Kinetic modelling of plant metabolic pathways

This paper provides a review of kinetic modelling of plant metabolic pathways as a tool for analysing their control and regulation. An overview of different modelling strategies is presented, starting with those approaches that only require a knowledge of the network stoichiometry; these are referred to as structural. Flux-balance analysis, metabolic flux analysis using isotope labelling, and elementary mode analysis are briefly mentioned as three representative examples. The main focus of this paper, however, is a discussion of kinetic modelling, which requires, in addition to the stoichiometry, a knowledge of the kinetic properties of the constituent pathway enzymes. The different types of kinetic modelling analysis, namely time-course simulation, steady-state analysis, and metabolic control analysis, are explained in some detail. An overview is presented of strategies for obtaining model parameters, as well as software tools available for simulation of such models. The kinetic modelling approach is exemplified with discussion of three models from the general plant physiology literature. With the aid of kinetic modelling it is possible to perform a control analysis of a plant metabolic system, to identify potential targets for biotechnological manipulation, as well as to ascertain the regulatory importance of different enzymes (including isoforms of the same enzyme) in a pathway. Finally, a framework is presented for extending metabolic models to the whole-plant scale by linking biochemical reactions with diffusion and advective flow through the phloem. Future challenges include explicit modelling of subcellular compartments, as well as the integration of kinetic models on the different levels of the cellular and organizational hierarchy.     

Comparing parametric solid modelling/reconfiguration, global shape modelling and free-form deformation for the generation of 3D digital models of femurs from X-ray images

At present, computer assisted surgery systems help orthopaedic surgeons both plan and perform surgical procedures. To enable these systems to function, it is crucial to have at one's disposal 3D models of anatomical structures, surgical tools and prostheses (if required). This paper analyses and compares three methods for generating 3D digital models of anatomical structures starting from X-ray images: parametric solid modelling/reconfiguration, global shape modelling and free-form deformation. Seven experiences involving the generation of a femur model were conducted by software developers and different skilled users. These experiences are described in detail and compared at different stages and from different points of view.     

Making do without selection—review essay of “Cultural Evolution: Conceptual Challenges” by Tim Lewens

Cultural evolution is a growing, interdisciplinary, and disparate field of research. In ‘Cultural evolution: conceptual challenges”, Tim Lewens offers an ambitious analytical survey of this field that aims to clarify and defend its epistemic contributions, and highlight the limitations and risks associated with them. One overarching contention is that a form of population thinking dubbed the ‘kinetic approach’ should be seen as a unifying and justifying principle for cultural evolution, especially when considering the role of formal modelling. This book makes a number of extremely valuable contributions to the literature. However, I argue that not all is as it may seem regarding the kinetic approach and that, while it does little to diminish the book’s value, the use which Lewens makes for it is problematic.     

Comparing parametric solid modelling/reconfiguration,global shape modelling and free-form deformation for the generation of 3D digital models of femurs from X-ray images

At present, computer assisted surgery systems help orthopaedic surgeons both plan and perform surgical procedures. To enable these systems to function, it is crucial to have at one's disposal 3D models of anatomical structures, surgical tools and prostheses (if required). This paper analyses and compares three methods for generating 3D digital models of anatomical structures starting from X-ray images: parametric solid modelling/reconfiguration, global shape modelling and free-form deformation. Seven experiences involving the generation of a femur model were conducted by software developers and different skilled users. These experiences are described in detail and compared at different stages and from different points of view.     

Simple Carrier Kinetics in Complex Membrane Transporters

The four-state simple carrier model (SCM) has been employed to describe facilitative transport of ligands across biological membranes. Two basic mechanisms have been invoked to account for carrier-mediated ligand translocation: (i) binding to a mobile carrier, and (ii) displacement determined by conformational changes of an integral protein. While translatory carriers may be accurately represented by a four-state diagram, it is unlikely that the transport process mediated by a complex membrane protein can be strictly described by the elementary SCM. The purpose of this article is to test whether facilitative transporters with a more complex kinetic design than the SCM can exhibit macroscopic kinetic properties indistinguishable from it. For this, I studied a ``general carrier model' (GCM), and evaluated whether the relevant kinetic parameters are subject to the same basic restrictions as in the SCM. The fundamental finding is that there is a general kinetic design embodied with SCM-like properties, that can be shared by many transporters. In particular, the classical SCM is shown here to represent a particular case of the GCM. A main conclusion of this work is therefore that the finding of a macroscopic SCM-like kinetic behavior for a particular process of facilitative transport does not represent a sufficient argument in favor of a particular type of mechanism, like the typical one involving a two-conformational single-site carrier. Received: 9 February 1998/Revised: 19 June 1998     

Evolving cell models for systems and synthetic biology

This paper proposes a new methodology for the automated design of cell models for systems and synthetic biology. Our modelling framework is based on P systems, a discrete, stochastic and modular formal modelling language. The automated design of biological models comprising the optimization of the model structure and its stochastic kinetic constants is performed using an evolutionary algorithm. The evolutionary algorithm evolves model structures by combining different modules taken from a predefined module library and then it fine-tunes the associated stochastic kinetic constants. We investigate four alternative objective functions for the fitness calculation within the evolutionary algorithm: (1) equally weighted sum method, (2) normalization method, (3) randomly weighted sum method, and (4) equally weighted product method. The effectiveness of the methodology is tested on four case studies of increasing complexity including negative and positive autoregulation as well as two gene networks implementing a pulse generator and a bandwidth detector. We provide a systematic analysis of the evolutionary algorithm’s results as well as of the resulting evolved cell models.     

Modelling of a continuous pilot photobioreactor for microalgae production

In this study, a model of a continuous pilot photobioreactor for microalgae production is proposed. Three aspects have been studied: the modelling of kinetic growth, the gas-liquid transfer and the hydrodynamics in the photobioreactor. The modelling of each aspect has been developed with the dynamic simulation software SpeedUp, after experimental studies, then validated step-by-step. The connection of these three aspects aims to predict and optimise biomass production of the pilot plant.     

ScrumPy: metabolic modelling with Python

ScrumPy is a software package used for the definition and analysis of metabolic models. It is written using the Python programming language that is also used as a user interface. ScrumPy has features for both kinetic and structural modelling, but the emphasis is on structural modelling and those features of most relevance to analysis of large (genome-scale) models. The aim is at describing ScrumPy's functionality to readers with some knowledge of metabolic modelling, but implementation, programming and other computational details are omitted. ScrumPy is released under the Gnu Public Licence, and available for download from http://mudshark.brookes.ac.uk/ ScrumPy.     

Comparison of plant and fungal gravitropic responses using imitational modelling

The mechanisms of gravity perception are still hypothetical, but there are sufficient data from experiments with plants to enable mathematical modelling to imitate the behaviour of gravitropic response systems. We have a much less complete picture of gravitropic kinetics in agaric mushrooms. However, some existing mathematical models which imitate plant responses are in principle universal because their conceptual components are not limited to any specific cellular entities. In this work we have used such models to compare plant and fungal gravitropism, using recently acquired kinetic data from the agarics Coprinus cinereius and Flammulina velutipes. The results show striking similarities between plants and fungi. First, it is evident that the basic assumptions of the plant models are logically applicable to fungi. Secondly, the mechanism of bending is the same (differential growth of opposite flanks of the growing organ). Thirdly, the distribution of growth seems very similar: in both plants and fungi growth of the organ is most intensive just behind the apex and is almost absent at the apex and at the base. Fourthly, in both fungi and plants the gravitropic response exhibits a substantial time delay suggesting that many time-consuming processes are involved in reception, transduction and realization of gravitropic stimuli. Important differences in plant and fungal gravitropism kinetics were: (i) the agaric stem apex always returned to the vertical, whereas some plant organs show stable plagiogravitropic growth; (ii) inflections were usually seen in C. cinereus stem gravitropism time courses suggesting that a curvature compensation process delayed bending for a time; (iii) C. cinercus stems very rarely overshot or oscillated around the vertical although many plant subjects oscillate and the (limited) data for F. velutipes showed a single, exaggerated overshoot and oscillation. In this latter case, experimental modelling with parameters characteristic of a low level of perception improved the fit to the F. velutipes data, indicating that the two fungi may differ in this factor. Application of the plant models focused future research attention on the urgent need for data bearing on angle-response and acceleration–response relationships in fungi, and their detection–level thresholds for gravitational acceleration. Since the modelling also highlighted some fundamental kinetic differences between the only two fungi for which sufficient data are available at the moment, it is also clear that detailed observations need to be made of gravitropism kinetics in a larger number and wider range of fungi.     

INSTAR,a discrete event model for simulating zooplankton population dynamics

In this paper we discuss the basic principles of discrete event, individual oriented, data based modelling in ecology, and we present an application of this modelling strategy. The strategy is contrasted with some more conventional modelling strategies with respect to its purpose, its basic units and its heuristic properties.INSTAR applies this modelling strategy to the simulation of the fluctuations of the population structure and density of microcrustaceans through the year. The model encompasses one microcrustacean species at a time, and its interface with the rest of the ecosystem; it has been applied to several Cladocera and Copepoda species in a shallow eutrophic lake in the Netherlands (Vijverberg & Richter 1982a, b). Possibilities for extending the model are discussed.     

Daphnicle dynamics based on kinetic theory: An analogue-modelling of swarming and behaviour of Daphnia

Attempts are presented of an analogue modelling of Daphnia responses to various influences and stimuli, as distribution of food and of predators. An aim of the study is to examine to what extent a statistical-mechanical approach may be useful as a tool in modelling of Daphnia swarms behaviour. In the modelling we follow a line close to test particle studies in physical sciences. A generalized kinetic equation of what we shall call daphnicles is derived. The modelling incorporates individual characteristics of daphnicles, as position, velocity, degree of food saturation and responses daphnicles have to outside influences. Each daphnicle we assume responds to some stimuli in ordered ways and to others in stochastic ways, and the degree or strength of reactions depends on the density of all daphnicles, the density of food available, the saturation level of daphnicles and the threat level in the environment, or background, the daphnicles are living on. Some fluid equations of daphnicle swarms are subsequently derived from the basic equation, and solutions are given of the model-equations, including a food distribution equation, in some particular cases that show peculiarities in reactions of daphnicles to food, degree of saturation and to threat, when these are acting alone, and in combination. The modelling results may be compared to results of laboratory experiments of Daphnia behaviour that soon will be performed.     

Combining model structure identification and hybrid modelling for photo-production process predictive simulation and optimisation

Integrating physical knowledge and machine learning is a critical aspect of developing industrially focused digital twins for monitoring, optimisation, and design of microalgal and cyanobacterial photo-production processes. However, identifying the correct model structure to quantify the complex biological mechanism poses a severe challenge for the construction of kinetic models, while the lack of data due to the time-consuming experiments greatly impedes applications of most data-driven models. This study proposes the use of an innovative hybrid modelling approach that consists of a simple kinetic model to govern the overall process dynamic trajectory and a data-driven model to estimate mismatch between the kinetic equations and the real process. An advanced automatic model structure identification strategy is adopted to simultaneously identify the most physically probable kinetic model structure and minimum number of data-driven model parameters that can accurately represent multiple data sets over a broad spectrum of process operating conditions. Through this hybrid modelling and automatic structure identification framework, a highly accurate mathematical model was constructed to simulate and optimise an algal lutein production process. Performance of this hybrid model for long-term predictive modelling, optimisation, and online self-calibration is demonstrated and thoroughly discussed, indicating its significant potential for future industrial application.     

Something from nothing: bridging the gap between constraint-based and kinetic modelling

Two divergent modelling methodologies have been adopted to increase our understanding of metabolism and its regulation. Constraint-based modelling highlights the optimal path through a stoichiometric network within certain physicochemical constraints. Such an approach requires minimal biological data to make quantitative inferences about network behaviour; however, constraint-based modelling is unable to give an insight into cellular substrate concentrations. In contrast, kinetic modelling aims to characterize fully the mechanics of each enzymatic reaction. This approach suffers because parameterizing mechanistic models is both costly and time-consuming. In this paper, we outline a method for developing a kinetic model for a metabolic network, based solely on the knowledge of reaction stoichiometries. Fluxes through the system, estimated by flux balance analysis, are allowed to vary dynamically according to linlog kinetics. Elasticities are estimated from stoichiometric considerations. When compared to a popular branched model of yeast glycolysis, we observe an excellent agreement between the real and approximate models, despite the absence of (and indeed the requirement for) experimental data for kinetic constants. Moreover, using this particular methodology affords us analytical forms for steady state determination, stability analyses and studies of dynamical behaviour.     

Identifiability: the first step in parameter estimation

The observations in an experiment define a set of observational parameters that are functions of the basic kinetic parameters of the model of the system. The problem of identifiability is concerned with whether the observational parameters uniquely specify the basic kinetic parameters. As such, it depends only on the functional relation between the two levels of parameters and not on errors of observation and the estimation procedure. It should be checked before doing the experiment. Given initial estimates of the basic kinetic parameters, identifiability can be checked, in a local sense, from data generated by simulating the experiment on the model.     

Changes in collagen stability and folding in lethal perinatal osteogenesis imperfecta. The effect of alpha 1 (I)-chain glycine-to-arginine substitutions.

The effect of glycine-to-arginine mutations in the alpha 1 (I)-chain on collagen triple-helix structure in lethal perinatal osteogenesis imperfecta was studied by determination of the helix denaturation temperature and by computerized molecular modelling. Arginine substitutions at glycine residues 391 and 667 resulted in similar small decreases in helix stability. Molecular modelling suggested that the glycine-to-arginine-391 mutant resulted in only a relatively small localized disruption to the helix structure. Thus the glycine-to-arginine substitutions may lead to only a small structural abnormality of the collagen helix, and it is most likely that the over-modification of lysine, poor secretion, increased degradation and other functional sequelae result from a kinetic defect in collagen helix formation resulting from the mutation.     

On a general model structure for macroscopic biological reaction rates

Macroscopic modelling of bioprocesses requires the determination of a biological reaction scheme and a kinetic model. The a priori selection of an appropriate kinetic model structure is usually made difficult by the lack of detailed bioprocess knowledge and the profusion of apparently similar biological kinetic laws. Moreover, parameter identification is made arduous and time-consuming by the strong non-linearities involved in kinetic laws. In most cases, these kinetic structures are non-linearizable and no first parameter estimation can be deduced easily. In order to avoid such identification problems, Bogaerts et al. [Bogaerts, Ph., Castillo, J., Hanus, R., 1999. A general mathematical modelling technique for bioprocesses in engineering applications. Syst. Anal. Model. Simul. 35, 87-113] have developed a general linearizable kinetic structure which allows the representation of activation and/or inhibition effects of each component in the culture. This paper further generalizes this structure in order to improve the way saturation effects are taken into account, and in turn, improve the biological interpretation of the model parameters. The main advantage of the proposed structure lies in an associated systematic estimation procedure. The usefulness of the proposed model is tested with simulated as well as with experimental data.     

Docking and electron transfer studies between rubredoxin and rubredoxin:oxygen oxidoreductase

The interaction and electron transfer (ET) between rubredoxin (Rd) and rubredoxin:oxygen oxidoreductase (ROO) from Desulfovibrio gigas is studied by molecular modelling techniques. Experimental kinetic assays using recombinant proteins show that the Rd reoxidation by ROO displays a bell-shaped dependence on ionic strength, suggesting a non-trivial electrostatic dependence of the interaction between these two proteins. Rigid docking studies reveal a prevalence for Rd to interact, in a very specific way, with the surface of the ROO dimer near its FMN cofactors. The optimization of the lowest energy complexes, using molecular dynamics simulation, shows a very tight interaction between the surface of the two proteins, with a high probability for Rd residues (but not the iron centre directly) to be in direct contact with the FMN cofactors of ROO. Both electrostatics and van der Waals interactions contribute to the final energy of the complex. In these complexes, the major contributions for complex formation are polar interactions between acidic residues of Rd and basic residues of ROO, plus substantial non-polar interactions between different groups. Important residues for this process are identified. ET estimates (using the Pathways model), in the optimized lowest energy complexes, suggest that these configurations are efficient for transferring electrons. The experimental bell-shaped dependence of kinetics on ionic strength is analysed in view of the molecular modelling results, and hypotheses for the molecular basis of this phenomenon are discussed.