Modelling the variable incorporation of aromatic amino acids in the tyrocidines and analogous cyclodecapeptides.

AIMS: A mathematical model of the nonribosomal synthesis of tyrocidines and analogues by Brevibacillus parabrevis was constructed using a competitive binding mechanism (CBM) for the incorporation of the three variable aromatic amino acid (Aaa) residues in their sequence. These antimicrobial peptides have a conserved structure (D-Phe1 -Pro2 -Aaa3 -D-Aaa4 -Asn5 -Gln6 -Aaa7 -Val8 -Orn9 -Leu10 ), apart from the Aaa in positions 3, 4 and 7 containing either Phe, Trp or Tyr. METHODS AND RESULTS: Ultra-performance liquid chromatography linked mass spectrometry was used to profile peptides from extracts of cultures grown in media with various Phe : Trp ratios. The CBM model describes the production of peptides as a function of growth medium Aaa concentration. The model accounts for variable Aaa incorporation by simultaneously considering the influence of maximal incorporation rate and cooperativity, despite similar KM' s of synthetase modules. CONCLUSIONS: Our CBM model can be utilized to predict the Aaa composition of produced peptides from the concentration of Aaas in the growth medium. SIGNIFICANCE AND IMPACT OF THE STUDY: Subtly exploiting the inherent promiscuity of the nontemplate coded peptide synthesis allows for external control of peptide identity, without using genetic manipulation. Such versatility is exploitable in the production of targeted peptide complexes and rare peptides where production processes are reliant on nonribosomal synthesis.

Flux balance analysis for ethylene formation in genetically engineered Saccharomyces cerevisiae.

Biosynthesis of ethylene (ethene) is mainly performed by plants and some bacteria and fungi, via two distinct metabolic routes. Plants use two steps, starting with S-adenosylmethionine, while the ethylene-forming microbes perform an oxygen dependent reaction using 2-oxoglutarate and arginine. Introduction of these systems into Saccharomyces cerevisiae was studied in silico. The reactions were added to a metabolic network of yeast and flux over the two networks was optimised for maximal ethylene formation. The maximal ethylene yields obtained for the two systems were similar in the range of 7-8 mol ethylene/10 mol glucose. The microbial metabolic network was used for testing different strategies to increase the ethylene formation. It was suggested that supplementation of exogenous proline, using a solely NAD-coupled glutamate dehydrogenase, and using glutamate as the nitrogen source, could increase the ethylene formation. Comparison of these in silico results with published experimental data for yeast expressing the microbial system confirmed an increased ethylene formation when changing nitrogen source from ammonium to glutamate. The theoretical analysis methods indicated a much higher maximal yield per glucose for ethylene than was experimentally observed. However, such high ethylene yields could only be obtained with a concomitant very high respiration (per glucose). Accordingly, when ethylene production was optimised under the additional constraint of restricted respiratory capacity (i.e. limited to experimentally measured values) the theoretical maximal ethylene yield was much lower at 0.2/10 mol glucose, and closer to the experimentally observed values.

Control of specific growth rate in Saccharomyces cerevisiae.

In this contribution we resolve the long-standing dispute whether or not the Monod constant (K(S)), describing the overall affinity of an organism for its growth-limiting substrate, can be related to the affinity of the transporter for that substrate (K(M)). We show how this can be done via the control of the transporter on the specific growth rate; they are identical if the transport step has full control. The analysis leads to the counter-intuitive result that the affinity of an organism for its substrate is expected to be higher than the affinity of the enzyme that facilitates its transport. Experimentally, we show this indeed to be the case for the yeast Saccharomyces cerevisiae, for which we determined a K(M) value for glucose more than two times higher than the K(S) value in glucose-limited chemostat cultures. Moreover, we calculated that at glucose concentrations of 0.03 and 0.29 mM, the transport step controls the specific growth rate at 78 and 49 %, respectively.

Control, responses and modularity of cellular regulatory networks: a control analysis perspective.

Cells adapt to changes in environmental conditions through the concerted action of signalling, gene expression and metabolic subsystems. The authors will discuss a theoretical framework addressing such integrated systems. This 'hierarchical analysis' was first developed as an extension to a metabolic control analysis. It builds on the phenomenon that often the communication between signalling, gene expression and metabolic subsystems is almost exclusively via regulatory interactions and not via mass flow interactions. This allows for the treatment of the said subsystems as 'levels' in a hierarchical view of the organisation of the molecular reaction network of cells. Such a hierarchical approach has as a major advantage that levels can be analysed conceptually in isolation of each other (from a local intra-level perspective) and at a later stage integrated via their interactions (from a global inter-level perspective). Hereby, it allows for a modular approach with variable scope. A number of different approaches have been developed for the analysis of hierarchical systems, for example hierarchical control analysis and modular response analysis. The authors, here, review these methods and illustrate the strength of these types of analyses using a core model of a system with gene expression, metabolic and signal transduction levels.

Pyruvate relieves the necessity of high induction levels of catalase and enables Campylobacter jejuni to grow under fully aerobic conditions.

AIMS: Several cases of campylobacteriosis reported worldwide seemingly conflict with the strict growth requirements and sensitivity to environmental stress of Campylobacter jejuni. In this study, the need for a micro-aerobic environment [dissolved oxygen tension (DOT): 0.1-90%; 100% air saturation)] and the adaptive responses to oxygen stress were studied. METHODS AND RESULTS: The growth of C. jejuni in continuous culture was assessed under different DOT in the presence or absence of pyruvate. In a medium without pyruvate, continuous cultures of C. jejuni showed typically micro-aerobic behaviour and cells were unable to grow under fully aerobic conditions. However in the presence of pyruvate (25 mmol l(-1)), continuous cultures of C. jejuni were able to grow in a broad DOT range, varying from 0.1% to at least 90%, and the catalase activity was decreased. CONCLUSIONS: Addition of pyruvate results in the decrease in the concentration of hydrogen peroxide, which enables C. jejuni to grow aerobically. SIGNIFICANCE AND IMPACT OF THE STUDY: New information on the oxidative physiology of C. jejuni and its ability to grow aerobically in media supplemented with pyruvate is presented.

BDI-modelling of complex intracellular dynamics.

A BDI-based continuous-time modelling approach for intracellular dynamics is presented. It is shown how temporalized BDI-models make it possible to model intracellular biochemical processes as decision processes. By abstracting from some of the details of the biochemical pathways, the model achieves understanding in nearly intuitive terms, without losing veracity: classical intentional state properties such as beliefs, desires and intentions are founded in reality through precise biochemical relations. In an extensive example, the complex regulation of Escherichia coli vis-à-vis lactose, glucose and oxygen is simulated as a discrete-state, continuous-time temporal decision manager. Thus a bridge is introduced between two different scientific areas: the area of BDI-modelling and the area of intracellular dynamics.

A comparative analysis of kinetic models of erythrocyte glycolysis.

Since the 1970s, with Heinrich as a pioneer in the field, numerous kinetic models of erythrocyte glycolysis have been constructed. A functional comparison of eight of these models indicates that the production of ATP and GSH in the red blood cell is largely controlled by the demand reactions. The rate characteristics for the supply and demand blocks indicate a good homeostatic control of ATP and GSH concentrations at different work loads for the pathway, while the production rates of ATP and GSH can be adjusted as needed by the demand reactions.

Summation theorems for flux and concentration control coefficients of dynamic systems.

Metabolic control analysis (MCA) was developed to quantify how system variables are affected by parameter variations in a system. In addition, MCA can express the global properties of a system in terms of the individual catalytic steps, using connectivity and summation theorems to link the control coefficients to the elasticity coefficients. MCA was originally developed for steady-state analysis and not all summation theorems have been derived for dynamic systems. A method to determine time-dependent flux and concentration control coefficients for dynamic systems by expressing the time domain as a function of percentage progression through any arbitrary fixed interval of time is reported. Time-dependent flux and concentration control coefficients of dynamic systems, provided that they are evaluated in this novel way, obey the same summation theorems as steady-state flux and concentration control coefficients, respectively.

Conditions for effective allosteric feedforward and feedback in metabolic pathways.

Whether an allosteric feedback or feedforward modifier actually has an effect on the steady-state properties of a metabolic pathway depends not only on the allosteric modifier effect itself, but also on the control properties of the affected allosteric enzyme in the pathway of which it is part. Different modification mechanisms are analysed: mixed inhibition, allosteric inhibition and activation of the reversible Monod-Wyman-Changeux and reversible Hill models. In conclusion, it is shown that, whereas a modifier effect on substrate and product binding (specific effects) can be an effective negative feedback mechanism, it is much less effective as a positive feedforward mechanism. The prediction is that catalytic effects that change the apparent limiting velocity would be more effective in feedforward activation.

Comparing the regulatory behaviour of two cooperative, reversible enzyme mechanisms.

It is shown that both the reversible Hill equation and a generalised, reversible Monod-Wyman-Changeux equation can give analogous regulatory behaviour when embedded in a model metabolic pathway.

Experimental evidence for allosteric modifier saturation as predicted by the bi-substrate Hill equation.

The cooperative enzyme reaction rates predicted by the bi-substrate Hill equation and the bi-substrate Monod-Wyman-Changeux (MWC) equation when allosterically inhibited are compared in silico. Theoretically, the Hill equation predicts that when the maximum inhibitory effect at a certain substrate condition has been reached, an increase in allosteric inhibitor concentration will have no effect on reaction rate, that is the Hill equation shows allosteric inhibitor saturation. This saturating inhibitory effect is not present in the MWC equation. Experimental in vitro data for pyruvate kinase, a bi-substrate cooperative enzyme that is allosterically inhibited, are presented. This enzyme also shows inhibitor saturation, and therefore serves as experimental evidence that the bi-substrate Hill equation predicts more realistic allosteric inhibitor behaviour than the bi-substrate MWC equation.

Evaluation of a simplified generic bi-substrate rate equation for computational systems biology.

The evaluation of a generic simplified bi-substrate enzyme kinetic equation, whose derivation is based on the assumption of equilibrium binding of substrates and products in random order, is described. This equation is much simpler than the mechanistic (ordered and ping-pong) models, in that it contains fewer parameters (that is, no K(i) values for the substrates and products). The generic equation fits data from both the ordered and the ping-pong models well over a wide range of substrate and product concentrations. In the cases where the fit is not perfect, an improved fit can be obtained by considering the rate equation for only a single set of product concentrations. Due to its relative simplicity in comparison to the mechanistic models, this equation will be useful for modelling bi-substrate reactions in computational systems biology.

Software tools that facilitate kinetic modelling with large data sets: an example using growth modelling in sugarcane.

A solution to manage cumbersome data sets associated with large modelling projects is described. A kinetic model of sucrose accumulation in sugarcane is used to predict changes in sucrose metabolism with sugarcane internode maturity. This results in large amounts of output data to be analysed. Growth is simulated by reassigning maximal activity values, specific to each internode of the sugarcane plant, to parameter attributes of a model object. From a programming perspective, only one model definition file is required for the simulation software used; however, the amount of input data increases with each extra interrnode that is modelled, and likewise the amount of output data that is generated also increases. To store, manipulate and analyse these data, the modelling was performed from within a spreadsheet. This was made possible by the scripting language Python and the modelling software PySCeS through an embedded Python interpreter available in the Gnumeric spreadsheet program.

Is there an optimal ribosome concentration for maximal protein production?

A core model is presented for protein production in Escherichia coli to address the question whether there is an optimal ribosomal concentration for non-ribosome protein production. Analysing the steady-state solution of the model over a range of mRNA concentrations, indicates that such an optimum ribosomal content exists, and that the optimum shifts to higher ribosomal contents at higher specific growth rates.

Experimental supply-demand analysis of anaerobic yeast energy metabolism.

Experimental supply-demand analysis of yeast fermentative energy metabolism shows that control of the glycolytic flux is shared between supply and demand. In glucose limited chemostat cultures the supply block was modulated in a dilution rate change and demand block via a benzoic acid titration. Under these conditions the supply block had a flux control of 0.90 and the demand block a flux control of 0.10.

Java Web Simulation (JWS); a web based database of kinetic models.

Software to make a database of kinetic models accessible via the internet has been developed and a core database has been set up at http://jjj.biochem.sun.ac.za/. This repository of models, available to everyone with internet access, opens a whole new way in which we can make our models public. Via the database, a user can change enzyme parameters and run time simulations or steady state analyses. The interface is user friendly and no additional software is necessary. The database currently contains 10 models, but since the generation of the program code to include new models has largely been automated the addition of new models is straightforward and people are invited to submit their models to be included in the database.

How to distinguish between the vacuum cleaner and flippase mechanisms of the lmrA multi-drug transporter in Lactococcus lactis.

A numerical model of the LmrA multi-drug transport system of Lactococcus lactis is used to explore the possibility of distinguishing experimentally between two putative transport mechanisms, i.e., the vacuum-cleaner and the flippase mechanisms. This comparative model also serves as an example of numerical simulation with the scripting language Python and its scientific add-on Scipy.

Time dependent responses of glycolytic intermediates in a detailed glycolytic model of Lactococcus lactis during glucose run-out experiments.

Glucose addition and subsequent run-out experiments were compared to simulations with a detailed glycolytic model of Lactococcus lactis. The model was constructed largely on bases of enzyme kinetic data taken from literature and not adjusted for the specific simulations shown here. Upon glucose depletion a rapid increase in PEP, inorganic phosphate and a gradual decrease in fructose 1,6-bisphosphate (FBP) were measured and predicted by simulation. The dynamic changes in these and other intermediate concentrations as measured in the experiments were well predicted by the kinetic model.

Control of glycolytic dynamics by hexose transport in Saccharomyces cerevisiae.

It is becoming accepted that steady-state fluxes are not necessarily controlled by single rate-limiting steps. This leaves open the issue whether cellular dynamics are controlled by single pacemaker enzymes, as has often been proposed. This paper shows that yeast sugar transport has substantial but not complete control of the frequency of glycolytic oscillations. Addition of maltose, a competitive inhibitor of glucose transport, reduced both average glucose consumption flux and frequency of glycolytic oscillations. Assuming a single kinetic component and a symmetrical carrier, a frequency control coefficient of between 0.4 and 0.6 and an average-flux control coefficient of between 0.6 and 0.9 were calculated for hexose transport activity. In a second approach, mannose was used as the carbon and free-energy source, and the dependencies on the extracellular mannose concentration of the transport activity, of the frequency of oscillations, and of the average flux were compared. In this case the frequency control coefficient and the average-flux control coefficient of hexose transport activity amounted to 0.7 and 0.9, respectively. From these results, we conclude that 1) transport is highly important for the dynamics of glycolysis, 2) most but not all control resides in glucose transport, and 3) there should at least be one step other than transport with substantial control.