A spatial-temporal map of glutamatergic neurogenesis in the murine embryonic cerebellar nuclei uncovers a high degree of cellular heterogeneity.

The nuclei are the main output structures of the cerebellum. Each and every cerebellar cortical computation reaches several areas of the brain by means of cerebellar nuclei processing and integration. Nevertheless, our knowledge of these structures is still limited compared to the cerebellar cortex. Here, we present a mouse genetic inducible fate-mapping study characterizing rhombic lip-derived glutamatergic neurons of the nuclei, the most conspicuous family of long-range cerebellar efferent neurons. Glutamatergic neurons mainly occupy dorsal and lateral territories of the lateral and interposed nuclei, as well as the entire medial nucleus. In mice, they are born starting from about embryonic day 9.5, with a peak between 10.5 and 12.5, and invade the nuclei with a lateral-to-medial progression. While some markers label a heterogeneous population of neurons sharing a common location (BRN2), others appear to be lineage specific (TBR1, LMX1a, and MEIS2). A comparative analysis of TBR1 and LMX1a distributions reveals an incomplete overlap in their expression domains, in keeping with the existence of separate efferent subpopulations. Finally, some tagged glutamatergic progenitors are not labeled by any of the markers used in this study, disclosing further complexity. Taken together, our results obtained in late embryonic nuclei shed light on the heterogeneity of the excitatory neuron pool, underlying the diversity in connectivity and functions of this largely unexplored cerebellar territory. Our findings contribute to laying the groundwork for a comprehensive functional analysis of nuclear neuron subpopulations.

Neuronal models of TDP-43 proteinopathy display reduced axonal translation, increased oxidative stress, and defective exocytosis.

Amyotrophic lateral sclerosis (ALS) is a progressive, lethal neurodegenerative disease mostly affecting people around 50-60 years of age. TDP-43, an RNA-binding protein involved in pre-mRNA splicing and controlling mRNA stability and translation, forms neuronal cytoplasmic inclusions in an overwhelming majority of ALS patients, a phenomenon referred to as TDP-43 proteinopathy. These cytoplasmic aggregates disrupt mRNA transport and localization. The axon, like dendrites, is a site of mRNA translation, permitting the local synthesis of selected proteins. This is especially relevant in upper and lower motor neurons, whose axon spans long distances, likely accentuating their susceptibility to ALS-related noxae. In this work we have generated and characterized two cellular models, consisting of virtually pure populations of primary mouse cortical neurons expressing a human TDP-43 fusion protein, wt or carrying an ALS mutation. Both forms facilitate cytoplasmic aggregate formation, unlike the corresponding native proteins, giving rise to bona fide primary culture models of TDP-43 proteinopathy. Neurons expressing TDP-43 fusion proteins exhibit a global impairment in axonal protein synthesis, an increase in oxidative stress, and defects in presynaptic function and electrical activity. These changes correlate with deregulation of axonal levels of polysome-engaged mRNAs playing relevant roles in the same processes. Our data support the emerging notion that deregulation of mRNA metabolism and of axonal mRNA transport may trigger the dying-back neuropathy that initiates motor neuron degeneration in ALS.

From Pavlov Conditioning to Hebb Learning.

Hebb's learning traces its origin in Pavlov's classical conditioning; however, while the former has been extensively modeled in the past decades (e.g., by the Hopfield model and countless variations on theme), as for the latter, modeling has remained largely unaddressed so far. Furthermore, a mathematical bridge connecting these two pillars is totally lacking. The main difficulty toward this goal lies in the intrinsically different scales of the information involved: Pavlov's theory is about correlations between concepts that are (dynamically) stored in the synaptic matrix as exemplified by the celebrated experiment starring a dog and a ringing bell; conversely, Hebb's theory is about correlations between pairs of neurons as summarized by the famous statement that neurons that fire together wire together. In this letter, we rely on stochastic process theory to prove that as long as we keep neurons' and synapses' timescales largely split, Pavlov's mechanism spontaneously takes place and ultimately gives rise to synaptic weights that recover the Hebbian kernel.

On the Thermodynamics of Particles Obeying Monotone Statistics.

The aim of the present paper is to provide a preliminary investigation of the thermodynamics of particles obeying monotone statistics. To render the potential physical applications realistic, we propose a modified scheme called block-monotone, based on a partial order arising from the natural one on the spectrum of a positive Hamiltonian with compact resolvent. The block-monotone scheme is never comparable with the weak monotone one and is reduced to the usual monotone scheme whenever all the eigenvalues of the involved Hamiltonian are non-degenerate. Through a detailed analysis of a model based on the quantum harmonic oscillator, we can see that: (a) the computation of the grand-partition function does not require the Gibbs correction factor n! (connected with the indistinguishability of particles) in the various terms of its expansion with respect to the activity; and (b) the decimation of terms contributing to the grand-partition function leads to a kind of "exclusion principle" analogous to the Pauli exclusion principle enjoined by Fermi particles, which is more relevant in the high-density regime and becomes negligible in the low-density regime, as expected.

Boltzmann Machines as Generalized Hopfield Networks: A Review of Recent Results and Outlooks.

The Hopfield model and the Boltzmann machine are among the most popular examples of neural networks. The latter, widely used for classification and feature detection, is able to efficiently learn a generative model from observed data and constitutes the benchmark for statistical learning. The former, designed to mimic the retrieval phase of an artificial associative memory lays in between two paradigmatic statistical mechanics models, namely the Curie-Weiss and the Sherrington-Kirkpatrick, which are recovered as the limiting cases of, respectively, one and many stored memories. Interestingly, the Boltzmann machine and the Hopfield network, if considered to be two cognitive processes (learning and information retrieval), are nothing more than two sides of the same coin. In fact, it is possible to exactly map the one into the other. We will inspect such an equivalence retracing the most representative steps of the research in this field.