Multivector Field Formulation of Hamiltonian Field Theories: Equations and Symmetries

We state the intrinsic form of the Hamiltonian equations of first-order Classical Field theories in three equivalent geometrical ways: using multivector fields, jet fields and connections. Thus, these equations are given in a form similar to that in which the Hamiltonian equations of mechanics are usually given. Then, using multivector fields, we study several aspects of these equations, such as the existence and non-uniqueness of solutions, and the integrability problem. In particular, these problems are analyzed for the case of Hamiltonian systems defined in a submanifold of the multimomentum bundle. Furthermore, the existence of first integrals of these Hamiltonian equations is considered, and the relation between {\sl Cartan-Noether symmetries} and {\sl general symmetries} of the system is discussed. Noether's theorem is also stated in this context, both the ``classical'' version and its generalization to include higher-order Cartan-Noether symmetries. Finally, the equivalence between the Lagrangian and Hamiltonian formalisms is also discussed.Comment: Some minor mistakes are corrected. Bibliography is updated. To be published in J. Phys. A: Mathematical and Genera

Non-standard connections in classical mechanics

In the jet-bundle description of first-order classical field theories there are some elements, such as the lagrangian energy and the construction of the hamiltonian formalism, which require the prior choice of a connection. Bearing these facts in mind, we analyze the situation in the jet-bundle description of time-dependent classical mechanics. So we prove that this connection-dependence also occurs in this case, although it is usually hidden by the use of the ``natural'' connection given by the trivial bundle structure of the phase spaces in consideration. However, we also prove that this dependence is dynamically irrelevant, except where the dynamical variation of the energy is concerned. In addition, the relationship between first integrals and connections is shown for a large enough class of lagrangians.Comment: 17 pages, Latex fil

PLA and PBAT-based electrospun fibers functionalized with antibacterial bio-based polymers

Antimicrobial fibers based on biodegradable polymers, poly(lactic acid) (PLA), and poly(butylene adipate-co-terephthalate) (PBAT) are prepared by electrospinning. For this purpose, a biodegradable/bio-based polyitaconate containing azoles groups (PTTI) is incorporated at 10 wt.% into the electrospinning formulations. The resulting fibers functionalized with azole moieties are uniform and free of beads. Then, the accessible azole groups are subjected to N-alkylation, treatment that provides cationic azolium groups with antibacterial activity at the surface of fibers. The positive charge density, roughness, and wettability of the cationic fibers are evaluated and compared with flat films. It is confirmed that these parameters exert an important effect on the antimicrobial properties, as well as the length of the alkylating agent and the hydrophobicity of the matrix. The quaternized PLA/PTTI fibers exhibit the highest efficiency against the tested bacteria, yielding a 4-Log reduction against S. aureus and 1.7-Log against MRSA. Then, biocompatibility and bioactivity of the fibers are evaluated in terms of adhesion, morphology and viability of fibroblasts. The results show no cytotoxic effect of the samples, however, a cytostatic effect is appreciated, which is ascribed to the strong electrostatic interactions between the positive charge at the fiber surface and the negative charge of the cell membranes

Biobased polymers derived from itaconic acid bearing clickable groups with potent antibacterial activity and negligible hemolytic activity.

Herein, we report, for the first time, the synthesis of clickable polymers derived from biobased itaconic acid, which was then used for the preparation of novel cationic polymers with antibacterial properties and low hemotoxicity via click chemistry. Itaconic acid (IA) was subjected to chemical modification by incorporating clickable alkyne groups on the carboxylic acids. The resulting monomer with pendant alkyne groups was easily polymerized and copolymerized with dimethyl itaconate (DMI) by radical polymerization. The feed molar ratio of comonomers was varied to precisely tune the content of alkyne groups in the copolymers and the amphiphilic balance. Subsequently, an azide with a thiazole group, which is a component of the vitamin thiamine (B1), was attached onto the polymers by copper-catalyzed azidealkyne cycloaddition (CuAAC) click chemistry leading to triazole linkages. N-Alkylation reactions of the thiazole and triazole groups with methyl and butyl iodides provide the corresponding itaconate derivatives with pendant azolium groups. The copolymers with variable cationic charge densities and hydrophobic/ hydrophilic balances, depending on the comonomer feed ratio, display potent antibacterial activity against Gram-positive bacteria, whereas the activity was almost null against Gram-negative bacteria. Hemotoxicity assays demonstrated that the copolymers exhibited negligible hemolysis and excellent selectivity, more than 1000-fold, for Gram-positive bacteria over human red blood cells.post-print1945 K

Higher-order Mechanics: Variational Principles and other topics

After reviewing the Lagrangian-Hamiltonian unified formalism (i.e, the Skinner-Rusk formalism) for higher-order (non-autonomous) dynamical systems, we state a unified geometrical version of the Variational Principles which allows us to derive the Lagrangian and Hamiltonian equations for these kinds of systems. Then, the standard Lagrangian and Hamiltonian formulations of these principles and the corresponding dynamical equations are recovered from this unified framework.Comment: New version of the paper "Variational principles for higher-order dynamical systems", which was presented in the "III Iberoamerican Meeting on Geometry, Mechanics and Control" (Salamanca, 2012). The title is changed. A detailed review is added. Sections containing results about variational principles are enlarged with additional comments, diagrams and summarizing results. Bibliography is update

Cloning, in silico structural characterization and expression analysis of MfAtr4, an ABC transporter from the banana pathogen Mycosphaerella fijiensis

ABC transporters are membrane proteins that use the energy released from the hydrolysis of ATP to drive the transport of compounds across biological membranes. In some plants, pathogenic fungi ABC transporters play a role as virulence factors by mediating the export of plant defense compounds or fungal virulence factors. Mycosphaerella fijiensis, the causal agent of black Sigatoka disease in banana, is the main constraint for the banana industry worldwide. So far, little is known about molecular mechanism that it uses to infect the host. In this study, degenerated primers designed from fungal ABC transporters known to be involved in virulence were used to isolate homologs from M. fijiensis. Here, we reported the full cloning of MfAtr4 a putative ortholog of MgAtr4, an ABC transporter of the related Mycosphaerella graminicola with a function in virulence. Similarities and differences with its presumed ortholog MgAtr4 are described, and the putative function of MfAtr4 are discussed. Analysis of MfAtr4 gene expression in field banana samples exhibiting visible symptoms of black Sigatoka disease indicated a higher expression of MfAtr4 during the first symptomatic stages in comparison to the late necrotrophic phases, suggesting a role for MfAtr4 in the early stages of pathogenic development of M. fijiensis.Key words: ABC transporters, virulence factors, MgAtr4 ortholog, Mycosphaerella fijiensis, black Sigatoka, Musa sp

Synergistic Combination of Antimicrobial Peptides and Cationic Polyitaconates in Multifunctional PLA Fibers

Combining different antimicrobial agents has emerged as a promising strategy to enhance efficacy and address resistance evolution. In this study, we investigated the synergistic antimicrobial effect of a cationic biobased polymer and the antimicrobial peptide (AMP) temporin L, with the goal of developing multifunctional electrospun fibers for potential biomedical applications, particularly in wound dressing. A clickable polymer with pendent alkyne groups was synthesized by using a biobased itaconic acid building block. Subsequently, the polymer was functionalized through click chemistry with thiazolium groups derived from vitamin B1 (PTTIQ), as well as a combination of thiazolium and AMP temporin L, resulting in a conjugate polymer-peptide (PTTIQ-AMP). The individual and combined effects of the cationic PTTIQ, Temporin L, and PTTIQ-AMP were evaluated against Gram-positive and Gram-negative bacteria as well as Candida species. The results demonstrated that most combinations exhibited an indifferent effect, whereas the covalently conjugated PTTIQ-AMP displayed an antagonistic effect, potentially attributed to the aggregation process. Both antimicrobial compounds, PTTIQ and temporin L, were incorporated into poly(lactic acid) electrospun fibers using the supercritical solvent impregnation method. This approach yielded fibers with improved antibacterial performance, as a result of the potent activity exerted by the AMP and the nonleaching nature of the cationic polymer, thereby enhancing long-term effectiveness.This work was funded by the MICINN (PID2019-104600RB- I00 and PID2021-123553OA-I00), the Agencia Estatal de Investigación (AEI, Spain), and Fondo Europeo de Desarrollo Regional (FEDER, EU) and by CSIC (LINKA20364). A. Chiloeches acknowledges MICIU for his FPU fellowship FPU18/01776. Cesar de la Fuente-Nunez holds a Presidential Professorship at the University of Pennsylvania and acknowl- edges funding from the Procter & Gamble Company, United Therapeutics, a BBRF Young Investigator Grant, the Nemirovsky Prize, Penn Health-Tech Accelerator Award, and the Dean’s Innovation Fund from the Perelman School of Medicine at the University of Pennsylvania. Research reported in this publication was supported by the Langer Prize (AIChE Foundation), the National Institute of General Medical Sciences of the National Institutes of Health under award number R35GM138201, and the Defense Threat Reduction Agency (DTRA; HDTRA11810041, HDTRA1-21-1-0014, and HDTRA1-23-1-0001). D. Placha and J. Zagora acknowledge the Doctoral grant competition VSB-Technical University of Ostrava (reg. no. CZ.02.2.69/0.0/0.0/19_073/0016945) with- in the Operational Programme Research, Development and Education, under project DGS/INDIVIDUAL/2020-001 “Development of antimicrobial biobased polymeric material using supercritical fluid technology”

Synthesis, crystal structure and cytotoxicity assays of a copper(II) nitrate complex with a tridentate ONO acylhydrazone ligand. Spectroscopic and theoretical studies of the complex and its ligand

The new copper complex, [Cu(HL)(OH2)2](NO3), including the tridentate N-acyhydrazone derived from 4-hydroxy-benzohydrazide and 2-hydroxy-3-methoxybenzaldehyde, (H2L), has been synthesized and characterized in the solid state and in solution by spectroscopic (FTIR, Ra, UV–vis, EPR) methods. The results were compared with those obtained for the hydrazone ligand and complemented with computational methods based on DFT. The crystal structure of the complex has been determined by X-ray diffraction. It crystallizes in the triclinic space group with Z = 2. The Cu(II) ion is in a distorted square pyramidal environment, coordinated to a planar HL- anion acting as a tridentate ligand. The 5-fold coordination is completed with two water molecules. It is arranged in the lattice as H-bonded ribbon-like polymers that extends along the [1 2 1] crystal direction. The cytotoxicity of the complex together with that of the H2L ligand and the copper ion were evaluated in vitro against five different human cancer cell lines namely A549 (lung), MG-63 (bone), MCF-7 and MDA-MB-231 (breast) and Jurkat (leukemia). The copper complex inhibits the cell viability in a dose dependent manner with a greater potency than the H2L ligand and the free copper ion displaying even higher antitumor activity than the well-known anticancer metallodrug cisplatin.CONICET (PIP 11220130100651CO and PIP 0034), UNLP (111/X673) and ANPCyT (PICT 2014-2223) of Argentina. Consejería de Educación CyL and FFEDER BU076U16, BU022G18 and Ministerio de Economía y Competitividad CTQ2016-75023-C2-1-P and CTQ2015-70371-REDTMetDrugs Network (Spain

Cu(ii) and Zn(ii) complexes with a poly-functional ligand derived from o-vanillin and thiophene. Crystal structure, physicochemical properties, theoretical studies and cytotoxicity assays against human breast cancer cells

The interaction of a poly-functional ligand derived from o-vanillin and 2-thiophenemethylamine (oVATPNH2) with transition metal ions Cu(II) and Zn(II) leads to the formation of stable coordination compounds, namely [Cu(oVATPNH2)2] and [Zn(oVATPNH2)2]. Their crystal structures have been determined by X-ray diffraction methods. Two molecules of the deprotonated ligand acting in a bidentate fashion build a nearly square planar environment around Cu(II) and a distorted tetrahedral coordination arrangement for Zn(II). The complexes were characterized by spectroscopic techniques, including solid state FTIR, Raman, EPR and diffuse reflectance and solution UV-vis and EPR. Their thermal behavior has been analyzed by means of TGA and DTA. DFT theoretical studies, using computational methods based on DFT, were employed to assist the interpretation and assignment of spectroscopic data. Cytotoxicity assays against two human breast cancer cell lines, namely MCF-7 and MDA-MB-231, revealed an enhancement of the effectiveness of the complexes as compared with both the ligand and the free metal ions. The results for the copper compound are promising, as its cytotoxic effect was stronger than the reference metallodrug cisplatin in both cancer cell lines tested.CONICET-CCT-La Plata (PIP 0651 and 0034), ANPCyT (PICT 2016-1574) and UNLP (11/X-473) (Argentina) and also by Consejerı´a de Educacio´n CyL and FFEDER BU076U16, BU022G18 and Ministerio de Economı´a y Competitividad CTQ2016-75023-C2-1-P and CTQ2015-70371- REDT MetDrugs Network (Spai

Symmetries in Classical Field Theory

The multisymplectic description of Classical Field Theories is revisited, including its relation with the presymplectic formalism on the space of Cauchy data. Both descriptions allow us to give a complete scheme of classification of infinitesimal symmetries, and to obtain the corresponding conservation laws.Comment: 70S05; 70H33; 55R10; 58A2