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The role of incidence rate is very important in the study of epidemiological models. In this article, the analysis of an epidemic problem for the transmission dynamic of HBV with saturated incidence rate is presented, which is more generalize than bilinear incidence rate. After formulating the new mathematical model, the threshold quantity reproduction number \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_0$$\end{document}R0 is investigated by using the well known approach i.e. next generation matrix and investigate the possible equilibriums such as disease free and endemic equilibria. Then for the local and global behavior of the proposed problem, the local asymptotic stability analysis as well as global asymptotic stability analysis are proved. To prove the global asymptotic stability at disease free equilibrium, the classic Lyapunov function theory is considered. Similarly to show global asymptotic stability at endemic equilibria, the geometrical approach is used, which is the generalization of Lyapunov theory. Finally, numeric of the proposed problem are carried out to show the feasibility of the obtained results and the role of saturated incidence rate.

WOS:000369327600007; International audience; SULF1/SULF2 enzymes regulate cell signalling that impacts the growth and differentiation of many tissues. To determine their possible role in cartilage and bone growth or repair, their expression was examined during development and bone fracture healing using RT-PCR and immunochemical analyses. Examination of epiphyseal growth plates revealed differential, inverse patterns of SULF1 and SULF2 expressions, with the former enriched in quiescent and the latter in hypertrophic chondrocyte zones. Markedly higher levels of both SULFs, however, were expressed in osteoblasts actively forming bone when compared with proliferating pre-osteoblasts in the periosteum or the entombed osteocytes which express the lowest levels. The increased expression of Sulf1 and Sulf2 in differentiating osteoblasts was further confirmed by RT-PCR analysis of mRNA levels in rat calvarial osteoblast cultures. SULF1 and SULF2 were expressed in most foetal articular chondrocytes but down-regulated in a larger subset of cells in the post-natal articular cartilage. Unlike adult articular chondrocytes, SULF1/SULF2 expression varied markedly in post-natal hypertrophic chondrocytes in the growth plate, with very high SULF2 expression compared with SULF1 apparent during neonatal growth in both primary and secondary centres of ossification. Similarly, hypertrophic chondrocytes expressed greatly higher levels of SULF2 but not SULF1 during bone fracture healing. SULF2 expression unlike SULF1 also spread to the calcifying matrix around the hypertrophic chondrocytes indicating its possible ligand inhibiting role through HSPG desulphation. Higher levels of SULF2 in both developing and healing bone closely correlated with parallel increases in hedgehog signalling analysed by ptc1 receptor expression.

Estrogen receptors critically regulate a number of steps in the pathways in osteoblasts and osteocytes activated by exposure to dynamic mechanical strain. It is these pathways that are responsible for converting the immediate effects of strain change into a coherent stimulus for (re)modelling. It is this stimulus that controls the (re)modelling responsible for matching bones’ architecture to their customary loading. Less effective processing of this strain-related stimulus will have the same downstream effects as the absence of strain. The (re)modelling consequences are the same as those of disuse; bone loss to a genetically determined minimum. Here we review studies showing involvement of the estrogen receptor in a number of bone cells’ early responses to mechanical stimulation. We hypothesise that the structurally inappropriate bone loss in post-menopausal women, and ageing men, that is associated with declining estrogen, is due in part to less effective processing of potentially osteogenic strain-related stimulation in osteoblasts and osteocytes due to reduced availability of estrogen receptors.

Postmenopausal osteoporosis represents a failure of the response by which bone cells adapt bone mass and architecture to be sufficiently strong to withstand loading without fracture. To address why this failure should be associated with oestrogen withdrawal, we investigated the ulna's adaptive response to mechanical loading in adult female mice lacking oestrogen receptor-alpha (ERalpha(-/-)), those lacking oestrogen receptor-beta (ERbeta(-/-)) and their wild-type littermates. In wild-type mice, short periods of physiologic cyclic compressive loading of the ulna in vivo over a 2-week period stimulates new bone formation. In ERalpha(-/-) and ERbeta(-/-) mice this osteogenic response was respectively threefold and twofold less (P

The ability of bones to withstand functional loading without damage depends upon their cell populations establishing and subsequently maintaining a mass and architecture that are appropriately robust for the purpose. In women, the rapid loss of bone associated with the menopause represents a steplike decline in the effectiveness of this process with consequent increase in bone fragility. In men, loss of bone tissue and reduction in bone strength are more gradual and the increased incidence of fragility fractures occurs later. In both sexes, bone mass is associated with levels of bioavailable estrogen. This poses the major question as to how the presence or concentration of the reproductive hormone estrogen influences the relationship between bone mass and bone loading. In this paper, we briefly review evidence of the mechanism(s) by which the mechanical strains engendered by loading influence bone cells to establish and maintain structurally competent bone architecture. We highlight the finding that at least one strain-related cascade responsible for adaptive control of bone architecture is mediated through estrogen receptor (ER) alpha, the number and activity of which are regulated by estrogen. We hypothesize that a major contributor to the rapid loss of bone mass that occurs in females, and the slower age-related fall in males and females, is reduced effectiveness of ER-mediated processing of strain-related information by resident bone cells.

Osteoblast-like cells in primary cultures derived from ER / mice do not proliferate in response to mechanical strain, unlike those from their ER / littermates. ER / cells also lack strain- related NO production and responsiveness to IGFs. Proliferative responsiveness to strain is rescued by transfection with functional ER .E R number or function in bone cells may limit bones' adaptability to mechanical loading. Introduction: In vivo, bones' osteogenic response to mechanical loading involves proliferation of surface osteo- blasts. This response is replicated in vitro and involves ERK-mediated activation of the estrogen receptor (ER) and upregulation of estrogen response element activity. This proliferative response can be blocked by selective estrogen receptor modulators and increased by transfection of additional ER. Materials and Methods: We have now investigated the mechanisms of ER involvement in osteoblast-like cells' early responses to strain by comparing the responses of primary cultures of these cells derived from homozygous ER knockout (ERKO) mice (ER / ) with those from their wildtype (ER / ) and heterozygous (ER / ) littermates and from ER knockout (BERKO) mice (ER / ,E R / , and ER / ). Results: Whereas ER / ,E R / ,E R / , and ER / cells proliferate in response to a single 10-minute period of cyclic strain, ER / cells do not. Transfection of fully functional, but not mutant, ER rescues the proliferative response to strain in these cells. The strain-related response of ER / cells is also deficient in that they show no increased activity of an AP-1 driven reporter vector and no strain-related increases in NO production. Their strain-related increase in prostacyclin production is retained. They proliferate in response to fibroblast growth factor-2 but not insulin-like growth factor (IGF)-I or IGF-II, showing the importance of ER in the IGF axis and the ability of ER / cells to proliferate normally in response to a mitogenic stimulus that does not require functional ER. Conclusions: These data indicate ER's obligatory involvement in a number of early responses to mechanical strain in osteoblast-like cells, including those that result in proliferation. They support the hypothesis that reduction in ER expression or activity after estrogen withdrawal results in a less osteogenic response to loading. This could be important in the etiology of postmenopausal osteoporosis. J Bone Miner Res 2004;19:938 -946. Published online on Month 00, 2004; doi: 10.1359/JBMR.

This manuscript is concerned to the existence and stability of HIV/AIDS infection model with fractional order derivative. The corresponding derivative is taken in Caputo-Fabrizio sense, which is a new approach for such type of biological models. With the help of Sumudu transform, some new results are handled. Further for the corresponding results, existence theory and uniqueness for the equilibrium solution are provided via using nonlinear functional analysis and fixed point theory due to Banach.

The involvement of the estrogen receptor in the early responses of bone cells to mechanical strain was investigated by subjecting subconfluent monolayer cultures of ROS.SMER #14 cells (ROS 17/2.8 cells stably transfected with additional ER alpha) to 17 beta-estradiol or a single short period of dynamic mechanical strain (600 cycles, 1 Hz). The basal proliferation rate of ROS.SMER #14 cells was similar to ROS 17/2.8 cells, whose proliferative responsiveness to strain and estrogen is similar to that of primary cultures of rat long bone-derived osteoblasts. At peak strains of 3400 mu epsilon, strain-related proliferation in ROS.SMER #14 cells was 1.4 times that of ROS 17/2.8 cells. At 10(-8) mol/L, 17 beta-estradiol-related proliferation was nearly twice greater. The ROS.SMER #14 cells were transiently transfected with an estrogen-responsive reporter, 2ERE-pS2-CAT, containing two consensus estrogen response elements (ERE) linked to a chloroamphenicol acetyl transferase gene. Strain increased normalized ERE-CAT activity threefold and estradiol (10(-8) mol/L) sixfold. Both strain-related and estradiol-related increases in proliferation and ERE-CAT activity were blocked by the estrogen antagonist ICI 182,780 (10(-6) mol/L). These data show that strain as well as estrogen stimulates increased proliferation in ROS 17/2.8 cells and increased ER alpha-related ERE activity in ROS cells transfected with ER alpha. Proliferation is greater in the cells with more estrogen receptors. Both strain- and estrogen-related proliferation and ERE activity are blocked by the estrogen antagonist ICI 182,780. This indicates that ROS cells' early responses to mechanical strain involve ER alpha and estrogen-responsive genes.

Heme oxygenases (HO) are responsible for the production of carbon monoxide, which has been suggested to act similarly to nitric oxide as a signaling molecule. Inducible HO-1 and constitutive HO-2 were located in sections of weight-bearing ulnae of the rat by immunocytochemistry. Intense HO-1 localization was restricted to peri- and endosteal sites, whereas HO-2 staining occurred in osteoblasts and osteocytes throughout the cortex. Northern blot hybridization of mRNA levels for HO-1 and HO-2 extracted from bones was also performed. Six hours after a single 10 min period of noninvasive mechanical loading of the ulna in vivo, generating physiological levels of strain sufficient to initiate an osteogenic response, the level of mRNA for the inducible HO-1 isoform was increased, but that of HO-2 was unchanged. The presence of a constitutive and strain-related upregulation of an inducible enzyme capable of producing carbon monoxide suggests that carbon monoxide may participate not only in bone cells' basal metabolism but also in their adaptive response to mechanical load.

Momani, Shaher M./0000-0002-6326-8456; Khan, Madad/0000-0003-0044-961X WOS: 000334264300010 In this paper, we consider the SEW (Susceptible-Exposed-Infected-Recovered) epidemic model by taking into account both standard and bilinear incidence rates of fractional order. First, the non-negative solution of the SEIR model of fractional order is presented. Then, the multi-step generalized differential transform method (MSGDTM) is employed to compute an approximation to the solution of the model of fractional order. Finally, the obtained results are compared with those obtained by the fourth-order Runge-Kutta method and non-standard finite difference (NSFD) method in the integer case.

In this work, an optimal control strategy is developed to eliminate the spread of HIV-1. To do this, two control variables are used such as the efficaciousness of drug therapy in reducing the infection of new cells and decreasing the production of new viruses. Existence for the optimal control pair is accomplished and the Pontryagins Maximum Principle is used to characterize these optimal controls. Objective functional is constituted to minimize the densities of infected cells and free virus and to maximize the density of healthy cells. The optimality system is derived and solved numerically.

The structural competence of the skeleton is maintained by an adaptive mechanism in which resident bone cells respond to load-induced strains. To investigate the possible role of the messenger molecule nitric oxide (NO) in this response, we studied NO production in well-characterized organ culture systems, rat long bone-derived osteoblast-like (LOBs) cells, and embryonic chick osteocytes (LOCYs) in monolayer culture. In superfused cancellous bone cores, loading (for 15 min) produces increases in NO2- (stable NO metabolite) release during the loading period, which paralleled those in PGI2 and PGE2. Loading of rat vertebrae and ulnae produces increases in NO2- release, and in ulnae NO synthase inhibitors diminish these responses. Transient rapid increases in NO release are stimulated by strain in both LOBs and LOCYs. Polymerase chain reaction amplification of extracted mRNA shows that rat ulnae, LOBs, and LOCYs express both the inducible and neuronal (constitutive) isoforms of NO synthase. Adaptability to mechanical strain relies on assessment of the strain environment followed by modification of bone architecture. Immediate increases in NO production induced by loading suggest the involvement of NO in strain measurement and cellular communication to establish strain distribution, as well as potentially in adaptive changes in bone cell behavior.

SULF1/SULF2 enzymes regulate the activities of several growth factors by selective hydrolysis of 6-O-sulphates of heparan sulphate proteoglycan co-receptors, the sulfation of which is essential for signal transduction of some ligand/receptor interactions but not others. This study demonstrates the existence of SULF1 variants with a wide spectrum of splicing patterns in mammalian tumours. The levels and relative proportions of SULF1/SULF2 splice variants markedly vary in different tumours with a potential to regulate cell growth differentially. Although mammalian Sulf1 compared with Sulf2 gene generates a much larger number of splice variants, both enzymes follow generally similar distribution and signalling association trends in hepatocellular carcinomas.

An existing model is extended to assess the impact of some antimalaria control measures, by re-formulating the model as an optimal control problem. This paper investigates the fundamental role of three type of controls, personal protection, treatment, and mosquito reduction strategies in controlling the malaria. We work in the nonlinear optimal control framework. The existence and the uniqueness results of the solution are discussed. A characterization of the optimal control via adjoint variables is established. The optimality system is solved numerically by a competitive Gauss-Seidel-like implicit difference method. Finally, numerical simulations of the optimal control problem, using a set of reasonable parameter values, are carried out to investigate the effectiveness of the proposed control measures.

In this paper, we consider a Holling type model, which describes the interaction between two preys with a common predator. First, we give some sufficient conditions for the globally asymptotic stability and prove that local stability implies global stability. Then, we present a set of sufficient conditions for the existence of a positive periodic solution with strictly positive components. Finally, the optimal control strategy is developed to minimize the number of predator and maximize the number of preys. We also show the existence of an optimal control for the optimal control problem and derive the optimality system. The technical tool used to determine the optimal strategy is the Pontryagin Maximum Principle. Finally, the numerical simulations of global stability and the optimal problem are given as the conclusion of this paper. Copyright © 2011 John Wiley & Sons, Ltd.

Highlights ► Sost down-regulation is stimulated by mechanical strain in osteoblastic cells. ► Sost/Osteocalcin regulation by strain in Saos2 osteoblastic cells requires Cox2. ► PGE2-mediated Sost regulation by strain in Saos2 cells requires EP4/ERK signaling. ► Osteocalcin regulation by strain in Saos2 cells requires EP2/PKC signaling., Sclerostin is a potent inhibitor of bone formation which is down-regulated by mechanical loading. To investigate the mechanisms involved we subjected Saos2 human osteoblastic cells to short periods of dynamic strain and used quantitative reverse transcriptase polymerase chain reaction to compare their responses to unstrained controls. Strain-induced Sost down-regulation was recapitulated by cyclo-oxygenase-2-mediated PGE2, acting through the EP4 receptor, whereas strain-related up-regulation of osteocalcin was mediated by the EP2 receptor. Strain-related Sost regulation required extracellular signal-regulated kinase signaling, whereas osteocalcin required protein kinase C. These findings indicate early divergence in the signaling pathways stimulated by strain and establish PGE2/EP4 as the pathway used by strain to regulate Sost expression.

Summary Osteocyte sclerostin is regulated by loading and disuse in mouse tibiae but is more closely related to subsequent local osteogenesis than the peak strains engendered. Introduction The purpose of this study was to assess the relationship between loading-related change in osteocyte sclerostin expression, local strain magnitude, and local bone modeling/remodeling. Methods The right tibiae of 19-week-old female C57BL/6 mice were subjected to non-invasive, dynamic axial loading and/or to sciatic neurectomy-induced disuse. The sclerostin status of osteocytes was evaluated immunohistochemically, changes in bone mass by micro-computed tomography, new bone formation by histomorphometry, and loading-induced strain by strain gauges and finite element analysis. Results In cortical bone of the tibial shaft, loading engendered strains of similar peak magnitude proximally and distally. Proximally, sclerostin-positive osteocytes decreased and new bone formation increased. Distally, there was neither decrease in sclerostin-positive osteocytes nor increased osteogenesis. In trabecular bone of the proximal secondary spongiosa, loading decreased sclerostin-positive osteocytes and increased bone volume. Neither occurred in the primary spongiosa. Disuse increased sclerostin-positive osteocytes and decreased bone volume at all four sites. Loading reversed this sclerostin upregulation to a level below baseline in the proximal cortex and secondary spongiosa. Conclusion Loading-related sclerostin downregulation in osteocytes of the mouse tibia is associated preferentially with regions where new bone formation is stimulated rather than where high peak strains are engendered. The mechanisms involved remain unclear, but could relate to peak surface strains not accurately reflecting the strain-related osteogenic stimulus or that sclerostin regulation occurs after sufficient signal processing to distinguish between local osteogenic and non-osteogenic responses.

Bones' functionally adaptive responses to mechanical loading can usefully be studied in the tibia by the application of loads between the knee and ankle in normal and genetically modified mice. Such loading also deforms the fibula. Our present study was designed to ascertain whether the fibula adapts to loading in a similar way to the tibia and could thus provide an additional bone in which to study functional adaptation. The right tibiae/fibulae in C57BL/6 mice were subjected to a single period of axial loading (40 cycles at 10 Hz with 10-second intervals between each cycle; approximately 7 min/day, 3 alternate days/week, 2 weeks). The left tibiae/fibulae were used as non-loaded, internal controls. Both left and right fibulae and tibiae were analyzed by micro-computed tomography at the levels of the mid-shaft of the fibula and 25% from its proximal and distal ends. We also investigated the effects of intermittent parathyroid hormone (iPTH) on the (re)modelling response to 2-weeks of loading and the effect of 2-consecutive days of loading on osteocytes' sclerostin expression. These in vivo experiments confirmed that the fibula showed similar loading-related (re)modelling responses to those previously documented in the tibia and similar synergistic increases in osteogenesis between loading and iPTH. The numbers of sclerostin-positive osteocytes at the proximal and middle fibulae were markedly decreased by loading. Collectively, these data suggest that the mouse fibula, as well as the tibia and ulna, is a useful bone in which to assess bone cells' early responses to mechanical loading and the adaptive (re)modelling that this engenders.

Outbreaks of spruce budworm are natural and common disturbance in the forest of North America and Canada. The large population of spruce budworm can cause significant change in the fir trees. Several strategies have been used to reduce the spruce budworm population. In this paper, we use constant yield harvesting techniques to reduce the spruce budworm population and develop new mathematical models.

Almost all mathematical models of diseases start from the same basic premise: the population can be subdivided into a set of distinct classes dependent upon experience with respect to the relevant disease. Most of these models classify individuals as either a susceptible individual S, infected individual I or recovered individual R. This is called the susceptible-infected-recovered (SIR) model. In this paper, we describe an SIR epidemic model with three components; S, I and R. We describe our study of stability analysis theory to find the equilibria for the model. Next in order to achieve control of the disease, we consider a control problem relative to the SIR model. A percentage of the susceptible populations is vaccinated in this model. We show that an optimal control exists for the control problem and describe numerical simulations using the Runge-Kutta fourth order procedure. Finally, we describe a real example showing the efficiency of this optimal control.

Mung bean was investigated as a novel source of lipoxygenase in the natural production of the green-note aroma compound hexanal. Lipoxygenase extracted from mung bean catalyzed the oxidative reaction of linoleic acid, after which the intermediate hydroperoxide compound was split via green bell pepper hydroperoxide lyase to produce hexanal. In comparison to soybean lipoxygenase, mung bean lipoxygenase was found to be a good substitute as it produced 15.4 mM (76% yield) hexanal while soybean gave 60% yield. The mung bean pH profile comprised a wide peak (optimum pH 6.5) representing lipoxygenase-2 and lipoxygenase-3 isozymes, whereas two narrower peaks representing lipoxygenase-1 and lipoxygenase-2/3 isozymes were observed for soybean (optimum pH 10). Extraction at pH 4.5 was preferred, at which specific lipoxygenase activity was also the highest.

The Wnt/beta-catenin pathway has been implicated in bone cell response to their mechanical environment. This response is the origin of the mechanism by which bone cells adjust bone architecture to maintain bone strength. Osteoporosis is the most widespread failure of this mechanism. The degree of osteoporotic bone loss in men and women is related to bio-available estrogen. Here we report that in osteoblastic ROS 17/2.8 cells and primary osteoblast cultures, a single short period of dynamic mechanical strain, as well as the glycogen synthase kinase-3beta (GSK-3beta) inhibitor LiCl, increased nuclear accumulation of activated beta-catenin and stimulated TCF/LEF reporter activity. This effect was blocked by the estrogen receptor (ER) modulators ICI 182,780 and tamoxifen and was absent in primary osteoblast cultures from mice lacking ERalpha. Microarray expression data for 25,000 genes from total RNA extracted from tibiae of wild-type mice within 24 h of being loaded in vivo showed differential gene regulation between loaded and contralateral non-loaded bones of 10 genes established to be involved in the Wnt pathway. Only 2 genes were involved in loaded tibiae from mice lacking ERalpha (ERalpha(-/-)). Together these data suggest that Wnt/beta-catenin signaling contributes to bone cell early responses to mechanical strain and that its effectiveness requires ERalpha. Reduced effectiveness of bone cell responses to bone loading, associated with estrogen-related decline in ERalpha, may contribute to the failure to maintain structurally appropriate bone mass in osteoporosis in both men and women.

The role of mechanical strain and estrogen status in regulating ERα levels in bone cells was studied in female rats. OVX is associated with decreased ERα protein expression/osteocyte, whereas habitual strain and artificial loading has only a small but positive effect, except on the ulna's medial surface, where artificial loading stimulates reversal of resorption to formation. Introduction: Osteoporosis is the most widespread failure of bones' ability to match their architectural strength to their habitual load bearing. In men and women, the severity of bone loss is associated with bioavailability of estrogen. This association could result from the estrogen receptor (ER) involvement in bone cells' adaptive response to loading. Materials and Methods: In vivo semiquantitative analysis of the amount of ERα protein per osteocyte was performed in immuno-cytochemically stained sections from control and loaded rat ulna, as well as tibias of ovariectomy (OVX) and sham-operated female rats. In vitro, the effect of exogenous estrogen (10−8 M) and mechanical strain (3400 μϵ, 1 Hz, 600 cycles) on the expression of ERα mRNA levels was assessed in ROS 17/2.8 cells in monolayers using real-time PCR and ER promoter activity. ERα translocation in response to exogenous estrogen and mechanical strain was assessed in both ROS 17/2.8 and MLO-Y4 cells. Results: More than 90 percent of tibial osteocytes express ERα, the level/osteocyte being higher in cortical than cancellous bone. OVX is associated with decreased ERα protein expression/osteocyte, whereas in the ulna habitual strain and that caused by artificial loading had only a small but positive effect, except on the medial surface, where loading stimulates reversal of resorption to formation. In unstimulated osteocytes and osteoblasts in situ, and osteocyte-like and osteoblast-like cells in vitro, ERα is predominantly cytoplasmic. In vitro, both strain and estrogen stimulate transient ERα translocation to the nucleus and transient changes in ERα mRNA. Strain but not estrogen also induces discrete membrane localization of ERα. Conclusions: Bone cells' responses to both strain and estrogen involve ERα, but only estrogen regulates its cellular concentration. This is consistent with the hypothesis that bone loss associated with estrogen deficiency is a consequence of reduction in ERα number/activity associated with lower estrogen concentration reducing the effectiveness of bone cells' anabolic response to strain.

In a recent paper [Anwar Zeb, Gul Zaman, Shaher Momani, Square-root Dynamics of a Giving Up Smoking Model, Appl. Math. Model., 37 (2013) 5326-5334], the authors presented a new model of giving up smoking model. In this paper, we introduce three control variables in the form of education campaign, anti-smoking gum, and anti-nicotive drugs/medicine for the eradication of smoking in a community. Using the optimal control theory, the optimal levels of the three controls are characterized, and then the existence and uniqueness for the optimal control pair are established. In order to do this, we minimize the number of potential and occasional smokers and maximize the number of quit smokers. We use Pontryagin's maximum principle to characterize the optimal levels of the three controls. The resulting optimality system is solved numerically by Matlab.

The mechanism by which mechanical strain and estrogen stimulate bone cell proliferation was investigated using monolayer cultures of human osteoblastic TE85 cells and female human primary (first-passage) osteoblasts (fHOBs). Both cell types showed small but statistically significant dose-dependent increases in [3H]thymidine incorporation in response to 17beta-estradiol and to a single 10-minute period of uniaxial cyclic strain (1 Hz). In both cell types, the peak response to 17beta-estradiol occurred at 10(-8) - 10(-7) M and the peak response to strain occurred at 3500 microstrain ((mu)epsilon). Both strain-related and 17beta-estradiol-related increases in [3H]thymidine incorporation were abolished by the estrogen receptor (ER) modulator ICI 182,780 (10-8 M). Tamoxifen (10(-9) - 10(-8) M) increased [3H]thymidine incorporation in both cell types but had no effect on their response to strain. In TE85 cells, tamoxifen reduced the increase in [3H]thymidine incorporation associated with 17beta-estradiol to that of tamoxifen alone but had no such effect in fHOBs. In TE85 cells, strain increased medium concentrations of insulin-like growth factor (IGF) II but not IGF-I, whereas 17beta-estradiol increased medium concentrations of IGF-I but not IGF-II. Neutralizing monoclonal antibody (MNAb) to IGF-I (3 microg/ml) blocked the effects of 17beta-estradiol and exogenous truncated IGF-I (tIGF-I; 50 ng/ml) but not those of strain or tIGF-II (50 ng/ml). Neutralizing antibody to IGF-II (3 microg/ml) blocked the effects of strain and tIGF-II but not those of 17beta-estradiol or tIGF-I. MAb aIR-3 (100 ng/ml) to the IGF-I receptor blocked the effects on [3H]thymidine incorporation of strain, tIGF-II, 17beta-estradiol, and tIGF-I. HOBs and TE85 cells, act similarly to rat primary osteoblasts and ROS 17/2.8 cells in their dose-related proliferative responses to strain and 17beta-estradiol, both of which can be blocked by the ER modulator ICI 182,780. In TE85 cells (as in rat primaries and ROS 17/2.8 cells), the response to 17beta-estradiol is mediated by IGF-I, and the response to strain is mediated by IGF-II. Human cells differ from rat cells in that tamoxifen does not block their response to strain and reduces the response to 17beta-estradiol in TE85s but not primaries. In both human cell types (unlike rat cells) the effects of strain and IGF-II as well as estradiol and IGF-I can be blocked at the IGF-I receptor.

Previous studies have indicated that physiological levels of dynamic mechanical strain produce rapid increases in nitric oxide (NO) release from rat ulna explants and primary cultures of osteoblast-like cells and embryonic chick osteocytes derived from long bones. To establish the mechanism by which loading-induced NO production may be regulated, we have examined: nitric oxide synthase (NOS) isoform mRNA and protein expression, the effect of mechanical loading in vivo on NOS mRNA expression, and the effect of mechanical strain on NO production by bone cells in culture. Using Northern blot analyses, in situ hybridization, and immunocytochemistry we have established that the predominant NOS isoform expressed in rat long bone periosteal osteoblasts and in a distinct population of cortical bone osteocytes is the endothelial form of NOS (eNOS), with little or no expression of the inducible NOS or neuronal NOS isoforms. In contrast, in non-load-bearing calvariae there are no detectable levels of eNOS in osteocytes and little in osteoblasts. Consistent with these observations, ulnar explants release NO rapidly in response to loading in vitro, presumably through the activation of eNOS, whereas calvarial explants do not. The relative contribution of different bone cells to these rapid increases in strain-induced NO release was established by assessment of medium nitrite (stable NO metabolite) concentration, which showed that purified populations of osteocytes produce significantly greater quantities of NO per cell in response to mechanical strain than osteoblast-like cells derived from the same bones. Using Northern blot hybridization, we have also shown that neither a single nor five consecutive daily periods of in vivo mechanical loading produced any significant effect on different NOS isoform mRNA expression in rat ulnae. In conclusion, our results indicate that eNOS is the prevailing isoform expressed by cells of the osteoblast/osteocyte lineage and that strain produces increases in the activity of eNOS without apparently altering the levels of eNOS mRNA.

In biological communities interaction among different species affect their stability. In this paper, we consider a nonlinear SIR model, which describes the dynamics of the interaction between susceptible and infected individuals in population. We establish stability techniques to find out the equilibria for the model and their numerical results are given. This work is based on the model first introduced by Kermack and Mckendrick [1]. The name of this class of models derives from the fact that they involve coupled equations relating the number of susceptible individuals S, the number of infected individuals I, and the number of recovered individuals R. The dynamics is described by a set of equations giving the change of population size of any one individual in terms of the population sizes of other individual in the system. It is much more complicated to know more from the qualitative structure of the isoclines, that whether the system is stable or unstable after the change in any population size. Therefore we introduce stability analysis in this paper to find out that the system is stable or not when individuals are in competition. 2 Stability analysis in the SIR model We consider a general epidemic model [2] and apply the stability analysis theory to find out the equilibria for the model [3]. The differential equations for the SIRmodel are dS(t) dt =( 1− V )μN − β I(t)S(t) N − μS(t), dI(t) dt = β I(t)S(t) N − (γ + μ)I(t), dR(t) dt = Vμ N+ γI(t) − μR(t).

Using differential display polymerase chain reaction, we cloned a novel cDNA named RoBo-1 from rat tibia. RoBo-1 is abundantly expressed in bone, including the hypertrophic chondrocytes of the growth plate where cartilage is remodeled into bone. RoBo-1 mRNA expression increased in response to two modulators of bone metabolism, estradiol and intermittent mechanical loading, suggesting a role in bone homeostasis. The 1.6-kilobase cDNA encodes a 240-amino acid protein with a cysteine spacing pattern, suggesting that RoBo-1 is a novel member of the urokinase plasminogen activator receptor/CD59/Ly-6/snake toxin family. Furthermore, the C-terminal contains a glycosyl-phosphatidylinositol attachment site, suggesting that it is a cell surface protein similar to other mammalian members of this family. The strongest homology of RoBo-1 is to the snake serum-derived phospholipase A2 inhibitors, which uniquely contain two of the cysteine domains but are secreted proteins. Interestingly, RoBo-1 is likely the first membrane-anchored member of this family containing two cysteine domains. Thus, the tissue specificity, responsiveness to bone protective mediators, along with its relationship to the multifunctional urokinase plasminogen activator receptor/CD59/Ly-6/snake toxin family suggests that RoBo-1 may play a novel role in the growth or remodeling of bone.

Explants of ulnae from 5-week-old male and female rats were cleaned of marrow and soft tissue and, in the presence and absence of 10 -8 M 17β-estradiol (E2) or 5α-dihydrotestosterone (DHT), mechanically loaded or treated with exogenous prostanoids previously shown to be produced during loading. Over an 18-h period, mechanical loading (peak strain 1300 μe, I Hz, 8 minutes, maximum strain rate 25,000 μe/s), prostaglandin E 2 (PGE 2 ) and prostacyclin (PGI 2 ) (10 -6 M), each separately produced quantitatively similar increases in cell proliferation and matrix production in bones from males and females, as indicated by incorporation of [ 3 H]thymidine into DNA and [ 3 H]proline into collagen. E2 and DHT both increased [ 3 H]thymidine and [ 3 H]proline incorporations, E2 producing greater increases in females than in males. Indomethacin abrogated the effects of loading, but had no effects on those of sex hormones. Loading, or prostanoids, together with sex hormones, produced responses generally equal to or greater than the addition of the individual influences acting independently. In females there was a synergistic response in [ 3 H]thymidine incorporation between loading and E2, which was quantitatively similar to the interaction between E2 and PGE 2 or PGI 2 . The interaction between loading and E2 for [ 3 H]proline incorporation was not mimicked by these prostanoids. In males the synergism in [ 3 H]proline incorporation seen between loading and DHT was mimicked by that between PGI 2 and DHT. We conclude that loading stimulates increased bone cell proliferation and matrix production in situ through a prostanoid-dependent mechanism. This response is equal in size in males and females. Estrogen and testosterone increase proliferation and matrix production through a mechanism independent of prostanoid production. The interactions between loading and hormones are reproduced in some but not all cases by E2 and prostaglandins. E2 with loading and prostaglandins has greater effects in female bones, while DHT with loading and prostaglandins has greater effects in males.

Mechanical loading of bone explants stimulates prostaglandin E2 (PGE2) and prostacyclin (PGI2) release and increases glucose 6-phosphate dehydrogenase (G6PD) activity. This response is blocked by indomethacin and imitated by exogenous PGs. In the experiments reported here, primary cultures of rat long bone-derived osteoblast-like cells were exposed to a dynamic strain and exogenous PGs in the culture dish. Strain (3400 mu epsilon, 600 cycles, 1 Hz) caused an immediate release of PGI2 into the culture medium but had no effect on PGE2. Strain also caused an increase in G6PD activity per cell and an increase in the smallest transcript of insulin-like growth factor II (IGF-II) (IGF-II T3) but had no effect on the expression of transforming growth factor-beta1 (TGF-beta1). Indomethacin inhibited strain-induced release of PGI2 and suppressed strain-induced stimulation of IGF-II T3 transcript. PGI2 (1 microM) increased G6PD activity and mRNA levels of all three transcripts of IGF-II but had no effect on the mRNA levels of IGF-I or TGF-beta1. PGE2 (1 microM) stimulated G6PD activity and caused a marked increase in IGF-I and the largest transcript of IGF-II (IGF-II T1) but had no effect on the IGF-II transcripts T2 and T3 or on TGF-beta1 mRNA levels. These findings show similarities in response between osteoblast-like cells strained in monolayer culture and bone cells in loaded bone explants in situ. They provide support for a role for IGF-II and PGI2 in the early strain-related response of osteoblasts in loading-related bone modeling/remodeling.

A number of early biochemical responses of bone cells to mechanical loading have been identified, but the full sequence of events from the sensing of strain to the formation of new bone is poorly characterized. Extracellular matrix proteins can modulate cell behavior and would be ideal molecules to amplify the early response to loading. The extracellular matrix protein, tenascin-C, supports differentiation of cultured osteoblast-like cells. The current study was carried out to investigate whether expression patterns of tenascin-C in loaded bones support a role for this protein as a mediator of the osteoregulatory response to loading. Tenascin-C expression was investigated by Northern blot analysis in rat ulnae subjected to an established noninvasive loading regimen engendering physiological strain levels. RNA extracted from loaded compared with contralateral control bones 6 h after loading showed a significant increase in tenascin-C transcript expression. The presence of tenascin-C was investigated by immunohistochemistry in bones of animals killed 3, 5, or 15 days after the initiation of daily loading. In animals killed at 3 or 5 days, periosteal surfaces undergoing load-induced reversal from resorption to formation showed enhanced tenascin-C staining. In animals killed at 15 days, the bone formed in response to loading was clearly demarcated from old bone by strong tenascin-C staining of reversal lines. Within this new bone, tenascin-C staining was seen in the lacunae of older but not more recently embedded osteocytes. The results presented here indicate that tenascin-C expression by bone cells is enhanced in the early osteogenic response to loading. This may indicate that tenascin-C acts as a mediator of the mechanically adaptive response.

A model was developed for the application of cyclic mechanical loads to 17 day embryonic chick tibiotarsi in culture. A single 20 minute period of intermittent loading at 0.4 Hz, producing physiologic peak strains and strain rates, resulted in two peak strain magnitude-related responses that were previously reported in vivo: (1) a rapid increase in glucose 6-phosphate dehydrogenase activity in osteoblasts and osteocytes and (2) increased RNA synthesis, as shown by increased incorporation of [3H]uridine into extracted RNA. The RNA response was detectable 8 h following loading but was more pronounced by 24 h. Both responses were blocked by indomethacin (10(-6) M). These results demonstrate that embryonic chick bones in organ culture exhibit cellular responses to loading similar to those previously identified in adult canine cancellous bone cultures in vitro and adult avian cortical bone in vivo. These findings are consistent with a sequence of events between loading and new bone formation that includes an immediate strain magnitude-related, prostanoid-dependent increase in activity of the pentose monophosphate shunt in osteoblasts and osteocytes, followed by a similarly strain magnitude-related increase in RNA synthesis over the subsequent 24 h.

Pairs of 17-day embryonic chick tibiotarsi were removed and maintained in organ culture. One of each pair was subjected to a single 20-minute period of intermittent loading at 0.4 Hz, producing peak longitudinal compressive strains of 650 microstrain (mu epsilon). In the 18-hour culture period following loading, alkaline phosphatase levels in the osteoblasts of the loaded tibiotarsi were maintained whereas in controls they declined. In situ hybridization using a collagen type I cRNA riboprobe showed a substantial increase in expression of mRNA for collagen type I in the periosteal tissue of bones that were cultured for 18 hours after loading compared with that in similarly cultured controls and bones cultured for 4 hours. These results demonstrate that appropriate loading of embryonic chick bones in organ culture elicits adaptive regulation of matrix synthesis as evidenced by increased expression of the gene for type I collagen and alkaline phosphatase activity. This model may be useful as it must contain all the obligatory steps between strain change in the matrix and modified osteogenic activity.

In this study, asymptotic analysis of an HIV-1 epidemic model with distributed intracellular delays is proposed. One delay term represents the latent period which is the time when the target cells are contacted by the virus particles and the time the contacted cells become actively infected and the second delay term represents the virus production period which is the time when the new virions are created within the cell and are released from the cell. The infection free equilibrium and the chronic-infection equilibrium have been shown to be locally asymptotically stable by using Rouths Hurwiths criterion and general theory of delay differential equations. Similarly, by using Lyapunov functionals and LaSalle’s invariance principle, it is proved that if the basic reproduction ratio is less than unity, then the infection-free equilibrium is globally asymptotically stable, and if the basic reproduction ratio is greater than unity, the chronic-infection equilibrium is globally asymptotically stable. Finally, numerical results with conclusion are discussed.

A mathematical model for HIV-1 infection with multiple delays is proposed. These delays account for (i) the delay in contact process between the uninfected cells virus, (ii) a latent period between the time target cells which are contacted by the virus particles and the time the virions enter the cells, and (iii) a virus production period for new virions to be produced within and released from the infected cells. For this model, the basic reproductive number is identified and its threshold property is discussed. The uninfected and infected steady states are shown to be locally as well as globally asymptotically stable. The value of the basic reproductive number shows that increasing any one of these delays will decrease this number. This may suggest a new direction for new drugs that can prolong the infection process and spreading of virus. The proved results have potential applications in HIV-1 therapy.