Computation and analysis of time-dependent sensitivities in Generalized Mass Action systems

Understanding biochemical system dynamics is becoming increasingly important for insights into the functioning of organisms and for biotechnological manipulations, and additional techniques and methods are needed to facilitate investigations of dynamical properties of systems. Extensions to the method of Ingalls and Sauro, addressing time-dependent sensitivity analysis, provide a new tool for executing such investigations. We present here the results of sample analyses using time-dependent sensitivities for three model systems taken from the literature, namely an anaerobic fermentation pathway in yeast, a negative feedback oscillator modeling cell-cycle phenomena, and the Mitogen Activated Protein (MAP) kinase cascade. The power of time-dependent sensitivities is particularly evident in the case of the MAPK cascade. In this example it is possible to identify the emergence of a concentration of MAPKK that provides the best response with respect to rapid and efficient activation of the cascade, while over- and under-expression of MAPKK relative to this concentration have qualitatively different effects on the transient response of the cascade. Also of interest is the quite general observation that phase-plane representations of sensitivities in oscillating systems provide insights into the manner with which perturbations in the envelope of the oscillation result from small changes in initial concentrations of components of the oscillator. In addition to these applied analyses, we present an algorithm for the efficient computation of time-dependent sensitivities for Generalized Mass Action (GMA) systems, the most general of the canonical system representations of Biochemical Systems Theory (BST). The algorithm is shown to be comparable to, or better than, other methods of solution, as exemplified with three biochemical systems taken from the literature.     

Metabolic Engineering with power-law and linear-logarithmic systems

Metabolic Engineering aims to improve the performance of biotechnological processes through rational manipulation rather than random mutagenesis of the organisms involved. Such a strategy can only succeed when a mathematical model of the target process is available. Simplifying assumptions are often needed to cope with the complexity of such models in an efficient way, and the choice of such assumptions often leads to models that fall within a certain structural template or formalism. The most popular formalisms can be grouped in two categories: power-law and linear-logarithmic. As optimization and analysis of a model strongly depends on its structure, most methods in Metabolic Engineering have been defined within a given formalism and never used in any other.In this work, the four most commonly used formalisms (two power-law and two linear-logarithmic) are placed in a common framework defined within Biochemical Systems Theory. This framework defines every model as matrix equations in terms of the same parameters, enabling the formulation of a common steady state analysis and providing means for translating models and methods from one formalism to another. Several Metabolic Engineering methods are analysed here and shown to be variants of a single equation. Particularly, two problem solving philosophies are compared: the application of the design equation and the solution of constrained optimization problems. Generalizing the design equation to all the formalisms shows it to be interchangeable with the direct solution of the rate law in matrix form. Furthermore, optimization approaches are concluded to be preferable since they speed the exploration of the feasible space, implement a better specification of the problem and exclude unrealistic results.Beyond consolidating existing knowledge and enabling comparison, the systematic approach adopted here can fill the gaps between the different methods and combine their strengths.     

A statistical light scattering approach to separating fast and slow dynamics

Light scattering is a powerful technique to study the structural and dynamical properties of biomolecular systems or other soft materials such as polymeric solutions and blends or gels. An important application of this technique is the study of the kinetics of formation of supramolecular structures. However, in such cases, the system under study is rapidly changing, and consequently the integration time for each measurement is limited. In order to overcome this difficulty, a statistical approach has been developed based on the analysis of the scattered light intensity distribution (Manno et al. 2006, 2004). Indeed the intensity distribution depends upon the ratio between the integration time of each measurement and the coherence time of scattered radiation. This method has been applied to protein aggregation (Manno et al. 2006) and to sol-gel transition (Manno et al. 2004), to obtain information on the heterogeneity of morphological and dynamical features during such processes. In the present work, we accurately test the validity of this approach by analyzing the statistical properties of the light scattered by a model system: a solution of polystyrene spherical macromolecules of different sizes. Each molecular size is related to a given diffusion coefficient and to a given coherence time of the scattered intensity. The effect of changing the experimental integration time is systematically investigated. A mixture of particles of two different sizes is also analyzed to test the validity and robustness of the model based on the convolution of a gaussian with an exponential distribution. Proceedings of the XVIII Congress of the Italian Society of Pure and Applied Biophysics (SIBPA), Palermo, Sicily, September 2006.     

Experimental and theoretical approaches for Cd(II) biosorption from aqueous solution using Oryza sativa biomass

Biomass of Oryza sativa (OS) was tested for the removal of Cd(II) ions from synthetic and real wastewater samples. Batch experiments were conducted to investigate the effects of operating parameters on Cd(II) biosorption. Fourier transform infrared spectroscopy, scanning electron microscopy, and energy-dispersive x-ray spectroscopy were used to examine the surface characteristics of the Cd(II)-loaded biomass. The maximum removal efficiency of Cd(II) was 89.4% at optimum pH 6.0, biosorbent dose 10.0 g L^?1, initial Cd(II) 50 mg L^?1, and biosorbent particle size 0.5 mm. The applicability of Langmuir and Freundlich isotherms to the sorbent system implied the existence of both monolayer and heterogeneous surface conditions. Kinetic studies revealed that the adsorption process of Cd(II) followed the pseudo-second-order model (r2: 0.99). On the theoretical side, an adaptive neuro-fuzzy inference system (ANFIS) was applied to select the operating parameter that mostly influences the Cd(II) biosorption process. Results from ANFIS indicated that pH was the most influential parameter affecting Cd(II) removal efficiency, indicating that the biomass of OS was strongly pH sensitive. Finally, the biomass was confirmed to adsorb Cd(II) from real wastewater samples with removal efficiency close to 100%. However, feasibility studies of such systems on a large-scale application remain to be investigated.