Identification of reaction networks for bioprocesses: determination of a partially unknown pseudo-stoichiometric matrix

In this paper we propose a methodology to determine the structure of the pseudo-stoichiometric coefficient matrix K in a mass balance-based model and to identify its coefficients from a set of available data. The first stage consists in estimating the number of reactions that must be taken into account to represent the main mass transfer within the bioreactor. This provides the dimension of K. Then we propose a method to directly determine the structure of the matrix (i.e. mainly its zeros and the signs of its coefficients). These methods are illustrated with simulations of a process of lipase production from olive oil by Candida rugosa.     

Empirical modelling of lake water-temperature relationships: a comparison of approaches

1.  As a result of the role that temperature plays in many aquatic processes, good predictive models of annual maximum near-surface lake water temperature across large spatial scales are needed, particularly given concerns regarding climate change. Comparisons of suitable modelling approaches are required to determine their relative merit and suitability for providing good predictions of current conditions. We developed models predicting annual maximum near-surface lake water temperatures for lakes across Canada using four statistical approaches: multiple regression, regression tree, artificial neural networks and Bayesian multiple regression.
2.  Annual maximum near-surface (from 0 to 2 m) lake water-temperature data were obtained for more than 13 000 lakes and were matched to geographic, climatic, lake morphology, physical habitat and water chemistry data. We modelled 2348 lakes and three subsets thereof encompassing different spatial scales and predictor variables to identify the relative importance of these variables at predicting lake temperature.
3.  Although artificial neural networks were marginally better for three of the four data sets, multiple regression was considered to provide the best solution based on the combination of model performance and computational complexity. Climatic variables and date of sampling were the most important variables for predicting water temperature in our models.
4.  Lake morphology did not play a substantial role in predicting lake temperature across any of the spatial scales. Maximum near-surface temperatures for Canadian lakes appeared to be dominated by large-scale climatic and geographic patterns, rather than lake-specific variables, such as lake morphology and water chemistry.     

CAMBIO: software for modelling and simulation of bioprocesses

CAMBIO, a software package devoted to bioprocess modelling,which runs on Apollo computers, is described. This softwareenables bioengineers to easily and interactively design appropriatemathematical models directly from their perception of the process.CAMBIO provides the user with a set of design symbols and mnemonicicons in order to interactively design a functional diagram.This diagram has to exhibit the most relevant components withtheir related interactions through biological and physico-chemicalreactions. Then, CAMBIO automatically generates the dynamicalmaterial balance equations of the process in the form of analgebraic-differential system by taking advantage of the knowledgeinvolved in the functional diagram. The model may be used forcontrol design purpose or completed by kinetics expressionswith a view to simulation. CAMBIO offers facilities to generatea simulation model (for coding of kinetics, introducing auxiliaryvariables, etc.). This model is automatically interfaced witha specialized simulation software which allows an immediatevisualization of the process dynamical behaviour under variousoperational conditions (possibly involving feedback controlstrategies). An example of an application dealing with yeastfermentation is given. Received on June 14, 1990; accepted on January 11, 1991     

Connection between stochastic and deterministic modelling of microbial growth

We present in this paper various links between individual and population cell growth. Deterministic models of the lag and subsequent growth of a bacterial population and their connection with stochastic models for the lag and subsequent generation times of individual cells are analysed. We derived the individual lag time distribution inherent in population growth models, which shows that the Baranyi model allows a wide range of shapes for individual lag time distribution. We demonstrate that individual cell lag time distributions cannot be retrieved from population growth data. We also present the results of our investigation on the effect of the mean and variance of the individual lag time and the initial cell number on the mean and variance of the population lag time. These relationships are analysed theoretically, and their consequence for predictive microbiology research is discussed.     

A comparison of statistical approaches for modelling fish species distributions

SUMMARY 1. The prediction of species distributions is of primary importance in ecology and conservation biology. Statistical models play an important role in this regard; however, researchers have little guidance when choosing between competing methodologies because few comparative studies have been conducted. 2. We provide a comprehensive comparison of traditional and alternative techniques for predicting species distributions using logistic regression analysis, linear discriminant analysis, classification trees and artificial neural networks to model: (1) the presence/absence of 27 fish species as a function of habitat conditions in 286 temperate lakes located in south‐central Ontario, Canada and (2) simulated data sets exhibiting deterministic, linear and non‐linear species response curves. 3. Detailed evaluation of model predictive power showed that approaches produced species models that differed in overall correct classification, specificity (i.e. ability to correctly predict species absence) and sensitivity (i.e. ability to correctly predict speciespresence) and in terms of which of the study lakes they correctly classified. Onaverage, neural networks outperformed the other modelling approaches, although all approaches predicted species presence/absence with moderate to excellent success. 4. Based on simulated non‐linear data, classification trees and neural networks greatly outperformed traditional approaches, whereas all approaches exhibited similar correct classification rates when modelling simulated linear data. 5. Detailed evaluation of model explanatory insight showed that the relative importance of the habitat variables in the species models varied among the approaches, where habitat variable importance was similar among approaches for some species and very different for others. 6. In general, differences in predictive power (both correct classification rate and identity of the lakes correctly classified) among the approaches corresponded with differences in habitat variable importance, suggesting that non‐linear modelling approaches (i.e. classification trees and neural networks) are better able to capture and model complex, non‐linear patterns found in ecological data. The results from the comparisons using simulated data further support this notion. 7. By employing parallel modelling approaches with the same set of data and focusing on comparing multiple metrics of predictive performance, researchers can begin to choose predictive models that not only provide the greatest predictive power, but also best fit the proposed application.     

Congruent epidemic models for unstructured and structured populations: analytical reconstruction of a 2003 SARS outbreak

Both the threat of bioterrorism and the natural emergence of contagious diseases underscore the importance of quantitatively understanding disease transmission in structured human populations. Over the last few years, researchers have advanced the mathematical theory of scale-free networks and used such theoretical advancements in pilot epidemic models. Scale-free contact networks are particularly interesting in the realm of mathematical epidemiology, primarily because these networks may allow meaningfully structured populations to be incorporated in epidemic models at moderate or intermediate levels of complexity. Moreover, a scale-free contact network with node degree correlation is in accord with the well-known preferred mixing concept. The present author describes a semi-empirical and deterministic epidemic modeling approach that (a) focuses on time-varying rates of disease transmission in both unstructured and structured populations and (b) employs probability density functions to characterize disease progression and outbreak controls. Given an epidemic curve for a historical outbreak, this modeling approach calls for Monte Carlo calculations (that define the average new infection rate) and solutions to integro-differential equations (that describe outbreak dynamics in an aggregate population or across all network connectivity classes). Numerical results are obtained for the 2003 SARS outbreak in Taiwan and the dynamical implications of time-varying transmission rates and scale-free contact networks are discussed in some detail.     

A comparison of approaches for modelling the occurrence of marine animals

Approaches for modelling the distribution of animals in relation to their environment can be divided into two basic types, those which use records of absence as well as records of presence and those which use only presence records. For terrestrial species, presence–absence approaches have been found to produce models with greater predictive ability than presence-only approaches. This study compared the predictive ability of both approaches for a marine animal, the harbour porpoise (Phoceoena phocoena). Using data on the occurrence of harbour porpoises in the Sea of Hebrides, Scotland, the predictive abilities of one presence–absence approach (generalised linear modelling—GLM) and three presence-only approaches (Principal component analysis—PCA, ecological niche factor analysis—ENFA and genetic algorithm for rule-set prediction—GARP) were compared. When the predictive ability of the models was assessed using receiver operating characteristic (ROC) plots, the presence–absence approach (GLM) was found to have the greatest predictive ability. However, all approaches were found to produce models that predicted occurrence significantly better than a random model and the GLM model did not perform significantly better than ENFA and GARP. The PCA had a significantly lower predictive ability than GLM but not the other approaches. In addition, all models predicted a similar spatial distribution. Therefore, while models constructed using presence–absence approaches are likely to provide the best understanding of species distribution within a surveyed area, presence-only models can perform almost as well. However, careful consideration of the potential limitations and biases in the data, especially with regards to representativeness, is needed if the results of presence-only models are to be used for conservation and/or management purposes. Guest editor: V. D. Valavanis Essential Habitat Mapping in the Mediterranean     

Development of a structured model for batch cultures of lactic acid bacteria

A combined stochastic-deterministic model able to predict the growth curve of microorganisms, from inoculation to death, is presented. The proposed model is based on the assumption that microorganisms can experience two different physiological states: non-proliferating and proliferating. The former being the physiological state of the cells right after their inoculation into the new extracellular environment; the latter the state of microorganisms after adaptation to the new medium. To validate the model, a Lactobacillus bulgaricus strain was tested in a medium at pH 4.6 at two different temperatures (42°C and 35°C). Curves representing the bacterial growth cycle were satisfactorily fitted by means of the proposed model. Moreover, due to the mechanistic structure of the proposed model, valuable quantitative information on the following was obtained: rate of conversion of non-proliferating cells into proliferating cells, growth and death rate of proliferating cells, and rate of nutrient consumption.     

Nanoconfined polymers: modelling and simulation approaches

In this article, application of molecular simulation methods for studying molecular pictures of nanoconfined polymers is reviewed and discussed. The simulation methods, covering a range from atomistic to systematically parameterised coarse-grained models, employed in the literature to study nanoconfined polymers are reviewed and their results are compared together. The effect of polymer–surface interactions, surface curvature and surface area on the alteration of polymer structure and dynamics from the unperturbed (bulk) polymer properties are discussed. The length scales over which the surface influences the polymer structure and dynamics and the magnitude of surface effect on dynamics deceleration in the interphase are addressed in terms of different local and global chain properties.     

Output regulation of a class of unstructured models of continuous bioreactors: steady-state approaches

This article deals with the output regulation of continuous bioreactors in the face of constant disturbances and inverse dynamics. Nonlinear controllers developed on the basis of approximate equilibrium manifolds can almost attenuate measurable or unmeasurable disturbances on the output. This nonlinear feed-forward/feedback control framework without any tuning parameters can be directly implemented to strictly nonlinear systems. Under dynamic actuator constraints and the availability of only output signals for use in the control law, closed-loop simulations demonstrate that the proposed control techniques are superior to a nonlinear PI control scheme based on the identified Hammerstein model.     

Parsimonious modelling of nutrient fluxes for a terrestrial ecosystem on Svalbard

MBL-MEL, a simple model of ecosystem biogeochemistry, is amended and applied to plant and soil C, ¹⁴N and ¹⁵N data for the summers of 2001–2003 from Brandalpynten, a maritime high Arctic site on Svalbard following the application of ¹⁵N (99 atom%) as ¹⁵NO₃-N at or ¹⁵NH₄-N at concentrations of 1 or 5 kg N ha⁻¹. Variants of this Parent model are also developed to incorporate: temperature dependence into equations describing nutrient fluxes (Temp model); cryptogams (Cryp model); both features combined (CrypTemp model). Goodness-of-fit (GOF) statistics suggest that the addition of temperature-dependence improves the utility of models with and without cryptogams: the residual weighted sums of squares per data point were 5.69, 3.91, 4.31 and 3.93 for the Parent, Temp, Cryp and CrypTemp models respectively. The application of model selection criteria confirm that the addition of temperature-dependence also improves model generalisability. Across all models, the principal discrepancies between observation and prediction are associated with the inorganic soil ¹⁵N pool. We conclude that models in which fluxes are described using simple equations that can be augmented to include additional complexity, are an ideal starting point from which the relationship between GOF and model generalisability can be assessed.     

Towards a structured approach to building qualitative reasoning models and simulations

Successful transfer and uptake of qualitative reasoning technology for modelling and simulation in a variety of domains has been hampered by the lack of a structured methodology to support formalisation of ideas. We present a framework that structures and supports the capture of conceptual knowledge about system behaviour using a qualitative reasoning approach. This framework defines a protocol for representing content that supports the development of a conceptual understanding of systems and how they behave. The framework supports modellers in two ways. First, it structures and explicates the work involved in building models. Second, it facilitates easier comparison and evaluation of intermediate and final results of modelling efforts. We show how this framework has been used in developing qualitative reasoning models about three case studies of sustainable development in different river systems.     

Customizing lipases for biocatalysis: a survey of chemical, physical and molecular biological approaches

Lipases (triacylglycerol ester hydrolases, EC 3.1.1.3) are ubiquitous enzymes that catalyze the breakdown of fats and oils with subsequent release of free fatty acids, diacylglycerols, monoglycerols and glycerol. Besides this, they are also efficient in various reactions such as esterification, transesterification and aminolysis in organic solvents. Therefore, those enzymes are nowadays extensively studied for their potential industrial applications. Examples in the literature are numerous concerning their use in different fields such as resolution of racemic mixtures, synthesis of new surfactants and pharmaceuticals, oils and fats bioconversion and detergency applications. However, the drawbacks of the extensive use of lipases (and biocatalysts in general) compared to classical chemical catalysts can be found in the relatively low stability of enzyme in their native state as well as their prohibitive cost. Consequently, there is a great interest in methods trying to develop competitive biocatalysts for industrial applications by improvement of their catalytic properties such as activity, stability (pH or temperature range) or recycling capacity. Such improvement can be carried out by chemical, physical or genetical modifications of the native enzyme. The present review will survey the different procedures that have been developed to enhance the properties of lipases. It will first focus on the physical modifications of the biocatalysts by adsorption on a carrier material, entrapment or microencapsulation. Chemical modifications and methods such as modification of amino acids residues, covalent coupling to a water-insoluble material, or formation of cross-linked lipase matrix, will also be reviewed. Finally, new and promising methods of lipases modifications by genetic engineering will be discussed.     

Genetic evaluation with uncertain parentage: a comparison of methods

Summary The most common method for genetic evaluation when parents are unknown is best linear unbiased prediction with genetic groups (BLUP-G). With this method unknown parents are assumed to be unrelated to any other animals in the population. This assumption is unrealistic in most situations. If a finite number of potential parents can be identified and the probabilities of being the true parent can be assigned to these, genetic evaluation can be obtained given the uncertainty of parentage without introducing genetic groups into the model. The correct numerator relationship matrix with uncertain parentage () is derived. Rules are given to efficiently compute and ^-1. Computer simulation was used to compare BLUP-G with BLUP using . The simulated population consisted of ten sires and 200 dams per breeding season. The dams were always known; the sires were unknown for 10% or 30% of the males and 30% of the females. The number of potential sires was three (BLUP-₁ or ten (BLUP-₂), including the true sire in both cases. Equal probabilities were assigned to each potential sire. The increase in response with BLUP-₁ and BLUP-₂ relative to BLUP-G ranged from 4% to 8% in the fifth breeding season. Selection with BLUP-₁ or BLUP-₂ resulted in higher inbreeding, 17% and 12%, respectively, than with BLUP-G. Estimates of response to selection were unbiased with BLUP-₁ and BLUP-₂, but not unbiased with BLUP-G. Mean square error of estimated genetic means and mean prediction error variance were higher with BLUP-G than with blup-₁ or BLUP-₂.     

Treatment and kinetic modelling of a simulated dye house effluent by enzymatic catalysis

Biocatalytic treatment of a synthetic dye house effluent, simulating a textile wastewater containing various reactive dyestuffs (Reactive Yellow 15, Reactive Red 239 and Reactive Black 5) and auxiliary chemicals, was investigated in a batch reactor using a commercial laccase. A high decolourisation (above 86%) was achieved at the maximum wavelength of Reactive Black 5. The decolourisation at the other dyes wavelengths (above 63% for RY15 and around 41% for RR239) and the total decolourisation based on all the visible spectrum (around 55%) were not so good, being somewhat lower than in the case of a mixture of the dyes (above 89% for RB5, 77% for RY15, 68% for RR239 and above 84% for total decolourisation). Even so, these results suggest the applicability of this method to treat textile dyeing wastewaters. Kinetic models were developed to simulate the synthetic effluent decolourisation by commercial laccase. The kinetic constants of the models were estimated by minimizing the difference between the predicted and the experimental time courses. The close correlation between the experimental data and the simulated values seems to demonstrate that the models are able to describe with remarkable accuracy the simulated effluent degradation. Water quality parameters such as TOC, COD, BOD₅ and toxicity were found to be under the maximum permissible discharge limits for textile industries wastewaters.     

Root respiration of barley in a semiarid Mediterranean agroecosystem: field and modelling approaches

Aims

Root respiration is a major contributor to soil CO₂ flux, and its response to management practices needs to be evaluated. The aim was to determine the effect of management practices (tillage systems and nitrogen fertilization levels) on root respiration and to develop a model able to simulate root respiration and its components.

Methods

The study was carried out during two contrasting growing seasons (2007–2008 and 2008–2009). Root respiration, including root tissue respiration (R _ts ) and rhizomicrobial respiration of exudates (R _rz ), was estimated as the difference between the soil CO₂ flux of cropped and bare soil (the so-called root exclusion technique). Additionally a novel sub-model of R _ts , was used to simulate root respiration based on root growth and specific root respiration rates.

Results

Root respiration was reduced under no-tillage. The model agreed well with the patterns and the amounts of the observed values of root respiration, although prior calibration was needed.

Conclusions

Root respiration was reduced by the long-term adoption of no-tillage, but was increased by N fertilizer. The root exclusion technique and the model were useful means to estimate root respiration on cropland under semiarid Mediterranean conditions. Additionally the model successfully separated out the theoretical contributions of R _ts and R _rz to root respiration.     

A biochemically structured model for ethanol fermentation by Kluyveromyces marxianus: A batch fermentation and kinetic study

Anaerobic batch fermentations of ricotta cheese whey (i.e. containing lactose) were performed under different operating conditions. Ethanol concentrations of ca. 22 g L⁻¹ were found from whey containing ca. 44 g L⁻¹ lactose, which corresponded to up to 95% of the theoretical ethanol yield within 15 h. The experimental data could be explained by means of a simple knowledge-driven biochemically structured model that was built on bioenergetics principles applied to the metabolic pathways through which lactose is converted into major products. Use of the model showed that the observed concentrations of ethanol, lactose, biomass and glycerol during batch fermentation could be described within a ca. 6% deviation, as could the yield coefficients for biomass and ethanol produced on lactose. The model structure confirmed that the thermodynamics considerations on the stoichiometry of the system constrain the metabolic coefficients within a physically meaningful range thereby providing valuable and reliable insight into fermentation processes.     

Mechanical power in running: a comparison of different approaches

The purposes of the present study were: (1) to compare four different methods of calculating mechanical power in running on the basis of comparable data over a wide range of running velocity; (2) to examine the linearity of the relation between mechanical power as calculated with the four methods and running velocity. Eight runners participated in the investigation (height: 1.82 +/- 0.03 m, body mass: 81.05 +/- 4.69 kg). A Kistler force platform registered all components of the ground reaction force (1000 Hz) during one foot ground contact, which was additionally video taped using two high-speed video cameras running at 120 Hz. Four different methods were used to calculate mechanical power. Two methods determined the mechanical power due to the work done on the athletes' center of mass and two were calculated from the motion of the athletes' segments. The four different methods provided different relations between mechanical power and running velocity. The calculations on the basis of kinematic data cannot be recommended to determine efficiency of movement. The methods based on ground reaction force measurements revealed significant linear relations (r = 0.90, r2 = 0.84) between running velocity and mechanical power.     

Empirical approaches to metacommunities: a review and comparison with theory

Metacommunity theory has advanced understanding of how spatial dynamics and local interactions shape community structure and biodiversity. Here, we review empirical approaches to metacommunities, both observational and experimental, pertaining to how well they relate to and test theoretical metacommunity paradigms and how well they capture the realities of natural ecosystems. First, we show that the species-sorting and mass-effects paradigms are the most commonly tested and supported paradigms. Second, the dynamics observed can often be ascribed to two or more of the four non-exclusive paradigms. Third, empirical approaches relate only weakly to the concise assumptions and predictions made by the paradigms. Consequently, we suggest major avenues of improvement for empirical metacommunity approaches, including the integration across theoretical approaches and the incorporation of evolutionary and meta-ecosystem dynamics. We hope for metacommunity ecology to thereby bridge existing gaps between empirical and theoretical work, thus becoming a more powerful framework to understand dynamics across ecosystems.