Non-Exponential Kinetics of Loop Formation in Proteins and Peptides: A Signature of Rugged Free Energy Landscapes?

The kinetics of loop formation, i.e., the occurrence of contact between two atoms of a polypeptide, remains the focus of continuing interest. One of the reasons is that contact formation is the elementary event underlying processes such as folding and binding. More importantly, it is experimentally measurable and can be predicted theoretically for ideal polymers. Deviations from single exponential kinetics have sometimes been interpreted as a signature of rugged, protein-like, free energy landscapes. Here we present simulations, with different atomistic models, of short peptides with varied structural propensity, and of a structured protein. Results show exponential contact formation kinetics (or relaxation) at long times, and a power law relaxation at very short times. At intermediate times a deviation from either power law or simple exponential kinetics is observed that appears to be characteristic of polypeptides with either specific or non-specific attractive interactions, but disappears if attractive interactions are absent. Our results agree with recent experimental measurements on peptides and proteins and offer a comprehensive interpretation for them

Pauli equation and the method of supersymmetric factorization

We consider different variants of factorization of a 2x2 matrix Schroedinger/Pauli operator in two spatial dimensions. They allow to relate its spectrum to the sum of spectra of two scalar Schroedinger operators, in a manner similar to one-dimensional Darboux transformations. We consider both the case when such factorization is reduced to the ordinary 2-dimensional SUSY QM quasifactorization and a more general case which involves covariant derivatives. The admissible classes of electromagnetic fields are described and some illustrative examples are given.Comment: 18 pages, Late

Multiparticle SUSY quantum mechanics and the representations of permutation group

The method of multidimensional SUSY Quantum Mechanics is applied to the investigation of supersymmetrical N-particle systems on a line for the case of separable center-of-mass motion. New decompositions of the superhamiltonian into block-diagonal form with elementary matrix components are constructed. Matrices of coefficients of these minimal blocks are shown to coincide with matrices of irreducible representations of permutations group S_N, which correspond to the Young tableaux (N-M,1^M). The connections with known generalizations of N-particle Calogero and Sutherland models are established.Comment: 20 pages, Latex,no figure

Application of new lysine-based peptide dendrimers D3K2 and D3G2 for gene delivery: Specific cytotoxicity to cancer cells and transfection in vitro

In order to enhance intracellular uptake and accumulation of therapeutic nucleic acids for improved gene therapy methods, numerous delivery vectors have been elaborated. Based on their origin, gene carriers are generally classified as viral or non-viral vectors. Due to their significantly reduced immunogenicity and highly optimized methods of synthesis, nanoparticles (especially those imitating natural biomolecules) constitute a promising alternative for virus-based delivery devices. Thus, we set out to develop innovative peptide dendrimers for clinical application as transfection agents and gene carriers. In the present work we describe the synthesis of two novel lysine-based dendritic macromolecules (D3K2 and D3G2) and their initial characterization for cytotoxicity/genotoxicity and transfection potential in two human cell line models: cervix adenocarcinoma (HeLa) and microvascular endothelial (HMEC-1). This approach allowed us to identify more cationic D3K2 as potent delivery agent, being able to increase intracellular accumulation of large nucleic acid molecules such as plasmids. Moreover, the dendrimers exhibited specific cytotoxicity towards cancer cell line without showing significant toxic effects on normal cells. These observations are promising prognosis for future clinical application of this type of nanoparticles. © 2019 The Author

COMPUTER SIMULATION OF LOCAL MOBILITY IN DENDRIMERS WITH ASYMMETRIC BRANCHING BY BROWNIAN DYNAMICS METHOD

The Brownian dynamics method has been used to study the effect of the branching asymmetry on the local orientational mobility of segments and bonds in dendrimers in good solvent. “Coarse-grained” models of flexible dendrimers with different branching symmetry but with the same average segment length were considered. The frequency dependences of the rate of the spin-lattice relaxation nuclear magnetic resonance (NMR) [1/T1H(H)] for segments or bonds located at different distances from terminal monomers were calculated. After the exclusion of the contribution of the overall dendrimer rotation the position of the maxima of the frequency dependences [1/T1H(ωH)] for different segments with the same length doesn’t depend on their location inside a dendrimer both for phantom models and for models with excluded volume interactions. This effect doesn’t depend also on the branching symmetry, but the position of the maximum [1/T1H(ωH))] is determined by the segment length. For bonds inside segments the positions of the maximum [1/T1H(ωH)] coincide for all models considered. Therefore, the obtained earlier conclusion about the weak influence of the excluded volume interactions on the local dynamics in the flexible symmetric dendrimers can be generalized for dendrimers with an asymmetric branching

Poly(lysine) Dendrimers Form Complexes with siRNA and Provide Its Effcient Uptake by Myeloid Cells: Model Studies for Therapeutic Nucleic Acid Delivery

The disruption of the cellular pathways of protein biosynthesis through the mechanism of RNA interference has been recognized as a tool of great diagnostic and therapeutic significance. However, in order to fully exploit the potential of this phenomenon, efficient and safe carriers capable of overcoming extra-and intracellular barriers and delivering siRNA to the target cells are needed. Recently, attention has focused on the possibility of the application of multifunctional nanoparticles, dendrimers, as potential delivery devices for siRNA. The aim of the present work was to evaluate the formation of dendriplexes using novel poly(lysine) dendrimers (containing lysine and arginine or histidine residues in their structure), and to verify the hypothesis that the use of these polymers may allow an efficient method of siRNA transfer into the cells in vitro to be obtained. The fluorescence polarization studies, as well as zeta potential and hydrodynamic diameter measurements were used to characterize the dendrimer:siRNA complexes. The cytotoxicity of dendrimers and dendriplexes was evaluated with the resazurin-based assay. Using the flow cytometry technique, the efficiency of siRNA transport to the myeloid cells was determined. This approach allowed us to determine the properties and optimal molar ratios of dendrimer:siRNA complexes, as well as to demonstrate that poly(lysine) dendrimers may serve as efficient carriers of genetic material, being much more effective than the commercially available transfection agent Lipofectamine 2000. This outcome provides the basis for further research on the application of poly(lysine) dendrimers as carriers for nucleic acids in the field of gene therapy. © 2020 by the authors

Equivalence of the super Lax and local Dunkl operators for Calogero-like models

Following Shastry and Sutherland I construct the super Lax operators for the Calogero model in the oscillator potential. These operators can be used for the derivation of the eigenfunctions and integrals of motion of the Calogero model and its supersymmetric version. They allow to infer several relations involving the Lax matrices for this model in a fast way. It is shown that the super Lax operators for the Calogero and Sutherland models can be expressed in terms of the supercharges and so called local Dunkl operators constructed in our recent paper with M. Ioffe. Several important relations involving Lax matrices and Hamiltonians of the Calogero and Sutherland models are easily derived from the properties of Dunkl operators.Comment: 25 pages, Latex, no figures. Accepted for publication in: Jounal of Physics A: Mathematical and Genera

Higher Order Matrix SUSY Transformations in Two-Dimensional Quantum Mechanics

The iteration procedure of supersymmetric transformations for the two-dimensional Schroedinger operator is implemented by means of the matrix form of factorization in terms of matrix 2x2 supercharges. Two different types of iterations are investigated in detail. The particular case of diagonal initial Hamiltonian is considered, and the existence of solutions is demonstrated. Explicit examples illustrate the construction.Comment: 15