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Topicality of the study is driven by the fact that the new fundamental mathematical ideas and methods of mathematics arise in the new era of mathematization of science and have a great influence on the formation of methodological culture of educational research in recent decades. The aim of the article is to identify the important aspects of the methodology of mathematization of pedagogical science. The leading approach to the study of this problem is a philosophical and mathematical analysis of aspects of the methodology of mathematization of pedagogical science that allows to consider in complex the aspects revealing in the light of mathematization of sciences. The analysis of the specified aspects describes the main features of a methodological interaction between mathematical and pedagogical science, the influence of the ideas and methods of modern mathematics and mathematical culture on pedagogical research, on the formation of conceptual and terminological bases of correct logic and of the reasoning of pedagogical research. The materials of the article can be used in the correct use of ideas and methods of modern mathematics during the study of the characteristic features of pedagogical objects, processes and phenomena.

The application of selenocysteine in a supported phase method to direct native folding and produce [alpha]-conotoxins efficiently with improved biophysical properties is reported. The results obtained provide insight into the development of more stable and potent nicotinic antagonists suitable for new drug therapies, and highlight the application of selenocysteine technology more broadly to disulfide-bonded peptides and proteins.

Abstract: N-methyl-d-aspartate (NMDA)-type glutamate receptors perform critical functions during the development of the nervous system and in the initiation of synaptic plasticity. An important mechanism in setting the gain of NMDA receptors involves the stimulation of G-protein-coupled receptors (GPCRs), which through activation of protein tyrosine kinases leads to an upregulation of NMDA receptors. In contrast, little is known about how NMDA receptors are downregulated. In the present study, we characterized a signaling pathway that mediates the depression of NMDA receptor function in response to stimulation of muscarinic acetylcholine receptors. Whole-cell patch-clamp recordings obtained from CA3 pyramidal cells in organotypic slice cultures revealed that under conditions of low intracellular calcium buffering application of muscarine-depressed NMDA receptor current. The sensitivity of this response to pirenzipine indicated that the M1 acetylcholine receptor is mediating this depression. The muscarine-induced depression of NMDA current was prevented by blocking G-protein function or after depleting intracellular Ca2+ stores with cyclopiazonic acid. Inhibitors of calmodulin prevented the depression whereas blocking calcineurin enhanced the depression of NMDA currents. Blocking tyrosine phosphatase activity with pervanandate converted the muscarine-induced depression into a potentiation of NMDA currents, whereas blocking protein kinase A (H-89), Src kinase (PP2, SU6656), or PKC (GF 109203X) failed to prevent the depression of NMDA currents. As Src tyrosine kinase is known to phosphorylate and upregulate NMDA receptors, we propose that a protein tyrosine phosphatase(s) counteracting the action of Src is the final target in the mAChR-dependent inhibitory signaling cascade. Our data are consistent with a transduction cascade comprising an M1 acetylcholine receptor→G-protein→Ca2+ release→calmodulin→tyrosine phosphatase. [Copyright &y& Elsevier]

Treatments for cognitive deficits associated with central nervous system (CNS) disorders such as Alzheimer disease and schizophrenia remain significant unmet medical needs that incur substantial pressure on the health care system. The α 7 nicotinic acetylcholine receptor (nAChR) has garnered substantial attention as a target for cognitive deficits based on receptor localization, robust preclinical effects, genetics implicating its involvement in cognitive disorders, and encouraging, albeit mixed, clinical data with α 7 nAChR orthosteric agonists. Importantly, previous orthosteric agonists at this receptor suffered from off-target activity, receptor desensitization, and an inverted U-shaped dose-effect curve in preclinical assays that limit their clinical utility. To overcome the challenges with orthosteric agonists, we have identified a novel selective α 7 positive allosteric modulator (PAM), BNC375. This compound is selective over related receptors and potentiates acetylcholine-evoked α 7 currents with only marginal effect on the receptor desensitization kinetics. In addition, BNC375 enhances long-term potentiation of electrically evoked synaptic responses in rat hippocampal slices and in vivo. Systemic administration of BNC375 reverses scopolamine-induced cognitive deficits in rat novel object recognition and rhesus monkey object retrieval detour (ORD) task over a wide range of exposures, showing no evidence of an inverted U-shaped dose-effect curve. The compound also improves performance in the ORD task in aged African green monkeys. Moreover, ex vivo 13 C-NMR analysis indicates that BNC375 treatment can enhance neurotransmitter release in rat medial prefrontal cortex. These findings suggest that α 7 nAChR PAMs have multiple advantages over orthosteric α 7 nAChR agonists for the treatment of cognitive dysfunction associated with CNS diseases. SIGNIFICANCE STATEMENT: BNC375 is a novel and selective α7 nicotinic acetylcholine receptor (nAChR) positive allosteric modulator (PAM) that potentiates acetylcholine-evoked α7 currents in in vitro assays with little to no effect on the desensitization kinetics. In vivo, BNC375 demonstrated robust procognitive effects in multiple preclinical models across a wide exposure range. These results suggest that α7 nAChR PAMs have therapeutic potential in central nervous system diseases with cognitive impairments., (Copyright © 2020 by The American Society for Pharmacology and Experimental Therapeutics.)

Non-native disulfide isomers of alpha-conotoxins are generally inactive although some unexpectedly demonstrate comparable or enhanced bioactivity. The actions of "globular" and "ribbon" isomers of alpha-conotoxin AuIB have been characterized on alpha3beta4 nicotinic acetylcholine receptors (nAChRs) heterologously expressed in Xenopus oocytes. Using two-electrode voltage clamp recording, we showed that the inhibitory efficacy of the ribbon isomer of AuIB is limited to approximately 50%. The maximal inhibition was stoichiometry-dependent because altering alpha3:beta4 RNA injection ratios either increased AuIB(ribbon) efficacy (10alpha:1beta) or completely abolished blockade (1alpha:10beta). In contrast, inhibition by AuIB(globular) was independent of injection ratios. ACh-evoked current amplitude was largest for 1:10 injected oocytes and smallest for the 10:1 ratio. ACh concentration-response curves revealed high (HS, 1:10) and low (LS, 10:1) sensitivity alpha3beta4 nAChRs with corresponding EC(50) values of 22.6 and 176.9 microM, respectively. Increasing the agonist concentration antagonized the inhibition of LS alpha3beta4 nAChRs by AuIB(ribbon), whereas inhibition of HS and LS alpha3beta4 nAChRs by AuIB(globular) was unaffected. Inhibition of LS and HS alpha3beta4 nAChRs by AuIB(globular) was insurmountable and independent of membrane potential. Molecular docking simulation suggested that AuIB(globular) is likely to bind to both alpha3beta4 nAChR stoichiometries outside of the ACh-binding pocket, whereas AuIB(ribbon) binds to the classical agonist-binding site of the LS alpha3beta4 nAChR only. In conclusion, the two isomers of AuIB differ in their inhibitory mechanisms such that AuIB(ribbon) inhibits only LS alpha3beta4 nAChRs competitively, whereas AuIB(globular) inhibits alpha3beta4 nAChRs irrespective of receptor stoichiometry, primarily by a non-competitive mechanism.