Homogeneous Chain Research Articles

Identification of Proteins Interacting with Ubiquitin Chains.

Ubiquitylation, the modification of proteins with ubiquitin (Ub), is one of the most versatile post-translational modifications in eukaryotic cells. Since Ub also serves as its own substrate, proteins can be modified by numerous different Ub chains, in which the individual moieties are linked via one or several of the seven lysines of Ub. Homogeneous Ub chains, in which the moieties are sequentially linked via the same residue, have been most extensively studied. However, due to their restricted availability, the functions of Ub chains linked via K27, K29, or K33 are poorly understood. We have developed an approach that, for the first time, allows the generation of all seven homogeneous Ub chains in large quantities. The potential of our approach is demonstrated by the identification of previously unknown interaction partners of K27-, K29-, and K33-linked Ub chains by affinity-based proteomics.

Universal scaling for the quantum Ising chain with a classical impurity

We study finite size scaling for the magnetic observables of an impurity residing at the endpoint of an open quantum Ising chain in a transverse magnetic field, realized by locally rescaling the magnetic field by a factor $\mu \neq 1$. In the homogeneous chain limit at $\mu = 1$, we find the expected finite size scaling for the longitudinal impurity magnetization, with no specific scaling for the transverse magnetization. At variance, in the classical impurity limit, $\mu = 0$, we recover finite scaling for the longitudinal magnetization, while the transverse one basically does not scale. For this case, we provide both analytic approximate expressions for the magnetization and the susceptibility as well as numerical evidences for the scaling behavior. At intermediate values of $\mu$, finite size scaling is violated, and we provide a possible explanation of this result in terms of the appearance of a second, impurity related length scale. Finally, on going along the standard quantum-to-classical mapping between statistical models, we derive the classical counterpart of the quantum Ising chain with an impurity at its endpoint as a classical Ising model on a square lattice wrapped on a half-infinite cylinder, with the links along the first circle modified as a function of $\mu$.

Entanglement entropy and Möbius transformations for critical fermionic chains

Entanglement entropy may display a striking new symmetry under Möbius transformations. This symmetry was analysed in our previous work for the case of a non-critical (gapped) free homogeneous fermionic chain invariant under parity and charge conjugation. In the present work we extend and analyse this new symmetry in several directions. First, we show that the above mentioned symmetry also holds when parity and charge conjugation invariance are broken. Second we extend this new symmetry to the case of critical (gapless) theories. Our results are further supported by numerical analysis. For some particular cases, analytical demonstrations show the validity of the extended symmetry. We finally discuss the intriguing parallelism of this new symmetry and space-time conformal transformations.

Inhomogeneous Josephson junction chains: a superconducting meta-material for superinductance optimization

We report a theoretical study of the low-frequency impedance of a Josephson junction chain whose parameters vary in space. Our goal is to find the optimal spatial profile which maximizes the total inductance of the chain without shrinking the low-frequency window where the chain behaves as an inductor. If the spatial modulation is introduced by varying the junction areas, we find that the best result is obtained for a spatially homogeneous chain, reported earlier in the literature. An improvement over the homogeneous result can be obtained by representing the junctions by SQUIDs with different loop areas, so the inductances can be varied by applying a magnetic field. Still, we find that this improvement becomes less important for longer chains.

Traveling and solitary waves in monodisperse and dimer granular chains

We provide a review of propagating traveling waves and solitary pulses in uncompressed one-dimensional ([Formula: see text]) ordered granular media. The first such solution in homogeneous granular media was discovered by Nesterenko in the form of a single-hump solitary pulse with energy-dependent profile and velocity. Considering directly the discrete, strongly nonlinear governing equations of motion of these media (i.e., without resorting to continuum approximation or homogenization), we show the existence of countably infinite families of stable multi-hump propagating traveling waves with arbitrary wavelengths. A semi-analytical approach is used to study the dependence of these waves on spatial periodicity (wavenumber) and energy, and to show that in a certain asymptotic limit, these families converge to the single-hump Nesterenko solitary wave. Then the study is extended in dimer granular chains composed of alternating “heavy” and “light” beads. For a set of specific mass ratios between the light and heavy beads, we show the existence of multi-hump solitary waves that propagate faster than the Nesterenko solitary wave in the corresponding homogeneous granular chain composed of only heavy beads. The existence of these waves has interesting implications in energy transmission in ordered granular chains.

Heparin and homogeneous model heparin oligosaccharides form distinct complexes with protamine: Light scattering and zeta potential analysis

Large multimolecular complexes of heparin with positively charged proteins such as platelet factor 4 (PF4) or protamine can initiate immune responses associated with heparin use in patients, including the most significant adverse event, heparin-induced thrombocytopenia (HIT). Current evidence suggests that platelet-activating antibodies that recognize large multi-molecular complexes (300–700kDa) of PF4 bound to heparin cause HIT [1] and in very rare cases anti-protamine-heparin antibodies can induce thrombocytopenia [2]. Heparin is administered as a mixture of sulfated glycosaminoglycans of variable lengths and sulfation levels. To date the potential impact of chain length, sulfation level and impurities on the formation, size and immunogenicity of heparin-protamine complexes has not been addressed due to the lack of purified, homogenous heparin chains for testing purposes. Here, a set of well-characterized model heparin oligosaccharides was used with protamine sulfate to evaluate the physicochemical properties of the resulting complexes. Hydrodynamic radii and zeta potential profiles of heparin-protamine complexes were observed to be dependent upon the sulfation location, size and concentration of the model heparin oligosaccharides. The well-characterized oligosaccharide-protamine complexes analyzed in this work will be useful for establishing links between heparin-protamine complex physiochemical attributes to their potential to illicit cellular immunogenicity.

Revisiting Bloch oscillations in homogeneous and binary chains from an exact quantum mechanical perspective

AbstractWe present an exact analytic approach to study Bloch oscillations which allows to study cases where the semiclassical arguments are not valid. The method is focused on the velocity operator V. Two representative examples are addressed here: (i) the superposition of AC and DC electric fields in a one‐dimensional chain and (ii) the binary uni‐dimensional chain under the action of a static electric field. For the first case, it is demonstrated that, depending on the frequency of the AC field, an unidirectional movement emerges whose velocity depends on the magnitude of the AC and DC fields, on the phase of the AC field and on the convolution of the initial wavepacket with itself displaced by one lattice spacement. We also show the limit where the semiclassical approach can be used. For the second case, we show that the transition between two mini‐bands plays a significant role in the dynamics of the electronic wavepacket. In this case, the Bloch oscillations are characterized by two main frequencies and combinations of them.

Evaluation of safety and reliability parameters of supervision and control systems

The aim of this article is the analytical evaluation of dependability and reliability indicators of vital facility supervision and control systems. Such indicators include: probability of no-failure, collective failure rate, wrong-side and right-side failure rate, average service life. The article considers systems with different redundancy rates (2-oo-2, 2-oo-3, 2-oo-2-by-2) ensuring recovery of failed equipment (channels) without interruption of operation. The paper covers such safety and reliability mechanisms as interchannel data comparison, mutual channel blocking and protection against negative failure development by mutual channel blocking. Methods . For the purpose of achieving the set goal, the article suggests a mathematical functional model based on absorbing homogenous Markovian continuous-time chains. The states of this chain reflect the number of good channels of the system, while state transition rates are identified based on the equipment failure rates of each channel and repair rates (subject to the mechanisms of interchannel data comparison and failed channel blocking). The absence of protection can be caused by such events as non-detection of failure by supervision facilities, disability of blocking mechanisms, protection tripping delay. In such case the failure of a channel (channels) causes the failure of the whole system and forces the Markovian chain into the absorbing state. The probabilities of transition into the absorbing state are divided into the probabilities of transition into state of right-side failure and state of wrong-side failure. As a failure occurrence in a situation of absent guaranteed protection against its possible negative consequences in a system that continues operating may cause undue inputs to the system’s executive mechanisms and on the assumption of the worst case scenario we deem such failure to be a wrong-side one. The used methods allow finding the probabilities of each state of the chain by solving a system of Kolmogorov-Chapman differential equations. Based on the given probabilities, the collective failure rate and average service life are identified along with the right-side and wrong-side failure rates. In order to ensure the usability of the presented methods, the authors provide approximate formulas of failure rates and approximation errors. Results . A mathematical model of operation of a multichannel microprocessor system has been developed. Formulas for calculation of system state probabilities, average service life, wrong-side and right-side failure rates have been obtained that allow evaluating the safety and fault tolerance of various systems with hot standby and in-operation operability recovery capabilities. The given formulas for calculation of system state probabilities allow increasing the number of safety and reliability indicators, if needed. The article presents the feasibility of simplified calculation of failure rates. Conclusions. The formulas given in the article can be used for evaluation of reliability, safety and longevity indicators of microprocessor-based supervision and control circuits of vital facilities (ship-borne technical facilities, trackside equipment in railway stations and open lines, fixed power facilities, etc.). In the development process they allow finding the rational system organization by means of comparative evaluation of performance of structures with various degrees of redundancy. In the context of system adaptation for application in various facilities as well as its modernization the formulas in question enable analytical calculation of the above indicators.

Infinite non homogeneous chain of harmonic oscillators: Large-time behavior of solutions

Infinite non homogeneous chain of harmonic oscillators: Large-time behavior of solutions

Fractional formalism to DNA chain and impact of the fractional order on breather dynamics

We have investigated the impact of the fractional order derivative on the dynamics of modulated waves of a homogeneous DNA chain that is based on site-dependent finite stacking and pairing enthalpies. We have reformulated the classical Lagrangian of the system by including the coordinates depending on the Riemann-Liouville time derivative of fractional order γ. From the Lagrange equation, we derived the fractional nonlinear equation of motion. We obtained the fractional breather as solutions by means of a fractional perturbation technique. The impact of the fractional order is investigated and we showed that depending on the values of γ, there are three types of waves that propagate in DNA. We have static breathers, breathers of small amplitude and high velocity, and breathers of high amplitude and small velocity.

Distribution and availability for aggregated second-order semi-Markov ternary system with working time omission

Discrete repairable degradation systems can be modeled by a homogeneous discrete-time second-order semi-Markov chain with finite state space for theoretical and practical sake. In the present paper, the state space can be divided into three subclasses, namely excellent states, good states (middle states) and failure states. The transitions among states may be driven by degradations and inside shocks of the system, repair actions, self-healings, energy supplement and other recovery ways. The Z-transform is used to give distributions for some interesting problems such as distributions of an I-period (oscillation & working time) and a gap between I-periods, and instantaneous and steady availabilities of the system. Finally, some numerical examples are given to illustrate the results obtained in the paper. The work may be used in reliability and maintenance analysis of discrete time repairable systems.

Transport properties through an aromatic molecular wire

The quantum transport properties through a finite homogeneous chain of aromatic molecules composed by benzene rings connected to two semi-infinite leads are investigated. The study is based on the tight-binding approach using semi-analytic methods of Green's function techniques within a real space renormalization scheme. The transmission probability and the characteristic diagram I−V of an aromatic molecular wire are calculated as a function of the molecule-leads coupling and the intra-rings coupling parameters. The obtained results show a good agreement with the previous reported DFT calculations.

Heat conduction in diatomic chains with correlated disorder

The paper considers heat transport in diatomic one-dimensional lattices, containing equal amounts of particles with different masses. Ordering of the particles in the chain is governed by single correlation parameter – the probability for two neighboring particles to have the same mass. As this parameter grows from zero to unity, the structure of the chain varies from regular staggering chain to completely random configuration, and then – to very long clusters of particles with equal masses. Therefore, this correlation parameter allows a control of typical cluster size in the chain. In order to explore different regimes of the heat transport, two interatomic potentials are considered. The first one is an infinite potential wall, corresponding to instantaneous elastic collisions between the neighboring particles. In homogeneous chains such interaction leads to an anomalous heat transport. The other one is classical Lennard–Jones interatomic potential, which leads to a normal heat transport. The simulations demonstrate that the correlated disorder of the particle arrangement does not change the convergence properties of the heat conduction coefficient, but essentially modifies its value. For the collision potential, one observes essential growth of the coefficient for fixed chain length as the limit of large homogeneous clusters is approached. The thermal transport in these models remains superdiffusive. In the Lennard–Jones chain the effect of correlation appears to be not monotonous in the limit of low temperatures. This behavior stems from the competition between formation of long clusters mentioned above, and Anderson localization close to the staggering ordered state.

Catalysis and autocatalysis of chemical synthesis and of hadronization

We compare the thermodynamics and catalysis of two important exothermic chemical reactions, the homogeneously catalyzed chain reaction of H2 oxidation and the heterogeneously catalyzed ammonia synthesis, with those of an important exothermic physical reaction, namely the proton or neutron synthesis from elementary particles, i.e. quarks or relativistic neutrinos, a process known as hadronization. We show that, surprisingly, hadronization has several similarities both with homogeneous autocatalytic chain reactions, as well as with heterogeneously catalyzed ammonia synthesis. In NH3 synthesis, the presence of electrical charge, namely alkali promoters or protons or electrons on transition metals, enhances the formation of catalytically active intermediate NH species, while in hadronization, free electrons or positrons lower the activation energy and facilitate the formation of catalytically active bosonic e±-neutrino intermediates. These entities liberate highly active neutrinos, creating, via their relativistic mass increase, a strong local gravitational field with all the mass-producing properties of the Higgs field. The main analogies and differences between the electric field effects in chemical catalysis and the electric and gravitational field effects in hadronization catalysis are identified and briefly discussed.

Evolution of a primary pulse in the granular dimers mounted on a linear elastic foundation: An analytical and numerical study.

In this exposition we consider the wave dynamics of a one-dimensional periodic granular dimer (diatomic) chain mounted on a damped and an undamped linear elastic foundation (otherwise called the on-site potential). It is very well known that periodic granular dimers support solitary wave propagation (similar to that in the homogeneous granular chains) for a specific discrete set of mass ratios. In this work we present the analytical investigation of the evolution of solitary waves and primary pulses in granular dimers when they are mounted on on-site potential with and without velocity proportional foundation damping. We invoke a methodology based on the multiple time-scale asymptotic analysis and partition the dynamics of the perturbed dimer chain into slow and fast components. The dynamics of the dimer chain in the limit of large mass mismatch (auxiliary chain) mounted on on-site potential and foundation damping is used as the basis for the analysis. A systematic analytical procedure is then developed for the slowly varying response of the beads and in estimating primary pulse amplitude evolution resulting in a nonlinear map relating the relative displacement amplitudes of two adjacent beads. The methodology is applicable for arbitrary mass ratios between the beads. We present several examples to demonstrate the efficacy of the proposed method. It is observed that the amplitude evolution predicted by the described methodology is in good agreement with the numerical simulation of the original system. This work forms a basis for further application of the considered methodology to weakly coupled granular dimers which finds practical relevance in designing shock mitigating granular layers.

A series of 1-D, 2-D and 3-D coordination polymers self-assembled from a flexible dicarboxylate and mixed N-donor ligands: syntheses, structural diversity, and luminescent properties

We have synthesized a series of metal–organic coordination frameworks under solvothermal conditions, formulated as [Cu(L)(phen)](1), [Co2(L)2(bib)]·CH3OH(2), [Co(L)(btmb)0.5](3), [Zn(L)(bib)]·2H2O(4), [Cu(L)(bib)]·DMF(5), and [Mn4(L)4(bimb)(CH3OH)](6) based on a flexible multicarboxylic bridging ligand 4,4′-methylenebis(oxy)-dibenzoic acid (H2L) and flexible N-donor ligands 1,4-bis (1H-imidazol-1-yl)-butane (bib), 1,4-bis(1H-1,2,4-triazol- 1-ylmethyl)benzene (btmb), and 1,4-bis(1H-imidazol-1-ylmethyl)benzene (bimb). The structures of the frameworks have been determined by single-crystal X-ray diffraction analyses and further characterized by elemental analyses, IR spectra, and thermogravimetric analyses. The crystal structure determinations reveal that 1 has a 1-D Z-shape chain. Compounds 2 and 3 are 2-D twofold parallel interpenetrating 4-connected net with the Schläfli symbol {44·62}. Compound 4 is a 2-D threefold parallel interpenetrating 4-connected nets with the Schläfli symbol {44·62}. Compound 5 is 3-D 4-connected net with the Schläfli symbol {65·8}. Compound 6 is characterized by a three-dimensional framework with one-dimensional homogeneous Mn-carboxylate chain. We found that flexible carboxylate ligands have different coordination modes under different synthetic conditions. The flexible skeleton of ligands and the coordination angle between the ligand and the metal ion is described. The luminescence and thermogravimetric properties of these compounds have been investigated.

Design of passive interconnections in tall buildings subject to earthquake disturbances to suppress inter-storey drifts

This paper studies the problem of passive control of a multi-storey building subjected to an earthquake disturbance. The building is represented as a homogeneous mass chain model, i.e., a chain of identical masses in which there is an identical passive connection between neighbouring masses and a similar connection to a movable point. The paper considers passive interconnections of the most general type, which may require the use of inerters in addition to springs and dampers. It is shown that the scalar transfer functions from the disturbance to a given inter-storey drift can be represented as complex iterative maps. Using these expressions, two graphical approaches are proposed: one gives a method to achieve a prescribed value for the uniform boundedness of these transfer functions independent of the length of the mass chain, and the other is for a fixed length of the mass chain. A case study is presented to demonstrate the effectiveness of the proposed techniques using a 10-storey building model. The disturbance suppression performance of the designed interconnection is also verified for a 10-storey building model which has a different stiffness distribution but with the same undamped first natural frequency as the homogeneous model.

Investigation of the bistability in J aggregates upon resonant optical excitation with inclusion of pair correlations between molecules

A theory of resonant interaction with radiation of J aggregates based on chains of two-level molecules coupled by the retarded dipole‒dipole interaction has been developed. The effect of pair correlations between the chain molecules on the bistable response of this system under the influence of external resonant radiation has been investigated within the homogeneous chain model. Traditionally, these systems have been described using single-particle density matrices corresponding to each molecule. In this description, twoparticle interactions are represented in the factorized form and do not include correlations between the interacting molecules. In this study, the correlation corrections have been estimated taking into account the influence of only the nearest neighbors, while their values have found to be of the same order of magnitude as the factorized two-particle expectation values for which these corrections have been calculated. As a result, the dipole‒dipole interaction of a particular molecule with the nearest neighbors is so strong that the description of this interaction in the factorized form becomes inappropriate and can be used only for a qualitative analysis of the response of the chain. In order to obtain correct quantitative characteristics, it is necessary to abandon the factorization of the two-particle expectation values, at least for nearest neighbors.

Electron–phonon interaction in quantum transport through quantum dots and molecular systems

The quantum transport and effects of decoherence properties are studied in quantum dots systems and finite homogeneous chains of aromatic molecules connected to two semi-infinite leads. We study these systems based on the tight-binding approach through Green's function technique within a real space renormalization and polaron transformation schemes. In particular, we calculate the transmission probability following the Landauer–Büttiker formalism, the I−V characteristics and the noise power of current fluctuations taken into account the decoherence. Our results may explain the inelastic effects through nanoscopic systems.

Entanglement negativity in free-fermion systems: An overlap matrix approach

In this paper, we calculate the entanglement negativity in free-fermion systems by use of the overlap matrices. For a tripartite system, if the ground state can be factored into triples of modes, we show that the partially transposed reduced density matrix can be factorized and the entanglement negativity has a simple form. However, the factorability of the ground state in a tripartite system does not hold in general. In this situation, the partially transposed reduced density matrix can be expressed in terms of the Kronecker product of matrices. We explicitly compute the entanglement negativity for the Su-Schrieffer-Heeger model, the integer Quantum Hall state, and a homogeneous one-dimensional chain. We find that the entanglement negativity for the integer quantum Hall states shows an area law behavior. For the entanglement negativity of two adjacent intervals in a homogeneous one-dimensional gas, we find agreement with the conformal field theory. Our method provides a numerically feasible way to study the entanglement negativity in free-fermion systems.