Inclusion bodies of fuculose-1-phosphate aldolase as stable and reusable biocatalysts.

Fuculose-1-phosphate aldolase (FucA) has been produced in Escherichia coli as active inclusion bodies (IBs) in batch cultures. The activity of insoluble FucA has been modulated by a proper selection of producing strain, culture media, and process conditions. In some cases, when an optimized defined medium was used, FucA IBs were more active (in terms of specific activity) than the soluble protein version obtained in the same process with a conventional defined medium, supporting the concept that solubility and conformational quality are independent protein parameters. FucA IBs have been tested as biocatalysts, either directly or immobilized into Lentikat beads, in an aldolic reaction between DHAP and (S)-Cbz-alaninal, obtaining product yields ranging from 65 to 76%. The production of an active aldolase as IBs, the possibility of tailoring IBs properties by both genetic and process approaches, and the reusability of IBs by further entrapment in appropriate matrices fully support the principle of using self-assembled enzymatic clusters as tunable mechanically stable and functional biocatalysts.

Extinction conditions for isolated populations with Allee effect.

One of the main ecological phenomenons is the Allee effect [1-3], in which a positive benefit from the presence of conspecifics arises. In this work we describe the dynamical behavior of a population with Allee effect in a finite domain that is surrounded by a completely hostile environment. Using spectral methods to rewrite the local density of habitants we are able to determine the critical patch size and the bifurcation diagram, hence characterizing the stability of possible solutions, for different ways to introduce the Allee effect in the reaction-diffusion equations.

Fourier series expansion for nonlinear Hamiltonian oscillators.

The problem of nonlinear Hamiltonian oscillators is one of the classical questions in physics. When an analytic solution is not possible, one can resort to obtaining a numerical solution or using perturbation theory around the linear problem. We apply the Fourier series expansion to find approximate solutions to the oscillator position as a function of time as well as the period-amplitude relationship. We compare our results with other recent approaches such as variational methods or heuristic approximations, in particular the Ren-He's method. Based on its application to the Duffing oscillator, the nonlinear pendulum and the eardrum equation, it is shown that the Fourier series expansion method is the most accurate.