Thomas Millat

A systems biology approach to investigate the effect of pH-induced gene regulation on solvent production by Clostridium acetobutylicum in continuous culture.

BackgroundClostridium acetobutylicum is an anaerobic bacterium which is known for its solvent-producing capabilities, namely regarding the bulk chemicals acetone and butanol, the latter being a highly efficient biofuel. For butanol production by C. acetobutylicum to be optimized and exploited on an industrial scale, the effect of pH-induced gene regulation on solvent production by C. acetobutylicum in continuous culture must be understood as fully as possible.ResultsWe present an ordinary differential equation model combining the metabolic network governing solvent production with regulation at the genetic level of the enzymes required for this process. Parameterizing the model with experimental data from continuous culture, we demonstrate the influence of pH upon fermentation products: at high pH (pH 5.7) acids are the dominant product while at low pH (pH 4.5) this switches to solvents. Through steady-state analyses of the model we focus our investigations on how alteration in gene expression of C. acetobutylicum could be exploited to increase butanol yield in a continuous culture fermentation.ConclusionsIncorporating gene regulation into the model of solvent production by C. acetobutylicum enables an accurate representation of the pH-induced switch to solvent production to be obtained and theoretical investigations of possible synthetic-biology approaches to be pursued. Steady-state analyses suggest that, to increase butanol yield, alterations in the expression of single solvent-associated genes are insufficient; a more complex approach targeting two or more genes is required.

A shift in the dominant phenotype governs the pH-induced metabolic switch of Clostridium acetobutylicumin phosphate-limited continuous cultures

In response to changing extracellular pH levels, phosphate-limited continuous cultures of Clostridium acetobutylicum reversibly switches its metabolism from the dominant formation of acids to the prevalent production of solvents. Previous experimental and theoretical studies have revealed that this pH-induced metabolic switch involves a rearrangement of the intracellular transcriptomic, proteomic and metabolomic composition of the clostridial cells. However, the influence of the population dynamics on the observations reported has so far been neglected. Here, we present a method for linking the pH shift, clostridial growth and the acetone–butanol–ethanol fermentation metabolic network systematically into a model which combines the dynamics of the external pH and optical density with a metabolic model. Furthermore, the recently found antagonistic expression pattern of the aldehyde/alcohol dehydrogenases AdhE1/2 and pH-dependent enzyme activities have been included into this combined model. Our model predictions reveal that the pH-induced metabolic shift under these experimental conditions is governed by a phenotypic switch of predominantly acidogenic subpopulation towards a predominantly solventogenic subpopulation. This model-driven explanation of the pH-induced shift from acidogenesis to solventogenesis by population dynamics casts an entirely new light on the clostridial response to changing pH levels. Moreover, the results presented here underline that pH-dependent growth and pH-dependent specific enzymatic activity play a crucial role in this adaptation. In particular, the behaviour of AdhE1 and AdhE2 seems to be the key factor for the product formation of the two phenotypes, their pH-dependent growth, and thus, the pH-induced metabolic switch in C. acetobutylicum.

Inverse bremsstrahlung of hot, weakly coupled plasmas

The free–free absorption coefficient for radiation in hot, weakly coupled plasmas is determined from a systematic approach to the dynamical conductivity. Based on a generalized linear-response theory, it is expressed in terms of determinants of equilibrium correlation functions permitting a perturbative treatment. Within a Gould–DeWitt-type approach, dynamical screening is accounted for by a partial summation of loop diagrams, while strong collisions are treated by a ladder approximation. Known expressions for the absorption coefficient are reproduced when considering certain limits. A comparison is made with simulation results.

Integrative modelling of pH-dependent enzyme activity and transcriptomic regulation of the acetone–butanol–ethanol fermentation of Clostridium acetobutylicum in continuous culture

In a continuous culture under phosphate limitation the metabolism of Clostridium acetobutylicum depends on the external pH level. By comparing seven steady‐state conditions between pH 5.7 and pH 4.5 we show that the switch from acidogenesis to solventogenesis occurs between pH 5.3 and pH 5.0 with an intermediate state at pH 5.1. Here, an integrative study is presented investigating how a changing external pH level affects the clostridial acetone–butanol–ethanol (ABE) fermentation pathway. This is of particular interest as the biotechnological production of n‐butanol as biofuel has recently returned into the focus of industrial applications. One prerequisite is the furthering of the knowledge of the factors determining the solvent production and their integrative regulations. We have mathematically analysed the influence of pH‐dependent specific enzyme activities of branch points of the metabolism on the product formation. This kinetic regulation was compared with transcriptomic regulation regarding gene transcription and the proteomic profile. Furthermore, both regulatory mechanisms were combined yielding a detailed projection of their individual and joint effects on the product formation. The resulting model represents an important platform for future developments of industrial butanol production based on C. acetobutylicum.

Coenzyme A-transferase-independent butyrate re-assimilation in Clostridium acetobutylicum—evidence from a mathematical model

The hetero-dimeric CoA-transferase CtfA/B is believed to be crucial for the metabolic transition from acidogenesis to solventogenesis in Clostridium acetobutylicum as part of the industrial-relevant acetone-butanol-ethanol (ABE) fermentation. Here, the enzyme is assumed to mediate re-assimilation of acetate and butyrate during a pH-induced metabolic shift and to faciliate the first step of acetone formation from acetoacetyl-CoA. However, recent investigations using phosphate-limited continuous cultures have questioned this common dogma. To address the emerging experimental discrepancies, we investigated the mutant strain Cac-ctfA398s::CT using chemostat cultures. As a consequence of this mutation, the cells are unable to express functional ctfA and are thus lacking CoA-transferase activity. A mathematical model of the pH-induced metabolic shift, which was recently developed for the wild type, is used to analyse the observed behaviour of the mutant strain with a focus on re-assimilation activities for the two produced acids. Our theoretical analysis reveals that the ctfA mutant still re-assimilates butyrate, but not acetate. Based upon this finding, we conclude that C. acetobutylicum possesses a CoA-tranferase-independent butyrate uptake mechanism that is activated by decreasing pH levels. Furthermore, we observe that butanol formation is not inhibited under our experimental conditions, as suggested by previous batch culture experiments. In concordance with recent batch experiments, acetone formation is abolished in chemostat cultures using the ctfa mutant.

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, σB‐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.

Mathematical modelling of clostridial acetone-butanol-ethanol fermentation

Clostridial acetone-butanol-ethanol (ABE) fermentation features a remarkable shift in the cellular metabolic activity from acid formation, acidogenesis, to the production of industrial-relevant solvents, solventogensis. In recent decades, mathematical models have been employed to elucidate the complex interlinked regulation and conditions that determine these two distinct metabolic states and govern the transition between them. In this review, we discuss these models with a focus on the mechanisms controlling intra- and extracellular changes between acidogenesis and solventogenesis. In particular, we critically evaluate underlying model assumptions and predictions in the light of current experimental knowledge. Towards this end, we briefly introduce key ideas and assumptions applied in the discussed modelling approaches, but waive a comprehensive mathematical presentation. We distinguish between structural and dynamical models, which will be discussed in their chronological order to illustrate how new biological information facilitates the ‘evolution’ of mathematical models. Mathematical models and their analysis have significantly contributed to our knowledge of ABE fermentation and the underlying regulatory network which spans all levels of biological organization. However, the ties between the different levels of cellular regulation are not well understood. Furthermore, contradictory experimental and theoretical results challenge our current notion of ABE metabolic network structure. Thus, clostridial ABE fermentation still poses theoretical as well as experimental challenges which are best approached in close collaboration between modellers and experimentalists.

Simulations of stressosome activation emphasize allosteric interactions between RsbR and RsbT

BackgroundThe stressosome is a bacterial signalling complex that responds to environmental changes by initiating a protein partner switching cascade, which leads to the release of the alternative sigma factor, σB. Stress perception increases the phosphorylation of the stressosome sensor protein, RsbR, and the scaffold protein, RsbS, by the protein kinase, RsbT. Subsequent dissociation of RsbT from the stressosome activates the σB cascade. However, the sequence of physical events that occur in the stressosome during signal transduction is insufficiently understood.ResultsHere, we use computational modelling to correlate the structure of the stressosome with the efficiency of the phosphorylation reactions that occur upon activation by stress. In our model, the phosphorylation of any stressosome protein is dependent upon its nearest neighbours and their phosphorylation status. We compare different hypotheses about stressosome activation and find that only the model representing the allosteric activation of the kinase RsbT, by phosphorylated RsbR, qualitatively reproduces the experimental data.ConclusionsOur simulations and the associated analysis of published data support the following hypotheses: (i) a simple Boolean model is capable of reproducing stressosome dynamics, (ii) different stressors induce identical stressosome activation patterns, and we also confirm that (i) phosphorylated RsbR activates RsbT, and (ii) the main purpose of RsbX is to dephosphorylate RsbS-P.

Proteolysis of beta-galactosidase following SigmaB activation in Bacillus subtilis

In Bacillus subtilis the σ(B) mediated general stress response provides protection against various environmental and energy related stress conditions. To better understand the general stress response, we need to explore the mechanism by which the components interact. Here, we performed experiments in B. subtilis wild type and mutant strains to test and validate a mathematical model of the dynamics of σ(B) activity. In the mutant strain BSA115, σ(B) transcription is inducible by the addition of IPTG and negative control of σ(B) activity by the anti-sigma factor RsbW is absent. In contrast to our expectations of a continuous β-galactosidase activity from a ctc::lacZ fusion, we observed a transient activity in the mutant. To explain this experimental finding, we constructed mathematical models reflecting different hypotheses regarding the regulation of σ(B) and β-galactosidase dynamics. Only the model assuming instability of either ctc::lacZ mRNA or β-galactosidase protein is able to reproduce the experiments in silico. Subsequent Northern blot experiments revealed stable high-level ctc::lacZ mRNA concentrations after the induction of the σ(B) response. Therefore, we conclude that protein instability following σ(B) activation is the most likely explanation for the experimental observations. Our results thus support the idea that B. subtilis increases the cytoplasmic proteolytic degradation to adapt the proteome in face of environmental challenges following activation of the general stress response. The findings also have practical implications for the analysis of stress response dynamics using lacZ reporter gene fusions, a frequently used strategy for the σ(B) response.

How quantitative measures unravel design principles in multi-stage phosphorylation cascades

We investigate design principles of linear multi-stage phosphorylation cascades by using quantitative measures for signaling time, signal duration and signal amplitude. We compare alternative pathway structures by varying the number of phosphorylations and the length of the cascade. We show that a model for a weakly activated pathway does not reflect the biological context well, unless it is restricted to certain parameter combinations. Focusing therefore on a more general model, we compare alternative structures with respect to a multivariate optimization criterion. We test the hypothesis that the structure of a linear multi-stage phosphorylation cascade is the result of an optimization process aiming for a fast response, defined by the minimum of the product of signaling time and signal duration. It is then shown that certain pathway structures minimize this criterion. Several popular models of MAPK cascades form the basis of our study. These models represent different levels of approximation, which we compare and discuss with respect to the quantitative measures.