Study of Endogen Substrates,Drug Substrates and Inhibitors Binding Conformations on MRP4 and Its Variants by Molecular Docking and Molecular Dynamics

Multidrug resistance protein-4 (MRP4) belongs to the ABC transporter superfamily and promotes the transport of xenobiotics including drugs. A non-synonymous single nucleotide polymorphisms (nsSNPs) in the ABCC4 gene can promote changes in the structure and function of MRP4. In this work, the interaction of certain endogen substrates, drug substrates, and inhibitors with wild type-MRP4 (WT-MRP4) and its variants G187W and Y556C were studied to determine differences in the intermolecular interactions and affinity related to SNPs using protein threading modeling, molecular docking, all-atom, coarse grained, and umbrella sampling molecular dynamics simulations (AA-MDS and CG-MDS, respectively). The results showed that the three MRP4 structures had significantly different conformations at given sites, leading to differences in the docking scores (DS) and binding sites of three different groups of molecules. Folic acid (FA) had the highest variation in DS on G187W concerning WT-MRP4. WT-MRP4, G187W, Y556C, and FA had different conformations through 25 ns AA-MD. Umbrella sampling simulations indicated that the Y556C-FA complex was the most stable one with or without ATP. In Y556C, the cyclic adenosine monophosphate (cAMP) and ceefourin-1 binding sites are located out of the entrance of the inner cavity, which suggests that both cAMP and ceefourin-1 may not be transported. The binding site for cAMP and ceefourin-1 is quite similar and the affinity (binding energy) of ceefourin-1 to WT-MRP4, G187W, and Y556C is greater than the affinity of cAMP, which may suggest that ceefourin-1 works as a competitive inhibitor. In conclusion, the nsSNPs G187W and Y556C lead to changes in protein conformation, which modifies the ligand binding site, DS, and binding energy.     

Spontaneous magnetization of the Ising model on a 4–8 lattice

The spontaneous magnetization of the Ising model on a 4–8 lattice with six different coupling constants and two different magnetic moments is studied. A formula for the spontaneous magnetization is proposed. The result agrees with the exact low-temperature series expansions up to the 12th order.     

An Analogue of Distributivity for Ungraded Lattices

In this paper, we study lattices that posess both the properties of being extremal (in the sense of Markowsky) and of being left modular (in the sense of Blass and Sagan). We call such lattices trim and show that they posess some additional appealing properties, analogous to those of a distributive lattice. For example, trimness is preserved under taking intervals and suitable sublattices. Trim lattices satisfy a weakened form of modularity. The order complex of a trim lattice is contractible or homotopic to a sphere; the latter holds exactly if the maximum element of the lattice is a join of atoms. Any distributive lattice is trim, but trim lattices need not be graded. The main example of ungraded trim lattices are the Tamari lattices and generalizations of them. We show that the Cambrian lattices in types A and B defined by Reading are trim; we conjecture that all Cambrian lattices are trim.     

Around Multicolour Disordered Lattice Gas

We consider a system of multicolour disordered lattice gas, following closely the (monocolour) introduced by Faggionato and Martinelli^(3,4). We study the projection on the monocolour system and we derive an estimate of the closeness between grand canonical and canonical Gibbs measures. AMS Classification: Primary: 60K35, 82C20, 82C22     

Economic Equilibrium: Optimality and Price Decentralization

Mathematical economics has a long history and covers many interdisciplinary areas between mathematics and economics. At its center lies the theory of market equilibrium. The purpose of this expository article is to introduce mathematicians to price decentralization in general equilibrium theory. In particular, it concentrates on the role of positivity in the theory of convex economic analysis and the role of normal cones in the theory of non-convex economies.     

A finite model property for RMImin

It is proved that the variety of relevant disjunction lattices has the finite embeddability property. It follows that Avron's relevance logic RMI _min has a strong form of the finite model property, so it has a solvable deducibility problem. This strengthens Avron's result that RMI _min is decidable. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

具有某种断面的半群的研究进展

本文综述了几类具有特殊断面的半群的近期研究结果。在介绍逆半群和正则半群的一般结构之后，概述了具有逆断面的正则半群的结构和同余格的研究成果。总结了作为逆断面的推广的可裂断面，纯正断面，正则^*－断面和恰当断面。提出了可以进一步研究的重要的问题。