A mathematical model for examining growth and sporulation processes of Bacillus subtilis

From the outer space to the inner cell: deconvoluting the complexity of Bacillus subtilis disulfide stress responses by redox state and absolute abundance quantification of extracellular, membrane, and cytosolic proteins

Understanding cellular mechanisms of stress management relies on omics data as a valuable resource. However, the lack of absolute quantitative data on protein abundances remains a significant limitation, particularly when comparing protein abundances across different cell compartments. In this study, we aimed to gain deeper insights into the proteomic responses of the Gram-positive model bacterium Bacillus subtilis to disulfide stress. We determined proteome-wide absolute abundances, focusing on different sub-cellular locations (cytosol and membrane) as well as the extracellular medium, and combined these data with redox state determination. To quantify secreted proteins in the culture medium, we developed a simple and straightforward protocol for the absolute quantification of extracellular proteins in bacteria. We concentrated extracellular proteins, which are highly diluted in the medium, using StrataClean beads along with a set of standard proteins to determine the extent of the concentration step. The resulting data set provides new insights into protein abundances in different sub-cellular compartments and the extracellular medium, along with a comprehensive proteome-wide redox state determination. Our study offers a quantitative understanding of disulfide stress management, protein production, and secretion in B. subtilis.

IMPORTANCE

Stress responses play a crucial role in bacterial survival and adaptation. The ability to quantitatively measure protein abundances and redox states in different cellular compartments and the extracellular environment is essential for understanding stress management mechanisms. In this study, we addressed the knowledge gap regarding absolute quantification of extracellular proteins and compared protein concentrations in various sub-cellular locations and in the extracellular medium under disulfide stress conditions. Our findings provide valuable insights into the protein production and secretion dynamics of B. subtilis, shedding light on its stress response strategies. Furthermore, the developed protocol for absolute quantification of extracellular proteins in bacteria presents a practical and efficient approach for future studies in the field. Overall, this research contributes to the quantitative understanding of stress management mechanisms and protein dynamics in B. subtilis, which can be used to enhance bacterial stress tolerance and protein-based biotechnological applications.

Dynamics of cell wall-binding proteins at a single molecule level: B. subtilis autolysins show different kinds of motion

The bacterial cell wall is a meshwork of crosslinked peptidoglycan strands, with a thickness of up to 50 nm in Firmicutes. Little is known about how proteins move through the cell wall to find sites of enzymatic activity. Cell wall synthesis for cell elongation involves the integration of new peptidoglycan strands by integral membrane proteins, as well as the degradation of existing strands by so-called autolysins, soluble proteins that are secreted through the cell membrane. Autolysins comprise different classes of proteases and glucanases and mostly contain cell-wall binding domains in addition to their catalytic domain. We have studied dynamics of Bacillus subtilis autolysins LytC, a major endopeptidase required for lateral cell wall growth, and LytF, a peptidase acting at the newly formed division site in order to achieve separation of daughter cells. We show that both proteins, fused to moxVenus are present as three distinct populations of different diffusion constants. The fastest population is compatible with free diffusion in a crowded liquid environment, that is similar to that of cytosolic enzymes, likely reflecting autolysins diffusing through the periplasm. The medium mobile fraction can be explained by constrained motion through a polymeric substance, indicating mobility of autolysins through the wall similar to that of DNA-binding proteins within the nucleoid. The slow-mobile fraction are most likely autolysins bound to their specific substrate sites. We show that LytF is more static during exponential phase, while LytC appears to be more active during the transition to stationary phase. Both autolysins became more static in backgrounds lacking redundant other autolysins, suggesting stochastic competition for binding sites. On the other hand, lack of inhibitor IseA or autolysin CwlS lead to an altered preference for polar localization of LytF within the cell wall, revealing that inhibitors and autolysins also affect each other's pattern of localization, in addition to their activity.

Design of a Porous Silicon Biosensor: Characterization, Modeling, and Application to the Indirect Detection of Bacteria

The design of a porous silicon (PSi) biosensor is not often documented, but is of the upmost importance to optimize its performance. In this work, the motivation behind the design choices of a PSi-based optical biosensor for the indirect detection of bacteria via their lysis is detailed. The transducer, based on a PSi membrane, was characterized and models were built to simulate the analyte diffusion, depending on the porous nanostructures, and to optimize the optical properties. Once all performances and properties were analyzed and optimized, a theoretical response was calculated. The theoretical limit of detection was computed as 104 CFU/mL, based on the noise levels of the optical setup. The experimental response was measured using 106 CFU/mL of Bacillus cereus as model strain, lysed by bacteriophage-coded endolysins PlyB221. The obtained signal matched the expected response, demonstrating the validity of our design and models.

A Central Role for Magnesium Homeostasis during Adaptation to Osmotic Stress

Osmotic stress is a significant physical challenge for free-living cells. Cells from all three domains of life maintain viability during osmotic stress by tightly regulating the major cellular osmolyte potassium (K+) and by import or synthesis of compatible solutes. It has been widely established that in response to high salt stress, many bacteria transiently accumulate high levels of K+, leading to bacteriostasis, with growth resuming only when compatible solutes accumulate and K+ levels are restored to biocompatible levels. Using Bacillus subtilis as a model system, we provide evidence that K+ fluxes perturb Mg2+ homeostasis: import of K+ upon osmotic upshift is correlated with Mg2+ efflux, and Mg2+ reimport is critical for adaptation. The transient growth inhibition resulting from hyperosmotic stress is coincident with loss of Mg2+ and a decrease in protein translation. Conversely, the reimport of Mg2+ is a limiting factor during resumption of growth. Furthermore, we show the essential signaling dinucleotide cyclic di-AMP fluctuates dynamically in coordination with Mg2+ and K+ levels, consistent with the proposal that cyclic di-AMP orchestrates the cellular response to osmotic stress. IMPORTANCE Environments with high concentrations of salt or other solutes impose an osmotic stress on cells, ultimately limiting viability by dehydration of the cytosol. A very common cellular response to high osmolarity is to immediately import high levels of potassium ion (K+), which helps prevent dehydration and allows time for the import or synthesis of biocompatible solutes that allow a resumption of growth. Here, using Bacillus subtilis as a model, we demonstrate that concomitant with K+ import there is a large reduction in intracellular magnesium (Mg2+) mediated by specific efflux pumps. Further, it is the reimport of Mg2+ that is rate-limiting for the resumption of growth. These coordinated fluxes of K+ and Mg2+ are orchestrated by cyclic-di-AMP, an essential second messenger in Firmicutes. These findings amend the conventional model for osmoadaptation and reveal that Mg2+ limitation is the proximal cause of the bacteriostasis that precedes resumption of growth.

Absolute Quantification of the Central Carbon Metabolome in Eight Commonly Applied Prokaryotic and Eukaryotic Model Systems

Absolute quantification of intracellular metabolite pools is a prerequisite for modeling and in-depth biological interpretation of metabolomics data. It is the final step of an elaborate metabolomics workflow, with challenges associated with all steps—from sampling to quantifying the physicochemically diverse metabolite pool. Chromatographic separation combined with mass spectrometric (MS) detection is the superior platform for high coverage, selective, and sensitive detection of metabolites. Herein, we apply our quantitative MS-metabolomics workflow to measure and present the central carbon metabolome of a panel of commonly applied biological model systems. The workflow includes three chromatographic methods combined with isotope dilution tandem mass spectrometry to allow for absolute quantification of 68 metabolites of glycolysis, the pentose phosphate pathway, the tricarboxylic acid cycle, and the amino acid and (deoxy) nucleoside pools. The biological model systems; Bacillus subtilis, Saccharomyces cerevisiae, two microalgal species, and four human cell lines were all cultured in commonly applied culture media and sampled in exponential growth phase. Both literature and databases are scarce with comprehensive metabolite datasets, and existing entries range over several orders of magnitude. The workflow and metabolite panel presented herein can be employed to expand the list of reference metabolomes, as encouraged by the metabolomics community, in a continued effort to develop and refine high-quality quantitative metabolomics workflows.

Membranes, energetics, and evolution across the prokaryote-eukaryote divide

The evolution of the eukaryotic cell marked a profound moment in Earth’s history, with most of the visible biota coming to rely on intracellular membrane-bound organelles. It has been suggested that this evolutionary transition was critically dependent on the movement of ATP synthesis from the cell surface to mitochondrial membranes and the resultant boost to the energetic capacity of eukaryotic cells. However, contrary to this hypothesis, numerous lines of evidence suggest that eukaryotes are no more bioenergetically efficient than prokaryotes. Thus, although the origin of the mitochondrion was a key event in evolutionary history, there is no reason to think membrane bioenergetics played a direct, causal role in the transition from prokaryotes to eukaryotes and the subsequent explosive diversification of cellular and organismal complexity.

Over time, life on Earth has evolved into three large groups: archaea, bacteria, and eukaryotes. The most familiar forms of life – such as fungi, plants and animals – all belong to the eukaryotes. Bacteria and archaea are simpler, single-celled organisms and are collectively referred to as prokaryotes.

The hallmark feature that distinguishes eukaryotes from prokaryotes is that eukaryotic cells contain compartments called organelles that are surrounded by membranes. Each organelle supports different activities in the cell. Mitochondria, for example, are organelles that provide eukaryotes with most of their energy by producing energy-rich molecules called ATP. Prokaryotes lack mitochondria and instead produce their ATP on their cell surface membrane.

Some researchers have suggested that mitochondria might actually be one of the reasons that eukaryotic cells are typically larger than prokaryotes and more varied in their shape and structure. The thinking is that producing ATP on dedicated membranes inside the cell, rather than on the cell surface, boosted the amount of energy available to eukaryotic cells and allowed them to diversify more. However, other researchers are not convinced by this view. Moreover, some recent evidence suggested that eukaryotes are no more efficient in producing energy than prokaryotes.

Lynch and Marinov have now used computational and comparative analysis to compare the energy efficiency of different organisms including prokaryotes and eukaryotes grown under defined conditions. To do the comparison, the results were scaled based on cell volume and the total surface area deployed in energy production.

From their findings, Lynch and Marinov concluded that mitochondria did not enhance how much energy eukaryotes could produce per unit of cell volume in any substantial way. Although the origin of mitochondria was certainly a key event in evolutionary history, it is unlikely to have been responsible for the diversity and complexity of today’s life forms.

How mathematical modelling elucidates signalling in Bacillus subtilis

Appropriate stimulus perception, signal processing and transduction ensure optimal adaptation of bacteria to environmental challenges. In the Gram-positive model bacterium Bacillus subtilis signalling networks and molecular interactions therein are well-studied, making this species a suitable candidate for the application of mathematical modelling. Here, we review systems biology approaches, focusing on chemotaxis, sporulation, σ(B) -dependent general stress response and competence. Processes like chemotaxis and Z-ring assembly depend critically on the subcellular localization of proteins. Environmental response strategies, including sporulation and competence, are characterized by phenotypic heterogeneity in isogenic cultures. The examples of mathematical modelling also include investigations that have demonstrated how operon structure and signalling dynamics are intricately interwoven to establish optimal responses. Our review illustrates that these interdisciplinary approaches offer new insights into the response of B. subtilis to environmental challenges. These case studies reveal modelling as a tool to increase the understanding of complex systems, to help formulating hypotheses and to guide the design of more directed experiments that test predictions.

Toward failure analyses in systems biology

Parallels between designed and biological systems with respect to formal failure analyses have been presented. Failure analysis in designed systems depends on an identified, limited set of parameters or operation variables with high predictive value. In contrast, the biological systems pose problems in identification of operation variables and the identified variables may not be accurate predictors of failure. The difficulty in parameter identification is because of large numbers of components and the inability to envelope variables at each compartment or contour level. Contour level maps for biological systems are currently non-existent, and most failure models are based on very limited, unilateral operation variables (a mutant gene). Operation variable identification within each contour level will enhance failure analyses of complex biological systems.

Metabolic flux distributions in Corynebacterium glutamicum during growth and lysine overproduction

The two main contributions of this are the solidification of Corynebacterium glutamicum biochemistry guided by bioreaction network analysis, and the determination of bansal metabolic flux distributions during growth and lysine synthesis. Employed methodology makes use of stoichiometrically based mass balances to determine flux distributions in the C. glutamicum metabolic network. Presented are a brief description of the methodology, a through literature review of glutamic acid bacteria biochemistry, and specific results obtained through a combination of fermentation studies and analysis-directed intracellular assays. The latter include the findings of the lack of activity of glyoxylate shunt, and that phosphoenolpyruvate carboxylase (PPC) is the only anaplerotic reaction expressed in C. glutamicum cultivated on glucose minimal media. Network simplifications afforded by the above findings facilitated the determination of metabolic flux distributions under a variety of culture conditions and led to the following conclusions. Both the pentose phosphate pathway and PPC support fluxes during growth and lysine overproduction branch point does not appear to limit lysine synthesis.

Mathematical modelling of the sporulation-initiation network in Bacillus subtilis revealing the dual role of the putative quorum-sensing signal molecule PhrA

Bacillus subtilis cells may opt to forgo normal cell division and instead form spores if subjected to certain environmental stimuli, for example nutrient deficiency or extreme temperature. The resulting spores are extremely resilient and can survive for extensive periods of time, importantly under particularly harsh conditions such as those mentioned above. The sporulation process is highly time and energy consuming and essentially irreversible. The bacteria must therefore ensure that this route is only undertaken under appropriate circumstances. The gene regulation network governing sporulation initiation accordingly incorporates a variety of signals and is of significant complexity. We present a model of this network that includes four of these signals: nutrient levels, DNA damage, the products of the competence genes, and cell population size. Our results can be summarised as follows: (i) the model displays the correct phenotypic behaviour in response to these signals; (ii) a basal level of sda expression may prevent sporulation in the presence of nutrients; (iii) sporulation is more likely to occur in a large population of cells than in a small one; (iv) finally, and of most interest, PhrA can act simultaneously as a quorum-sensing signal and as a timing mechanism, delaying sporulation when the cell has damaged DNA, possibly thereby allowing the cell time to repair its DNA before forming a spore.

Artificial neural networks in bioprocess state estimation

The application of artificial neural networks to the estimation and prediction of bioprocess variables is presented in this paper. A neural network methodology is discussed, which uses environmental and physiological information available from on-line sensors, to estimate concentration of species in the bioreactor. Two case studies are presented, both based on the ethanol production by Zymomonas mobilis. An efficient optimization algorithm which reduces the number of iterations required for convergence is proposed. Results are presented for different training sets and different training methodologies. It is shown that the neural network estimator provides good on-line bioprocess state estimations.

Toward large-scale modeling of the microbial cell for computer simulation

In the post-genomic era, the large-scale, systematic, and functional analysis of all cellular components using transcriptomics, proteomics, and metabolomics, together with bioinformatics for the analysis of the massive amount of data generated by these "omics" methods are the focus of intensive research activities. As a consequence of these developments, systems biology, whose goal is to comprehend the organism as a complex system arising from interactions between its multiple elements, becomes a more tangible objective. Mathematical modeling of microorganisms and subsequent computer simulations are effective tools for systems biology, which will lead to a better understanding of the microbial cell and will have immense ramifications for biological, medical, environmental sciences, and the pharmaceutical industry. In this review, we describe various types of mathematical models (structured, unstructured, static, dynamic, etc.), of microorganisms that have been in use for a while, and others that are emerging. Several biochemical/cellular simulation platforms to manipulate such models are summarized and the E-Cell system developed in our laboratory is introduced. Finally, our strategy for building a "whole cell metabolism model", including the experimental approach, is presented.

Role of the Bacillus methanolicus citrate synthase II gene, citY, in regulating the secretion of glutamate in L-lysine-secreting mutants

The thermotolerant, restrictive methylotroph Bacillus methanolicus MGA3 (ATCC 53907) can secrete 55 g of glutamate per liter (maximum yield, 0.36 g/g) at 50 degrees C with methanol as a carbon source and a source of ammonia in fed-batch bioreactors. A homoserine dehydrogenase mutant, 13A52-8A66, secreting up to 35 g of L-lysine per liter in fed-batch fermentations had minimal 2-oxoglutarate dehydrogenase activity [7.3 nmol min(-1) (mg of protein)(-1)], threefold-increased pyruvate carboxylase activity [535 nmol min(-1) (mg of protein)(-1)], and elevated citrate synthase (CS) activity [292 nmol min(-1) (mg of protein)(-1)] and simultaneously secreted glutamate (20 to 30 g per liter) and L-lysine. The flow of carbon from oxaloacetate is split between transamination to aspartate and formation of citrate. To investigate the regulation of this branch point, the B. methanolicus gene citY encoding a CSII protein with activity at 50 degrees C was cloned from 13A52-8A66 into a CS-deficient Escherichia coli K2-1-4 strain. A citY-deficient B. methanolicus mutant, NCS-L-7, was also isolated from the parent strain of 13A52-8A66 by N-methyl-N'-nitro-N-nitrosoguanidine mutagenesis, followed by selection with monofluoroacetate disks on glutamate plates. Characterization of these strains confirmed that citY in strain 13A52-8A66 was not altered and that B. methanolicus possessed several forms of CS. Analysis of citY cloned from NCS-L-7 showed that the reduced CS activity resulted from a frameshift mutation. The level of glutamate secreted by NCS-L-7 was reduced sevenfold and the ratio of L-lysine to glutamate secreted was increased 4.5-fold compared to the wild type in fed-batch cultures with glutamate feeding. This indicates that glutamate secretion in L-lysine-overproducing mutants can be altered in favor of increased L-lysine secretion by regulating in vivo CS activity.

A mathematical model of the cell cycle of a hybridoma cell line

A one-dimensional age-based population balance model of the cell cycle is proposed for a mouse-mouse hybridoma cell line (mm321) producing immunoglobulin G antibody to paraquat. It includes the four conventional cell cycle phases, however, G1 is divided into two parts (G1a and G1b). Two additional phases have been added, a non-cycling state G1', and a pre-death phase D. The duration of these additional phases is determined by cumulative glutamine content and ammonia concentration, respectively. It is assumed that glutamine is only consumed during G1 and antibody is only produced during G1b and S, the kinetics are assumed to be zero-order. Glucose is consumed throughout the cell cycle at a rate that is dependent upon its prevalent concentration. Ammonia and lactate are produced in direct proportion to glutamine and glucose consumption, respectively. Parameters in the model have been determined from experimental data or from fitting the model to post-synchronisation data. The model thus fitted has been used to successfully predict this cell lines behaviour in conventional batch culture at different initial glutamine concentrations, and in chemostat culture at steady-state and in response to a glutamine pulse. The model predicts viable cell, glutamine, glucose and lactate kinetics well, but there are some discrepancies in the prediction for ammonia and antibody. Overall, the results obtained support the assumptions made in the model relating to the regulation of cell cycle progression. It is concluded that this approach has the potential to be exploited with other cell lines and used in a model-based control scheme.

Characterization study of the sporulation kinetics of Bacillus thuringiensis

A wild-type and an rDNA strain of Bacillus thuringiensis were cultured in a net-draft-tube modified 20-L airlift bioreactor. A comparison of the sporulation patterns suggests that the early sporulation strain has a lower final spore count. Results from off-gas analysis suggests that the CO(2) profile could be an alternative indication to spore counts for the examination of fermentation performance or even the mortality in bioassay of the cultivation product. The difference in mortality tests exhibited by the microorganism was attributed to different patterns of sporulation as well as different levels of gene control inside the cell itself. The sporulation kinetics of B. thuringiensis was simulated by a simple modified Hill equation, where the initial glucose concentration could affect the timing of the onset of sporulation. The equation matches well with the experimental sporulation data for B. thuringiensis in both wild-type and rDNA strains.

Single-cell models: promise and limitations

This article describes the development of single-cell models, their uses and accomplishments, the barriers to the greater adoption, and a perspective on challenges to the biochemical engineering community where the single-cell model approach may be used advantageously. In particular, it may become an important tool in relating genomic information to cellular regulation and dynamics.

BacSim, a simulator for individual-based modelling of bacterial colony growth

The generic, quantitative, spatially explicit, individual-based model BacSim was developed to simulate growth and behaviour of bacteria. The potential of this approach is in relating the properties of microscopic entities - cells - to the properties of macroscopic, complex systems such as biofilms. Here, the growth of a single Escherichia coli cell into a colony was studied. The object-oriented program BacSim is an extension of Gecko, an ecosystem dynamics model which uses the Swarm toolkit for multi-agent simulations. The model describes bacterial properties including substrate uptake, metabolism, maintenance, cell division and death at the individual cell level. With the aim of making the model easily applicable to various bacteria under different conditions, the model uses as few as eight readily obtainable parameters which can be randomly varied. For substrate diffusion, a two-dimensional diffusion lattice is used. For growth-rate-dependent cell size variation, a conceptual model of cell division proposed by Donachie was examined. A mechanistic version of the Donachie model led to unbalanced growth at higher growth rates, whereas including a minimum period between subsequent replication initiations ensured balanced growth only if this period was unphysiologically long. Only a descriptive version of the Donachie model predicted cell sizes correctly. For maintenance, the Herbert model (constant specific rate of biomass consumption) and for substrate uptake, the Michaelis-Menten or the Best equations were implemented. The simulator output faithfully reproduced all input parameters. Growth characteristics when maintenance and uptake rates were proportional to either cell mass or surface area are compared. The authors propose a new generic measure of growth synchrony to quantify the loss of synchrony due to random variation of cell parameters or spatial heterogeneity. Variation of the maximal uptake rate completely desynchronizes the simulated culture but variation of the volume-at-division does not. A new measure for spatial heterogeneity is introduced: the standard deviation of substrate concentrations as experienced by the cells. Spatial heterogeneity desynchronizes population growth by subdividing the population into parts synchronously growing at different rates. At a high enough spatial heterogeneity, the population appears to grow completely asynchronously.

Intracellular compounds quantification by means of flow cytometry in bacteria: application to xanthan production by Xanthomonas campestris

The use of flow cytometry (FCM) to quantitatively analyze intracellular compounds is studied. FCM is a very useful technique for individual cell studies in microbial systems, and gives access to information which cannot be obtained in any other way. Nevertheless, it provides data in arbitrary units, that is, relative data. This analytical technique could be employed for kinetic modeling of microbial systems and even for internal phenomena analysis, but for this purpose, absolute data-that is concentration of intracellular compounds-must be used. In this work, relative flow cytometry data are transformed into absolute data by means of calibrations employing the same fluorochromes with another technique: spectrofluorymetry. Calibrations of DNA, RNA, and protein intracellular concentrations are presented for the bacteria, Xanthomonas campestris. Other analytical methods, based on biochemical determinations, were also employed to quantify intracellular compounds, but the results obtained are very poor compared with those achieved by means of spectrofluorymetry (SFM). Calibration equations and data obtained by both techniques are given. Evolutions of protein and nucleic acids during Xanthomonas campestris growth and xanthan gum production are shown.

Respiration of Pseudomonas fluorescens as a function of intracellular substrate concentration

A kinetic method to measure the intracellular concentration of respiratory substrates in short-term starvation-enrichment experiments is proposed. Samples of bacterial suspension from steady-state chemostat cultures were subjected to 25 min starvation, followed by pulse addition of [14C]glucose. Residual substrate utilization rates and respiration rates (uptake of dissolved O2) before and after amendment were recorded. Increases in pool sizes (δL) during transients were calculated on the basis of C balance. The dependence of respiration rate qresp on δL was found to obey modified Michaelis-Menten kinetics: q resp = Q resp (LC+δL)/(K L+LC+δL) [Q resp is maximal respiration rate (29.1 mmol O2 h-1per g biomass C), K L = 12.14 mg C per g biomass C], where LC is the absolute value of the pool size before amendment. Direct chemical determination of LC in cold TCA extracts revealed two fractions. The first fraction was mobile and showed a close correlation with both respiration and L. The second, ‘stable’, fraction did not correlate with respiration dynamics and was interpreted as material formed artifactually by acid degradation of polymeric cell components.

Modelling and analysis of metabolic pathways

Modelling and analysis of metabolic pathways has received an increasing amount of attention over the past few years. Progress has been made in many aspects such as the identification of rate-controlling steps, applications of optimization principles, and stoichiometric analyses. In addition, the scope of modelling has also expanded. These efforts have led to an improved understanding of metabolic pathways and have facilitated their manipulation.

Transport regulation of recombinant gene expression in E. coli and B. subtilis

Expression kinetics of the lactose (lac) operon in Escherichia coli are reviewed for both wild-type and recombinant cell cultures under chemostatic conditions. A unified model which involves regulation of active inducer (lactose) transport, promoter-operator regulated expression of the lac operon, glucose-mediated inducer exclusion, and catabolite repression is summarized and supporting data is shown to verify its accuracy. The synthesis of alpha-amylase with a recombinant form of Bacillus subtilis is also reviewed to point out generic features in transport regulation, the lac operon model providing a point of departure. While there are many similarities in the influence of transport on both regulating models, there are also important differences. In a chemostat system, the synthesis of alpha-amylase is nongrowth associated, while beta-galactosidase is a growth-associated enzyme. Nevertheless, transport regulation is an important feature in both instances.

A structured model for vegetative growth and sporulation in Bacillus thuringiensis

A mathematical model has been developed for the delta-endotoxin producing Bacillus thuringiensis. The structure of the model involves the processes taking place during vegetative growth, those leading to the initiation of sporulation under conditions of carbon and/or nitrogen limitation, and the sporulation events. The key features in the model are the pools of compounds, such as PRPP, IMP, ADP/ATP, GDP/GTP, pyrimidine nucleotides, NAD/NADH2, amino acids, nucleic acids, cell wall, and vegetative and sporulation proteins. These, along with sigma-factors that control the nature of RNA-polymerase during the different phases, effectively stimulate the vegetative growth and sporulation. The initiation of sporulation is controlled by the intracellular concentration of GTP. Results of simulation of vegetative growth, initiation of sporulation, spore protein formation, and production of delta-endotoxin under C- or N-limitation are presented.