Convex Representation of Metabolic Networks with Michaelis-Menten Kinetics.

Polyhedral models of metabolic networks are computationally tractable and can predict some cellular functions. A longstanding challenge is incorporating metabolites without losing tractability. In this paper, we do so using a new second-order cone representation of the Michaelis-Menten kinetics. The resulting model consists of linear stoichiometric constraints alongside second-order cone constraints that couple the reaction fluxes to metabolite concentrations. We formulate several new problems around this model: conic flux balance analysis, which augments flux balance analysis with metabolite concentrations; dynamic conic flux balance analysis; and finding minimal cut sets of networks with both reactions and metabolites. Solving these problems yields information about both fluxes and metabolite concentrations. They are second-order cone or mixed-integer second-order cone programs, which, while not as tractable as their linear counterparts, can nonetheless be solved at practical scales using existing software.

Consideration of Maintenance in Wine Fermentation Modeling.

We show that a simple model with a maintenance term can satisfactorily reproduce the simulations of several existing models of wine fermentation from the literature, as well as experimental data. The maintenance describes a consumption of the nitrogen that is not entirely converted into biomass. We show also that considering a maintenance term in the model is equivalent to writing a model with a variable yield that can be estimated from data.

Nutritive value of three tropical forage legumes and their influence on growth performance, carcass traits and organ weights of pigs.

The effects of tropical forage legumes on feed intake, growth performance and carcass traits were investigated in 16 groups of two Large White × Duroc pigs. The diets consisted of a commercial corn-soybean meal diet as the basal diet and three forage-supplemented diets. Four groups of control pigs received daily 4 % of body weight of the basal diet, and 12 groups of experimental pigs were fed the basal diet at 3.2 % of body weight completed with fresh leaves of one of the three forage legumes (Psophocarpus scandens, Stylosanthes guianensis and Vigna unguiculata) ad libitum. The study lasted 90 days. The in vitro digestion and fermentation of the forage legumes were also determined. The in vitro digestible energy content of the legumes was between 0.72 and 0.77 that of the basal diet (14.4 MJ/kg dry matter (DM)). V . unguiculata was the most digestible forage legume expected for crude protein digestibility. Feeding forage legumes lowered the dry matter intake by 4.5 to 9.6 % (P < 0.05), final body weight (P = 0.013), slaughter weight, average daily gain and hot carcass weight (P < 0.05) without affecting the feed conversion ratio (FCR), dressing percentage and back fat thickness. In conclusion, using forage to feed pig could be interesting in pig smallholder production with limited access to concentrate, as FCR was not significantly affected.

Long run coexistence in the chemostat with multiple species.

In this work we analyze the transient behavior of the dynamics of multiple species competing in a chemostat for a single resource, presenting slow/fast characteristics. We prove that coexistence among a subset of species, with growth functions close to each other, can last for a substantially long time. For these cases, we also show that the proportion of non-dominant species can be increasing before decreasing, under certain conditions on the initial distribution.

Modeling for the optimal biodegradation of toxic wastewater in a discontinuous reactor.

The degradation of toxic compounds in Sequencing Batch Reactors (SBRs) poses inhibition problems. Time Optimal Control (TOC) methods may be used to avoid such inhibition thus exploiting the maximum capabilities of this class of reactors. Biomass and substrate online measurements, however, are usually unavailable for wastewater applications, so TOC must use only related variables as dissolved oxygen and volume. Although the standard mathematical model to describe the reaction phase of SBRs is good enough for explaining its general behavior in uncontrolled batch mode, better details are needed to model its dynamics when the reactor operates near the maximum degradation rate zone, as when TOC is used. In this paper two improvements to the model are suggested: to include the sensor delay effects and to modify the classical Haldane curve in a piecewise manner. These modifications offer a good solution for a reasonable complexification tradeoff. Additionally, a new way to look at the Haldane K-parameters (micro(o),K(I),K(S)) is described, the S-parameters (micro*,S*,S(m)). These parameters do have a clear physical meaning and, unlike the K-parameters, allow for the statistical treatment to find a single model to fit data from multiple experiments.

A simplified method to assess structurally identifiable parameters in Monod-based activated sludge models.

The first step in the estimation of parameters of models applied for data interpretation should always be an investigation of the identifiability of the model parameters. In this study the structural identifiability of the model parameters of Monod-based activated sludge models (ASM) was studied. In an illustrative example it was assumed that respirometric (dissolved oxygen or oxygen uptake rates) and titrimetric (cumulative proton production) measurements were available for the characterisation of nitrification. Two model structures, including the presence and absence of significant growth for description of long- and short-term experiments, respectively, were considered. The structural identifiability was studied via the series expansion methods. It was proven that the autotrophic yield becomes uniquely identifiable when combined respirometric and titrimetric data are assumed for the characterisation of nitrification. The most remarkable result of the study was, however, that the identifiability results could be generalised by applying a set of ASM1 matrix based generalisation rules. It appeared that the identifiable parameter combinations could be predicted directly based on the knowledge of the process model under study (in ASM1-like matrix representation), the measured variables and the biodegradable substrate considered. This generalisation reduces the time-consuming task of deriving the structurally identifiable model parameters significantly and helps the user to obtain these directly without the necessity to go too deeply into the mathematical background of structural identifiability.

Modeling aerobic carbon source degradation processes using titrimetric data and combined respirometric-titrimetric data: structural and practical identifiability.

The structural and practical identifiability of a model for description of respirometric-titrimetric data derived from aerobic batch substrate degradation experiments of a C(x)H(y)O(z) carbon source with activated sludge was evaluated. The model processes needed to describe titrimetric data included substrate uptake, CO(2) production, and NH(3) uptake for biomass growth. The structural identifiability was studied using the Taylor series method and a recently proposed generalization method. It showed that combining respirometric and titrimetric data allows structural identifiability of one extra parameter combination, the biomass yield, Y(H), compared to estimation on separate data sets, on condition that the nitrogen fraction in biomass (i(XB)) is known. However, data from short-term batch substrate degradation experiments were not sufficiently informative to allow practical identification of all structurally identifiable parameters. Combining respirometry and titrimetry resulted in improvements of parameter confidence intervals compared to estimation on separate respirometric or titrimetric data sets. However, the level of the improvement seems to be substrate dependent: parameter confidence intervals improved considerably more for dextrose than for acetate degradation models. Noteworthy is the finding that the half-saturation substrate concentrations can be different depending on whether they are estimated from respirometric or titrimetric data. Moreover, this difference appears to be dependent on the carbon source considered: for dextrose, titrimetry-based K(S) values are higher than respirometry-based values while for acetate the opposite was found. It was hypothesized that this can be explained by the different point in cell metabolism where the proton production or consumption takes place, leading to a corresponding difference in timing between pH effect and oxygen consumption. Finally, the biomass yield Y(H) and the nitrogen content of the biomass i(XB) could be estimated from combined respirometric-titrimetric data obtained with addition of a known amount of carbon source. Y(H) can also be estimated from r(O) data when the initial substrate concentration S(S)(0) is known. The values found correspond to values reported in literature, but, interestingly, also seem able to reflect the occurrence of storage processes when pulses of acetate and dextrose are added.