Fractional variational calculus of variable order

We study the fundamental problem of the calculus of variations with variable order fractional operators. Fractional integrals are considered in the sense of Riemann-Liouville while derivatives are of Caputo type.Comment: Submitted 26-Sept-2011; accepted 18-Oct-2011; withdrawn by the authors 21-Dec-2011; resubmitted 27-Dec-2011; revised 20-March-2012; accepted 13-April-2012; to 'Advances in Harmonic Analysis and Operator Theory', The Stefan Samko Anniversary Volume (Eds: A. Almeida, L. Castro, F.-O. Speck), Operator Theory: Advances and Applications, Birkh\"auser Verlag (http://www.springer.com/series/4850

Genetically engineered-MSC therapies for non-unions, delayed unions and critical-size bone defects

The normal bone regeneration process is a complex and coordinated series of events involving different cell types and molecules. However, this process is impaired in critical-size/large bone defects, with non-unions or delayed unions remaining a major clinical problem. Novel strategies are needed to aid the current therapeutic approaches. Mesenchymal stem/stromal cells (MSCs) are able to promote bone regeneration. Their beneficial effects can be improved by modulating the expression levels of specific genes with the purpose of stimulating MSC proliferation, osteogenic differentiation or their immunomodulatory capacity. In this context, the genetic engineering of MSCs is expected to further enhance their pro-regenerative properties and accelerate bone healing. Herein, we review the most promising molecular candidates (protein-coding and non-coding transcripts) and discuss the different methodologies to engineer and deliver MSCs, mainly focusing on in vivo animal studies. Considering the potential of the MSC secretome for bone repair, this topic has also been addressed. Furthermore, the promising results of clinical studies using MSC for bone regeneration are discussed. Finally, we debate the advantages and limitations of using MSCs, or genetically-engineered MSCs, and their potential as promoters of bone fracture regeneration/repair.This project is supported by Fundação para a Ciência e a Tecnologia (FCT)—in the framework of the project POCI-01-0145-FEDER-031402-R2Bone, under the PORTUGAL 2020 Partnership Agreement, through ERDF, co-funded by FEDER/FNR, and national funding (through FCT – Fundação para a Ciência e a Tecnologia, I.P., provided by the contract-program and according to numbers 4, 5 and 6 of art. 23 of Law No. 57/2016 of 29 August 2016, as amended by Law No. 57/2017 of 19 July 2017). RG, JHT, and MIA are supported by FCT, through the FCT Investigator Program (IF/00638/2014), SFRH/BD/112832/2015, and DL 57/2016/CP1360/CT0008, respectively

Long noncoding RNAs: a missing link in osteoporosis

Osteoporosis is a systemic disease that results in loss of bone density and increased fracture risk, particularly in the vertebrae and the hip. This condition and associated morbidity and mortality increase with population ageing. Long noncoding (lnc) RNAs are transcripts longer than 200 nucleotides that are not translated into proteins, but play important regulatory roles in transcriptional and post-transcriptional regulation. Their contribution to disease onset and development is increasingly recognized. Herein, we present an integrative revision on the studies that implicate lncRNAs in osteoporosis and that support their potential use as therapeutic tools. Firstly, current evidence on lncRNAs involvement in cellular and molecular mechanisms linked to osteoporosis and its major complication, fragility fractures, is reviewed. We analyze evidence of their roles in osteogenesis, osteoclastogenesis, and bone fracture healing events from human and animal model studies. Secondly, the potential of lncRNAs alterations at genetic and transcriptomic level are discussed as osteoporosis risk factors and as new circulating biomarkers for diagnosis. Finally, we conclude debating the possibilities, persisting difficulties, and future prospects of using lncRNAs in the treatment of osteoporosis.This project has been supported by Portuguese funds through FCT—Fundação para a Ciência e a Tecnologia/Ministério da Ciência, Tecnologia e Ensino Superior in the framework of the project POCI-01-0145-FEDER-031402—R2Bone, under the PORTUGAL 2020 Partnership Agreement, through ERDF. Authors would like to thank to FCT DL 57/2016/CP1360/CT0008 (M.I.A.) and SFRH/BD/112832/2015 (J.H.T)

Mesenchymal Stromal Cell Secretome: Influencing Therapeutic Potential by Cellular Pre-conditioning

Mesenchymal stromal cells (MSCs) are self-renewing, culture-expandable adult stem cells that have been isolated from a variety of tissues, and possess multipotent differentiation capacity, immunomodulatory properties, and are relatively non-immunogenic. Due to this unique set of characteristics, these cells have attracted great interest in the field of regenerative medicine and have been shown to possess pronounced therapeutic potential in many different pathologies. MSCs' mode of action involves a strong paracrine component resulting from the high levels of bioactive molecules they secrete in response to the local microenvironment. For this reason, MSCs' secretome is currently being explored in several clinical contexts, either using MSC-conditioned media (CM) or purified MSC-derived extracellular vesicles (EVs) to modulate tissue response to a wide array of injuries. Rather than being a constant mixture of molecular factors, MSCs' secretome is known to be dependent on the diverse stimuli present in the microenvironment that MSCs encounter. As such, the composition of the MSCs' secretome can be modulated by preconditioning the MSCs during in vitro culture. This manuscript reviews the existent literature on how preconditioning of MSCs affects the therapeutic potential of their secretome, focusing on MSCs' immunomodulatory and regenerative features, thereby providing new insights for the therapeutic use of MSCs' secretome.We would like to acknowledge Norte Portugal Regional Operational Programme (NORTE 2020) in the framework of the project “Bioengineered Therapies for Infectious Diseases and Tissue Regeneration” (NORTE-01-0145-FEDER-000012). We also acknowledge Fundação para a Ciência e a Tecnologia (FCT) and Fundo Europeu de Desenvolvimento Regional (FEDER) funds through the COMPETE 2020-Operacional Programme for Competitiveness and Internationalization (POCI), Portugal 2020-in the framework of the project “Institute for Research and Innovation in Health Sciences” (POCI-01-0145-FEDER-007274). We also acknowledge EUROSPINE TRF for the funded project “Disc Regeneration, Immuno, and Neuro Modulation” , ref. 2017_05 . In addition, JF and RG also acknowledge FCT for funding the BiotechHealth Ph.D. fellowship (PD/BD/135486/2018) and the FCT Investigator Grant (IF/00638/2014), respectively

A note on boundedness of operators in Grand Grand Morrey spaces

In this note we introduce grand grand Morrey spaces, in the spirit of the grand Lebesgue spaces. We prove a kind of \textit{reduction lemma} which is applicable to a variety of operators to reduce their boundedness in grand grand Morrey spaces to the corresponding boundedness in Morrey spaces. As a result of this application, we obtain the boundedness of the Hardy-Littlewood maximal operator and Calder\'on-Zygmund operators in the framework of grand grand Morrey spaces.Comment: 8 page

The systemic immune response to collagen-induced arthritis and the impact of bone injury in inflammatory conditions

Rheumatoid arthritis (RA) is a systemic disease that affects the osteoarticular system, associated with bone fragility and increased risk of fractures. Herein, we aimed to characterize the systemic impact of the rat collagen-induced arthritis (CIA) model and explore its combination with femoral bone defect (FD). The impact of CIA on endogenous mesenchymal stem/stromal cells (MSC) was also investigated. CIA induction led to enlarged, more proliferative, spleen and draining lymph nodes, with altered proportion of lymphoid populations. Upon FD, CIA animals increased the systemic myeloid cell proportions, and their expression of co-stimulatory molecules CD40 and CD86. Screening plasma cytokine/chemokine levels showed increased tumor necrosis factor-a (TNF-a), Interleukin (IL)-17, IL-4, IL-5, and IL-12 in CIA, and IL-2 and IL-6 increased in CIA and CIA+FD, while Fractalkine and Leptin were decreased in both groups. CIA-derived MSC showed lower metabolic activity and proliferation, and significantly increased osteogenic and chondrogenic differentiation markers. Exposure of control-MSC to TNF-a partially mimicked the CIA-MSC phenotype in vitro. In conclusion, inflammatory conditions of CIA led to alterations in systemic immune cell proportions, circulating mediators, and in endogenous MSC. CIA animals respond to FD, and the combined model can be used to study the mechanisms of bone repair in inflammatory conditions.This research was funded by the project NORTE-01-0145-FEDER-000012, supported by Norte Portugal Regional Operational Programme (NORTE 2020), under the PORTUGAL 2020 Partnership Agreement, through the European Regional Development Fund (ERDF), and AO Foundation-Switzerland (project S-15-83S). J.H.T, A.M.S, M.B.G, M.I.A and C.C were supported by FCT-Fundação para a Ciência e a Tecnologia, through the fellowships SFRH/BD/112832/2015, SFRH/BD/85968/2012, PD/BD/135489/2018, DL 57/2016/CP1360/CT0008 and DL 57/2016/CP1360/CT0004, respectively

Variable order Mittag-Leffler fractional operators on isolated time scales and application to the calculus of variations

We introduce new fractional operators of variable order on isolated time scales with Mittag-Leffler kernels. This allows a general formulation of a class of fractional variational problems involving variable-order difference operators. Main results give fractional integration by parts formulas and necessary optimality conditions of Euler-Lagrange type.Comment: This is a preprint of a paper whose final and definite form is with Springe

Profiling the circulating miRnome reveals a temporal regulation of the bone injury response

Bone injury healing is an orchestrated process that starts with an inflammatory phase followed by repair and remodelling of the bone defect. The initial inflammation is characterized by local changes in immune cell populations and molecular mediators, including microRNAs (miRNAs). However, the systemic response to bone injury remains largely uncharacterized. Thus, this study aimed to profile the changes in the plasma miRnome after bone injury and determine its biological implications. Methods: A rat model of femoral bone defect was used, and animals were evaluated at days 3 and 14 after injury. Non-operated (NO) and sham operated animals were used as controls. Blood and spleen were collected and peripheral blood mononuclear cells (PBMC) and plasma were separated. Plasma miRnome was determined by RT-qPCR array and bioinformatics Ingenuity pathway analysis (IPA) was performed. Proliferation of bone marrow mesenchymal stem/stromal cells (MSC) was evaluated by Ki67 staining and high-throughput cell imaging. Candidate miRNAs were evaluated in splenocytes by RT-qPCR, and proteins found in the IPA analysis were analysed in splenocytes and PBMC by Western blot. Results: Bone injury resulted in timely controlled changes to the miRNA expression profile in plasma. At day 3 there was a major down-regulation of miRNA levels, which was partially recovered by day 14 post-injury. Interestingly, bone injury led to a significant up-regulation of let-7a, let-7d and miR-21 in plasma and splenocytes at day 14 relative to day 3 after bone injury, but not in sham operated animals. IPA predicted that most miRNAs temporally affected were involved in cellular development, proliferation and movement. MSC proliferation was analysed and found significantly increased in response to plasma of animals days 3 and 14 post-injury, but not from NO animals. Moreover, IPA predicted that miRNA processing proteins Ago2 and Dicer were specifically inhibited at day 3 post-injury, with Ago2 becoming activated at day 14. Protein levels of Ago2 and Dicer in splenocytes were increased at day 14 relative to day 3 post-bone injury and NO animals, while in PBMC, levels were reduced at day 3 (albeit Dicer was not significant) and remained low at day 14. Ephrin receptor B6 followed the same tendency as Ago2 and Dicer, while Smad2/3 was significantly decreased in splenocytes from day 14 relative to NO and day 3 post-bone injury animals. Conclusion: Results show a systemic miRNA response to bone injury that is regulated in time and is related to inflammation resolution and the start of bone repair/regeneration, unravelling candidate miRNAs to be used as biomarkers in the monitoring of healthy bone healing and as therapeutic targets for the development of improved bone regeneration therapies.This work was funded by project NORTE-01-0145-FEDER-000012, supported by Norte Portugal Regional Operational Programme (NORTE 2020), under the PORTUGAL 2020 Partnership Agreement, through the European Regional Development Fund (ERDF), and AO Foundation-Switzerland (project S-15-83S). AMS, MIA, CC and JHT were supported by FCT-Fundação para a Ciência e a Tecnologia, through fellowships SFRH/BD/ 85968/2012, SFRH/BPD/91011/2012, SFRH/BDP/ 87071/2012 and SFRH/BD/112832/2015, respecttively. Work in Dr. Calin's laboratory is supported by National Institutes of Health (NIH/NCATS) grant UH3TR00943-01 through the NIH Common Fund, Office of Strategic Coordination (OSC), the NIH/NCI grant 1R01CA182905-01, a U54 grant-UPR/MDACC Partnership for Excellence in Cancer Research 2016 Pilot Project, a Team DOD (CA160445P1) grant, a Ladies Leukemia League grant, a CLL Moonshot Flagship project, a SINF 2017 grant, and the Estate of C. G. Johnson, J

On the renormalization of multiparton webs

We consider the recently developed diagrammatic approach to soft-gluon exponentiation in multiparton scattering amplitudes, where the exponent is written as a sum of webs - closed sets of diagrams whose colour and kinematic parts are entangled via mixing matrices. A complementary approach to exponentiation is based on the multiplicative renormalizability of intersecting Wilson lines, and their subsequent finite anomalous dimension. Relating this framework to that of webs, we derive renormalization constraints expressing all multiple poles of any given web in terms of lower-order webs. We examine these constraints explicitly up to four loops, and find that they are realised through the action of the web mixing matrices in conjunction with the fact that multiple pole terms in each diagram reduce to sums of products of lower-loop integrals. Relevant singularities of multi-eikonal amplitudes up to three loops are calculated in dimensional regularization using an exponential infrared regulator. Finally, we formulate a new conjecture for web mixing matrices, involving a weighted sum over column entries. Our results form an important step in understanding non-Abelian exponentiation in multiparton amplitudes, and pave the way for higher-loop computations of the soft anomalous dimension.Comment: 60 pages, 15 figure