Class Of Chains Research Articles

Calcium inhibition as an intracellular signal for actin-myosin interaction.

Intracellular signaling pathways include both the activation and the inhibition of biological processes. The activation of Ca2+ regulation of actin-myosin interactions was examined first, whereas it took 20 years for the author to clarify the inhibitory mode by using Physarum polycephalum, a lower eukaryote. This review describes the investigation of the inhibitory mode since 1980. The inhibitory effect of Ca2+ on myosin was detected chemically by ATPase assays and mechanically by in vitro motility assays. The Ca2+-binding ability of Physarum myosin is as high as that of scallop myosin. Ca2+ inhibits Physarum myosin, whereas it activates scallop myosin. We cloned cDNA of the myosin heavy chain and light chains to express a hybrid of Physarum and scallop myosin, and found that the Ca-binding light chain (CaLc), which belongs to an alkali light chain class, plays a major role in Ca inhibition. The role of CaLc was confirmed by mutating its EF-hand, Ca-binding structure and expressing Physarum myosin as a recombinant protein. Thus, the data obtained by classical protein purification were confirmed by the results obtained with the modern recombinant techniques. However, there are some discrepancies that remain to be solved as described in Section XII.

N-soliton interactions in an extended Schrödinger equation with higher order of nonlinearities

We investigate the existence of N-solitons in an extended general nonlinear Schrödinger equation with third and fourth order dispersive terms that is most important for applications, such as the dynamics of a general class of anisotropic Heisenberg ferromagnetic spin chain with different magnetic interactions, the alpha helical proteins, and in media that offer interactions in biophysics. We have transformed the model to a homogeneous model that is utilized to show the existence of interactions of N-soliton solutions. We analyzed, and gave specific forms of these new class of N-solitons in a new simple form and discussed the interactions of these N-solitons. We have shown the existence of three types of head-on collisions, head-on collisions with or without over-taking or splitting into two solitons.

160 LIPIDOME SIGNATURES IN EARLY BOVINE EMBRYO DEVELOPMENT

Mammalian pre-implantation embryonic development is a complex, conserved, and well-orchestrated process involving dynamic molecular and structural changes. Understanding the membrane lipid profile fluctuation during this crucial period is fundamental to address cellular and molecular mechanisms governing embryogenesis. A full understanding of stage-specific lipid signatures in early bovine embryo development is, however, still lacking. The aim of the present work was to characterise stage-specific changes in lipid profiles during early bovine embryonic development. Immature oocytes were recovered from slaughterhouse-derived bovine ovaries and assigned among 5 in vitro developmental stages for lipid characterisation: immature oocytes, 2-cell embryos (32–40 h post-insemination), 8 to 16-cell embryos (72 h post-insemination), morulas (120 h post-insemination), and blastocysts (168 h post-insemination). Two different culture media were used for in vitro embryo production, SOFaaci medium supplemented with 2.5% of serum and serum-free SOF-BE1 medium. Cytoplasmic lipid droplets content and membrane phospholipids profiles for each development stage were assessed by lipid staining (Nile red; n = 5–9) and matrix-assisted laser desorption ionization as a mass spectrometry imaging (MALDI-MS; n = 5–9), respectively. For statistical analysis, univariate and multivariate models were used to compare lipid droplets content and membrane phospholipids profiles. Cytoplasmic lipid droplets content increased from minimum in the immature oocyte stage to maximum at the morula stage, followed by a sharp drop at the blastocyst stage (58.4 ± 10.5ac, 62.5 ± 9.4ac, 85.9 ± 8.2a, 148.3 ± 7.4b, 37.4 ± 9.9c of fluorescence intensity per embryo area, respectively, for immature oocyte, 2-cells, 8 to 16-cells, morulas, and blastocysts; abcP < 0.05). More cytoplasmic lipid droplets were detected in morulas and blastocyts cultured in SOFaaci than in SOF-BE1 (morulas, 162.6 ± 11.3 v. 137.1 ± 9.2 of fluorescence intensity per embryo area, respectively, P < 0.05; blastocysts, 49.9 ± 9.9 v. 20.7 ± 9.9 of fluorescence intensity per embryo area, respectively, P < 0.05). Characteristic dynamic changes of unsaturation level, acyl chain length and class composition (phosphatidylcholines, sphingomyelins, and phosphatidylethanolamines) of phospholipid profiles were observed during early embryo development. This study provides a comprehensive analysis, involving lipid staining and mass spectrometry evaluation, of stage-specific lipid signatures during bovine in vitro embryo development. These results may be useful for assessing the role of specific lipid species during important events of embryogenesis. Research was supported by CNPq, FAPESP, and FAPERGS.

Mean convergence of Markovian spherical averages for measure-preserving actions of the free group

Mean convergence of Markovian spherical averages is established for a measure-preserving action of a finitely-generated free group on a probability space. We endow the set of generators with a generalized Markov chain and establish the mean convergence of resulting spherical averages in this case under mild nondegeneracy assumptions on the stochastic matrix $\Pi$ defining our Markov chain. Equivalently, we establish the triviality of the tail sigma-algebra of the corresponding Markov operator. This convergence was previously known only for symmetric Markov chains, while the conditions ensuring convergence in our paper are inequalities rather than equalities, so mean convergence of spherical averages is established for a much larger class of Markov chains.

RETRACTED ARTICLE: Fixed point theorems and explicit estimates for convergence rates of continuous time Markov chains

Abstract In this paper we give Banach fixed point theorems and explicit estimates on the rates of convergence of the transition function to the stationary distribution for a class of exponential ergodic Markov chains. Our results are different from earlier estimates using coupling theory, and from estimates using stochastically monotone one. Our estimates show a noticeable improvement on existing results if Markov chains contain instantaneous states or nonconservative states. The proof uses existing results of discrete time Markov chains together with h-skeleton. At last, we apply this result, Ray-Knight compactification and Itô excursion theory to two examples: a class of singular Markov chains and Kolmogorov matrix.

Dynamical class of a two-dimensional plasmonic Dirac system.

A current goal in plasmonic science and technology is to figure out how to manage the relaxational dynamics of surface plasmons in graphene since its damping constitutes a hinder for the realization of graphene-based plasmonic devices. In this sense we believe it might be of interest to enlarge the knowledge on the dynamical class of two-dimensional plasmonic Dirac systems. According to the recurrence relations method, different systems are said to be dynamically equivalent if they have identical relaxation functions at all times, and such commonality may lead to deep connections between seemingly unrelated physical systems. We employ the recurrence relations approach to obtain relaxation and memory functions of density fluctuations and show that a two-dimensional plasmonic Dirac system at long wavelength and zero temperature belongs to the same dynamical class of standard two-dimensional electron gas and classical harmonic oscillator chain with an impurity mass.

Rescaling Entropy and Divergence Rates

Based on rescaling by some suitable sequence instead of the number of time units, the usual notion of divergence rate is here extended to define and determine meaningful generalized divergence rates. Rescaling entropy rates appears as a special case. Suitable rescaling is naturally induced by the asymptotic behavior of the marginal divergences. Closed-form formulas are obtained as soon as the marginal divergences behave like powers of some analytical functions. A wide class of countable Markov chains is proved to satisfy this property. Most divergence and entropy functionals defined in the literature are concerned, e.g., the classical Shannon, Kullback–Leibler, Renyi, and Tsallis. For illustration purposes, Ferreri or Basu–Harris–Hjort–Jones—among others—are also considered.

G.P.413 - Enhancement of myosin heavy chain class I (MHC I) mRNA expression in C2C12 myocyte by multivalent cations

G.P.413 - Enhancement of myosin heavy chain class I (MHC I) mRNA expression in C2C12 myocyte by multivalent cations

Renal AH Amyloidosis Associated With a Truncated Immunoglobulin Heavy Chain Undetectable by Immunostaining

AH amyloidosis is a rare type of amyloidosis caused by deposition of monoclonal immunoglobulin heavy chain. The key diagnostic feature is positive immunostaining for a single class of immunoglobulin heavy chain. We report a case of AH amyloidosis with immunoglobulin G (IgG) λ monoclonal gammopathy that was diagnosed by liquid chromatography-tandem mass spectrometry (LC-MS/MS) after immunostaining of renal tissue for immunoglobulin heavy chain gave negative results. The molecular weight of the purified renal amyloid protein was ∼11kDa, which was determined by LC-MS/MS analysis to correspond to an amino acid sequence comprising the variable region and a truncated portion of the constant region of IgG heavy chain. The exact same truncated heavy chain was detected by LC-MS/MS of a protein isolated from the patient's serum, suggesting that the truncated serum protein was the precursor of the amyloid protein. Because antibodies to immunoglobulin heavy chain recognize the Fc portion, the large deletion in the constant region could explain the negative results upon immunostaining. Direct protein detection by LC-MS/MS is a powerful aid to diagnose renal AH amyloidosis, particularly when the findings of immunoglobulin staining are inconsistent with the background monoclonal gammopathy.

Random matrix theory and critical phenomena in quantum spin chains.

We compute critical properties of a general class of quantum spin chains which are quadratic in the Fermi operators and can be solved exactly under certain symmetry constraints related to the classical compact groups U(N),O(N), and Sp(2N). In particular we calculate critical exponents s,ν, and z, corresponding to the energy gap, correlation length, and dynamic exponent, respectively. We also compute the ground state correlators 〈σ_{i}^{x}σ_{i+n}^{x}〉_{g},〈σ_{i}^{y}σ_{i+n}^{y}〉_{g}, and 〈∏_{i=1}^{n}σ_{i}^{z}〉_{g}, all of which display quasi-long-range order with a critical exponent dependent upon system parameters. Our approach establishes universality of the exponents for the class of systems in question.

Recursive Learning for Sparse Markov Models

Markov chains of higher order are popular models for a wide variety of applications in natural language and DNA sequence processing. However, since the number of parameters grows exponentially with the order of a Markov chain, several alternative model classes have been proposed that allow for stability and higher rate of data compression. The common notion to these models is that they cluster the possible sample paths used to predict the next state into invariance classes with identical conditional distributions assigned to the same class. The models vary in particular with respect to constraints imposed on legitime partitions of the sample paths. Here we consider the class of sparse Markov chains for which the partition is left unconstrained a priori. A recursive computation scheme based on Delaunay triangulation of the parameter space is introduced to enable fast approximation of the posterior mode partition. Comparisons with stochastic optimization, k-means and nearest neighbor algorithms show that our approach is both considerably faster and leads on average to a more accurate estimate of the underlying partition. We show additionally that the criterion used in the recursive steps for comparison of triangulation cell contents leads to consistent estimation of the local structure in the sparse Markov model.

Reversible Markov structures on divisible set partitions

We studyk-divisible partition structures, which are families of random set partitions whose block sizes are divisible by an integerk= 1, 2, …. In this setting, exchangeability corresponds to the usual invariance under relabeling by arbitrary permutations; however, fork> 1, the ordinary deletion maps on partitions no longer preserve divisibility, and so a random deletion procedure is needed to obtain a partition structure. We describe explicit Chinese restaurant-type seating rules for generating families of exchangeablek-divisible partitions that are consistent under random deletion. We further introduce the notion ofMarkovian partition structures, which are ensembles of exchangeable Markov chains onk-divisible partitions that are consistent under a random process ofMarkovian deletion. The Markov chains we study are reversible and refine the class of Markov chains introduced in Crane (2011).

Reversible Markov structures on divisible set partitions

We study k-divisible partition structures, which are families of random set partitions whose block sizes are divisible by an integer k = 1, 2, …. In this setting, exchangeability corresponds to the usual invariance under relabeling by arbitrary permutations; however, for k > 1, the ordinary deletion maps on partitions no longer preserve divisibility, and so a random deletion procedure is needed to obtain a partition structure. We describe explicit Chinese restaurant-type seating rules for generating families of exchangeable k-divisible partitions that are consistent under random deletion. We further introduce the notion of Markovian partition structures, which are ensembles of exchangeable Markov chains on k-divisible partitions that are consistent under a random process of Markovian deletion. The Markov chains we study are reversible and refine the class of Markov chains introduced in Crane (2011).

Solving the Pareto front for multiobjective Markov chains using the minimum Euclidean distance gradient-based optimization method

A novel method based on minimizing the Euclidean distance is proposed for generating a well-distributed Pareto set in multi-objective optimization for a class of ergodic controllable Markov chains. The proposed approach is based on the concept of strong Pareto policy. We consider the case where the search space is a non-strictly convex set. For solving the problem we introduce the Tikhonov’s regularization method and implement the Lagrange principle. We formulate the original problem introducing linear constraints over the nonlinear problem employing the c-variable method and constraining the cost-functions allowing points in the Pareto front to have a small distance from one another. As a result, the proposed method generates an even representation of the entire Pareto surface. Then, we propose an algorithm to compute the Pareto front and provide all the details needed to implement the method in an efficient and numerically stable way. As well, we prove the main Theorems for describing the dependence of the saddle point for the regularizing parameter and analyzes its asymptotic behavior. Moreover, we analyze the step size parameter of the Lagrange principle and also its asymptotic behavior. The suggested approach is validated theoretically and verified by a numerical example related to security patrolling that present a technique for visualizing the Pareto front.

The repetitive portion of the Xenopus IgH Mu switch region mediates orientation-dependent class switch recombination.

Vertebrates developed immunoglobulin heavy chain (IgH) class switch recombination (CSR) to express different IgH constant regions. Most double-strand breaks for Ig CSR occur within the repetitive portion of the switch regions located upstream of each set of constant domain exons for the Igγ, Igα or Igϵ heavy chain. Unlike mammalian switch regions, Xenopus switch regions do not have a high G-density on the non-template DNA strand. In previous studies, when Xenopus Sμ DNA was moved to the genome of mice, it is able to support substantial CSR when it is used to replace the murine Sγ1 region. Here, we tested both the 2kb repetitive portion and the 4.6 kb full-length portions of the Xenopus Sμ in both their natural (forward) orientation relative to the constant domain exons, as well as the opposite (reverse) orientation. Consistent with previous work, we find that the 4.6 kb full-length Sμ mediates similar levels of CSR in both the forward and reverse orientations. Whereas, the forward orientation of the 2kb portion can restore the majority of the CSR level of the 4.6 kb full-length Sμ, the reverse orientation poorly supports R-looping and no CSR. The forward orientation of the 2kb repetitive portion has more GG dinucleotides on the non-template strand than the reverse orientation. The correlation of R-loop formation with CSR efficiency, as demonstrated in the 2kb repetitive fragment of the Xenopus switch region, confirms a role played by R-looping in CSR that appears to be conserved through evolution.

Quantitative Convergence Rates for Subgeometric Markov Chains

We provide explicit expressions for the constants involved in the characterisation of ergodicity of subgeometric Markov chains. The constants are determined in terms of those appearing in the assumed drift and one-step minorisation conditions. The results are fundamental for the study of some algorithms where uniform bounds for these constants are needed for a family of Markov kernels. Our results accommodate also some classes of inhomogeneous chains.

Quantitative Convergence Rates for Subgeometric Markov Chains

We provide explicit expressions for the constants involved in the characterisation of ergodicity of subgeometric Markov chains. The constants are determined in terms of those appearing in the assumed drift and one-step minorisation conditions. The results are fundamental for the study of some algorithms where uniform bounds for these constants are needed for a family of Markov kernels. Our results accommodate also some classes of inhomogeneous chains.

Codimension one structurally stable chain classes

The well-known stability conjecture of Palis and Smale states that if a diffeomorphism is structurally stable, then the chain recurrent set is hyperbolic. It is natural to ask if this type of result is true for an individual chain class, that is, whether or not every structurally stable chain class is hyperbolic. Regarding the notion of structural stability, there is a subtle difference between the case of a whole system and the case of an individual chain class. The latter is more delicate and contains additional difficulties. In this paper we prove a result of this type for the latter, with an additional assumption of codimension 1. Precisely, let f f be a diffeomorphism of a closed manifold M M and let p p be a hyperbolic periodic point of f f of index 1 or dim ⁡ M − 1 \dim M-1 . We prove if the chain class of p p is structurally stable, then it is hyperbolic. Since the chain class of p p is not assumed in advance to be locally maximal, and since the counterpart of it for the perturbation g g is defined not canonically but indirectly through the continuation p g p_g of p p , the proof is quite delicate.

Quantum state transfer in disordered spin chains: How much engineering is reasonable?

The transmission of quantum states through spin chains is an important element in the implementation of quantum information technologies. Speed and fidelity of transfer are the main objectives which have to be achieved by the devices even in the presence of imperfections which are unavoidable in any manufacturing process. To reach these goals, several kinds of spin chains have been suggested, which differ in the degree of fine-tuning, or engineering, of the system parameters. In this work we present a systematic study of two important classes of such chains. In one class only the spin couplings at the ends of the chain have to be adjusted to a value different from the bulk coupling constant, while in the other class every coupling has to have a specific value. We demonstrate that configurations from the two different classes may perform similarly when subjected to the same kind of disorder in spite of the large difference in the engineering effort necessary to prepare the system. We identify the system features responsible for these similarities and we perform a detailed study of the transfer fidelity as a function of chain length and disorder strength, yielding empirical scaling laws for the fidelity which are similar for all kinds of chain and all disorder models. These results are helpful in identifying the optimal spin chain for a given quantum information transfer task. In particular, they help in judging whether it is worthwhile to engineer all couplings in the chain as compared to adjusting only the boundary couplings.

Two-Sided Bounds on the Rate of Convergence for Continuous-Time nite Inhomogeneous Markov Chains

Abstract We suggest an approach to obtain general two-sided bounds on the rate of convergence in terms of special “weighted” norms related to total variation. Some important classes of continuous-time Markov chains are considered: birth–death–catastrophes processes, queueing models with batch arrivals and group services, chains with absorption in zero.