Steady-state global optimization of metabolic non-linear dynamic models through recasting into power-law canonical models

Background: Design of newly engineered microbial strains for biotechnological purposes would greatly benefit from the development of realistic mathematical models for the processes to be optimized. Such models can then be analyzed and, with the development and application of appropriate optimization techniques, one could identify the modifications that need to be made to the organism in order to achieve the desired biotechnological goal. As appropriate models to perform such an analysis are necessarily non-linear and typically non-convex, finding their global optimum is a challenging task. Canonical modeling techniques, such as Generalized Mass Action (GMA) models based on the power-law formalism, offer a possible solution to this problem because they have a mathematical structure that enables the development of specific algorithms for global optimization. Results: Based on the GMA canonical representation, we have developed in previous works a highly efficient optimization algorithm and a set of related strategies for understanding the evolution of adaptive responses in cellular metabolism. Here, we explore the possibility of recasting kinetic non-linear models into an equivalent GMA model, so that global optimization on the recast GMA model can be performed. With this technique, optimization is greatly facilitated and the results are transposable to the original non-linear problem. This procedure is straightforward for a particular class of non-linear models known as Saturable and Cooperative (SC) models that extend the power-law formalism to deal with saturation and cooperativity. Conclusions: Our results show that recasting non-linear kinetic models into GMA models is indeed an appropriate strategy that helps overcoming some of the numerical difficulties that arise during the global optimization task.

Power spectral changes of the superimposed M wave during isometric voluntary contractions of increasing strength.

INTRODUCTION: We examined the power spectral changes of the compound muscle action potential (M wave) evoked during isometric contractions of increasing strength. METHODS: Surface electromyography (sEMG) of the vastus lateralis and medialis was recorded from 20 volunteers who performed 4-s step-wise isometric contractions of different intensities. A maximal M wave was elicited by a single stimulus to the femoral nerve and superimposed on the voluntary contractions. The spectral characteristics (Fmean and Fmedian) of sEMG and M-wave signals were calculated. RESULTS: M-wave spectral indicators increased systematically with contraction intensity up to 60% MVC and then leveled off at higher forces. Over the 10-60% MVC range, the increase in spectral indicators was 3 times higher for M waves (36%) than for sEMG (12%). CONCLUSIONS: The consistent increase in M-wave spectral characteristics with force is due to the fact that the number of motor units recruited by the superimposed supramaximal stimulus is approximately stable.