The Emerging Role of Epigenetic Methylation in Kidney Disease.

Kidney disease has complex and multifactorial pathophysiology and pathogenesis. Recent studies have revealed that epigenetic methylation changes, namely DNA methylation, histone methylation and non-histone methylation, are strongly implicated in various forms of kidney diseases. This review provides a perspective on the emerging role of epigenetic methylation in kidney disease, including the effects of DNA methylation in diverse promoter regions, regulation and implication of histone methylation, and recent advances and potential directions related to non-histone methylation. Monitoring or targeting epigenetic methylation has the potential to contribute to development of therapeutic approaches for multiple kidney diseases.

Selective EZH2 inhibitor zld1039 alleviates inflammation in cisplatin-induced acute kidney injury partially by enhancing RKIP and suppressing NF-κB p65 pathway.

Enhancer of zeste homolog 2 (EZH2), a component of polycomb repressive complex 2 (PRC2), is a histone lysine methyltransferase mediating trimethylation of histone H3 at lysine 27 (H3K27me3), which is a repressive marker at the transcriptional level. EZH2 sustains normal renal function and its overexpression has bad properties. Inhibition of EZH2 overexpression exerts protective effect against acute kidney injury (AKI). A small-molecule compound zld1039 has been developed as an efficient and selective EZH2 inhibitor. In this study, we evaluated the efficacy of zld1039 in the treatment of cisplatin-induced AKI in mice. Before injection of cisplatin (20 mg/kg, i.p.), mice were administered zld1039 (100, 200 mg/kg, i.g.) once, then in the following 3 days. We found that cisplatin-treated mice displayed serious AKI symptoms, evidenced by kidney dysfunction and kidney histological injury, accompanied by EZH2 upregulation in the nucleus of renal tubular epithelial cells. Administration of zld1039 dose-dependently alleviated renal dysfunction as well as the histological injury, inflammation and cell apoptosis in cisplatin-treated mice. We revealed that zld1039 administration exerted an anti-inflammatory effect in kidney of cisplatin-treated mice via H3K27me3 inhibition, raf kinase inhibitor protein (RKIP) upregulation and NF-κB p65 repression. In the cisplatin-treated mouse renal tubular epithelial (TCMK-1) cells, silencing of RKIP with siRNA did not abolish the anti-inflammatory effect of EZH2 inhibition, suggesting that RKIP was partially involved in the anti-inflammatory effect of zld1039. Collectively, EZH2 inhibition alleviates inflammation in cisplatin-induced mouse AKI via upregulating RKIP and blocking NF-κB p65 signaling in cisplatin-induced AKI. The potent and selective EZH2 inhibitor zld1039 has the potential as a promising agent for the treatment of AKI.

Conservative epitope of human papillomavirus type 31 L2 can induce broad-spectrum neutralizing antibodies / 基础医学与临床

Objective To detect the immunogenicity of conservative neutralizing epitope from human papilloma-virus type 31 ( HPV31) minor capsid protein L2, and analyze the neutralizing antibody spectrum of its immune sera.Methods Synthesize HPV31 L2 aa.17-40 peptide and conjugate with KLH by EDC.Immunize New Zeal-and white rabbits with HPV31 L2-KLH and Freud's Adjuvant.Analyze the neutralizing antibody titers of immune sera against HPVs from α4,α7,α9,α10 and β1 species by pseudovirus neutralization assay.Results In rabbits, HPV31 L2-KLH induced broad-spectrum neutralizing antibodies against at least 17 types of HPV, among which the neutralizing antibody titers against HPV31 are the highest, followed by that of HPV5/45/57. Conclusions The broad-spectrum neutralizing activity of the immune sera of HPV31 L2 is stimulated by conser-vative neutralizing epitope.The results lay the foundation of the development of broad-spectrum HPV vaccines based on HPV31 L2 neutralizing epitope.

Geometry of inertial manifolds probed via a Lyapunov projection method.

A method for determining the dimension and state space geometry of inertial manifolds of dissipative extended dynamical systems is presented. It works by projecting vector differences between reference states and recurrent states onto local linear subspaces spanned by the Lyapunov vectors. A sharp characteristic transition of the projection error occurs as soon as the number of basis vectors is increased beyond the inertial manifold dimension. Since the method can be applied using standard orthogonal Lyapunov vectors, it provides a possible way to also determine experimentally inertial manifolds and their geometric characteristics.

Covariant Lyapunov vectors from reconstructed dynamics: the geometry behind true and spurious Lyapunov exponents.

The estimation of Lyapunov exponents from time series suffers from the appearance of spurious Lyapunov exponents due to the necessary embedding procedure. Separating true from spurious exponents poses a fundamental problem which is not yet solved satisfactorily. We show, in this Letter, analytically and numerically that covariant Lyapunov vectors associated with true exponents lie in the tangent space of the reconstructed attractor. Therefore, we use the angle between the covariant Lyapunov vectors and the tangent space of the reconstructed attractor to identify the true Lyapunov exponents. The usefulness of our method, also for noisy situations, is demonstrated by applications to data from model systems and a NMR laser experiment.

Hyperbolic decoupling of tangent space and effective dimension of dissipative systems.

We show, using covariant Lyapunov vectors, that the tangent space of spatially extended dissipative systems is split into two hyperbolically decoupled subspaces: one comprising a finite number of frequently entangled "physical" modes, which carry the physically relevant information of the trajectory, and a residual set of strongly decaying "spurious" modes. The decoupling of the physical and spurious subspaces is defined by the absence of tangencies between them and found to take place generally; we find evidence in partial differential equations in one and two spatial dimensions and even in lattices of coupled maps or oscillators. We conjecture that the physical modes may constitute a local linear description of the inertial manifold at any point in the global attractor.

Comparison between covariant and orthogonal Lyapunov vectors.

Two sets of vectors, covariant Lyapunov vectors (CLVs) and orthogonal Lyapunov vectors (OLVs), are currently used to characterize the linear stability of chaotic systems. A comparison is made to show their similarity and difference, especially with respect to the influence on hydrodynamic Lyapunov modes (HLMs). Our numerical simulations show that in both Hamiltonian and dissipative systems HLMs formerly detected via OLVs survive if CLVs are used instead. Moreover, the previous classification of two universality classes works for CLVs as well, i.e., the dispersion relation is linear for Hamiltonian systems and quadratic for dissipative systems, respectively. The significance of HLMs changes in different ways for Hamiltonian and dissipative systems with the replacement of OLVs with CLVs. For general dissipative systems with nonhyperbolic dynamics the long-wavelength structure in Lyapunov vectors corresponding to near-zero Lyapunov exponents is strongly reduced if CLVs are used instead, whereas for highly hyperbolic dissipative systems the significance of HLMs is nearly identical for CLVs and OLVs. In contrast the HLM significance of Hamiltonian systems is always comparable for CLVs and OLVs irrespective of hyperbolicity. We also find that in Hamiltonian systems different symmetry relations between conjugate pairs are observed for CLVs and OLVs. Especially, CLVs in a conjugate pair are statistically indistinguishable in consequence of the microreversibility of Hamiltonian systems. Transformation properties of Lyapunov exponents, CLVs, and hyperbolicity under changes of coordinate are discussed in appendices.

Lyapunov modes in extended systems.

Hydrodynamic Lyapunov modes, which have recently been observed in many extended systems with translational symmetry, such as hard sphere systems, dynamic XY models or Lennard-Jones fluids, are nowadays regarded as fundamental objects connecting nonlinear dynamics and statistical physics. We review here our recent results on Lyapunov modes in extended system. The solution to one of the puzzles, the appearance of good and 'vague' modes, is presented for the model system of coupled map lattices. The structural properties of these modes are related to the phase space geometry, especially the angles between Oseledec subspaces, and to fluctuations of local Lyapunov exponents. In this context, we report also on the possible appearance of branches splitting in the Lyapunov spectra of diatomic systems, similar to acoustic and optical branches for phonons. The final part is devoted to the hyperbolicity of partial differential equations and the effective degrees of freedom of such infinite-dimensional systems.

Hyperbolicity and the effective dimension of spatially extended dissipative systems.

Using covariant Lyapunov vectors, we reveal a split of the tangent space of standard models of one-dimensional dissipative spatiotemporal chaos: A finite extensive set of N dynamically entangled vectors with frequent common tangencies describes all of the physically relevant dynamics and is hyperbolically separated from possibly infinitely many isolated modes representing trivial, exponentially decaying perturbations. We argue that N can be interpreted as the number of effective degrees of freedom, which has to be taken into account in numerical integration and control issues.

Hydrodynamic Lyapunov modes and strong stochasticity threshold in the dynamic XY model: an alternative scenario.

Crossover from weak to strong chaos in high-dimensional Hamiltonian systems at the strong stochasticity threshold (SST) was anticipated to indicate a global transition in the geometric structure of phase space. Our recent study of Fermi-Pasta-Ulam models showed that corresponding to this transition the energy density dependence of all Lyapunov exponents is identical apart from a scaling factor. The current investigation of the dynamic XY model discovers an alternative scenario for the energy dependence of the system dynamics at SSTs. Though similar in tendency, the Lyapunov exponents now show individually different energy dependencies except in the near-harmonic regime. Such a finding restricts the use of indices such as the largest Lyapunov exponent and the Ricci curvatures to characterize the global transition in the dynamics of high-dimensional Hamiltonian systems. These observations are consistent with our conjecture that the quasi-isotropy assumption works well only when parametric resonances are the dominant sources of dynamical instabilities. Moreover, numerical simulations demonstrate the existence of hydrodynamical Lyapunov modes (HLMs) in the dynamic XY model and show that corresponding to the crossover in the Lyapunov exponents there is also a smooth transition in the energy density dependence of significance measures of HLMs. In particular, our numerical results confirm that strong chaos is essential for the appearance of HLMs.

When can one observe good hydrodynamic Lyapunov modes?

Inspired by recent results on differences in fluctuations of finite-time Lyapunov exponents between hard-core and soft-potential systems we surmise that partial domination of the Oseledec splitting (DOS) with respect to subspaces associated with near-zero Lyapunov exponents is essential for observing good hydrodynamic Lyapunov modes (HLMs). Numerical results for coupled map lattices are presented to show the importance of DOS for observing good HLMs. This is achieved by relating splitting parameters to the maximum value of the Lyapunov mode structure factor.

Lyapunov spectral gap and branch splitting of Lyapunov modes in a diatomic system.

Lyapunov instability of a "diatomic" system of coupled map lattices is studied and the dynamics of Lyapunov modes (LMs) is compared with phonon dynamics. Similar to the phonon case mass differences between neighboring sites induce gaps in the Lyapunov spectrum and LMs split into two types correspondingly. An unexpected finding is that contrary to the phonon case a nontrivial threshold value for the mass difference is required for the occurrence of the spectral gap and the splitting of LMs. A possible origin of such a nontrivial threshold value of mass differences is suggested.

Hydrodynamic Lyapunov modes and strong stochasticity threshold in Fermi-Pasta-Ulam models.

The existence of a strong stochasticity threshold (SST) has been detected in many Hamiltonian lattice systems, including the Fermi-Pasta-Ulam (FPU) model, which is characterized by a crossover of the system dynamics from weak to strong chaos with increasing energy density epsilon. Correspondingly, the relaxation time to energy equipartition and the largest Lyapunov exponent exhibit different scaling behavior in the regimes below and beyond the threshold value. In this paper, we attempt to go one step further in this direction to explore further changes in the energy density dependence of other Lyapunov exponents and of hydrodynamic Lyapunov modes (HLMs). In particular, we find that for the FPU-beta and FPU-alpha(beta) models the scalings of the energy density dependence of all Lyapunov exponents experience a similar change at the SST as that of the largest Lyapunov exponent. In addition, the threshold values of the crossover of all Lyapunov exponents are nearly identical. These facts lend support to the point of view that the crossover in the system dynamics at the SST manifests a global change in the geometric structure of phase space. They also partially answer the question of why the simple assumption that the ambient manifold representing the system dynamics is quasi-isotropic works quite well in the analytical calculation of the largest Lyapunov exponent. Furthermore, the FPU-beta model is used as an example to show that HLMs exist in Hamiltonian lattice models with continuous symmetries. Some measures are defined to indicate the significance of HLMs. Numerical simulations demonstrate that there is a smooth transition in the energy density dependence of these variables corresponding to the crossover in Lyapunov exponents at the SST. In particular, our numerical results indicate that strong chaos is essential for the appearance of HLMs and those modes become more significant with increasing degree of chaoticity.

Universal features of hydrodynamic Lyapunov modes in extended systems with continuous symmetries.

Numerical and analytical evidence is presented to show that hydrodynamic Lyapunov modes (HLMs) do exist in lattices of coupled Hamiltonian and dissipative maps. More importantly, we find that HLMs in these two classes of systems are different with respect to their spatial structure and their dynamical behavior. To be concrete, the corresponding dispersion relations of Lyapunov exponent versus wave number are characterized by lambda approximately k and lambda approximately k2, respectively. The HLMs in Hamiltonian systems are propagating, whereas those of dissipative systems show only diffusive motion. Extensive numerical simulations of various systems confirm that the existence of HLMs is a very general feature of extended dynamical systems with continuous symmetries and that the above-mentioned differences between the two classes of systems are universal in large extent.

Hydrodynamic Lyapunov modes in coupled map lattices.

In this paper, numerical and analytical results are presented which indicate that hydrodynamic Lyapunov modes (HLMs) also exist for coupled map lattices (CMLs). The dispersion relations for the HLMs of CMLs are found to fall into two different universality classes. It is characterized by lambda approximately k for coupled standard maps and lambda approximately k2 for coupled circle maps. The conditions under which HLMs can be observed are discussed. The role of the Hamiltonian structure, conservation laws, translational invariance, and damping is elaborated. Our results are as follows: (1) The Hamiltonian structure is not a necessary condition for the existence of HLMs. (2) Conservation laws or the translational invariance alone cannot guarantee the existence of HLMs. (3) Including a damping term in the system of coupled Hamiltonian maps does not destroy the HLMs. The lambda-k dispersion relation of HLMs, however, changes to the universality class with lambda-k2 under damping. In contrast, no HLMs survives in the system of coupled circle maps under damping. (4) An on-site potential destroys the HLMs. (5) The study of zero-value Lyapunov exponents (LEs) and associated Lyapunov vectors (LVs) shows that translational invariance and conservation laws play different roles in the tangent space dynamics. (6) The dynamics of the coordinate and momentum parts of LVs in Hamiltonian systems are related but different. Furthermore, numerical results for a two-dimensional system show that the appearance of HLMs in CMLs is not restricted to the one-dimensional case.

Dynamical behavior of hydrodynamic Lyapunov modes in coupled map lattices.

In our previous study of hydrodynamic Lyapunov modes (HLMs) in coupled map lattices, we found that there are two classes of systems with different lambda-k dispersion relations. For coupled circle maps we found the quadratic dispersion relations lambda approximately k2 and lambda approximately k for coupled standard maps. Here, we carry out further numerical experiments to investigate the dynamic Lyapunov vector (LV) structure factor which can provide additional information on the Lyapunov vector dynamics. The dynamic LV structure factor of coupled circle maps is found to have a single peak at omega=0 and can be well approximated by a single Lorentzian curve. This implies that the hydrodynamic Lyapunov modes in coupled circle maps are nonpropagating and show only diffusive motion. In contrast, the dynamic LV structure factor of coupled standard maps possesses two visible sharp peaks located symmetrically at +/- omega. The spectrum can be well approximated by the superposition of three Lorentzian curves centered at omega=0 and +/-omegau, respectively. In addition, the omega-k dispersion relation takes the form omegau=cuk for k --> 2pi/L. These facts suggest that the hydrodynamic Lyapunov modes in coupled standard maps are propagating. The HLMs in the two classes of systems are shown to have different dynamical behavior besides their difference in spatial structure. Moreover, our simulations demonstrate that adding damping to coupled standard maps turns the propagating modes into diffusive ones alongside a change of the lambda-k dispersion relation from lambda approximately k to lambda approximately k2. In cases of weak damping, there is a crossover in the dynamic LV structure factors; i.e., the spectra with smaller k are akin to those of coupled circle maps while the spectra with larger k are similar to those of coupled standard maps.

Lyapunov instabilities of Lennard-Jones fluids.

Recent work on many-particle systems reveals the existence of regular collective perturbations corresponding to the smallest positive Lyapunov exponents (LEs), called hydrodynamic Lyapunov modes. Until now, however, these modes have been found only for hard-core systems. Here we report results on Lyapunov spectra and Lyapunov vectors (LVs) for Lennard-Jones fluids. By considering the Fourier transform of the coordinate fluctuation density u((alpha)) (x,t) , it is found that the LVs with lambda approximately equal to 0 are highly dominated by a few components with low wave numbers. These numerical results provide strong evidence that hydrodynamic Lyapunov modes do exist in soft-potential systems, although the collective Lyapunov modes are more vague than in hard-core systems. In studying the density and temperature dependence of these modes, it is found that, when the value of the Lyapunov exponent lambda((alpha)) is plotted as function of the dominant wave number k(max) of the corresponding LV, all data from simulations with different densities and temperatures collapse onto a single curve. This shows that the dispersion relation lambda((alpha)) vs k(max) for hydrodynamical Lyapunov modes appears to be universal for the low-density cases studied here. Despite the wavelike character of the LVs, no steplike structure exists in the Lyapunov spectrum of the systems studied here, in contrast to the hard-core case. Further numerical simulations show that the finite-time LEs fluctuate strongly. We have also investigated localization features of LVs and propose a length scale to characterize the Hamiltonian spatiotemporal chaotic states.

Oscillatory and rotatory synchronization of chaotic autonomous phase systems.

The existence of rotatory, oscillatory, and oscillatory-rotatory synchronization of two coupled chaotic phase systems is demonstrated in the paper. We find four types of transition to phase synchronization depending on coherence properties of motions, characterized by phase variable diffusion. When diffusion is small the onset of phase synchronization is accompanied by a change in the Lyapunov spectrum; one of the zero Lyapunov exponents becomes negative shortly before this onset. If the diffusion of the phase variable is strong then phase synchronization and generalized synchronization, occur simultaneously, i.e., one of the positive Lyapunov exponents becomes negative, or generalized synchronization even sets in before phase synchronization. For intermediate diffusion the phase synchronization appears via interior crisis of the hyperchaotic set. Soft and hard transitions to phase synchronization are discussed.