Simultaneous Conjugation Research Articles

On m-tuples of nilpotent 2 × 2 matrices over an arbitrary field

The algebra of [Formula: see text]-invariants of [Formula: see text]-tuples of [Formula: see text] matrices with respect to the action by simultaneous conjugation is a classical topic in case of infinite base field. On the other hand, in case of a finite field generators of polynomial invariants are not known even for a pair of [Formula: see text] matrices. Working over an arbitrary field we classified all [Formula: see text]-orbits on [Formula: see text]-tuples of [Formula: see text] nilpotent matrices for all [Formula: see text]. As a consequence, we obtained a minimal separating set for the algebra of [Formula: see text]-invariant polynomial functions of [Formula: see text]-tuples of [Formula: see text] nilpotent matrices. We also described the least possible number of elements of a separating set for an algebra of invariant polynomial functions over a finite field.

Covalent Attachment of Functional Proteins to Microfiber Surfaces via a General Strategy for Site-Selective Tetrazine Ligation.

Surface modification of materials with proteins has various biological applications, and hence the methodology for surface modification needs to accommodate a wide range of proteins that differ in structure, size, and function. Presented here is a methodology that uses the Affinity Bioorthogonal Chemistry (ABC) tag, 3-(2-pyridyl)-6-methyltetrazine (PyTz), for the site-selective modification and purification of proteins and subsequent attachment of the protein to trans-cyclooctene (TCO)-functionalized hydrogel microfibers. This method of surface modification is shown to maintain the functionality of the protein after conjugation with proteins of varying size and functionalities, namely, HaloTag, NanoLuc luciferase (NanoLuc), and fibronectin type III domains 9-10 (FNIII 9-10). The method also supports surface modification with multiple proteins, which is shown by the simultaneous conjugation of HaloTag and NanoLuc on the microfiber surface. The ability to control the relative concentrations of multiple proteins presented on the surface is shown with the use of HaloTag and superfolder GFP (sfGFP). This application of the ABC-tagging methodology expands on existing surface modification methods and provides flexibility in the site-selective protein conjugation methods used along with the rapid kinetics of tetrazine ligation.

Solvent-Free Fabrication of Anisotropic Microparticles with Precise 3D Shape Control Using Dipping-Based Micromolding.

We present an innovative solvent-free micromolding technique for rapidly fabricating complex polymer microparticles with three-dimensional (3D) shapes utilizing a surface tension-induced dipping process. Our fabrication process involves loading a photocurable solution into micromolds through mold dipping. The loaded solution, induced by surface tension, undergoes spatial deformation upon mold removal caused by surface forces, ultimately acquiring an anisotropic shape before photopolymerization. Results show that the amount of photocurable solution loaded depends on the degree of capillary penetration, which can be adjusted by varying the dipping time and mold height. It enables the production of polymer particles with precisely controlled 3D shapes without diluting them with volatile organic solvents. Sequential micromolding enables the spatial stacking of the polymer domain through a bottom-up approach, facilitating the creation of complex multicompartmental microparticles with independently controlled compartments. Finally, we demonstrated the successful simultaneous conjugation of multiple model-fluorescent proteins through the biofunctionalization of microparticles, indicating functional stability and effective conjugation of hydrophilic molecules such as proteins. We also extend our capacity to create bicompartmental microparticles with distinct functionalities in each compartment, revealing spatially controlled functional structures. In summary, these findings demonstrate a straightforward, rapid, and reliable method for producing highly uniform complex particles with precise control over the 3D shape and compartmentalization, all accomplished without the use of organic solvents.

Simultaneous conjugation of commuting foliation preserving torus maps

We prove the simultaneous conjugation of commuting foliation preserving torus maps by the KAM method. We also explore the relationship between the conjugation theory and the existence and analyticity of solutions for differential equations with time-varying delays.

Optimization of the Process for Preparing Bivalent Polysaccharide Conjugates to Develop Multivalent Conjugate Vaccines against Streptococcus pneumoniae or Neisseria meningitidis and Comparison with the Corresponding Licensed Vaccines in Animal Models.

This study aimed to describe, optimize and evaluate a method for preparing multivalent conjugate vaccines by simultaneous conjugation of two different bacterial capsular polysaccharides (CPs) with tetanus toxoid (TT) as bivalent conjugates. Different molecular weights (MWs) of polysaccharides, activating agents and capsular polysaccharide/protein (CP/Pro) ratio that may influence conjugation and immunogenicity were investigated and optimized to prepare the bivalent conjugate bulk. Using the described method and optimized parameters, a 20-valent pneumococcal conjugate vaccine and a bivalent meningococcal vaccine were developed and their effectiveness was compared to that of corresponding licensed vaccines in rabbit or mouse models. The immunogenicity test revealed that polysaccharides with lower MWs were better for Pn1-TT-Pn3 and MenA-TT-MenC, while higher MWs were superior for Pn4-TT-Pn14, Pn6A-TT-Pn6B, Pn7F-TT-Pn23F and Pn8-TT-Pn11A. For activating polysaccharides, 1-cyano-4-dimethylaminopyridinium tetrafluoroborate (CDAP) was superior to cyanogen bromide (CNBr), but for Pn1, Pn3 and MenC, N-(3-dimethylaminopropyl)-N'-ethylcarbodiimide hydrochloride (EDAC) was the most suitable option. For Pn6A-TT-Pn6B and Pn8-TT-Pn11A, rabbits immunized with bivalent conjugates with lower CP/Pro ratios showed significantly stronger CP-specific antibody responses, while for Pn4-TT-Pn14, higher CP/Pro ratio was better. Instead of interfering with the respective immunological activity, our bivalent conjugates usually induced higher IgG titers than their monovalent counterparts. The result indicated that the described conjugation technique was feasible and efficacious to prepare glycoconjugate vaccines, laying a solid foundation for developing extended-valent multivalent or combined conjugate vaccines without potentially decreased immune function.

The separating variety for 2 × 2 matrix invariants

Let G be a linear algebraic group acting linearly on a vector space (or more generally, an affine variety) V , and let k [ V ] G be the corresponding algebra of invariant polynomial functions. A separating set S ⊆ k [ V ] G is a set of polynomials with the property that for all v , w ∈ V , if there exists f ∈ k [ V ] G separating $v$ and $w$, then there exists f ∈ S separating $v$ and $w$. In this article, we consider the action of G = GL 2 ⁡ ( C ) on the C -vector space M 2 n of n-tuples of 2 × 2 matrices by simultaneous conjugation. Minimal generating sets S n of C [ M 2 n ] G are well known and | S n | = 1 6 ( n 3 + 11 n ) . In recent work, Kaygorodov et al. [Kaygorodov I, Lopatin A, Popov Y. Separating invariants for 2 × 2 matrices. Linear Algebra Appl. 2018;559:114-124.] showed that for all n ≥ 1 , S n is a minimal separating set by inclusion, i.e. that no proper subset of S n is a separating set. This does not necessarily mean that S n has minimum cardinality among all separating sets for C [ M 2 n ] G . Our main result shows that any separating set for C [ M 2 n ] G has cardinality ≥ 5 n − 5 . In particular, there is no separating set of size dim ⁡ ( C [ M 2 n ] G ) = 4 n − 3 for n ≥ 3 . Further, S 3 has indeed minimum cardinality as a separating set, but for n ≥ 4 there may exist a smaller separating set than S n . We show that a smaller separating set does in fact exist for all n ≥ 5 . We also prove similar results for the left–right action of SL 2 ⁡ ( C ) × SL 2 ⁡ ( C ) on M 2 n .

High-stability conducting polymer-based conformal electrodes for bio-/iono-electronics

Compared to conventional rigid electronics, polymer-based soft electronics conformal to organisms of irregular shapes have emerged as the next-generation devices, especially benefiting long-term bio-interface interactions that avoid mechanical mismatch and consequent adverse immune responses. Highly conductive poly(3,4-ethylenedioxythiophene):poly(styrenesulfonate) (PEDOT:PSS) has become a promising candidate for building soft conductors/electrodes due to its good conductance, tunable mechanical stiffness, good biocompatibility and facile fabrication into various structures. However, their high instability towards alkaline, reductants and applied voltage has not yet been fully addressed, which inevitably leads to deteriorated performance in complex physiological environments or weather conditions (e.g., humidity). Such intolerances are rooted in unstable electronic/molecular structures of PEDOT caused by de-doping. Besides the low electrical stability, PEDOT:PSS films also exhibit an impaired overall conductance due to its phase separation into PSS-rich and PEDOT-rich domains. Herein, a general and effective coating strategy is proposed, based on a mechanism of simultaneous molecular rejection and electron conjugation, to improve the stability and boost the conductance. Specifically, a reduced-graphene-oxide (rGO) thin layer can not only protect PEDOT: PSS from being de-doped by alkali, bio-reductants and applied voltage through molecular rejection, to maintain its conductivity and ensure stable functions, but also further boost the overall conductance through a bridging effect with its large conjugated domain. This strategy is compatible with various material fabrication techniques, including blade-coating, dip-coating and extrusion-based printing techniques, enabling the fabrication of conductors/electrodes with different structures. Finally, the advantages of excellent stability and high conformability of the composite films as soft conductors have been demonstrated through practical applications in tissue stimulation, electrophysiological recording and proprioceptive hydrogel skins, exhibiting great promise in bio/iono-electronics and human–machine interactions.

Titanium oxide bonded Zeolite and Bentonite composites for adsorptive removal of phosphate

An increase in the global population has increased the use of chemically formulated products, which indirectly increases the release of toxic chemicals into the effluent. Phosphate is one such pollutant, which leads to multiple environmental and health effects. In this study, we have formulated two novel composites to enhance the phosphate removal process. Zeolite and Bentonite were used as base materials for simultaneous surface conjugation of titanium oxide particles to synthesize novel titanium oxide composites. Characterizations were performed to understand the physical and chemical nature of the composites. Parameters affecting the process were optimized conventionally (pH, contact time, initial concentration, and adsorbent dosages), which revealed pH to be the most influential parameter. The study of adsorption isotherms and kinetics aided in understanding the adsorption patterns and the nature of reaction over the composites. Response surface methodology with central composite design was applied to enhance phosphate removal, which significantly defined the process. TB and TZ composites were able to remove up to 84 % and 83% of phosphate at pH 3, respectively. Additionally, a desorption study was carried for the safe disposal of pollutants. Obtained results indeed states that these composites could be upcoming competent novel materials for variant pollutants, particularly phosphate.

Dual Antibody-Conjugated Amyloid Nanorods to Promote Selective Cell-Cell Interactions.

Grafting biomolecules on nanostructures’ surfaces is an increasingly used strategy to target pathogenic cells, with both diagnostic and therapeutic applications. However, nanomaterials monofunctionalized by conjugating a single type of ligand find limited uses in pathologies/therapies that require two or more targets/receptors to be targeted and/or activated with a single molecular entity simultaneously. Therefore, multivalent nanomaterials for dual- or multitargeting are attracting significant interest. This study provides a proof of concept of such nanostructures. We have recently developed a modular methodology that allows obtaining amyloid-based materials decorated with active globular domains. Here, this approach is exploited to generate functional amyloid fibrils displaying antibody capture moieties. A high antibody binding affinity and capacity for the resulting nanofibrils, whose size can be manipulated to obtain homogeneous nanorods with high biocompatibility, are demonstrated. These nanorods are then used for specific antibody-mediated targeting of different cell types. Simultaneous conjugation of these nanorods with different antibodies allows obtaining a mimic of a bispecific antibody that redirects T lymphocytes to tumoral cells, holding high potential for immunotherapy. Overall, the work illustrates a modular and straightforward strategy to obtain preparative quantities of multivalent antibody-functionalized nanomaterials with multitargeting properties without the need for covalent modification.

Multifunctional surfaces through synergistic effects of heparin and nitric oxide release for a highly efficient treatment of blood-contacting devices

Thrombosis and inflammation after implantation remain unsolved problems associated with various medical devices with blood-contacting applications. In this study, we develop a multifunctional biomaterial with enhanced hemocompatibility and anti-inflammatory effects by combining the anticoagulant activity of heparin with the vasodilatory and anti-inflammatory properties of nitric oxide (NO). The co-immobilization of these two key molecules with distinct therapeutic effects is achieved by simultaneous conjugation of heparin (HT) and copper nanoparticles (Cu NPs), an NO-generating catalyst, via a simple tyrosinase (Tyr)-mediated reaction. The resulting immobilized surface showed long-term, stable and adjustable NO release for 14 days. Importantly, the makeup of the material endows the surface with the ability to promote endothelialization and to inhibit coagulation, platelet activation and smooth muscle cell proliferation. In addition, the HT/Cu NP co-immobilized surface enhanced macrophage polarization towards the M2 phenotype in vitro, which can reduce the inflammatory response and improve the adaptation of implants in vivo. This study demonstrated a simple but efficient method of developing a multifunctional surface for blood-contacting devices.

Indecomposable orthogonal invariants of several matrices over a field of positive characteristic

We consider the algebra of invariants of [Formula: see text]-tuples of [Formula: see text] matrices under the action of the orthogonal group by simultaneous conjugation over an infinite field of characteristic [Formula: see text] different from two. It is well known that this algebra is generated by the coefficients of the characteristic polynomial of all products of generic and transpose generic [Formula: see text] matrices. We establish that in case [Formula: see text] the maximal degree of indecomposable invariants tends to infinity as [Formula: see text] tends to infinity. In other words, there does not exist a constant [Formula: see text] such that it only depends on [Formula: see text] and the considered algebra of invariants is generated by elements of degree less than [Formula: see text] for any [Formula: see text]. This result is well-known in case of the action of the general linear group. On the other hand, for the rest of [Formula: see text] the given phenomenon does not hold. We investigate the same problem for the cases of symmetric and skew-symmetric matrices.

Algorithms for orbit closure separation for invariants and semi-invariants of matrices

We consider two group actions on $m$-tuples of $n \times n$ matrices. The first is simultaneous conjugation by $\operatorname{GL}_n$ and the second is the left-right action of $\operatorname{SL}_n \times \operatorname{SL}_n$. We give efficient algorithms to decide if the orbit closures of two points intersect. We also improve the known bounds for the degree of separating invariants in these cases.

Hybrid DNA-Carbon Dot-Poly(vinylpyrrolidone) Hydrogel with Self-Healing and Shape Memory Properties for Simultaneous Trackable Drug Delivery and Visible-Light-Induced Antimicrobial Photodynamic Inactivation.

A two-step methodology for simultaneous conjugation of DNA and poly(vinylpyrrolidone) (PVP) polymer to a single carbon quantum dot (CD) is demonstrated for the first time to fabricate a pH-responsive DNA-CD-PVP hybrid hydrogel. Cross-linking in the hydrogel was achieved using CD as the common nucleus through the formation of DNA I-motif conformation at neutral to acidic pH and noncovalent interaction of PVP that infuse self-healing and shape memory properties in the hydrogel. The hydrogel is capable of loading and sustained delivery of drugs for more than 2 weeks as demonstrated using a model drug, Hemin. The quenching of fluorescence of CD by Hemin was trackable even through simple visual monitoring, which showed that Hemin can diffuse from the loaded part to the unloaded part of the hydrogel during the self-healing process. Most significantly, the chosen CD generates reactive oxygen species (ROS) upon visible light irradiation, armoring the hydrogel with worthy antimicrobial activity. Biocompatibility of the DNA-CD-PVP hydrogel was established on human fibroblast cells, indicating their potential use in biomedical area pertaining to wound healing.

Investigating Ugi/Passerini Multicomponent Reactions for the Site-Selective Conjugation of Native Trastuzumab*.

Site-selective modification of proteins has been the object of intense studies over the past decades, especially in the therapeutic field. Prominent results have been obtained with recombinant proteins, for which site-specific conjugation is made possible by the incorporation of particular amino acid residues or peptide sequences. In parallel, methods for the site-selective and site-specific conjugation of native and natural proteins are starting to thrive, allowing the controlled functionalization of various types of amino acid residues. Pursuing the efforts in this field, we planned to develop a new type of site-selective method, aiming at the simultaneous conjugation of two amino acid residues. We reasoned that this should give higher chances of developing a site-selective strategy compared to the great majority of existing methods that solely target a single residue. We opted for the Ugi four-centre three-component reaction to implement this idea, with the aim of conjugating the side-chain amine and carboxylate groups of two neighbouring lysine and aspartate/glutamate. Herein, we show that this strategy can give access to valuable antibody conjugates bearing several different payloads; furthermore, the approach limits the potential conjugation sites to only six on the model antibody trastuzumab.

Separating invariants of three nilpotent 3 × 3 matrices

The algebra O(Nnd)GLn of GLn-invariants of d-tuple of n×n nilpotent matrices with respect to the action by simultaneous conjugation is generated by the traces of products of nilpotent generic matrices in the case of an algebraically closed field of characteristic zero. We describe a minimal separating set for this algebra in case n=d=3.

ON RELATIVE COMPLETE REDUCIBILITY

Abstract Let $K$ be a reductive subgroup of a reductive group $G$ over an algebraically closed field $k$. The notion of relative complete reducibility, introduced in [M. Bate, B. Martin, G. Röhrle, R. Tange, Complete reducibility and conjugacy classes of tuples in algebraic groups and Lie algebras, Math. Z.269 (2011), no. 1, 809–832], gives a purely algebraic description of the closed $K$-orbits in $G^n$, where $K$ acts by simultaneous conjugation on $n$-tuples of elements from $G$. This extends work of Richardson and is also a natural generalization of Serre’s notion of $G$-complete reducibility. In this paper we revisit this idea, giving a characterization of relative $G$-complete reducibility, which directly generalizes equivalent formulations of $G$-complete reducibility. If the ambient group $G$ is a general linear group, this characterization yields representation-theoretic criteria. Along the way, we extend and generalize several results from [M. Bate, B. Martin, G. Röhrle, R. Tange, Complete reducibility and conjugacy classes of tuples in algebraic groups and Lie algebras, Math. Z.269 (2011), no. 1, 809–832].

Conjugacy classes of commuting nilpotents

We consider the space M q , n \mathcal {M}_{q,n} of regular q q -tuples of commuting nilpotent endomorphisms of k n k^n modulo simultaneous conjugation. We show that M q , n \mathcal {M}_{q,n} admits a natural homogeneous space structure, and that it is an affine space bundle over P q − 1 {\mathbb {P}}^{q-1} . A closer look at the homogeneous structure reveals that, over C {\mathbb {C}} and with respect to the complex*1pt topology, M q , n \mathcal {M}_{q,n} is a smooth vector bundle over P q − 1 {\mathbb {P}}^{q-1} . We prove that, in this case, M q , n \mathcal {M}_{q,n} is diffeomorphic to a direct sum of twisted tangent bundles. We also prove that M q , n \mathcal {M}_{q,n} possesses a universal property and represents a functor of ideals, and we use it to identify M q , n \mathcal {M}_{q,n} with an open subscheme of a punctual Hilbert scheme. Using a result of A. Iarrobino’s, we show that M q , n → P q − 1 \mathcal {M}_{q,n} \to {\mathbb {P}}^{q-1} is not a vector bundle, hence giving a family of affine space bundles that are not vector bundles.

Simultaneous Photoradiochemical Labeling of Antibodies for Immuno-Positron Emission Tomography

SummaryA method for the simultaneous (one-step) photochemical conjugation and 89Zr-radiolabeling of antibodies is introduced. A photoactivatable chelate based on the functionalization of desferrioxamine B with an arylazide moiety (DFO-ArN3, [1]) was synthesized. The radiolabeled complex, 89Zr-1+, was produced and characterized. Density functional theory calculations were used to investigate the mechanism of arylazide photoactivation. 89Zr-radiolabeling experiments were also used to determine the efficiency of photochemical conjugation. A standard two-step approach gave a measured conjugation efficiency of 3.5% ± 0.4%. In contrast, the one-step process gave a higher photoradiolabeling efficiency of ∼76%. Stability measurements, cellular saturation binding assays, positron emission tomographic imaging, and biodistribution studies in mice bearing SK-OV-3 tumors confirmed the biochemical viability and tumor specificity of photoradiolabeled [89Zr]ZrDFO-azepin-trastuzumab. Experimental data support the conclusion that the combination of photochemistry and radiochemistry is a viable strategy for producing radiolabeled proteins for imaging and therapy.

Polynomial bound for the nilpotency index of finitely generated nil algebras

Working over an infinite field of positive characteristic, an upper bound is given for the nilpotency index of a finitely generated nil algebra of bounded nil index $n$ in terms of the maximal degree in a minimal homogenous generating system of the ring of simultaneous conjugation invariants of tuples of $n$ by $n$ matrices. This is deduced from a result of Zubkov. As a consequence, a recent degree bound due to Derksen and Makam for the generators of the ring of matrix invariants yields an upper bound for the nilpotency index of a finitely generated nil algebra that is polynomial in the number of generators and the nil index. Furthermore, a characteristic free treatment is given to Kuzmin's lower bound for the nilpotency index.

Optical Time Reversal from Time-Dependent Epsilon-Near-Zero Media.

Materials with a spatially uniform but temporally varying optical response have applications ranging from magnetic field-free optical isolators to fundamental studies of quantum field theories. However, these effects typically become relevant only for time variations oscillating at optical frequencies, thus presenting a significant hurdle that severely limits the realization of such conditions. Here we present a thin-film material with a permittivity that pulsates (uniformly in space) at optical frequencies and realizes a time-reversing medium of the form originally proposed by Pendry [Science 322, 71 (2008)SCIEAS0036-807510.1126/science.1162087]. We use an optically pumped, 500nm thick film of epsilon-near-zero (ENZ) material based on Al-doped zinc oxide. An incident probe beam is both negatively refracted and time reversed through a reflected phase-conjugated beam. As a result of the high nonlinearity and the refractive index that is close to zero, the ENZ film leads to time reversed beams (simultaneous negative refraction and phase conjugation) with near-unit efficiency and greater-than-unit internal conversion efficiency. The ENZ platform therefore presents the time-reversal features required, e.g., for efficient subwavelength imaging, all-optical isolators and fundamental quantum field theory studies.