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In this paper we discuss the existence of a solution between well-ordered subsolution and supersolution of the Kirchhoff equation. Using the sub-supersolution method together with a Rabinowitz-type global bifurcation theory, we establish the existence of positive solutions for Kirchhoff-type problems when the nonlinearity is singular or sign-changing. Moreover, we obtain some necessary and sufficient conditions for the existence of positive solutions for the problem when N = 1. [ABSTRACT FROM AUTHOR]

Background: As common progenitor cells of osteoblasts and adipocytes, bone marrow mesenchymal (stromal) stem cells (BMSCs) play key roles in bone homeostasis, tissue regeneration, and global energy homeostasis; however, the intrinsic mechanism of BMSC differentiation is not well understood. Plasticity in energy metabolism allows BMSCs to match the divergent demands of osteo-adipogenic differentiation. Targeting BMSC metabolic pathways may provide a novel therapeutic perspective for BMSC differentiation unbalance related diseases. Scope of review: This review covers the recent studies of glucose, fatty acids, and amino acids metabolism fuel the BMSC differentiation. We also discuss recent findings about energy metabolism in BMSC differentiation. Major conclusions: Glucose, fatty acids, and amino acids metabolism provide energy to fuel BMSC differentiation. Moreover, some well-known regulators including environmental stress, hormone drugs, and biological and pathological factors may also influence BMSC differentiation by altering metabolism. This offers insight to the significance of metabolism on BMSC fate determination and provides the possibility of treating diseases related to BMSC differentiation, such as obesity and osteoporosis, from a metabolic perspective.

Osteoarthritis (OA) is a chronic joint disease characterized by the degeneration of articular cartilage and thickening and sclerosis of the subchondral bone. Mechanical factors play significant roles in the development and progression of OA, but it is still controversial whether exercise or rest is a more effective treatment for OA patients. In this study, we compared the effects of swimming and immobilization at different stages of OA in mice. Four weeks (the middle stage of OA) or eight weeks (the late stage of OA) after DMM (destabilization of the medial meniscus) surgery, the mice were subjected to four-week immobilization or swimming. Ink blot analysis and a beam walking test were performed to measure the gait and balance ability. Histological analysis was performed to determine the trabecular bone area, the thickness of subchondral bone, the thickness of the cartilage, the OARSI score, and the expression of MMP13 (matrix metalloproteinases) and IL-6 (interleukin). The results showed that at the middle stage of OA, both immobilization and swimming slowed down the progression of OA. Immobilization relieved OA to a certain extent by decreasing the production of regulatory factors to attenuate the degeneration of cartilage, which partly relieved the effects of DMM on gait, mainly in the hindlimb. Swimming mainly attenuated the thickening and rescued the area of subchondral bone.

Osteoporosis and sarcopenia (termed “Osteosarcopenia”), the twin-aging diseases, are major contributors to reduced bone mass and muscle weakness in the elderly population. Connexin 43 (Cx43) in osteocytes has been previously reported to play vital roles in bone homeostasis and muscle function in mature mice. The Cx43-formed gap junctions (GJs) and hemichannels (HCs) in osteocytes are important portals for the exchange of small molecules in cell-to-cell and cell-to-extracellular matrix, respectively. However, the roles of Cx43-based GJs and HCs in both bone and muscle aging are still unclear. Here, we used two transgenic mouse models with overexpression of the dominant negative Cx43 mutants primarily in osteocytes driven by the 10-kb Dmp1 promoter, R76W mice (inhibited gap junctions but enhanced hemichannels) and Δ130–136 mice (both gap junction and hemichannels are inhibited), to determine the actions of Cx43-based hemichannels (HCs) and gap junctions (GJs) in the regulation of bone and skeletal muscle from aged mice (18 months) as compared with those from adult mice (10 months). We demonstrated that enhancement of Cx43 HCs reduces bone mass due to increased osteoclast surfaces while the impairment of Cx43 HCs increases osteocyte apoptosis in aged mice caused by reduced PGE2 levels. Furthermore, altered mitochondrial homeostasis with reduced expression of Sirt-1, OPA-1, and Drp-1 resulted in excessive ROS level in muscle soleus (SL) of aged transgenic mice. In vitro, the impairment of Cx43 HCs in osteocytes from aged mice also promoted muscle collagen synthesis through activation of TGFβ/smad2/3 signaling because of reduced PGE2 levels in the PO CM. These findings indicate that the enhancement of Cx43 HCs while GJs are inhibited reduces bone mass, and the impairment of Cx43 HCs inhibits PGE2 level in osteocytes and this reduction promotes muscle collagen synthesis in skeletal muscle through activation of TGFβ/smad2/3 signaling, which together with increased ROS level contributes to reduced muscle force in aged mice.

Bone marrow mesenchymal stem cells (BMSCs) are multi-potent cell populations and are capable of maintaining bone and body homeostasis. The stemness and potential therapeutic effect of BMSCs have been explored extensively in recent years. However, diverse cell surface antigens and complex gene expression of BMSCs have indicated that BMSCs represent heterogeneous populations, and the natural characteristics of BMSCs make it difficult to identify the specific subpopulations in pathological processes which are often obscured by bulk analysis of the total BMSCs. Meanwhile, the therapeutic effect of total BMSCs is often less effective partly due to their heterogeneity. Therefore, understanding the functional heterogeneity of the BMSC subpopulations under different physiological and pathological conditions could have major ramifications for global health. Here, we summarize the recent progress of functional heterogeneity of BMSC subpopulations in physiology and pathology. Targeting tissue-resident single BMSC subpopulation offers a potentially innovative therapeutic strategy and improves BMSC effectiveness in clinical application.

Osteocytes could release some small molecules (≤ 1 kDa) through gap junctions and hemichannels to extracellular environment, such as prostaglandin E2 (PGE2), nitric oxide (NO) and adenosine triphosphate (ATP), which play key roles in transferring signals between bone cells and other tissue cells. Connexin (Cx) 43 is the most abundant connexin in osteocytes. To further discover molecules released by osteocytes through Cx43 channels and better understand the regulatory function of Cx43 channels in osteocytes, we performed non-targeted global metabolomics analysis using liquid chromatography-tandem mass spectrometry (LC-MS/MS) on conditioned medium collected from osteocytes isolated from two transgenic mouse models with Cx43 dominant negative mutants driven by a 10 kb-DMP1 promoter: R76W (gap junctions are blocked, whereas hemichannels are promoted) and Δ130-136 (both gap junctions and hemichannels are blocked). The results revealed that several new categories of molecules, such as “fatty acyls” and “carboxylic acids and derivatives”, could be released through osteocytic Cx43 channels. In addition, alteration of Cx43 channel function affected the release of metabolites related to inflammatory reaction and oxidative stress. Pathway analysis further showed that citric acid cycle was the most differential metabolic pathway regulated by Cx43 channels. In sum, these results isolated new potential metabolites released by osteocytes through Cx43 channels, and offered a novel perspective to understand the regulatory mechanisms of osteocytes on themselves and other cells as well.

Exposure to high altitude environment leads to skeletal muscle atrophy. As a hormone secreted by skeletal muscles after exercise, irisin contributes to promoting muscle regeneration and ameliorating skeletal muscle atrophy, but its role in hypoxia-induced skeletal muscle atrophy is still unclear. Our results showed that 4 w of hypoxia exposure significantly reduced body weight and gastrocnemius muscle mass of mice, as well as grip strength and the duration time of treadmill exercise. Hypoxic treatment increased HIF-1α expression and decreased both the circulation level of irisin and its precursor protein FNDC5 expression in skeletal muscle. In in vitro, CoCl2-induced chemical hypoxia and 1% O2 ambient hypoxia both reduced FNDC5, along with the increase in HIF-1α. Moreover, the decline in the area and diameter of myotubes caused by hypoxia were rescued by inhibiting HIF-1α via YC-1. Collectively, our research indicated that FNDC5/irisin was negatively regulated by HIF-1α and could participate in the regulation of muscle atrophy caused by hypoxia.

In this paper, using fixed point index and the mixed monotone technique, we present some multiplicity and uniqueness results for the singular nonlocal boundary value problems involving nonlinear integral conditions. Our nonlinearity may be singular in its dependent variable and it is allowed to change sign. [ABSTRACT FROM AUTHOR]

In this paper, using fixed-point index theory and approximation techniques, we consider the existence and multiplicity of fixed points of some nonlinear operators with singular perturbation. As an application we consider the existence and multiplicity of positive solutions of singular systems of multi-point boundary value problems, which improve the results in the literature. [ABSTRACT FROM AUTHOR]

Abstract  The existence of at least one positive solution and the existence of multiple positive solutions are established for the singular second-order boundary value problem $$\left\{\begin{array}{l}{\frac{1}{p(t)}(p(t)x'(t))'}+\Phi(t)f(t,x,px')=0,\quad 0 using the fixed point index, where f may be singular at x=0 and px′=0. [ABSTRACT FROM AUTHOR]

nUsing the fixed point theorem in cones, this paper shows the existence of multiple positive solutions for the singular m-point boundary-value problem x"(t)+a(t)f(t,x(t), x' (t)) = 0, 0 ∑i=1m-2ai < 1 and f maybe singular at x = 0 and x' = 0. [ABSTRACT FROM AUTHOR]

Positive solutions to the singular initial-boundary value problems x″ = - f(t, xt), 0 < t < 1, x0 = 0, x(1) = 0, are obtained by applying the Schauder fixed-point theorem, where xt(u) = x(t+u) (0 ≤ t ≤ 1) on [-r, 0] and f(.,.) : (0, 1) × (C+\{0})→R+(C+ = {x ϵ C([-r, 0], R), x(t) ≥ 0, ∀t ϵ [-r, 0]}) may be singular at φ(u) = 0 (-r ≤ u ≤ 0) and t = 0. As an application, an example is given to demonstrate our result. [ABSTRACT FROM AUTHOR]

Abstract  The existence of multiple positive solutions is presented for the singular second-order boundary value problems $$\left\{\begin{array}{ll} x^{\prime\prime}\Phi(t)f(t,x,x') =0, 0 using the fixed point index, where f may be singular at x  =  0 and x′  = 0. [ABSTRACT FROM AUTHOR]

Using a fixed point theorem in cones, this paper shows the existence of positive solutions for the singular three-point boundary-value problem x″(t) + a(t)f(t, x(t), x′(t)) = 0, 0 < t < 1, x′(0) = 0, x(1) = αx(η), where 0 < &alpah; < 1, 0 < η < 1, and f may change sign and may be singular at x = 0 and x′ = 0. [ABSTRACT FROM AUTHOR]

Abstract??This paper presents a lower and upper solution approach for singular second order boundary value problems on the half line and establishes the existence of positive, unbounded and monotone solutions. [ABSTRACT FROM AUTHOR]

Using the theory of fixed point index, this article discusses the existence of positive solutions for singular second-order boundary value problems, where f may be singular at x = 0 and x'=0, and f may change sign. [ABSTRACT FROM AUTHOR]

Bone–muscle crosstalk plays an important role in skeletal biomechanical function, the progression of numerous pathological conditions, and the modulation of local and distant cellular environments. Previous work has revealed that the deletion of connexin (Cx) 43 in osteoblasts, and consequently, osteocytes, indirectly compromises skeletal muscle formation and function. However, the respective roles of Cx43-formed gap junction channels (GJs) and hemichannels (HCs) in the bone–muscle crosstalk are poorly understood. To this end, we used two Cx43 osteocyte-specific transgenic mouse models expressing dominant negative mutants, Δ130–136 (GJs and HCs functions are inhibited), and R76W (only GJs function is blocked), to determine the effect of these two types of Cx43 channels on neighboring skeletal muscle. Blockage of osteocyte Cx43 GJs and HCs in Δ130–136 mice decreased fast-twitch muscle mass with reduced muscle protein synthesis and increased muscle protein degradation. Both R76W and Δ130–136 mice exhibited decreased muscle contractile force accompanied by a fast-to-slow fiber transition in typically fast-twitch muscles. In vitro results further showed that myotube formation of C2C12 myoblasts was inhibited after treatment with the primary osteocyte conditioned media (PO CM) from R76W and Δ130–136 mice. Additionally, prostaglandin E2 (PGE2) level was significantly reduced in both the circulation and PO CM of the transgenic mice. Interestingly, the injection of PGE2 to the transgenic mice rescued fast-twitch muscle mass and function; however, this had little effect on protein synthesis and degradation. These findings indicate a channel-specific response: inhibition of osteocytic Cx43 HCs decreases fast-twitch skeletal muscle mass alongside reduced protein synthesis and increased protein degradation. In contrast, blockage of Cx43 GJs results in decreased fast-twitch skeletal muscle contractile force and myogenesis, with PGE2 partially accounting for the measured differences.

Using the theory of fixed point index, this paper discusses the existence of at least one positive solution and the existence of multiple positive solutions for the singular three-point boundary value problem: y"(t) + a(t)f(t, y(t), y'(t)) = 0, 0 < t < 1, y'(0) = 0, y(1) = αy(η), where 0 < α < 1, 0 < η < 1, and f may be singular at y = 0 and y' = 0. [ABSTRACT FROM AUTHOR]