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Abstract Background Tactile and mechanical pain are crucial to our interaction with the environment, yet the underpinning molecular mechanism is still elusive. Endophilin A2 (EndoA2) is an evolutionarily conserved protein that is documented in the endocytosis pathway. However, the role of EndoA2 in the regulation of mechanical sensitivity and its underlying mechanisms are currently unclear. Methods Male and female C57BL/6 mice (8–12 weeks) and male cynomolgus monkeys (7–10 years old) were used in our experiments. Nerve injury-, inflammatory-, and chemotherapy-induced pathological pain models were established for this study. Behavioral tests of touch, mechanical pain, heat pain, and cold pain were performed in mice and nonhuman primates. Western blotting, immunostaining, co-immunoprecipitation, proximity ligation and patch-clamp recordings were performed to gain insight into the mechanisms. Results The results showed that EndoA2 was primarily distributed in neurofilament-200-positive (NF200+) medium-to-large diameter dorsal root ganglion (DRG) neurons of mice and humans. Loss of EndoA2 in mouse NF200+ DRG neurons selectively impaired the tactile and mechanical allodynia. Furthermore, EndoA2 interacted with the mechanically sensitive ion channel Piezo2 and promoted the membrane trafficking of Piezo2 in DRG neurons. Moreover, as an adaptor protein, EndoA2 also bound to kinesin family member 5B (KIF5B), which was involved in the EndoA2-mediated membrane trafficking process of Piezo2. Loss of EndoA2 in mouse DRG neurons damaged Piezo2-mediated rapidly adapting mechanically activated currents, and re-expression of EndoA2 rescued the MA currents. In addition, interference with EndoA2 also suppressed touch sensitivity and mechanical hypersensitivity in nonhuman primates. Conclusions Our data reveal that the KIF5B/EndoA2/Piezo2 complex is essential for Piezo2 trafficking and for sustaining transmission of touch and mechanical hypersensitivity signals. EndoA2 regulates touch and mechanical allodynia via kinesin-mediated Piezo2 trafficking in sensory neurons. Our findings identify a potential new target for the treatment of mechanical pain.

Abstract The main goal of this paper is to study a class of differential nonlinear system involving parabolic variational and history-dependent hemivariational inequalities in Banach spaces by using the penalty method. We first construct a penalized problem for such a nonlinear system and then derive the existence and uniqueness of its solution to obtain an approximating sequence for the nonlinear system. Moreover, we prove the strong convergence of the obtained approximating sequence to the solution of the original nonlinear system when the penalty parameter converges to zero. Finally, we apply the obtained convergence result to a long-memory elastic frictional contact problem with wear and damage in mechanics. First part title: Introduction Second part title: Preliminaries Third part title: Convergence result for (1.1) Fourth part title: An application

The molecular mechanisms mediating nociception are unclear. Here, the authors show that the Activating Transcription Factor 4 (ATF4) is important for the response to heat nociception in mice and ATF4 role in mediating protein trafficking in dorsal root ganglion neurons.

Abstract In (J. Optim. Theory Appl. 183:139–157, 2019) we introduced and studied the concept of well-posedness in the sense of Tykhonov for abstract problems formulated on metric spaces. Our aim of this current paper is to extend the results in (J. Optim. Theory Appl. 183:139–157, 2019) to a system which consists of two independent problems denoted by P and Q, coupled by a nonlinear equation. Following the terminology used in literature we refer to such a system as a split problem. We introduce the concept of well-posedness for the abstract split problem and provide its characterization in terms of metric properties for a family of approximating sets and in terms of the well-posedness for the problems P and Q, as well. Then we illustrate the applicability of our results in the study of three relevant particular cases: a split variational–hemivariational inequality, an elliptic variational inequality and a history-dependent variational inequality. We describe each split problem and clearly indicate the family of approximating sets. We provide necessary and sufficient conditions which guarantee the well-posedness of the split variational–hemivariational inequality. Moreover, under appropriate assumptions on the data, we prove the well-posedness of the split elliptic variational inequality as well as the well-posedness of the split history-dependent variational inequality. We illustrate our abstract results with various examples, part of them arising in contact mechanics.

We consider a class of elliptic variational-hemivariational inequalities in an abstract Banach space for which we introduce the concept of well-posedness in the sense of Tykhonov. We characterize the well-posedness in terms of metric properties of a family of associated sets. Our results, which provide necessary and sufficient conditions for the well-posedness of inequalities under consideration, are valid under mild assumptions on the data. Their proofs are based on arguments of monotonicity, lower semicontinuity and properties of the Clarke directional derivative. For well-posed inequalities we also prove a continuous dependence result of the solution with respect to the data. We illustrate our abstract results in the study of one-dimensional examples, then we focus on some relevant particular cases, including variational-hemivariational inequalities with strongly monotone operators. Finally, we consider a model variational-hemivariational inequality which arises in Contact Mechanics for which we discuss its well-posedness and provide the corresponding mechanical interpretations.

Consider an abstract Problem P in a metric space (X; d) assumed to have a unique solution u. The aim of this paper is to compare two convergence results u'n → u and u''n → u, both in X, and to construct a relevant example of convergence result un → u such that the two convergences above represent particular cases of this third convergence. To this end, we use the concept of Tykhonov triple. We illustrate the use of this new and nonstandard mathematical tool in the particular case of hemivariational inequalities in reflexive Banach space. This allows us to obtain and to compare various convergence results for such inequalities. We also specify these convergences in the study of a mathematical model, which describes the contact of an elastic body with a foundation and provide the corresponding mechanical interpretations.

Abstract In this paper, we generalize the concept of well-posedness to a class of split hemivariational inequalities. By imposing very mild assumptions on involved operators, we establish some metric characterizations of the well-posedness for the split hemivariational inequality. The obtained results generalize some related theorems on well-posedness for hemivariational inequalities and variational inequalities in the literature.

In this paper, we study a class of partial differential variational inequalities. A general stability result for the partial differential variational inequality is provided in the case the perturbed parameters are involved in both the nonlinear mapping and the set of constraints. The main tools are theory of semigroups, theory of monotone operators, and variational inequality techniques.

This paper deals with the extinction and nonextinction properties of the fast diffusion equation of homogeneous Dirichlet boundary condition in a bounded domain of RN with N>2. For 0

By using surjectivity theorem of pseudomonotone and coercive operators rather than the KKM theorem and fixed point theorem used in recent literatures, we obtain some conditions under which a system of generalized variational-hemivariational inequalities concerning set-valued mappings, which includes as special cases many problems of hemivariational inequalities studied in recent literatures, is solvable. As an application, we prove an existence theorem of solutions for a system of generalized variational-hemivariational inequalities involving integrals of Clarke's generalized directional derivatives.

This paper is devoted to the convergence of the implicit Ishikawa iteration processes for approximating a common fixed point of nonexpansive semigroup in CAT(0) spaces. We obtain the Δ-convergence results of the implicit Ishikawa iteration sequences for a family of nonexpansive mappings in CAT(0) spaces. Under certain and different conditions, we also get the strong convergence theorems of implicit Ishikawa iteration sequences for nonexpansive semigroups in the CAT(0) spaces. The results presented in this paper extend and generalize some previous results.

We generalize the concept of well-posedness by perturbations for optimization problem to a class of variational-hemivariational inequalities. We establish some metric characterizations of the well-posedness by perturbations for the variational-hemivariational inequality and prove their equivalence between the well-posedness by perturbations for the variational-hemivariational inequality and the well-posedness by perturbations for the corresponding inclusion problem.