Distal hereditary motor neuropathies (HMNs) and axonal Charcot-Marie-Tooth neuropathy (CMT2) are clinically and genetically heterogeneous diseases characterized primarily by motor neuron degeneration and distal weakness. The genetic cause for about half of the individuals affected by HMN/CMT2 remains unknown. Here, we report the identification of pathogenic variants in GBF1 (Golgi brefeldin A-resistant guanine nucleotide exchange factor 1) in four unrelated families with individuals affected by sporadic or dominant HMN/CMT2. Genomic sequencing analyses in seven affected individuals uncovered four distinct heterozygous GBF1 variants, two of which occurred de novo . Other known HMN/CMT2-implicated genes were excluded. Affected individuals show HMN/CMT2 with slowly progressive distal muscle weakness and musculoskeletal deformities. Electrophysiological studies confirmed axonal damage with chronic neurogenic changes. Three individuals had additional distal sensory loss. GBF1 encodes a guanine-nucleotide exchange factor that facilitates the activation of members of the ARF (ADP-ribosylation factor) family of small GTPases. GBF1 is mainly involved in the formation of coatomer protein complex (COPI) vesicles, maintenance and function of the Golgi apparatus, and mitochondria migration and positioning. We demonstrate that GBF1 is present in mouse spinal cord and muscle tissues and is particularly abundant in neuropathologically relevant sites, such as the motor neuron and the growth cone. Consistent with the described role of GBF1 in Golgi function and maintenance, we observed marked increase in Golgi fragmentation in primary fibroblasts derived from all affected individuals in this study. Our results not only reinforce the existing link between Golgi fragmentation and neurodegeneration but also demonstrate that pathogenic variants in GBF1 are associated with HMN/CMT2.

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In this study, we consider spring-mass systems subjected to piecewise constant forces. We investigate sucient conditions for the existence of periodic solutions of homogeneous and nonhomogeneous damped spring-mass systems with the help of the Floquet theory. In addition to determining conditions for the existence of periodic solutions, stability analysis is performed for the solutions of the homogeneous system. The Floquet multipliers are taken into account for the stability analysis [3]. The results are stated in terms of the parameters of the systems. These results are illustrated and supported by simulations for dierent values of the parameters.

In this study, we develop a model of recurrent neural networks with functional dependence on piecewise constant argument of generalized type. Using the theoretical results obtained for functional differential equations with piecewise constant argument, we investigate conditions for existence and uniqueness of solutions, bounded solutions, and exponential stability of periodic solutions. We provide conditions based on the parameters of the model.

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