A general kinetic model for biological nutrient removal activated sludge systems: model evaluation

Hu et al. (2007) presented a general kinetic model for biological nutrient removal (BNR) activated sludge (AS) systems in general, but for external nitrification (EN) BNRAS (ENBNRAS) systems in particular. In this article, this model is evaluated against a large number of experimental data sets. In this evaluation, the model is first used to simulate a wide variety of conventional internal nitrification (IN) BNRAS systems to evaluate its predictions and also evaluate the model parameters suggested by Hu et al. (2007), and to calibrate those constants for which values are not available in the literature. Simulation results indicate that the model, with appropriately calibrated parameters, is capable of predicting COD removal, nitrification and denitrification and two types of biological excess phosphorus removal (BEPR), namely aerobic and anoxic/aerobic P uptake BEPR. The model is then used to simulate the ENBNRAS systems to evaluate its capacity of simulating the behaviour of this system. Simulation results show that the model is capable of simulating the behaviour of the ENBNRAS systems, including COD, nitrification, denitrification and BEPR, particularly anoxic P uptake BEPR, with the values of kinetic and stoichiometric parameters obtained in modelling conventional BNRAS systems, except for micro(NIT), K(MP), eta(PAO) and eta(H) which required calibration.     

Model building and model checking for biochemical processes

A central claim of computational systems biology is that, by drawing on mathematical approaches developed in the context of dynamic systems, kinetic analysis, computational theory and logic, it is possible to create powerful simulation, analysis, and reasoning tools for working biologists to decipher existing data, devise new experiments, and ultimately to understand functional properties of genomes, proteomes, cells, organs, and organisms. In this article, a novel computational tool is described that achieves many of the goals of this new discipline. The novelty of this system involves an automaton-based semantics of the temporal evolution of complex biochemical reactions starting from the representation given as a set of differential equations. The related tools also provide ability to qualitatively reason about the systems using a propositional temporal logic that can express an ordered sequence of events succinctly and unambiguously. The implementation of mathematical and computational models in the Simpathica and XSSYS systems is described briefly. Several example applications of these systems to cellular and biochemical processes are presented: the two most prominent are Leibler et al.'s repressilator (an artificial synthesized oscillatory network), and Curto-Voit-Sorribas-Cascante's purine metabolism reaction model.     

A kinetic model for binding protein-mediated arabinose transport.

A kinetic model is presented based on the simplest plausible mechanism for bacterial binding protein-dependent transport. The transport phenotypes of the 18 variant arabinose-binding proteins analyzed by Kehres and Hogg (1992, Protein Sci. 1, 1652-1660) (wild type and 17 mutants) are interpreted to mean that in wild-type arabinose uptake the forward transport rate (k(for)) greatly exceeds the dissociation rate (kund) of a binding protein docked with the AraG:AraH membrane complex, and that k(for) dominance is preserved in all of the binding protein surface mutants. The assumptions and predictions of the model are consistent with existing data from other periplasmic transport systems.     

Mixing s orbitals into p and d orbitals. An attempt at bridging the angular overlap model and the valence shell electron pair repulsion model. Critique of the cellular ligand-field model

The stereochemistries of main group molecules have been discussed by using the angular overlap model in its molecular orbital oriented form (MO-AOM). Either ligand-field stabilisation of the ground state s²p^q−2 configuration, or s-p mixing, or both, provide a consistent bonding model for the stereochemistries. The transformation of the non-bonding orbitals into equivalent orbitals leads invariably to agreement with the lone-pair locations of the valence shell electron pair repulsion (VSEPR) model. The concepts of Hamiltonian-generated hybrids and pseudohemispherical molecular systems are found useful in this context. The MO-AOM formalism is also used for discussing s-d mixing in transition metal systems, and the energetic consequences within the ligand-field AOM (LF-AOM) are included. This is a second-order effect, which depends on squares and cross-products of radial parameters. It may still be quite large for tetragonal systems and for systems that deviate strongly from orthoaxiality. The usual ligand-additive property of the AOM is lost when the symmetry is lower than tetragonal and so is the energy separability into angular and radial factors. The cellular ligand-field model is found to be identical with the LF-AOM, except that its users consider it important not to acknowledge the formal hierarchy, MO-AOMLF-AOM, as relevant. The unintelligible concept of an active coordination void is found to be unnecessary and insufficient.     

A model of biofilm detachment

A general mathematical framework for modeling biofilm detachment is presented. The approach is founded on a material balance on biomass that equates the detachment rate to the product of a detachment frequency and a detaching particle mass. The model provides a theoretical basis for deriving many of the empirical detachment rate expressions in common use and can thus lend some insight into their physical and biological significance. By allowing for variation in the detachment frequency with depth in the biofilm, the model permits derivation of detachment expressions that reflect a dependence on chemical or physiological gradients in the biofilm. Analysis of literature data sets from two different biofilm systems suggests, in both cases, that detachment is a growth-associated phenomenon. (c) 1993 John Wiley & Sons, Inc.     

A functionally based model for hydrolysis of cellulose by fungal cellulase

A new functionally based kinetic model for enzymatic hydrolysis of pure cellulose by the Trichoderma cellulase system is presented. The model represents the actions of cellobiohydrolases I, cellobiohydrolase II, and endoglucanase I; and incorporates two measurable and physically interpretable substrate parameters: the degree of polymerization (DP) and the fraction of beta-glucosidic bonds accessible to cellulase, F(a) (Zhang and Lynd, 2004). Initial enzyme-limited reaction rates simulated by the model are consistent with several important behaviors reported in the literature, including the effects of substrate characteristics on exoglucanase and endoglucanase activities; the degree of endo/exoglucanase synergy; the endoglucanase partition coefficient on hydrolysis rates; and enzyme loading on relative reaction rates for different substrates. This is the first cellulase kinetic model involving a single set of kinetic parameters that is successfully applied to a variety of cellulosic substrates, and the first that describes more than one behavior associated with enzymatic hydrolysis. The model has potential utility for data accommodation and design of industrial processes, structuring, testing, and extending understanding of cellulase enzyme systems when experimental date are available, and providing guidance for functional design of cellulase systems at a molecular scale. Opportunities to further refine cellulase kinetic models are discussed, including parameters that would benefit from further study.     

Multiple imputation for discrete data: Evaluation of the joint latent normal model

Missing data are ubiquitous in clinical and social research, and multiple imputation (MI) is increasingly the methodology of choice for practitioners. Two principal strategies for imputation have been proposed in the literature: joint modelling multiple imputation (JM‐MI) and full conditional specification multiple imputation (FCS‐MI). While JM‐MI is arguably a preferable approach, because it involves specification of an explicit imputation model, FCS‐MI is pragmatically appealing, because of its flexibility in handling different types of variables. JM‐MI has developed from the multivariate normal model, and latent normal variables have been proposed as a natural way to extend this model to handle categorical variables. In this article, we evaluate the latent normal model through an extensive simulation study and an application on data from the German Breast Cancer Study Group, comparing the results with FCS‐MI. We divide our investigation in four sections, focusing on (i) binary, (ii) categorical, (iii) ordinal, and (iv) count data. Using data simulated from both the latent normal model and the general location model, we find that in all but one extreme general location model setting JM‐MI works very well, and sometimes outperforms FCS‐MI. We conclude the latent normal model, implemented in the R package jomo , can be used with confidence by researchers, both for single and multilevel multiple imputation.     

A goodness-of-fit test for capture-recapture model Mt under closure

A new, fully efficient goodness-of-fit test for the time-specific closed-population capture-recapture model Mt is presented. This test is based on the residual distribution of the capture history data given the maximum likelihood parameter estimates under model Mt, is partitioned into informative components, and is based on chi-square statistics. Comparison of this test with Leslie's test (Leslie, 1958, Journal of Animal Ecology 27, 84-86) for model Mt, using Monte Carlo simulations, shows the new test generally outperforms Leslie's test. The new test is frequently computable when Leslie's test is not, has Type I error rates that are closer to nominal error rates than Leslie's test, and is sensitive to behavioral variation and heterogeneity in capture probabilities. Leslie's test is not sensitive to behavioral variation in capture probabilities but, when computable, has greater power to detect heterogeneity than the new test.     

A dissipative particle dynamics model of carbon nanotubes

A mesoscale dissipative particle dynamics model of single wall carbon nanotubes (CNTs) is designed and demonstrated. The coarse-grained model is produced by grouping together carbon atoms and by bonding the new lumped particles through pair and triplet forces. The mechanical properties of the simulated tube are determined by the bonding forces, which are derived by virtual experiments. Through the introduction of van der Waals interactions, tube–tube interactions were studied. Owing to the reduced number of particles, this model allows the simulation of relatively large systems. The applicability of the presented scheme to model CNT based mechanical devices is discussed.     

The structural identifiability and parameter estimation of a multispecies model for the transmission of mastitis in dairy cows with postmilking teat disinfection

A mathematical model for the transmission of two interacting classes of mastitis causing bacterial pathogens in a herd of dairy cows is presented and applied to a specific data set. The data were derived from a field trial of a specific measure used in the control of these pathogens, where half the individuals were subjected to the control and in the others the treatment was discontinued. The resultant mathematical model (eight non-linear simultaneous ordinary differential equations) therefore incorporates heterogeneity in the host as well as the infectious agent and consequently the effects of control are intrinsic in the model structure. A structural identifiability analysis of the model is presented demonstrating that the scope of the novel method used allows application to high order non-linear systems. The results of a simultaneous estimation of six unknown system parameters are presented. Previous work has only estimated a subset of these either simultaneously or individually. Therefore not only are new estimates provided for the parameters relating to the transmission and control of the classes of pathogens under study, but also information about the relationships between them. We exploit the close link between mathematical modelling, structural identifiability analysis, and parameter estimation to obtain biological insights into the system modelled.     

Metabolic model for glycogen-accumulating organisms in anaerobic/aerobic activated sludge systems

Glycogen-accumulating organisms (GAO) have the potential to directly compete with polyphosphate-accumulating organisms (PAO) in EBPR systems as both are able to take up VFA anaerobically and grow on the intracellular storage products aerobically. Under anaerobic conditions GAO hydrolyse glycogen to gain energy and reducing equivalents to take up VFA and to synthesise polyhydroxyalkanoate (PHA). In the subsequent aerobic stage, PHA is being oxidised to gain energy for glycogen replenishment (from PHA) and for cell growth. This article describes a complete anaerobic and aerobic model for GAO based on the understanding of their metabolic pathways. The anaerobic model has been developed and reported previously, while the aerobic metabolic model was developed in this study. It is based on the assumption that acetyl-CoA and propionyl-CoA go through the catabolic and anabolic processes independently. Experimental validation shows that the integrated model can predict the anaerobic and aerobic results very well. It was found in this study that at pH 7 the maximum acetate uptake rate of GAO was slower than that reported for PAO in the anaerobic stage. On the other hand, the net biomass production per C-mol acetate added is about 9% higher for GAO than for PAO. This would indicate that PAO and GAO each have certain competitive advantages during different parts of the anaerobic/aerobic process cycle.     

Numerical model (switchable/dual model) of the human head for rigid body and finite elements applications

In this paper, a methodology for the development and validation of a numerical model of the human head using generic procedures is presented. All steps required, starting with the model generation, model validation and applications will be discussed. The proposed model may be considered as a dual one due to its capabilities to switch from deformable to a rigid body according to the application's requirements. The first step is to generate the numerical model of the human head using geometry files or medical images. The required stiffness and damping for the elastic connection used for the rigid body model are identified by performing a natural frequency analysis. The presented applications for model validation are related to impact analysis. The first case is related to Nahum's (Nahum and Smith 1970) experiments pressure data being evaluated and a pressure map generated using the results from discrete elements. For the second case, the relative displacement between the brain and the skull is evaluated according to Hardy's (Hardy WH, Foster CD, Mason, MJ, Yang KH, King A, Tashman S. 2001.Investigation of head injury mechanisms using neutral density technology and high-speed biplanar X-ray. Stapp Car Crash J. 45:337–368, SAE Paper 2001-22-0016) experiments. The main objective is to validate the rigid model as a quick and versatile tool for acquiring the input data for specific brain analyses.     

A “parallel plate” electrostatic model for bimolecular rate constants applied to electron transfer proteins

A “parallel plate” model describing the electrostatic potential energy of protein-protein interactions is presented that provides an analytical representation of the effect of ionic strength on a bimolecular rate constant. The model takes into account the asymmetric distribution of charge on the surface of the protein and localized charges at the site of electron transfer that are modeled as elements of a parallel plate condenser. Both monopolar and dipolar interactions are included. Examples of simple (monophasic) and complex (biphasic) ionic strength dependencies obtained from experiments with several electron transfer protein systems are presented, all of which can be accommodated by the model. The simple cases do not require the use of both monopolar and dipolar terms (i.e., they can be fit well by either alone). The biphasic dependencies can be fit only by using dipolar and monopolar terms of opposite sign, which is physically unreasonable for the molecules considered. Alternatively, the high ionic strength portion of the complex dependencies can be fit using either the monopolar term alone or the complete equation; this assumes a model in which such behavior is a consequence of electron transfer mechanisms involving changes in orientation or site of reaction as the ionic strength is varied. Based on these analyses, we conclude that the principal applications of the model presented here are to provide information about the structural properties of intermediate electron transfer complexes and to quantify comparisons between related proteins or site-specific mutants. We also conclude that the relative contributions of monopolar and dipolar effects to protein electron transfer kinetics cannot be evaluated from experimental data by present approximations.     

Accounting for multiplicities in assessing drug safety: a three-level hierarchical mixture model

Multiple comparisons and other multiplicities are among the most difficult of problems that face statisticians, frequentists, and Bayesians alike. An example is the analysis of the many types of adverse events (AEs) that are recorded in drug clinical trials. We propose a three-level hierarchical mixed model. The most basic level is type of AE. The second level is body system, each of which contains a number of types of possibly related AEs. The highest level is the collection of all body systems. Our analysis allows for borrowing across body systems, but there is greater potential-depending on the actual data-for borrowing within each body system. The probability that a drug has caused a type of AE is greater if its rate is elevated for several types of AEs within the same body system than if the AEs with elevated rates were in different body systems. We give examples to illustrate our method and we describe its application to other types of problems.     

A model for long-term potentiation and depression

A computational model of long-term potentiation (LTP) and long-term depression (LTD) in the hippocampus is presented. The model assumes the existence of retrograde signals, is in good agreement with several experimental data on LTP, LTD, and their pharmacological manipulations, and shows how a simple kinetic scheme can capture the essential characteristics of the processes involved in LTP and LTD. We propose that LTP and LTD could be two different but conceptually similar processes, induced by the same class of retrograde signals, and maintained by two distinct mechanisms. An interpretation of a number of experiments in terms of the molecular processes involved in LTP and LTD induction and maintenance, and the roles of a retrograde signal are presented and discussed.     

Minimizing model fitting objectives that contain spurious local minima by bootstrap restarting

Objective functions that arise when fitting nonlinear models often contain local minima that are of little significance except for their propensity to trap minimization algorithms. The standard methods for attempting to deal with this problem treat the objective function as fixed and employ stochastic minimization approaches in the hope of randomly jumping out of local minima. This article suggests a simple trick for performing such minimizations that can be employed in conjunction with most conventional nonstochastic fitting methods. The trick is to stochastically perturb the objective function by bootstrapping the data to be fit. Each bootstrap objective shares the large-scale structure of the original objective but has different small-scale structure. Minimizations of bootstrap objective functions are alternated with minimizations of the original objective function starting from the parameter values with which minimization of the previous bootstrap objective terminated. An example is presented, fitting a nonlinear population dynamic model to population dynamic data and including a comparison of the suggested method with simulated annealing. Convergence diagnostics are discussed.     

Mathematical model of self-cycling fermentation

This article presents a mathematical model for biomass, limiting substrate, and dissolved oxygen concentrations during stable operation of self-cycling fermentation (SCF). Laboratory experiments using the bacterium Acinetobacter calcoaceticus RAG-1 and ethanol as the limiting substrate were performed to validate the model. A computer simulation developed from the model successfully matched experimental SCF intracycle trends and end-of-cycle results and, most importantly, settled into an unimposed periodicity characteristic of stable SCF operation. (c) 1995 John Wiley & Sons, Inc.     

Dynamics of a mechanistically derived stoichiometric producer-grazer model

One of the simplest predator-prey models that tracks the quantity and the quality of prey is the one proposed by [I. Loladze, Y. Kuang, and J.J. Elser, Stoichiometry in producer-grazer systems: Linking energy flow with element cycling, Bull. Math. Biol. 62 (2000) pp. 1137–1162.] (LKE model). In it, the ratio of two essential chemical elements, carbon to phosphorus, C:P, represents prey quality. However, that model does not explicitly track P neither in the prey nor in the media that supports the prey. Here, we extend the LKE model by mechanistically deriving and accounting for P in both the prey and the media. Bifurcation diagrams and simulations show that our model behaves similarly to the LKE model. However, in the intermediate range of the carrying capacity, especially near the homoclinic bifurcation point for the carrying capacity, quantitative behaviour of our model is different. We analyze positive invariant region and stability of boundary steady states. We show that as the uptake rate of P by producer becomes infinite, LKE models become the limiting case of our model. Furthermore, our model can be readily extended to multiple producers and consumers.