TRP Channels and calcium signalling in dental pulp stem cells

Introduction: Ca2+ ion is an important intracellular messenger essential for the regulation of various cellular functions including proliferation, differentiation and apoptosis. Transient Receptor Potential (TRP) channels are calcium permeable cationic channels that play important role in regulation of free intracellular calcium ([Ca2+]i) in response to thermal, physical and chemical stimuli. Ca2+ signalling in human dental pulp stem cells (hDPSCs) and the ion channels regulating Ca2+ are largely not known. Objectives: Investigate changes in [Ca2+]i and determine the ion channels that regulate calcium signalling in hDPSCs. Methods: DPSCs were derived from immature third molars and cells less than passage 6 were used in all the experiments. Changes in [Ca2+]i were studied with Fura2 calcium imaging. RNA was extracted from DPSCs and a panel of TRP channel gene expression was determined by qPCR employing custom designed FAM TRP specific primers and probes (Roche, UK) and the Light Cycler 480 Probes Master (Roche). Results: hDPSCs express gene transcripts for all TRP families including TRPV1, V2, V4, TRPA1, TRPC3, TRPC5, TRPC6, TRPM3, TRPM7 and TRPP2. Stimulation of cells with appropriate TRP channel agonist induced increase in [Ca2+]i and similar responses were obtained when cell were mechanically stimulated by membrane stretch with application of hypotonic solution. Conclusion: TRP channels mediate calcium signalling in hDPSCs that merit further investigation.

Osteoprotegerin Expression in the Dental Pulp

Objectives: The inflammatory response to pulpal injury or infection has major clinical significance. Osteoprotegerin (OPG) is a soluble decoy receptor for Receptor Activator of NF kappa B Ligand (RANKL), preventing ligand binding to its receptor (RANK), thus inhibiting clastic cell formation. The aim of the study is to investigate the expression of OPG in human dental pulp and the effects of inflammatory mediators. This study will specifically investigate the effects of Transforming Growth Factor Beta-1 (TGF-β1) and Interleukin 1-Beta (IL-1β) on the expression of OPG on pulp fibroblasts in vitro. Method: Five primary pulp fibroblast populations were obtained by explant culture of healthy pulp tissue. Triplicate cultures were grown to confluence in 12-well plates and stimulated for 48 hours with IL-1β (10ng/ml) or TGF-β1 (10ng/ml). The conditioned media was collected and OPG levels detected by ELISA (R+D Systems, UK). Results: All fibroblast populations produced quantifiable levels of OPG in a time-dependant fashion. IL-1β significantly increased the expression of OPG (p<0.05) in all cultures. In contrast, TGF-β1 had no significant effect on OPG expression levels. In addition, previous work in our laboratory demonstrated both TGF-β1 and IL-1β stimulated OPG expression by periodontal ligament fibroblasts. Conclusion: These data indicate that IL-1β-regulated expression of OPG by pulpal fibroblasts may mediate hard tissue turnover in the inflamed dental pulp.

Substance P production by human dental pulp fibroblasts

The inflammatory response to pulpal injury or infection has major clinical significance. Neurogenic inflammation describes the local release of neuropeptides, notably substance P (SP), from afferent neurones, and may play a role in the pathogenesis of pulpal disease. The fibroblast is the most numerous cell type in the dental pulp and recent work has suggested that it is involved in the inflammatory response. Objectives: The aims of the study were to determine whether pulp fibroblasts could produce SP, and to investigate the expression of the SP receptor, NK-1, by these cells. Methods: Primary pulp fibroblast cell populations were isolated by enzymatic digestion from non-carious teeth extracted for orthodontic reasons. Whole pulp tissue was obtained from freshly extracted sound (n=35) and carious (n=39) teeth. Expression of SP and NK-1 mRNA was determined by RT-PCR. The effects of interleukin-1β (IL-1β) and transforming growth factor-β1 (TGF-β1) on SP and NK-1 expression were also determined. The presence of NK-1 on fibroblast cell membranes was established by western blotting. The effects of the cytokines on each parameter were analysed by ANOVA. Radioimmunoassay (RIA) was carried out to quantify SP expression by pulp fibroblasts and in whole pulp tissue. Results: SP was expressed by pulpal fibroblasts both at the mRNA level and the protein level. In addition, NK-1 was detected in fibroblast cultures at the mRNA level and appeared as a double band on western blots of membrane extracts. IL-1β and TGF-β1 significantly stimulated the expression of SP and NK-1. SP levels were significantly greater (p<0.05) in carious compared to sound teeth. Conclusion: Pulp fibroblasts are capable of synthesising and secreting SP, as well as expressing the SP receptor, NK-1. These findings suggest that pulp fibroblasts play a role in neurogenic inflammation in pulpal disease. (Supported by the European Society of Endodontology.)

Co-expression of NPY and VIP in human dental pulp

Introduction: The regulation of pulpal haemodynamics in health and disease involves sympathetic and parasympathetic mechanisms in which both neuropeptide Y (NPY; a sympathetic vasoconstrictor) and vasoactive intestinal polypeptide (VIP; a parasympathetic vasodilator) may play potential pathophysiological roles. We have previously investigated the levels of NPY or VIP present in human dental pulp tissue and shown that their expression is up-regulated in caries induced pulpal inflammation. Objectives: The aim of this study was to investigate the potential correlation between NPY and VIP levels measured in the same dental pulp samples using radioimmunoassay (RIA). Methods: Pulp tissue was obtained from extracted teeth, classified as follows; healthy (n=22), moderately carious (n=20) and grossly carious (n=26). Samples were processed for RIA by boiling in acetic acid as previously described. The levels of NPY and VIP, measured by RIA, were expressed as ng/gram of pulp tissue. The nature of the relationship between NPY and VIP levels in human pulp tissue was tested by calculating Pearson's product moment correlation coefficient using the linear regression test. Results: Calculation of Pearson product moment correlation coefficient showed a significant negative correlation between NPY and VIP levels in pulp tissue samples from non-carious teeth (p = 0.02, r = -.48). This negative correlation in non-carious teeth changed to a significant positive correlation in carious teeth when the levels of NPY and VIP were compared (p = 0.03, r= 0.311). Conclusions: In non-carious teeth, the negative correlation between NPY and VIP levels is in keeping with the previously described modulatory influence of cholinergic nerves on sympathetic function which may be perturbed as caries develops.

Vasoactive Intestinal Polypeptide (VIP) in Human Dental Pulps

Pulpal innervation is not exclusively sensory and there are potential roles for other neuropeptides such as vasoactive intestinal polypeptide (VIP) in pulpal health and disease. In the systemic circulation VIP relaxes vascular smooth muscles leading to vasodilatation. It has been shown that VIP fibres are associated with pulpal blood vessels and therefore VIP may mediate vasoactivity in the dental pulp. A growing body of evidence has now demonstrated that an additional major physiological role of VIP is to act as a survival factor. In order to gain a better understanding of the role of neuropeptides in the caries process it is of interest to specifically examine a role for VIP. Objectives: The aim of the present study was to determine the levels of VIP in carious (moderately carious and grossly carious) compared with non-carious teeth. Methods: A total of 68 teeth were included in the study (22 non-carious, 20 moderately carious and 26 grossly carious). VIP was measured in all samples using a sensitive and specific radioimmunoassay. Results: The mean concentration of VIP in the pulps of non-carious teeth was 7.69 ng/g (9.41 SD) compared to 14.93 ng/g (15.58 SD) in carious teeth. Pair-wise comparisons of VIP levels using Tukey’s test showed statistically significant differences in VIP expression between non-carious and moderately carious teeth (p=0.002) and between moderately and grossly carious teeth, (p=0.002). Conclusion: The significantly increased levels of VIP in moderately carious pulps compared with either non-carious or grossly carious pulps may suggest a role for VIP as a protective or survival factor.

Radioimmunoassay Quantitation of Neuropeptide Y (NPY) in Human Dental Pulps

Neuropeptide Y (NPY) is a 36 amino acid peptide that is abundantly expressed in both the central and peripheral nervous systems. NPY has previously been shown to be present in human dental pulp although its exact role in pulpal health and disease remains to be fully elucidated. In addition to serving a neurotransmitter role, NPY may also have a role in modulating the pulpal response to injury and inflammation. Indeed NPY is known to be a potent vasoconstrictor in a range of tissues. Recent work by our research group has demonstrated changes in sensory neuropeptide levels measured by radioimmunoassay (RIA) in healthy and carious teeth. In addition to elevated levels of sensory neuropeptides, it is also possible that the carious process is associated with increased levels of autonomic neuropeptides such as NPY. Objectives: The aim of the present study was to undertake a comprehensive quantitative RIA analysis of NPY expression in human dental pulps from carious and non-carious teeth. Methods: A total of 22 non-carious and 46 carious teeth were included in the study. NPY was measured in all samples using RIA. Briefly, the RIA system consisted of a total volume of 400 ul, comprising 100 ul anti-NPY antibody (Peninsula Laboratories), 200 ul human NPY synthetic standard or pulp sample, and 100 ul of 125I-labelled NPY as radioactive tracer. Results: The mean concentration of NPY in non-carious teeth was found to be 4.28 ng/g (4.34 SD) compared to 9.57 ng/g (9.39 SD) in carious teeth. Using ANOVA the difference in NPY levels between the non-carious group and the carious group was found to be statistically significant (p= 0.003). Conclusion: The significant increase in the levels of NPY in carious dental pulps reported in this study provides evidence for a role for NPY in the pulpal response to caries.

Neuropeptide Receptors in the Dental Pulp

Objectives: The inflammatory response to pulpal injury or infection has major clinical significance. The aim of the study is to investigate the presence and regulation of expression of neuropeptide receptors on human pulp fibroblasts and whole pulp tissue. This study will investigate the expression of Substance P (NK-1) and Neuropeptide Y (NPY-Y1) receptors on pulp fibroblasts, determine the effects of Transforming Growth Factor Beta-1 (TGF-b1) and Interleukin 1-Beta (IL-1b) on the expression of NK-1 and NPY-Y1 receptors on pulp fibroblasts and examine the levels of receptor expression in whole pulp samples. Methods: Primary pulp fibroblast cell lines were obtained from patients undergoing extractions for orthodontic reasons. The cells were grown to confluence and stimulated for 5 days with IL-1b or TGF-b1. Pulp tissue fragments were obtained from freshly extracted sound and carious teeth, snap frozen in liquid nitrogen and cracked open using a vice. The monolayer was removed with cell scrapers and pelleted. The cell membranes of the cultured cells and the whole tissue were isolated using a Mem-PER® Eukaryotic Membrane Protein Extraction Reagent Kit (Pierce, UK). The membrane proteins were separated by SDS-PAGE and Western blotting was used to detect the presence of NK-1 and NPY-Y1. Results: Initial results demonstrated the presence of NK-1 and NPY-Y1 in cultured pulp fibroblasts. Following the 5 day incubation with TGF-b1, the cells appeared not to express NK-1. IL-1b had a slight stimulatory effect on NK-1 expression. The NPY-Y1 expression was not affected by either TGF-b1 or IL-1b. In whole pulp samples, levels of NK-1 were increased in carious teeth compared to caries-free teeth. The NPY-Y1 levels were similar in carious and non-carious teeth. Conclusion: These findings give an insight into how pulp cells react to inflammatory stimuli with regards to neuropeptide receptor expression and their roles in health and disease

Calculus of variations on time scales and discrete fractional calculus

Estudamos problemas do cálculo das variações e controlo óptimo no contexto das escalas temporais. Especificamente, obtemos condições necessárias de optimalidade do tipo de Euler–Lagrange tanto para lagrangianos dependendo de derivadas delta de ordem superior como para problemas isoperimétricos. Desenvolvemos também alguns métodos directos que permitem resolver determinadas classes de problemas variacionais através de desigualdades em escalas temporais. No último capítulo apresentamos operadores de diferença fraccionários e propomos um novo cálculo das variações fraccionário em tempo discreto. Obtemos as correspondentes condições necessárias de Euler– Lagrange e Legendre, ilustrando depois a teoria com alguns exemplos.

Fractional calculus on time scales - Cálculo fraccional em escalas temporais

Introduzimos um cálculo das variações fraccional nas escalas temporais ℤ e (hℤ)!. Estabelecemos a primeira e a segunda condição necessária de optimalidade. São dados alguns exemplos numéricos que ilustram o uso quer da nova condição de Euler–Lagrange quer da nova condição do tipo de Legendre. Introduzimos também novas definições de derivada fraccional e de integral fraccional numa escala temporal com recurso à transformada inversa generalizada de Laplace.

Symmetric quantum calculus

Generalizamos o cálculo Hahn variacional para problemas do cálculo das variações que envolvem derivadas de ordem superior. Estudamos o cálculo quântico simétrico, nomeadamente o cálculo quântico alpha,beta-simétrico, q-simétrico e Hahn-simétrico. Introduzimos o cálculo quântico simétrico variacional e deduzimos equações do tipo Euler-Lagrange para o cálculo q-simétrico e Hahn simétrico. Definimos a derivada simétrica em escalas temporais e deduzimos algumas das suas propriedades. Finalmente, introduzimos e estudamos o integral diamond que generaliza o integral diamond-alpha das escalas temporais.

Computational methods in the fractional calculus of variations and optimal control

The fractional calculus of variations and fractional optimal control are generalizations of the corresponding classical theories, that allow problem modeling and formulations with arbitrary order derivatives and integrals. Because of the lack of analytic methods to solve such fractional problems, numerical techniques are developed. Here, we mainly investigate the approximation of fractional operators by means of series of integer-order derivatives and generalized finite differences. We give upper bounds for the error of proposed approximations and study their efficiency. Direct and indirect methods in solving fractional variational problems are studied in detail. Furthermore, optimality conditions are discussed for different types of unconstrained and constrained variational problems and for fractional optimal control problems. The introduced numerical methods are employed to solve some illustrative examples.

Calculus of variations on time scales and applications to economics

We consider some problems of the calculus of variations on time scales. On the beginning our attention is paid on two inverse extremal problems on arbitrary time scales. Firstly, using the Euler-Lagrange equation and the strengthened Legendre condition, we derive a general form for a variation functional that attains a local minimum at a given point of the vector space. Furthermore, we prove a necessary condition for a dynamic integro-differential equation to be an Euler-Lagrange equation. New and interesting results for the discrete and quantum calculus are obtained as particular cases. Afterwards, we prove Euler-Lagrange type equations and transversality conditions for generalized infinite horizon problems. Next we investigate the composition of a certain scalar function with delta and nabla integrals of a vector valued field. Euler-Lagrange equations in integral form, transversality conditions, and necessary optimality conditions for isoperimetric problems, on an arbitrary time scale, are proved. In the end, two main issues of application of time scales in economic, with interesting results, are presented. In the former case we consider a firm that wants to program its production and investment policies to reach a given production rate and to maximize its future market competitiveness. The model which describes firm activities is studied in two different ways: using classical discretizations; and applying discrete versions of our result on time scales. In the end we compare the cost functional values obtained from those two approaches. The latter problem is more complex and relates to rate of inflation, p, and rate of unemployment, u, which inflict a social loss. Using known relations between p, u, and the expected rate of inflation π, we rewrite the social loss function as a function of π. We present this model in the time scale framework and find an optimal path π that minimizes the total social loss over a given time interval.

Mathematica in the classroom: new tools for exploring precalculus and differential calculus

Prémio de Melhor Artigo de Jovem Investigador atribuído pela empresa Timberlake, apresentado na 1ª Conferência Nacional sobre Computação Simbólica no Ensino e na Investigação - CSEI2012, que decorreu no IST nos dias 2 e 3 de Abril.

Influência da espessura do substrato dental sobre a eficácia clareadora e citotoxicidade de diferentes protocolos de clareamento

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

On development of fractional calculus during the last fifty years

Fractional calculus generalizes integer order derivatives and integrals. During the last half century a considerable progress took place in this scientific area. This paper addresses the evolution and establishes an assertive measure of the research development.