the clinical phenotype of EA1

Extrasynaptic Glutamate Spillover in the Hippocampus: Dependence on Temperature and the Role of Active Glutamate Uptake

AbstractAt excitatory synapses on CA1 pyramidal cells of the hippocampus, a larger quantal content is sensed by N-methyl-D-aspartic acid receptors (NMDARs) than by α-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid receptors (AMPARs). A novel explanation for this discrepancy is that glutamate released from terminals presynaptic to one cell can diffuse to and activate NMDARs, but not AMPARs, on a neighboring cell. If this occurs in the living brain, it could invalidate the view that glutamatergic synapses function as private communication channels between neurons. Here, we show that the discrepancy in quantal content mediated by the two receptors is greatly decreased at physiological temperature, compared with conventional recording conditions. This effect of temperature is not due to changes in release probability or uncovering of latent AMPARs. It is, however, partially reversed by the glutamate uptake inhibitor dihydrokainate. The results suggest that glutamate transporters play a critical role in limiting the extrasynaptic diffusion of glutamate, thereby minimizing cross-talk between neighboring excitatory synapses

Spike-Timing Dependent Plasticity in Inhibitory Circuits

Inhibitory circuits in the brain rely on GABA-releasing interneurons. For long, inhibitory circuits were considered weakly plastic in the face of patterns of neuronal activity that trigger long-term changes in the synapses between excitatory principal cells. Recent studies however have shown that GABAergic circuits undergo various forms of long-term plasticity. For the purpose of this review, we identify three major long-term plasticity expression sites. The first locus is the glutamatergic synapses that excite GABAergic inhibitory cells and drive their activity. Such synapses, on many but not all inhibitory interneurons, exhibit long-term potentiation (LTP) and depression (LTD). Second, GABAergic synapses themselves can undergo changes in GABA release probability or postsynaptic GABA receptors. The third site of plasticity is in the postsynaptic anion gradient of GABAergic synapses; coincident firing of GABAergic axons and postsynaptic neurons can cause a long-lasting change in the reversal potential of GABAA receptors mediating fast inhibitory postsynaptic potentials. We review the recent literature on these forms of plasticity by asking how they may be triggered by specific patterns of pre- and postsynaptic action potentials, although very few studies have directly examined spike-timing dependent plasticity (STDP) protocols in inhibitory circuits. Plasticity of interneuron recruitment and of GABAergic signaling provides for a rich flexibility in inhibition that may be central to many aspects of brain function. We do not consider plasticity at glutamatergic synapses on Purkinje cells and other GABAergic principal cells

Monosynaptic GABAergic Signaling from Dentate to CA3 with a Pharmacological and Physiological Profile Typical of Mossy Fiber Synapses

AbstractMossy fibers are the sole excitatory projection from dentate gyrus granule cells to the hippocampus, where they release glutamate, dynorphin, and zinc. In addition, mossy fiber terminals show intense immunoreactivity for the inhibitory neurotransmitter GABA. Fast inhibitory transmission at mossy fiber synapses, however, has not previously been reported. Here, we show that electrical or chemical stimuli that recruit dentate granule cells elicit monosynaptic GABAA receptor–mediated synaptic signals in CA3 pyramidal neurons. These inhibitory signals satisfy the criteria that distinguish mossy fiber–CA3 synapses: high sensitivity to metabotropic glutamate receptor agonists, facilitation during repetitive stimulation, and NMDA receptor–independent long-term potentiation. GABAergic transmission from the dentate gyrus to CA3 has major implications not only for information flow into the hippocampus but also for developmental and pathological processes involving the hippocampus

On SAT representations of XOR constraints

We study the representation of systems S of linear equations over the two-element field (aka xor- or parity-constraints) via conjunctive normal forms F (boolean clause-sets). First we consider the problem of finding an "arc-consistent" representation ("AC"), meaning that unit-clause propagation will fix all forced assignments for all possible instantiations of the xor-variables. Our main negative result is that there is no polysize AC-representation in general. On the positive side we show that finding such an AC-representation is fixed-parameter tractable (fpt) in the number of equations. Then we turn to a stronger criterion of representation, namely propagation completeness ("PC") --- while AC only covers the variables of S, now all the variables in F (the variables in S plus auxiliary variables) are considered for PC. We show that the standard translation actually yields a PC representation for one equation, but fails so for two equations (in fact arbitrarily badly). We show that with a more intelligent translation we can also easily compute a translation to PC for two equations. We conjecture that computing a representation in PC is fpt in the number of equations.Comment: 39 pages; 2nd v. improved handling of acyclic systems, free-standing proof of the transformation from AC-representations to monotone circuits, improved wording and literature review; 3rd v. updated literature, strengthened treatment of monotonisation, improved discussions; 4th v. update of literature, discussions and formulations, more details and examples; conference v. to appear LATA 201

Dendritic NMDA receptors in parvalbumin neurons enable strong and stable neuronal assemblies

Parvalbumin-expressing (PV+) GABAergic interneurons mediate feedforward and feedback inhibition and have a key role in gamma oscillations and information processing. The importance of fast synaptic recruitment, action potential initiation and repolarization, and rapid synchronous GABA release by PV+ cells is well established. In contrast, the functional significance of PV+ cell NMDA receptors (NMDARs), which generate relatively slow postsynaptic currents, is unclear. Underlining their importance, several studies implicate PV+ cell NMDAR disruption in impaired network function and circuit pathologies. Here, we show that dendritic NMDARs underlie supralinear integration of feedback excitation from local pyramidal neurons onto mouse CA1 PV+ cells. Furthermore, by incorporating NMDARs at feedback connections onto PV+ cells in spiking networks, we show that these receptors enable cooperative recruitment of PV+ interneurons, strengthening and stabilising principal cell assemblies. Failure of this phenomenon provides a parsimonious explanation for cognitive and sensory gating deficits in pathologies with impaired PV+ NMDAR signalling

Dysfunction of the CaV2.1 calcium channel in cerebellar ataxias

Mutations in the CACNA1A gene are associated with episodic ataxia type 2 (EA2) and spinocerebellar ataxia type 6 (SCA6). CACNA1A encodes the α-subunit of the P/Q-type calcium channel or CaV2.1, which is highly enriched in the cerebellum. It is one of the main channels linked to synaptic transmission throughout the human central nervous system. Here, we compare recent advances in the understanding of the genetic changes that underlie EA2 and SCA6 and what these new findings suggest about the mechanism of the disease

An Improved Exact Algorithm for the Exact Satisfiability Problem

The Exact Satisfiability problem, XSAT, is defined as the problem of finding a satisfying assignment to a formula $\varphi$ in CNF such that exactly one literal in each clause is assigned to be "1" and the other literals in the same clause are set to "0". Since it is an important variant of the satisfiability problem, XSAT has also been studied heavily and has seen numerous improvements to the development of its exact algorithms over the years. The fastest known exact algorithm to solve XSAT runs in $O(1.1730^n)$ time, where $n$ is the number of variables in the formula. In this paper, we propose a faster exact algorithm that solves the problem in $O(1.1674^n)$ time. Like many of the authors working on this problem, we give a DPLL algorithm to solve it. The novelty of this paper lies on the design of the nonstandard measure, to help us to tighten the analysis of the algorithm further