Improving Coarse Grain Models of Protein Folding through Weighting of Polar-polar/hydrophobic-hydrophobic Interactions into Crowded Spaces

In this piece of work were tested 7 Hydrophobic-Polar sequences in two types of 2D-square space lattices, homogeneous and correlated, the latter simulating molecular crowding included as a geometric boundary restriction. The optimization of the 2D structures was carried out using a variant of Dill's model, inspired by the convex function, which takes into account both the hydrophobic (Dill’s model) and polar interactions, aimed to include more structural information to reach better folding solutions. While using correlated networks, the degrees of freedom in the folding of sequences were limited, and as a result in all cases more successful structural trials were found in comparison to the homogeneous lattice. In particular, the S5 sequence turned out to be the most difficult sequence of the seven folded, this perhaps due to the intrinsic i) degrees of freedom and ii) motifs of the expected 2D HP structure. Regarding S2 and S6 sequences, although optimal folding was not achieved for neither of the two approaches, folding with correlated network approach not only produced better results than homogeneous space, but for both sequences the best values found with crowding were very close to the expected optimal fitness. The sequences S1-S4 and S6 were better folded with medium lattice units for the correlated media, instead, S5 and S7 were better folded with a bit larger degree of lattice unit, revealing that depending on the degrees of freedom and particular folding motifs in each sequence would require particular crowding to achieve better folding. Finally, we claim that in all folded sequences in crowded spaces achieve better results than homogeneous ones.

‘POSITIVELY HOMOGENEOUS LATTICE HOMOMORPHISMS BETWEEN RIESZ SPACES NEED NOT BE LINEAR’

This note furnishes an example showing that the main result (Theorem 4) in Toumi [‘When lattice homomorphisms of Archimedean vector lattices are Riesz homomorphisms’, J. Aust. Math. Soc. 87 (2009), 263–273] is false.

EXTENDING LOCAL PASSIVITY THEORY AND HOPF BIFURCATION AT THE EDGE OF CHAOS IN OREGONATOR CNN

The fundamental local passivity theory asserts that a wide spectrum of complex behaviors may exist if the cells in the reaction–diffusion are not locally passive. This local passivity principle has provided a powerful tool for studying the complexity in a homogeneous lattice formed by coupled cells. In this paper, the complexity matrix YQ(s), which is the tool for testing the local passivity theory, is modified based on the characteristic polynomial AQ(λ). Then, the local passivity theory is applied to the study of the Oregonator CNN to judge if the cell parameters of a CNN are chosen at the edge of chaos. Analysis of the bifurcation and the numerical simulations show that nonzero diffusion term in Oregonator CNN may cause a reaction–diffusion equation oscillating under the appropriate choice of diffusion coefficient if the local passivity theory is not satisfied. That is, if the cell parameters of a CNN are chosen at the edge of chaos, the system is potentially unstable.

Relation between Structural Size and the Discretization Density of Brittle Homogeneous Lattice Models

This paper contains the results of an investigation into the effect of the discretization of lattice models. The study is performed with homogeneous models where all elements share the same strength. Elemental constitutive law is linearly-brittle, meaning that elements behave linearly but are completely removed from the structure as soon as they reach the limit of their strength. The relation between structural size and discretization density is studied with unnotched beams loaded in three point bending (modulus of rupture test). We report the results for regular discretization and irregular networks obtained via Voronoi tessellation. This is carried out for two types of models: these being with and without rotational springs (normal and shear springs are always present). The numerically obtained dependence of strength on discretization density is compared to the analytical size effect formula.

Phase Field Simulation of the Collapse of the Rafted Structure in Ni-Based Superalloys

Microstructural evolution in single crystal Ni-based superalloys is investigated by the phase field simulation. During creep, the morphology of theγphase changed from the cuboidal shape to the rafted one, and the rafted structure was collapsed in the late stage of creep. The simulation on the microstructural evolution is based on thermodynamic information, diffusion equation, elastic anisotropy and a homogeneous lattice misfit. It is found that caused by external stress result in the morphological change of theγphase to the rafted structure, and this rafted structure is collapsed by inhomogeneous lattice misfit. These morphological changes can be explained by the change in stable morphology of theγphase.

Theorems and Application of Local Activity of CNN with Five State Variables and One Port

Coupled nonlinear dynamical systems have been widely studied recently. However, the dynamical properties of these systems are difficult to deal with. The local activity of cellular neural network (CNN) has provided a powerful tool for studying the emergence of complex patterns in a homogeneous lattice, which is composed of coupled cells. In this paper, the analytical criteria for the local activity in reaction-diffusion CNN with five state variables and one port are presented, which consists of four theorems, including a serial of inequalities involving CNN parameters. These theorems can be used for calculating the bifurcation diagram to determine or analyze the emergence of complex dynamic patterns, such as chaos. As a case study, a reaction-diffusion CNN of hepatitis B Virus (HBV) mutation-selection model is analyzed and simulated, the bifurcation diagram is calculated. Using the diagram, numerical simulations of this CNN model provide reasonable explanations of complex mutant phenomena during therapy. Therefore, it is demonstrated that the local activity of CNN provides a practical tool for the complex dynamics study of some coupled nonlinear systems.