Characterization of invertase entrapped into calcium alginate beads

A solution of 10 g/L of sodium alginate (Satialgine® types used [Sanofi trademark]: SG800® and S1100® with manuronic/guluronic ratio of 0.5 and 1.2, respectively) containing invertase (0.08 g of protein/L) was dropped into 0.1 M CaCl₂ solution buffered at pH 4.0, 7.0, or 8.0. The beads were left to harden in CaCl₂ solution for 24 h. The high immobilization yield of 60% occurred with SG800 at pH8.0. The activity of soluble and insoluble invertase was measured against pH (2.8–8.0), sucrose concentration (4.5–45 mM), and temperature (30–60°C). Both forms presented an optimum pH of 4.6. However, the soluble invertase was stable at the overall pH interval studied, whereas insoluble invertase lost 30% of its original activity at pH > 5.0. At temperatures above 40°C, the insoluble form was more stable than the soluble one. The kinetic constants and activation energies (E _a ) for free invertase were K _M =41.2 mM, V _max=0.10 mg of TRS/(min · mL), and E _a 28 kJ/mol for entrapped invertase they were (K _M ) _ap =7.2 mM, (V _max) _ap =0.060 mg of TRS/(min · mL), and (E _a )_ap=24 kJ/mol.     

On the Phragmén-Lindelöf principle for second-order elliptic equations

This paper is concerned with the maximum principle for subsolutions of second-order elliptic equations in non-divergence form in unbounded domains. Eventually the zero-order term can change sign and the involved functions can be unbounded at infinity with an admissible growth depending on the geometric properties of the domain. Following Gilbarg and Hopf, we also show a Phragmén-Lindelöf principle in angular sectors and give an example of an interesting field of application to nonlinear equations, deriving comparison principles for quasi-linear operators.     

Invertase immobilization onto radiation-induced graft copolymerized polyethylene pellets

The graft copolymer poly(ethylene-g-acrylic acid) (LDPE-g-AA) was prepared by radiation-induced graft copolymerization of acrylic acid onto low density polyethylene (LDPE) pellets, and characterized by infrared photoacoustic spectroscopy and scanning electron microscopy (SEM). The presence of the grafted poly(acrylic acid) (PAA) was established. Invertase was immobilized onto the graft polymer and the thermodynamic parameters of the soluble and immobilized enzyme were determined. The Michaelis constant, K_m, and the maximum reaction velocity, V_max, were determined for the free and the immobilized invertase. The Michaelis constant, K_m was larger for the immobilized invertase than for the free enzyme, whereas V_max was smaller for the immobilized invertase. The thermal stability of the immobilized invertase was higher than that of the free enzyme.     

Quasi-periodic bifurcations of invariant circles in low-dimensional dissipative dynamical systems

This paper first summarizes the theory of quasi-periodic bifurcations for dissipative dynamical systems. Then it presents algorithms for the computation and continuation of invariant circles and of their bifurcations. Finally several applications are given for quasiperiodic bifurcations of Hopf, saddle-node and period-doubling type.     

Ethanol production by Saccharomyces cerevisiae grown in sugarcane blackstrap molasses through a fed-batch process

We studied the effect of reactor filling time (T) (3-5 h), initial mass of inoculum (M) (1000-2100 g), and exponential time decay constant for the substrate feed rate (K) (0.6-1.6 h-1) on ethanol production by Saccharomyces cerevisiae grown in sugarcane blackstrap molasses through a fed-batch culture. The highest ethanol productivity (16.9 g/[L x h]) occurred at T = 3 h, K = 1.6 h-1, and M = 1300 g. In addition, productivity was affected by both M (for T = 3 and 4 h) and K (for T = 3 h) and varied inversely with T under any value fixed for M and K. By the quadratic regression multivariable analysis method, equations were determined to estimate ethanol yield and productivity as function of the variables studied (T, K, and M).     

Purification of glucose-6-phosphate dehydrogenase from baker’s yeast in aqueous two-phase systems with free triazine dyes as affinity ligands

To improve the selectivity of glucose-6-phosphate dehydrogenase (G6PDH) extraction by an aqueous two-phase system, a simple and inexpensive affinity aqueous two-phase system using unbound reactive triazine dyes as ligands was introduced. In a polyethylene glycol (PEG)/hydroxypropyl starch (PES) system, the unbound free triazine dyes, Cibacron Blue F3GA and Procion Red HE3B, partitioned unevenly in the top PEG-rich phase and thus showed an affinity effect on G6PDH, but no influence on hexokinase. The various parameters investigated were pH of the system, buffers, molecular weight of PEG, and ligand type and concentration. A two-step affinity extraction process was established for the purification of G6PDH from baker’s yeast. The total yield of G6PDH was 66.9% and purification factor was 2.35.     

Zymomonas mobilis as catalyst for the biotechnological production of sorbitol and gluconic acid

The conversion of glucose and fructose into gluconic acid (GA) and sorbitol (SOR) was conducted in a batch reactor with free (CTAB-treated or not) or immobilized cells of Zymomonas mobilis. High yields (more than 90%) of gluconic acid and sorbitol were attained at initial substrate concentration of 600 g/L (glucose plus fructose at 1:1 ratio), using cells with glucose-fructose-oxidoreductase activity of 75 U/L. The concentration of the products varied hyperbolically with time according to the equations (GA)=t(GA)_max/(W_GA +t), (SOR)=t (SOR)_max/(W_Sor+t), v_GA=[W_GA (GA)_max]/(W_GA+t)² and V_SOR=[W_SOR (SOR)_max]/(W_SOR+t)². Taking the test carried out with free CTAB-treated cells as an example, the constant parameters were (GA)_max= 541 g/L, (SOR)_max=552 g/L, W_GA=4.8h, W_SOR=4.9h, υ_GA=112.7 g/L· and υ_SOR=112.7 g/L·.     

The Alexandrov-Bakelman-Pucci Weak Maximum Principle for Fully Nonlinear Equations in Unbounded Domains

ABSTRACT

We obtain Alexandrov-Bakelman-Pucci type estimates for semicontinuous viscosity solutions of fully nonlinear elliptic inequalities in unbounded domains. Under suitable assumptions relating the geometry of the domain with structural conditions on the differential operator, we establish the validity of the weak maximum principle for solutions which are bounded from above. Two variants are also given, namely one for unbounded solutions in narrow domains and one for operators with possibly changing sign zero order coefficients in domains of small measure.