Molecular Dynamics Simulation of HIV-1 Integrase Dimer Complexed with Viral DNA

The biological function of HIV‐1 integrase (IN) is to integrate viral DNA into the host cell chromosome, and the specific binding of IN with viral DNA is a precondition for IN to function correctly. Beforehand, the binding mode of IN dimer (IN₂) with the 27 bp segment of viral DNA before 3′ processing (3′‐P) was obtained via a molecular docking method. Based on the binding mode, the aim of this article was to explore the changes of motive mode and correlative motion for the IN₂ and DNA systems after their binding through dynamical cross‐correlation map (DCCM) and principal component analysis (PCA). Finally, solvent effect during the association was analyzed briefly. The results show that there is a significantly increased positive correlation in the interface region between IN₂ and viral DNA, and some obvious motive mode changes of the two systems (IN₂ and DNA) were also observed after their binding. It was found that water molecules played an important role in the recognition between IN₂ and viral DNA through analyzing the water‐mediated hydrogen bonds.     

Sugarcane proteomics: Establishment of a protein extraction method for 2‐DE in stalk tissues and initiation of sugarcane proteome reference map

Sugarcane is an important commercial crop cultivated for its stalks and sugar is a prized commodity essential in human nutrition. Proteomics of sugarcane is in its infancy, especially when dealing with the stalk tissues, where there is no study to date. A systematic proteome analysis of stalk tissue yet remains to be investigated in sugarcane, wherein the stalk tissue is well known for its rigidity, fibrous nature, and the presence of oxidative enzymes, phenolic compounds and extreme levels of carbohydrates, thus making the protein extraction complicated. Here, we evaluated five different protein extraction methods in sugarcane stalk tissues. These methods are as follows: direct extraction using lysis buffer (LB), TCA/acetone precipitation followed by solubilization in LB, LB containing thiourea (LBT), and LBT containing tris, and phenol extraction. Both quantitative and qualitative protein analyses were performed for each method. 2‐DE analysis of extracted total proteins revealed distinct differences in protein patterns among the methods, which might be due to their physicochemical limitations. Based on the 2‐D gel protein profiles, TCA/acetone precipitation‐LBT and phenol extraction methods showed good results. The phenol method showed a shift in pI values of proteins on 2‐D gel, which was mostly overcome by the use of 2‐D cleanup kit after protein extraction. Among all the methods tested, 2‐D cleanup‐phenol method was found to be the most suitable for producing high number of good‐quality spots and reproducibility. In total, 30 and 12 protein spots commonly present in LB, LBT and phenol methods, and LBT method were selected and subjected to eLD‐IT‐TOF‐MS/MS and nESI‐LC‐MS/MS analyses, respectively, and a reference map has been established for sugarcane stalk tissue proteome. A total of 36 nonredundant proteins were identified. This is a very first basic study on sugarcane stalk proteome analysis and will promote the unexplored areas of sugarcane proteome research.     

A completely iterative method for the infinite domain electrostatic problem with nonlinear dielectric media

We present an iterative method for the solution of the exterior all-space electrostatic problem for nonlinear dielectric media. The electric potential is specified on interior boundaries and the electric field decays at infinity. Our approach uses a natural variational formulation based on the total energy of the nonlinear dielectric medium subject to boundary conditions. The problem is decomposed into an exterior calculation and an interior calculation with the boundary-specified electric potentials imposed as constraints between them. Together, these enable an iterative method that is based on the variational formulation. In contrast to direct solution of the electrostatic problems, we avoid the construction, storage and solution of dense and large linear systems. This provides important advantages for multiphysics problems that couple the linear electrostatic Poisson problem to nonlinear physics: the latter necessarily involves iterative approaches, and our approach replaces a large number of direct solves for the electrostatics with an iterative algorithm that can be coupled to the iterations of the nonlinear problem. We present examples applying the method to inhomogeneous, anisotropic nonlinear dielectrics. A key advantage of our variational formulation is that we require only the free-space, isotropic, homogeneous Greens function for all these settings.     

Image encryption scheme by using iterative random phase encoding in gyrator transform domains

An image encryption is discussed based on the random phase encoding method in gyrator domains. An iterative structure of image encryption is designed for introducing more random phases to encrypt image. These random phase functions are generated by a two-dimensional chaotic mapping with the help of computer. The random phases are utilized for increasing the security of this encryption algorithm. In the chaotic mapping relation, the initial value and expression can serve as the key of algorithm. The mapping relation is considered secretly for storage and transmission in practical application in comparison to traditional algorithms. The angle parameter of gyrator transform is an additional key. Some numerical simulations have been given to validate the performance of the encryption scheme.     

The solution of the global relation for the derivative nonlinear Schrödinger equation on the half-line

We consider initial-boundary value problems for the derivative nonlinear Schrödinger (DNLS) equation on the half-line x>0. In a previous work, we showed that the solution q(x,t) can be expressed in terms of the solution of a Riemann-Hilbert problem with jump condition specified by the initial and boundary values of q(x,t). However, for a well-posed problem, only part of the boundary values can be prescribed; the remaining boundary data cannot be independently specified, but are determined by the so-called global relation. In general, an effective solution of the problem therefore requires solving the global relation. Here, we present the solution of the global relation in terms of the solution of a system of nonlinear integral equations. This also provides a construction of the Dirichlet-to-Neumann map for the DNLS equation on the half-line.     

Continuous symmetry reduction and return maps for high-dimensional flows

We present two continuous symmetry reduction methods for reducing high-dimensional dissipative flows to local return maps. In the Hilbert polynomial basis approach, the equivariant dynamics is rewritten in terms of invariant coordinates. In the method of moving frames (or method of slices) the state space is sliced locally in such a way that each group orbit of symmetry-equivalent points is represented by a single point. In either approach, numerical computations can be performed in the original state space representation, and the solutions are then projected onto the symmetry-reduced state space. The two methods are illustrated by reduction of the complex Lorenz system, a five-dimensional dissipative flow with rotational symmetry. While the Hilbert polynomial basis approach appears unfeasible for high-dimensional flows, symmetry reduction by the method of moving frames offers hope.     

Boundary crisis and transient in a dissipative relativistic standard map

Some dynamical properties for a problem concerning the acceleration of particles in a wave packet are studied. The model is described in terms of a two-dimensional nonlinear map obtained from a Hamiltonian which describes the motion of a relativistic standard map. The phase space is mixed in the sense that there are regular and chaotic regions coexisting. When dissipation is introduced, the property of area preservation is broken and attractors emerge. We have shown that a tiny increase of the dissipation causes a change in the phase space. A chaotic attractor as well as its basin of attraction are destroyed thereby leading the system to experience a boundary crisis. We have characterized such a boundary crisis via a collision of the chaotic attractor with the stable manifold of a saddle fixed point. Once the chaotic attractor is destroyed, a chaotic transient described by a power law with exponent −1 is observed.     

Linearization of vector fields and embedding of diffeomorphisms in flows via Nash–Moser theorem

In the first part of this paper we give suitable spectral properties of the adjoint operators induced by appropriate perturbations of some hyperbolic linear vector fields. These properties are useful to prove general facts based on the Nash–Moser inverse function theorem. In the second part of this work we study circumstances where a global linearization of a vector field X$X$ in a real numerical space is feasible and where some diffeomorphisms which are close to exp(X)$exp\left(X\right)$ can be embedded in a flow.     

Public policy structuring incorporating reciprocal expectation analysis

This paper proposes a method of structuring public policy by incorporating reciprocal expectation analysis. The proposed method is characterized by three components: identification of the problem structure perceived by stakeholders using cognitive maps, policy structuring analysis with a value–driver matrix and a reciprocal expectation matrix, and feasibility analysis of agreements among the stakeholders. The three types of relationship among stakeholders are derived from the feasibility analysis, which are “Dosho-imu”, “Isho-imu”, and “Domu”. Three tests of feasibility to reach the agreement are then proposed: “information-sharing test”, “bargaining test”, and “reframing test”. A case study is presented, applying the method to strategic transportation planning in the Kanto region of Japan. Finally, the potential functions of the proposed method in practice are discussed.     

On the number of limit cycles in general planar piecewise linear systems of node–node types

We investigate the existence and number of limit cycles in a class of general planar piecewise linear systems constituted by two linear subsystems with node–node dynamics. Using the Liénard-like canonical form with seven parameters, some sufficient and necessary conditions for the existence of limit cycles are given by studying the fixed points of proper Poincaré maps. In particular, we prove the existence of at least two nested limit cycles and describe some parameter regions where two limit cycles exist. The main results are applied to the PWL Morris–Lecar neural model to determine the existence and stability of the limit cycles.