Application of mathematical optimization methods in microbiology

Abstract

Mathematical methods of experiment design have so far found little use in the optimization of microbiological processes. The conventional optimization procedure is still the transformation of functional relationship of n variables into n unidimensional optimizations; furthermore, the Box-Wilson gradient method is often used. This paper presents a review of methods used in other fields, and their application in microbiological practice. The methods are classified according to whether they require, besides the simple determination of the objective function (direct search methods), also the finding of its first (gradient methods) or second derivative (Newton-Raphson method). A modified Rosenbrock's method of direct optimum search and the gradient Box-Wilson method were used in parallel for the optimization of yeast growth on methanol. Their comparison showed that Rosenbrock's method is more suitbale for multiparameter systems.

Activity of quinolizidine alkaloids from three Mexican Lupinus against the lepidopteran crop pest Spodoptera frugiperda

“…Parameters of the regression were calculated and the likelihood of convergence determined according to a quasi-Newton method. In order to reach minima of PROBIT regression functions, a search for the Rosenbrock structure was performed prior to applying this method in order to reduce weight of extreme values (Pilat et al 1976;De Schamphelaere et al 2004). In order to separate the 30 samples into 3 sets of 10, a random sort (repeated 509) of 3 9 10 was performed independently on each series.…”

Bioprocess optimization using design‐of‐experiments methodology

“…Statistical experimental planning, factorial design, and design‐of‐experiments (DoE), are more or less synonymous concepts for investigating the mathematical relationships between input and output variables of a system. Although the fundamentals of the methodology have been known since the early 1900s,1–3 it was not until recent years that it was widely applied in biotechnology.…”

Biodegradation of formaldehyde under saline conditions by a moderately halophilic bacterial consortium

“…The growth of the consortium increased from 4 x 10 3 to 7 x 10 7 in case of 5 % NaCl, complete degradation of formaldehyde was achieved within 96 h. Growth of the bacterial consortium and degradation efficiency of formaldehyde (100 mg/L) at different NaCl concentrations is presented in (Figure1). Pilat and Prokop, (1976) where the concentration of formaldehyde was less than 400 mg/L and were conducted under non-saline conditions. In the present study, we have used a bacterial consortium to examine the growth and utilization of formaldehyde at different concentrations of NaCl (1%, 3%, 5% and 7%).…”