Modeling the dynamics of E. coli populations in the three-dimensional turbulent field of a stirred-tank bioreactor—A structured–segregated approach

From single cells to microbial population dynamics: modelling in biotechnology based on measurements of individual cells

The development of dynamic modelling of microbial populations in bioprocesses is reviewed. In the 1960s Arnold Fredrickson established the theoretical basis of such models, and other researchers have subsequently advanced them. This review explores the relationships that describe cell proliferation and evaluates the importance of the application of flow cytometry to the fundamental parameterisation of the models for their use in bioprocess engineering. The section "Individual-Based Modelling" discusses recent theoretical developments. Delay-differential equations are demonstrated to describe accurately temporal variation of the cell proliferation cycle and specialised approaches and related iconography are applied to stochastic and deterministic modelling of stages of cellular development. Synchronised cultures of the bacterium Cupriavidus necator were prepared and monitored using a flow cytometer. The data obtained demonstrate that cell proliferation could be simulated quantitatively using the developed model.

A multi-paradigm modeling framework to simulate dynamic reciprocity in a bioreactor

Despite numerous technology advances, bioreactors are still mostly utilized as functional black-boxes where trial and error eventually leads to the desirable cellular outcome. Investigators have applied various computational approaches to understand the impact the internal dynamics of such devices has on overall cell growth, but such models cannot provide a comprehensive perspective regarding the system dynamics, due to limitations inherent to the underlying approaches. In this study, a novel multi-paradigm modeling platform capable of simulating the dynamic bidirectional relationship between cells and their microenvironment is presented. Designing the modeling platform entailed combining and coupling fully an agent-based modeling platform with a transport phenomena computational modeling framework. To demonstrate capability, the platform was used to study the impact of bioreactor parameters on the overall cell population behavior and vice versa. In order to achieve this, virtual bioreactors were constructed and seeded. The virtual cells, guided by a set of rules involving the simulated mass transport inside the bioreactor, as well as cell-related probabilistic parameters, were capable of displaying an array of behaviors such as proliferation, migration, chemotaxis and apoptosis. In this way the platform was shown to capture not only the impact of bioreactor transport processes on cellular behavior but also the influence that cellular activity wields on that very same local mass transport, thereby influencing overall cell growth. The platform was validated by simulating cellular chemotaxis in a virtual direct visualization chamber and comparing the simulation with its experimental analogue. The results presented in this paper are in agreement with published models of similar flavor. The modeling platform can be used as a concept selection tool to optimize bioreactor design specifications.

Characterization and control of fungal morphology for improved production performance in biotechnology

Filamentous fungi have been widely applied in industrial biotechnology for many decades. In submerged culture processes, they typically exhibit a complex morphological life cycle that is related to production performance--a link that is of high interest for process optimization. The fungal forms can vary from dense spherical pellets to viscous mycelia. The resulting morphology has been shown to be influenced strongly by process parameters, including power input through stirring and aeration, mass transfer characteristics, pH value, osmolality and the presence of solid micro-particles. The surface properties of fungal spores and hyphae also play a role. Due to their high industrial relevance, the past years have seen a substantial development of tools and techniques to characterize the growth of fungi and obtain quantitative estimates on their morphological properties. Based on the novel insights available from such studies, more recent studies have been aimed at the precise control of morphology, i.e., morphology engineering, to produce superior bio-processes with filamentous fungi.

Real-time monitoring of metabolic shift and transcriptional induction of yciG::luxCDABE E. coli reporter strain to a glucose pulse of different concentrations

Ineffective mixing entailing heterogeneity issue within industrial bioreactors has been reported to affect microbial physiology and consequently bioprocess performances. Alteration of these performances results from microorganism ability to modulate their physiology at metabolic and/or transcriptional levels in order to survive in a given environment. Until now, dynamics of both metabolic and transcriptional microbial response to external stimuli have been investigated using mainly ex situ measurements with sampling and/or quenching constraints. This work showed an in situ bioluminescence approach for real-time monitoring of characteristic stress responses of Escherichia coli containing yciG::luxCDABE reporter to glucose pulses in well-controlled steady-state chemostat cultures. Reproducibility of in situ bioluminescence profiles was assessed. A dramatic transient increase in the bioluminescence intensity (sharp peak) was observed for a complete depletion of sugars and for a sudden decrease in the dilution rate. This response was connected to a sudden change of the metabolic activity. On the contrary a bell curve of bioluminescence intensity, dose-dependent, was related to an induction of transcriptional activity. Real-time monitoring of the bioluminescence signal with time-span less than a second gave access to the characteristic times of the metabolic shift and transcriptional induction of the stress response.

Scale-down simulators for metabolic analysis of large-scale bioprocesses

Analytical approaches for a comprehensive understanding of the metabolic networks in microbial cultures are mostly based on small-scale cultures which are in a steady state or undergo dynamic changes. For drawing conclusions to industrial-scale bioprocesses, however, it is important to understand that cells in large-scale bioreactors are exposed steadily to fast changes, because of an inhomogeneous environment. Analytical approaches that aim for large-scale bioprocess understanding need to apply specific laboratory simulators. Recent developments in cell cultivation techniques and computational tools provide improved possibilities to evaluate how a process will behave in the final scale. These simulators will pave the way for screening robust strains and process conditions.

Multi-scale spatio-temporal modeling: lifelines of microorganisms in bioreactors and tracking molecules in cells

Agent-based models are rigorous tools for simulating the interactions of individual entities, such as organisms or molecules within cells and assessing their effects on the dynamic behavior of the system as a whole. In context with bioprocess and biosystems engineering there are several interesting and important applications. This contribution aims at introducing this strategy with the aid of two examples characterized by striking distinctions in the scale of the individual entities and the mode of their interactions. In the first example a structured-segregated model is applied to travel along the lifelines of single cells in the environment of a three-dimensional turbulent field of a stirred bioreactor. The modeling approach is based on an Euler-Lagrange formulation of the system. The strategy permits one to account for the heterogeneity present in real reactors in both the fluid and cellular phases, respectively. The individual response of the cells to local variations in the extracellular concentrations is pictured by a dynamically structured model of the key reactions of the central metabolism. The approach permits analysis of the lifelines of individual cells in space and time.The second application of the individual modeling approach deals with dynamic modeling of signal transduction pathways in individual cells. Usually signal transduction networks are portrayed as being wired together in a spatially defined manner. Living circuitry, however, is placed in highly malleable internal architecture. Creating a homogenous bag of molecules, a well-mixed system, the dynamic behavior of which is modeled with a set of ordinary differential equations is normally not valid. The dynamics of the MAP kinase and a steroid hormone pathway serve as examples to illustrate how single molecule tracking can be linked with the stochasticity of biochemical reactions, where diffusion and reaction occur in a probabilistic manner. The problem of hindered diffusion caused by macromolecular crowding is also taken into account.

Global transcription and metabolic flux analysis of Escherichia coli in glucose-limited fed-batch cultivations

A time series of whole-genome transcription profiling of Escherichia coli K-12 W3110 was performed during a carbon-limited fed-batch process. The application of a constant feed rate led to the identification of a dynamic sequence of diverse carbon limitation responses (e.g., the hunger response) and at the same time provided a global view of how cellular and extracellular resources are used: the synthesis of high-affinity transporters guarantees maximal glucose influx, thereby preserving the phosphoenolpyruvate pool, and energy-dependent chemotaxis is reduced in order to provide a more economic "work mode." sigma(S)-mediated stress and starvation responses were both found to be of only minor relevance. Thus, the experimental setup provided access to the hunger response and enabled the differentiation of the hunger response from the general starvation response. Our previous topological model of the global regulation of the E. coli central carbon metabolism through the crp, cra, and relA/spoT modulons is supported by correlating transcript levels and metabolic fluxes and can now be extended. The substrate is extensively oxidized in the tricarboxylic acid (TCA) cycle to enhance energy generation. However, the general rate of oxidative decarboxylation within the pentose phosphate pathway and the TCA cycle is restricted to a minimum. Fine regulation of the carbon flux through these pathways supplies sufficient precursors for biosyntheses. The pools of at least three precursors are probably regulated through activation of the (phosphoenolpyruvate-)glyoxylate shunt. The present work shows that detailed understanding of the genetic regulation of bacterial metabolism provides useful insights for manipulating the carbon flux in technical production processes.

In vitro synthesis and characterization of guanosine 3',5'-bis(diphosphate)

The intracellular alarmone guanosine 3',5'-bis(diphosphate) (ppGpp) has been thoroughly investigated over the past 40 years and has become one of the best-known effectors in bacterial physiology. ppGpp is also of great importance for biotechnological applications. Systems biology research, involving experimental and mathematical approaches, has contributed a great deal to uncovering the alarmone's complex regulatory effects. HPLC analysis and UV detection are used to quantify intracellular ppGpp. The samples analyzed also contain other phosphorylated guanine nucleotides and, therefore, are spiked with a standard ppGpp solution. A rapidly growing number of laboratories are turning to synthesizing the nucleotide in vitro involving time-consuming protocols and yielding only low amounts of ppGpp. The current article provides a protocol for the preparation of large quantities of a ribosome extract that contains high ppGpp synthesis activity. The demonstrated upscaling from shaking flask to bioreactor cultivation involves the continuous and refrigerated harvest of the biomass. (13)C NMR analysis enabled the structural characterization of the synthesis product and was complemented by mass spectrometry and methods that are commonly used to identify ppGpp.

Topology of the global regulatory network of carbon limitation in Escherichia coli

One fundamental shortcoming of biotechnological processes operating under carbon-limiting conditions is the high-energy demand (maintenance) of the cells. Although the function of the central carbon metabolism in supplying precursors and energy for biosynthesis has been thoroughly characterized, its regulation and dynamic behaviour during carbon-limited growth has not yet been revealed. The current work demonstrates a time series of metabolic flux distributions during fed-batch cultivation of Escherichia coli K-12 W3110 applying a constant feed rate. The fluxes in glycolysis, pentose phosphate pathway and biosynthesis fell significantly, whereas TCA cycle fluxes remained constant. The flux redistribution resulted in an enhanced energy generation in the TCA cycle and consequently, in a 20% lower biomass yield. The intracellular alarmones ppGpp and cAMP accumulated in large quantities after the onset of nutrient limitation, subsequently declining to basal levels. The network topology of the regulation of the central metabolic pathways was identified so that the observed metabolic and regulatory behaviour can be described. This provides novel aspects of global regulation of the metabolism by the cra, crp and relA/spoT modulons. The work constitutes an important step towards dynamic mathematical modelling of regulation and metabolism, which is needed for the rational optimization of biotechnological processes.