Kunitzins: Prototypes of a new class of protease inhibitor from the skin secretions of European and Asian frogs

Amphibian skin secretions contain biologically-active compounds, such as anti-microbial peptides and trypsin inhibitors, which are used by biomedical researchers as a source of potential novel drug leads or pharmacological agents. Here, we report the application of a recently developed technique within our laboratory to “shotgun” clone the cDNAs encoding two novel but structurally-related peptides from the lyophilized skin secretions of one species of European frog, Rana esculenta and one species of Chinese frog, Odorrana schmackeri. Bioanalysis of the peptides established the structure of a 17-mer with an N-terminal Ala (A) residue and a C-terminal Cys (C) residue with a single disulphide bridge between Cys 12 and 17, which is a canonical Kunitz-type protease inhibitor motif (-CKAAFC-). Due to the presence of this structural attribute, these peptides were named kunitzin-RE (AAKIILNPKFRCKAAFC) and kunitzin-OS (AVNIPFKVHLRCKAAFC). Synthetic replicates of these two novel peptides were found to display a potent inhibitory activity against Escherichia coli but were ineffective at inhibiting the growth of Staphylococcus aureus and Candida albicans at concentrations up to 160 μM, and both showed little haemolytic activity at concentrations up to 120 μM. Subsequently, kunitzin-RE and kunitzin-OS were found to be a potent inhibitor of trypsin with a Ki of 5.56 μM and 7.56 μM that represent prototypes of a novel class of highly-attenuated amphibian skin protease inhibitor. Substitution of Lys-13, the predicted residue occupying the P1 position within the inhibitory loop, with Phe (F) resulted in decrease in trypsin inhibitor effectiveness and antimicrobial activity against Esherichia coli, but exhibits a potential inhibition activity against chymotrypsin.

On the zeros of the Abelian integrals for a class of Liénard systems

A planar polynomial differential system has a finite number of limit cycles. However, finding the upper bound of the number of limit cycles is an open problem for the general nonlinear dynamical systems. In this paper, we investigated a class of Liénard systems of the form x'=y, y'=f(x)+y g(x) with deg f=5 and deg g=4. We proved that the related elliptic integrals of the Liénard systems have at most three zeros including multiple zeros, which implies that the number of limit cycles bifurcated from the periodic orbits of the unperturbed system is less than or equal to 3.

A Numerical Solution Using an Adaptively Preconditioned Lanczos Method for a Class of Linear Systems Related with the Fractional Poisson Equation

This study considers the solution of a class of linear systems related with the fractional Poisson equation (FPE) (−∇2)α/2φ=g(x,y) with nonhomogeneous boundary conditions on a bounded domain. A numerical approximation to FPE is derived using a matrix representation of the Laplacian to generate a linear system of equations with its matrix A raised to the fractional power α/2. The solution of the linear system then requires the action of the matrix function f(A)=A−α/2 on a vector b. For large, sparse, and symmetric positive definite matrices, the Lanczos approximation generates f(A)b≈β0Vmf(Tm)e1. This method works well when both the analytic grade of A with respect to b and the residual for the linear system are sufficiently small. Memory constraints often require restarting the Lanczos decomposition; however this is not straightforward in the context of matrix function approximation. In this paper, we use the idea of thick-restart and adaptive preconditioning for solving linear systems to improve convergence of the Lanczos approximation. We give an error bound for the new method and illustrate its role in solving FPE. Numerical results are provided to gauge the performance of the proposed method relative to exact analytic solutions.

Changing pedagogic codes in a class of landscape architects learning 'ecologically sustainable development'

Professional discourse in education has been the focus of research conducted mostly with teachers and professional practitioners but the work of students in the built environment has largely been ignored. This article presents an analysis of students’ visual discourse in the final professional year of a landscape architecture course in Brisbane, Australia. The study has a multi-method design and includes drawings, interviews and documentary materials, but focuses on the drawings in this paper. Using the theory of Bernstein, the analysis considers student representations as interrelations between professional identity and discretionary space for legitimate knowledge formation in landscape planning. It shows a shift in how students persuade the teacher of their expanding views of this field. The discussion of this shift centres on the professional knowledge that students choose rather than need to learn. It points to the differences within a class that a teacher must address in curriculum design in a contemporary professional course.

Optimisation of a class of transportation problems using genetic algorithms

This paper presents a Genetic Algorithms (GA) approach to search the optimized path for a class of transportation problems. The formulation of the problems for suitable application of GA will be discussed. Exchanging genetic information in the sense of neighborhoods will be introduced for generation reproduction. The performance of the GA will be evaluated by computer simulation. The proposed algorithm use simple coding with population size 1 converged in reasonable optimality within several minutes.

An analytical method to solve a general class of nonlinear reactive transport models

Three recent papers published in Chemical Engineering Journal studied the solution of a model of diffusion and nonlinear reaction using three different methods. Two of these studies obtained series solutions using specialized mathematical methods, known as the Adomian decomposition method and the homotopy analysis method. Subsequently it was shown that the solution of the same particular model could be written in terms of a transcendental function called Gauss’ hypergeometric function. These three previous approaches focused on one particular reactive transport model. This particular model ignored advective transport and considered one specific reaction term only. Here we generalize these previous approaches and develop an exact analytical solution for a general class of steady state reactive transport models that incorporate (i) combined advective and diffusive transport, and (ii) any sufficiently differentiable reaction term R(C). The new solution is a convergent Maclaurin series. The Maclaurin series solution can be derived without any specialized mathematical methods nor does it necessarily involve the computation of any transcendental function. Applying the Maclaurin series solution to certain case studies shows that the previously published solutions are particular cases of the more general solution outlined here. We also demonstrate the accuracy of the Maclaurin series solution by comparing with numerical solutions for particular cases.