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Abstract In their natural habitats, microbes rarely exist in isolation; instead, they thrive in consortia, where various interactions occur. In this study, a defined synthetic co-culture of the cyanobacterium S. elongatus cscB, which supplies sucrose to the heterotrophic P. putida cscRABY, is investigated to identify potential interactions. Initial experiments reveal a remarkable growth-promoting effect of the heterotrophic partner on the cyanobacterium, resulting in an up to 80% increase in the growth rate and enhanced photosynthetic capacity. Vice versa, the presence of the cyanobacterium has a neutral effect on P. putida cscRABY, highlighting the resilience of pseudomonads against stress and their potential as co-culture partners. Next, a suitable reference process reinforcing the growth-promoting effect is established in a parallel photobioreactor system, which sets the basis for the analysis of the co-culture at the transcriptome, proteome, and metabolome levels. In addition to several moderate changes, including alterations in the metabolism and stress response in both microbes, this comprehensive multi-OMICs approach strongly hints towards the exchange of further molecules beyond the unidirectional feeding with sucrose. Taken together, these findings provide valuable insights into the complex dynamics between both co-culture partners, indicating multi-level interactions, which can be employed for further streamlining of the co-cultivation system.

Abstract Rationally designed synthetic microbial consortia carry a vast potential for biotechnological applications. The application of such a consortium in a bioprocess, however, requires tight and individual controllability of the involved microbes. Here, we present the streamlining of a co‐cultivation process consisting of Synechococcus elongatus cscB and Pseudomonas putida for the production of polyhydroxyalkanoates (PHA) from light and CO2. First, the process was improved by employing P. putida cscRABY, a strain with a higher metabolic activity towards sucrose. Next, the individual controllability of the co‐culture partners was addressed by providing different nitrogen sources, each exclusively available for one strain. By this, the growth rate of the co‐culture partners could be regulated individually, and defined conditions could be set. The molC/molN ratio, a key value for PHA accumulation, was estimated from the experimental data, and the necessary feeding rates to obtain a specific ratio could be predicted. This information was then implemented in the co‐cultivation process, following the concept of a DBTL‐cycle. In total, the streamlining of the process resulted in an increased maximal PHA titer of 393 mg/L and a PHA production rate of 42.1 mg/(L•day).

Abstract Biotechnological production processes are sustainable approaches for the production of biobased components such as amino acids for food and feed industry. Scale‐up from ideal lab‐scale bioreactors to large‐scale processes is often accompanied by loss in productivity. This may be related to population heterogeneities of cells originating from isogenic cultures that arise due to dynamic non‐ideal conditions in the bioreactor. To better understand this phenomenon, deeper insights into single‐cell physiologies in bioprocesses are mandatory before scale‐up. Here, a triple reporter strain (3RP) was developed by chromosomally integrating the fluorescent proteins mEmerald, CyOFP1, and mTagBFP2 into the L‐phenylalanine producing Escherichia coli strain FUS4 (pF81kan) to allow monitoring of growth, oxygen availability, and general stress response of the single cells. Functionality of the 3RP was confirmed in well‐mixed lab‐scale fed‐batch processes with glycerol as carbon source in comparison to the strain without fluorescent proteins, leading to no difference in process performance. Fluorescence levels could successfully reflect the course of related process state variables, revealed population heterogeneities during the transition between different process phases and potentially subpopulations that exhibit superior process performance. Furthermore, indications were found for noise in gene expression as regulation strategy against environmental perturbation.

The application of naturally-derived biomolecules in everyday products, replacing conventional synthetic manufacturing, is an ever-increasing market. An example of this is the compatible solute ectoine, which is contained in a plethora of treatment formulations for medicinal products and cosmetics. As of today, ectoine is produced in a scale of tons each year by the natural producer Halomonas elongata. In this work, we explore two complementary approaches to obtain genetically improved producer strains for ectoine production. We explore the effect of increased precursor supply (oxaloacetate) on ectoine production, as well as an implementation of increased ectoine demand through the overexpression of a transporter. Both approaches were implemented on an already genetically modified ectoine-excreting strain H. elongata KB2.13 (ΔteaABC ΔdoeA) and both led to new strains with higher ectoine excretion. The supply driven approach led to a 45% increase in ectoine titers in two different strains. This increase was attributed to the removal of phosphoenolpyruvate carboxykinase (PEPCK), which allowed the conversion of 17.9% of the glucose substrate to ectoine. For the demand driven approach, we investigated the potential of the TeaBC transmembrane proteins from the ectoine-specific Tripartite ATP-Independent Periplasmic (TRAP) transporter as export channels to improve ectoine excretion. In the absence of the substrate-binding protein TeaA, an overexpression of both subunits TeaBC facilitated a three-fold increased excretion rate of ectoine. Individually, the large subunit TeaC showed an approximately five times higher extracellular ectoine concentration per dry weight compared to TeaBC shortly after its expression was induced. However, the detrimental effect on growth and ectoine titer at the end of the process hints toward a negative impact of TeaC overexpression on membrane integrity and possibly leads to cell lysis. By using either strategy, the ectoine synthesis and excretion in H. elongata could be boosted drastically. The inherent complementary nature of these approaches point at a coordinated implementation of both as a promising strategy for future projects in Metabolic Engineering. Moreover, a wide variation of intracelllular ectoine levels was observed between the strains, which points at a major disruption of mechanisms responsible for ectoine regulation in strain KB2.13.

Mathematical modeling is a promising tool for better understanding of cellular processes. In recent years, the development of coarse-grained models has gained attraction since these simple models are able to capture and describe a broad range of growth conditions. Coarse-grained models often comprise only two cellular components, a low molecular component as representative for central metabolism and energy generation and a macromolecular component, representing the entire proteome. A framework is presented that presents a strict mass conservative model for bacterial growth during a biotechnological production process. After providing interesting properties for the steady-state solution, applications are presented 1) for a production process of an amino acid and 2) production of a metabolite from central metabolism.

The halophilic γ-proteobacterium Halomonas elongata DSM 2581T thrives at salt concentrations well above 10 % NaCl (1.7 M NaCl). A well-known osmoregulatory mechanism is the accumulation of the compatible solute ectoine within the cell in response to osmotic stress. While ectoine accumulation is central to osmoregulation and promotes resistance to high salinity in halophilic bacteria, ectoine has this effect only to a much lesser extent in non-halophiles. We carried out transcriptome analysis of H. elongata grown on two different carbon sources (acetate or glucose), and low (0.17 M NaCl), medium (1 M), and high salinity (2 M) to identify additional mechanisms for adaptation to high saline environments. To avoid a methodological bias, the transcripts were evaluated by applying two methods, DESeq2 and Transcripts Per Million (TPM). The differentially transcribed genes in response to the available carbon sources and salt stress were then compared to the transcriptome profile of Chromohalobacter salexigens, a closely related moderate halophilic bacterium. Transcriptome profiling supports the notion that glucose is degraded via the cytoplasmic Entner-Doudoroff pathway, whereas the Embden-Meyerhoff-Parnas pathway is employed for gluconeogenesis. The machinery of oxidative phosphorylation in H. elongata and C. salexigens differs greatly from that of non-halophilic organisms, and electron flow can occur from quinone to oxygen along four alternative routes. Two of these pathways via cytochrome bo' and cytochrome bd quinol oxidases seem to be upregulated in salt stressed cells. Among the most highly regulated genes in H. elongata and C. salexigens are those encoding chemotaxis and motility proteins, with genes for chemotaxis and flagellar assembly severely downregulated at low salt concentrations. We also compared transcripts at low and high-salt stress (low growth rate) with transcripts at optimal salt concentration and found that the majority of regulated genes were down-regulated in stressed cells, including many genes involved in carbohydrate metabolism, while ribosome synthesis was up-regulated, which is in contrast to what is known from non-halophiles at slow growth. Finally, comparing the acidity of the cytoplasmic proteomes of non-halophiles, extreme halophiles and moderate halophiles suggests adaptation to an increased cytoplasmic ion concentration of H. elongata. Taken together, these results lead us to propose a model for salt tolerance in H. elongata where ion accumulation plays a greater role in salt tolerance than previously assumed.

Order reduction methods are important tools for systems engineering and can be used, for example, for parameter estimation of kinetic models for systems biology applications. In particular, the Proper Orthogonal Decomposition (POD) method produces a reduced-order model of a system that is used for solving inverse problems (parameter estimation). POD is an intrusive model order reduction method that is aimed to obtain a lower-dimensional system for a high-dimensional system while preserving the main features of the original system. We use a singular value decomposition (SVD) to compute a reduced basis as it is usually numerically more robust to compute the singular values of the snapshot matrix instead of the eigenvalues of the corresponding correlation matrix. The reduced basis functions are then used to construct a data-fitting function that fits a known experimental data set of system substance concentrations. The method is applied to calibrate a kinetic model of carbon catabolite repression (CCR) in Escherichia coli, where the regulatory mechanisms on the molecular side are well understood and experimental data for a number of state variables is available. In particular, we show that the method can be used to estimate the uptake rate constants and other kinetic parameters of the CCR model.

Summary Using agricultural wastes as a substrate for biotechnological processes is of great interest in industrial biotechnology. A prerequisite for using these wastes is the ability of the industrially relevant microorganisms to metabolize the sugars present therein. Therefore, many metabolic engineering approaches are directed towards widening the substrate spectrum of the workhorses of industrial biotechnology like Escherichia coli, yeast or Pseudomonas putida. For instance, neither xylose or arabinose from cellulosic residues, nor sucrose, the main sugar in waste molasses, can be metabolized by most E. coli and P. putida wild types. We evaluated a new, so far uncharacterized gene cluster for sucrose metabolism from Pseudomonas protegens Pf‐5 and showed that it enables P. putida to grow on sucrose as the sole carbon and energy source. Even when integrated into the genome of P. putida, the resulting strain grew on sucrose at rates similar to the rate of the wild type on glucose – making it the fastest growing, plasmid‐free P. putida strain known so far using sucrose as substrate. Next, we elucidated the role of the porin, an orthologue of the sucrose porin ScrY, in the gene cluster and found that in P. putida, a porin is needed for sucrose transport across the outer membrane. Consequently, native porins were not sufficient to allow unlimited growth on sucrose. Therefore, we concluded that the outer membrane can be a considerable barrier for substrate transport, depending on strain, genotype and culture conditions, all of which should be taken into account in metabolic engineering approaches. We additionally showed the potential of the engineered P. putida strains by growing them on molasses with efficiencies twice as high as obtained with the wild‐type P. putida. This can be seen as a further step towards the production of low‐value chemicals and biofuels with P. putida from alternative and more affordable substrates in the future.

In the recent years, engineering new-to-nature CO2- and C1-fixing metabolic pathways made a leap forward. New, artificial pathways promise higher yields and activity than natural ones like the Calvin-Benson-Bassham (CBB) cycle. The question remains how to best predict their in vivo performance and what actually makes one pathway “better” than another. In this context, we explore aerobic carbon fixation pathways by a computational approach and compare them based on their specific activity and yield on methanol, formate, and CO2/H2 considering the kinetics and thermodynamics of the reactions. Besides pathways found in nature or implemented in the laboratory, this included two completely new cycles with favorable features: the reductive citramalyl-CoA cycle and the 2-hydroxyglutarate-reverse tricarboxylic acid cycle. A comprehensive kinetic data set was collected for all enzymes of all pathways, and missing kinetic data were sampled with the Parameter Balancing algorithm. Kinetic and thermodynamic data were fed to the Enzyme Cost Minimization algorithm to check for respective inconsistencies and calculate pathway-specific activities. The specific activities of the reductive glycine pathway, the CETCH cycle, and the new reductive citramalyl-CoA cycle were predicted to match the best natural cycles with superior product-substrate yield. However, the CBB cycle performed better in terms of activity compared to the alternative pathways than previously thought. We make an argument that stoichiometric yield is likely not the most important design criterion of the CBB cycle. Still, alternative carbon fixation pathways were paretooptimal for specific activity and product-substrate yield in simulations with C1 substrates and CO2/H2 and therefore hold great potential for future applications in Industrial Biotechnology and Synthetic Biology.

Salt tolerance in the γ-proteobacterium Halomonas elongata is linked to its ability to produce the compatible solute ectoine. The metabolism of ectoine production is of great interest since it can shed light on the biochemical basis of halotolerance as well as pave the way for the improvement of the biotechnological production of such compatible solute. Ectoine belongs to the biosynthetic family of aspartate-derived amino-acids. Aspartate is formed from oxaloacetate, thereby connecting ectoine production to the anaplerotic reactions that refill carbon into the tricarboxylic acid cycle (TCA cycle). This places a high demand on these reactions and creates the need to regulate them not only in response to growth but also in response to extracellular salt concentration. In this work, we combine modeling and experiments to analyze how these different needs shape the anaplerotic reactions in H. elongata. First, the stoichiometric and thermodynamic factors that condition the flux distributions are analyzed, then the optimal patterns of operation for oxaloacetate production are calculated. Finally, the phenotype of two deletion mutants lacking potentially relevant anaplerotic enzymes: phosphoenolpyruvate carboxylase (Ppc) and oxaloacetate decarboxylase (Oad) are experimentally characterized. The results show that the anaplerotic reactions in H. elongata are indeed subject to evolutionary pressures that differ from those faced by other gram-negative bacteria. Ectoine producing halophiles must meet a higher metabolic demand for oxaloacetate and the reliance of many marine bacteria on the Entner-Doudoroff pathway compromises the anaplerotic efficiency of Ppc, which is usually one of the main enzymes fulfilling this role. The anaplerotic flux in H. elongata is contributed not only by Ppc but also by Oad, an enzyme that has not yet been shown to play this role in vivo. Ppc is necessary for H. elongata to grow normally at low salt concentrations but it is not required to achieve near maximal growth rates as long as there is a steep sodium gradient. On the other hand, the lack of Oad presents serious difficulties to grow at high salt concentrations. This points to a shared role of these two enzymes in guaranteeing the supply of oxaloacetate for biosynthetic reactions.

One of the major challenges for the present and future generations is to find suitable substitutes for the fossil resources we rely on today. In this context, cyanobacterial carbohydrates have been discussed as an emerging renewable feedstock in industrial biotechnology for the production of fuels and chemicals. Based on this, we recently presented a synthetic bacterial co-culture for the production of medium-chain-length polyhydroxyalkanoates (PHAs) from CO2. This co-cultivation system is composed of two partner strains: Synechococcus elongatus cscB which fixes CO2, converts it to sucrose and exports it into the culture supernatant, and a Pseudomonas putida strain that metabolizes this sugar and accumulates PHAs in the cytoplasm. However, these biopolymers are preferably accumulated under conditions of nitrogen limitation, a situation difficult to achieve in a co-culture as the other partner, at best, should not perceive any limitation. In this article, we will present an approach to overcome this dilemma by uncoupling the PHA production from the presence of nitrate in the medium. This is achieved by the construction of a P. putida strain that is no longer able to grow with nitrate as nitrogen source -is thus nitrate blind, and able to grow with sucrose as carbon source. The deletion of the nasT gene encoding the response regulator of the NasS/NasT two-component system resulted in such a strain that has lost the ability use nitrate, but growth with ammonium was not affected. Subsequently, the nasT deletion was implemented in P. putida cscRABY, an efficient sucrose consuming strain. This genetic engineering approach introduced an artificial unilateral nitrogen limitation in the co-cultivation process, and the amount of PHA produced from light and CO2 was 8.8 fold increased to 14.8% of its CDW compared to the nitrate consuming reference strain. This nitrate blind strain, P. putidaΔnasT attTn7:cscRABY, is not only a valuable partner in the co-cultivation but additionally enables the use of other nitrate containing substrates for medium-chain-length PHA production, like for example waste-water.

Abstract Background One of the major challenges for the present and future generations is to find suitable substitutes for the fossil resources we rely on today. Cyanobacterial carbohydrates have been discussed as an emerging renewable feedstock in industrial biotechnology for the production of fuels and chemicals, showing promising production rates when compared to crop-based feedstock. However, intrinsic capacities of cyanobacteria to produce biotechnological compounds are limited and yields are low. Results Here, we present an approach to circumvent these problems by employing a synthetic bacterial co-culture for the carbon-neutral production of polyhydroxyalkanoates (PHAs) from CO2. The co-culture consists of two bio-modules: Bio-module I, in which the cyanobacterial strain Synechococcus elongatus cscB fixes CO2, converts it to sucrose, and exports it into the culture supernatant; and bio-module II, where this sugar serves as C-source for Pseudomonas putida cscAB and is converted to PHAs that are accumulated in the cytoplasm. By applying a nitrogen-limited process, we achieved a maximal PHA production rate of 23.8 mg/(L day) and a maximal titer of 156 mg/L. We will discuss the present shortcomings of the process and show the potential for future improvement. Conclusions These results demonstrate the feasibility of mixed cultures of S. elongatus cscB and P. putida cscAB for PHA production, making room for the cornucopia of possible products that are described for P. putida. The construction of more efficient sucrose-utilizing P. putida phenotypes and the optimization of process conditions will increase yields and productivities and eventually close the gap in the contemporary process. In the long term, the co-culture may serve as a platform process, in which P. putida is used as a chassis for the implementation of synthetic metabolic pathways for biotechnological production of value-added products.

Systems biology applies concepts from engineering in order to understand biological networks. If such an understanding was complete, biologists would be able to design ad hoc biochemical components tailored for different purposes, which is the goal of synthetic biology. Needless to say that we are far away from creating biological subsystems as intricate and precise as those found in nature, but mathematical models and high throughput techniques have brought us a long way in this direction. One of the difficulties that still needs to be overcome is finding the right values for model parameters and dealing with uncertainty, which is proving to be an extremely difficult task. In this work, we take advantage of ensemble modeling techniques, where a large number of models with different parameter values are formulated and then tested according to some performance criteria. By finding features shared by successful models, the role of different components and the synergies between them can be better understood. We will address some of the difficulties often faced by ensemble modeling approaches, such as the need to sample a space whose size grows exponentially with the number of parameters, and establishing useful selection criteria. Some methods will be shown to reduce the predictions from many models into a set of understandable "design principles" that can guide us to improve or manufacture a biochemical network. Our proposed framework formulates models within standard formalisms in order to integrate information from different sources and minimize the dimension of the parameter space. Additionally, the mathematical properties of the formalism enable a partition of the parameter space into independent subspaces. Each of these subspaces can be paired with a set of criteria that depend exclusively on it, thus allowing a separate sampling/screening in spaces of lower dimension. By applying tests in a strict order where computationally cheaper tests are applied first to each subspace and applying computationally expensive tests to the remaining subset thereafter, the use of resources is optimized and a larger number of models can be examined. This can be compared to a complex database query where the order of the requests can make a huge difference in the processing time. The method will be illustrated by analyzing a classical model of a metabolic pathway with end-product inhibition. Even for such a simple model, the method provides novel insight.

Since biotechnological research becomes more and more important for industrial applications, there is an increasing need for scalable and controllable laboratory procedures. A widely used approach in biotechnological research to improve the performance of a process is to vary the growth rates in order to find the right balance between growth and the production. This can be achieved by the application of a suitable feeding strategy. During this initial bioprocess development, it is beneficial to have at hand cheap and easy setups that work in parallel (e.g. in shaking flasks). Unfortunately, there is a gap between these easy setups and defined and controllable processes, which are necessary for up-scaling to an industrial relevant volume. One prerequisite to test and evaluate different process strategies apart from batch-mode is the availability of pump systems that allow for defined feeding profiles in shaking flasks. To our knowledge, there is no suitable dosing device on the market which fulfils the requirements of being cheap, precise, programmable, and parallelizable. Commercially available dosing units are either already integrated in bioreactors and therefore inflexible, or not programmable, or expensive, or a combination of those. Here, we present a LEGO-MINDSTORMS-based syringe pump, which has the potential of being widely used in daily laboratory routine due to its low price, programmability, and parallelisability. The acquisition costs do not exceed 350 € for up to four dosing units, that are independently controllable with one EV3 block. The system covers flow rates ranging from 0.7 μL min-1 up to 210 mL min-1 with a reliable flux. One dosing unit can convey at maximum a volume of 20 mL (using all 4 units even up to 80 mL in total) over the whole process time. The design of the dosing unit enables the user to perform experiments with up to four different growth rates in parallel (each measured in triplicates) per EV3-block used. We estimate, that the LEGO-MINDSTORMS-based dosing unit with 12 syringes in parallel is reducing the costs up to 50-fold compared to a trivial version of a commercial pump system (~1500 €) which fits the same requirements. Using the pump, we set the growth rates of a E. coli HMS174/DE3 culture to values between 0.1 and 0.4 h-1 with a standard deviation of at best 0.35% and an average discrepancy of 13.2%. Additionally, we determined the energy demand of a culture for the maintenance of the pTRA-51hd plasmid by quantifying the changes in biomass yield with different growth rates set. Around 25% of total substrate taken up is used for plasmid maintenance. To present possible applications and show the flexibility of the system, we applied a constant feed to perform microencapsulation of Pseudomonas putida and an individual dosing profile for the purification of a his-tagged eGFP via IMAC. This smart and versatile dosing unit, which is ready-to-use without any prior knowledge in electronics and control, is affordable for everyone and due to its flexibility and broad application range a valuable addition to the laboratory routine.

During the last 10 years, systems biology has matured from a fuzzy concept combining omics, mathematical modeling and computers into a scientific field on its own right. In spite of its incredible potential, the multilevel complexity of its objects of study makes it very difficult to establish a reliable connection between data and models. The great number of degrees of freedom often results in situations, where many different models can explain/fit all available datasets. This has resulted in a shift of paradigm from the initially dominant, maybe naive, idea of inferring the system out of a number of datasets to the application of different techniques that reduce the degrees of freedom before any data set is analyzed. There is a wide variety of techniques available, each of them can contribute a piece of the puzzle and include different kinds of experimental information. But the challenge that remains is their meaningful integration. Here we show some theoretical results that enable some of the main modeling approaches to be applied sequentially in a complementary manner, and how this workflow can benefit from evolutionary reasoning to keep the complexity of the problem in check. As a proof of concept, we show how the synergies between these modeling techniques can provide insight into some well studied problems: Ammonia assimilation in bacteria and an unbranched linear pathway with end-product inhibition.

Random fluctuations in the amount of cellular components like mRNA and protein molecules are inevitable due to the stochastic and discrete nature of biochemical reactions. If large enough, this so-called "cellular noise" can lead to random transitions between the expression states of a multistable genetic circuit. That way, heterogeneity within isogenic populations is created. Our aim is to understand which dynamical features of a simple autoregulatory system determine its intrinsic noise level, and how they can be modified in order to regulate state-transitions. To that end, novel mathematical methods for the state-dependent characterization and prediction of noise in multistable systems are developed. First, we introduce the hybrid LNA, a modified version of the Linear Noise Approximation. It yields good predictions on variances of mRNA and protein fluctuations, even for reaction systems comprising low-copy-number components (e.g. mRNA) and highly nonlinear reaction rates. Furthermore, the temporal structure of fluctuations and the skewness of the protein distribution are characterized via state-dependent protein burst sizes and burst frequencies. Based on this mathematical framework, we develop graphical methods which support the intuitive design of regulatory circuits with a desired noise pattern. The methods are then used to predict how overall noise in the system can be adapted, and how state-specific noise modifications are possible that allow, e.g., the generation of unidirectional transitions. Our considerations are validated by stochastic simulations. This way, a design of genetic circuits is possible that takes population heterogeneity into account and is valuable in applications of synthetic biology and biotechnology. Moreover, natural phenomena like the bimodal development of genetic competence can be studied.

The presence of standardised tools and methods to measure and represent accurately biological parts and functions is a prerequisite for successful metabolic engineering and crucial to understand and predict the behaviour of synthetic genetic circuits. Many synthetic gene networks are based on transcriptional circuits, thus information on transcriptional and translational activity is important for understanding and fine-tuning the synthetic function. To this end, we have developed a toolkit to analyse systematically the transcriptional and translational activity of a specific synthetic part in vivo. It is based on the plasmid pTRA and allows the assignment of specific transcriptional and translational outputs to the gene(s) of interest (GOI) and to compare different genetic setups. By this, the optimal combination of transcriptional strength and translational activity can be identified. The design is tested in a case study using the gene encoding the fluorescent mCherry protein as GOI. We show the intracellular dynamics of mRNA and protein formation and discuss the potential and shortcomings of the pTRA plasmid.

The time-scale hierarchies of a very general class of models in differential equations is analyzed. Classical methods for model reduction and time-scale analysis have been adapted to this formalism and a complementary method is proposed. A unified theoretical treatment shows how the structure of the system can be much better understood by inspection of two sets of singular values: one related to the stoichiometric structure of the system and another to its kinetics. The methods are exemplified first through a toy model, then a large synthetic network and finally with numeric simulations of three classical benchmark models of real biological systems.

In the mathematical modeling of biochemical reactions, a convenient standard approach is to use ordinary differential equations (ODEs) that follow the law of mass action. However, this deterministic ansatz is based on simplifications; in particular, it neglects noise, which is inherent to biological processes. In contrast, the stochasticity of reactions is captured in detail by the discrete chemical master equation (CME). Therefore, the CME is frequently applied to mesoscopic systems, where copy numbers of involved components are small and random fluctuations are thus significant. Here, we compare those two common modeling approaches, aiming at identifying parallels and discrepancies between deterministic variables and possible stochastic counterparts like the mean or modes of the state space probability distribution. To that end, a mathematically flexible reaction scheme of autoregulatory gene expression is translated into the corresponding ODE and CME formulations. We show that in the thermodynamic limit, deterministic stable fixed points usually correspond well to the modes in the stationary probability distribution. However, this connection might be disrupted in small systems. The discrepancies are characterized and systematically traced back to the magnitude of the stoichiometric coefficients and to the presence of nonlinear reactions. These factors are found to synergistically promote large and highly asymmetric fluctuations. As a consequence, bistable but unimodal, and monostable but bimodal systems can emerge. This clearly challenges the role of ODE modeling in the description of cellular signaling and regulation, where some of the involved components usually occur in low copy numbers. Nevertheless, systems whose bimodality originates from deterministic bistability are found to sustain a more robust separation of the two states compared to bimodal, but monostable systems. In regulatory circuits that require precise coordination, ODE modeling is thus still expected to provide relevant indications on the underlying dynamics.

Metabolism and signalling are tightly coupled in bacteria. Combining several theoretical approaches, a core model is presented that describes transcriptional and allosteric control of glycolysis in Escherichia coli. Experimental data based on microarrays, signalling components and extracellular metabolites are used to estimate kinetic parameters. A newly designed strain was used that adjusts the incoming glucose flux into the system and allows a kinetic analysis. Based on the results, prediction for intracelluar metabolite concentrations over a broad range of the growth rate could be performed and compared with data from literature.

KdpD and KdpE form a histidine kinase/response regulator system that senses K(+) limitation and induces the kdpFABC operon, which encodes a high-affinity K(+) uptake complex. To define the primary stimulus perceived by KdpD we focused in this study on the dynamics of the Kdp response. Escherichia coli cells were subjected to severe K(+) limitation, and all relevant parameters of the Kdp response, i.e., levels of kdpFABC transcripts and KdpFABC proteins, as well as extra- and intracellular K(+) concentrations, were quantitatively analysed over time (0 to 180 min). Unexpectedly, induction of kdpFABC was found to follow a non-monotonic time-course. To interpret this unusual behaviour, a mathematical model that adequately captures the dynamics of the Kdp system was established and used for simulations. We found a strong correlation between KdpD/KdpE activation and the intracellular K(+) concentration, which is influenced by the uptake of K(+) via the KdpFABC complex. Based on these results a model is proposed in which KdpD/KdpE phosphorylation is inversely correlated with the intracellular K(+) concentration. To corroborate this hypothesis an isogenic mutant that produces a defective KdpFABC complex, and the trans-complemented mutant that expresses the KtrAB high-affinity K(+) uptake system of Vibrio alginolyticus were quantitatively analysed. Experimental data and simulations for the mutants consistently support the tight correlation between KdpD/KdpE activation and the intracellular K(+) concentration. This study presents a striking example of the non-intuitive dynamics of a functional unit comprising signalling proteins and a transporter with K(+) as mediator.