Modelling of microbial kinetics

PhysioFit: a software to quantify cell growth parameters and extracellular fluxes

SUMMARY

Quantification of growth parameters and extracellular uptake and production fluxes is central in systems and synthetic biology. Fluxes can be estimated using various mathematical models by fitting time-course measurements of the concentration of cells and extracellular substrates and products. A single tool is available to non-computational biologists to calculate extracellular fluxes, but it is hardly interoperable and is limited to a single hard-coded growth model. We present our open-source flux calculation software, PhysioFit, which can be used with any growth model and is interoperable by design. PhysioFit includes some of the most common growth models, and advanced users can implement additional models to calculate extracellular fluxes and other growth parameters for metabolic systems or experimental setups that follow alternative kinetics. PhysioFit can be used as a Python library and offers a graphical user interface for intuitive use by end-users and a command-line interface to streamline integration into existing pipelines.

AVAILABILITY AND IMPLEMENTATION

PhysioFit v3 is implemented in Python 3 and was tested on Windows, Unix, and MacOS platforms. The source code and the documentation are freely distributed under GPL3 license at https://github.com/MetaSys-LISBP/PhysioFit/ and https://physiofit.readthedocs.io/.

The closure issue related to liquid-cell mass transfer and substrate uptake dynamics in biological systems

An original dynamic model for substrate uptake under transient conditions is established and used to simulate a variety of biological responses to external perturbations. The actual uptake and growth rates, treated as cell properties, are part of the model variables as well as the substrate concentration at the cell-liquid interface. Several regulatory loops inspired by the structure of the glycolytic chain are considered to establish a set of ordinary differential equations. The uptake rate evolves so as to reach an equilibrium between the cell demand and the environmental supply. This model does not contain any of the usual algebraic closure laws relating to the instantaneous uptake, growth rates, and the substrate concentration, nor does it enforce the continuity of mass fluxes at the liquid-cell interface. However, these relationships are found in the steady-state solution. Previously unexplained experimental observations are well reproduced by this model. Also, the model structure is suitable for further coupling with flux-based metabolic models and fluid-flow equations.

Using a genome-scale metabolic model of Enterococcus faecalis V583 to assess amino acid uptake and its impact on central metabolism

Increasing antibiotic resistance in pathogenic bacteria necessitates the development of new medication strategies. Interfering with the metabolic network of the pathogen can provide novel drug targets but simultaneously requires a deeper and more detailed organism-specific understanding of the metabolism, which is often surprisingly sparse. In light of this, we reconstructed a genome-scale metabolic model of the pathogen Enterococcus faecalis V583. The manually curated metabolic network comprises 642 metabolites and 706 reactions. We experimentally determined metabolic profiles of E. faecalis grown in chemically defined medium in an anaerobic chemostat setup at different dilution rates and calculated the net uptake and product fluxes to constrain the model. We computed growth-associated energy and maintenance parameters and studied flux distributions through the metabolic network. Amino acid auxotrophies were identified experimentally for model validation and revealed seven essential amino acids. In addition, the important metabolic hub of glutamine/glutamate was altered by constructing a glutamine synthetase knockout mutant. The metabolic profile showed a slight shift in the fermentation pattern toward ethanol production and increased uptake rates of multiple amino acids, especially l-glutamine and l-glutamate. The model was used to understand the altered flux distributions in the mutant and provided an explanation for the experimentally observed redirection of the metabolic flux. We further highlighted the importance of gene-regulatory effects on the redirection of the metabolic fluxes upon perturbation. The genome-scale metabolic model presented here includes gene-protein-reaction associations, allowing a further use for biotechnological applications, for studying essential genes, proteins, or reactions, and the search for novel drug targets.

High cell density cultivation of Pseudomonas putida KT2440 using glucose without the need for oxygen enriched air supply

High Cell Density (HCD) cultivation of bacteria is essential for the majority of industrial processes to achieve high volumetric productivity (g L(-1) h(-1) ) of a bioproduct of interest. This study developed a fed batch bioprocess using glucose as sole carbon and energy source for the HCD of the well described biocatalyst Pseudomonas putida KT2440 without the supply of oxygen enriched air. Growth kinetics data from batch fermentations were used for building a bioprocess model and designing feeding strategies. An exponential followed by linearly increasing feeding strategy of glucose was found to be effective in maintaining biomass productivity while also delaying the onset of dissolved oxygen (supplied via compressed air) limitation. A final cell dry weight (CDW) of 102 g L(-1) was achieved in 33 h with a biomass productivity of 3.1 g L(-1) h(-1) which are the highest ever reported values for P. putida strains using glucose without the supply of pure oxygen or oxygen enriched air. The usefulness of the biomass as a biocatalyst was demonstrated through the production of the biodegradable polymer polyhydroxyalkanoate (PHA). When nonanoic acid (NA) was supplied to the glucose grown cells of P. putida KT2440, it accumulated 32% of CDW as PHA in 11 h (2.85 g L(-1) h(-1) ) resulting in a total of 0.56 kg of PHA in 18 L with a yield of 0.56 g PHA g NA(-1) .

Morphogenesis of Streptomyces in submerged cultures

Members of the genus Streptomyces are mycelial bacteria that undergo a complex multicellular life cycle and propagate via sporulation. Streptomycetes are important industrial microorganisms, as they produce a plethora of medically relevant natural products, including the majority of clinically important antibiotics, as well as a wide range of enzymes with industrial application. While development of Streptomyces in surface-grown cultures is well studied, relatively little is known of the parameters that determine morphogenesis in submerged cultures. Here, growth is characterized by the formation of mycelial networks and pellets. From the perspective of industrial fermentations, such mycelial growth is unattractive, as it is associated with slow growth, heterogeneous cultures, and high viscosity. Here, we review the current insights into the genetic and environmental factors that determine mycelial growth and morphology in liquid-grown cultures. The genetic factors include cell-matrix proteins and extracellular polymers, morphoproteins with specific roles in liquid-culture morphogenesis, with the SsgA-like proteins as well-studied examples, and programmed cell death. Environmental factors refer in particular to those dictated by process engineering, such as growth media and reactor set-up. These insights are then integrated to provide perspectives as to how this knowledge can be applied to improve streptomycetes for industrial applications.

Optimal control analysis of the dynamic growth behavior of microorganisms

Understanding the growth behavior of microorganisms using modeling and optimization techniques is an active area of research in the fields of biochemical engineering and systems biology. In this paper, we propose a general modeling framework, based on Monod model, to model the growth of microorganisms. Utilizing the general framework, we formulate an optimal control problem with the objective of maximizing a long-term cellular goal and solve it analytically under various constraints for the growth of microorganisms in a two substrate batch environment. We investigate the relation between long term and short term cellular goals and show that the objective of maximizing cellular concentration at a fixed final time is equivalent to maximization of instantaneous growth rate. We then establish the mathematical connection between the generalized framework and optimal and cybernetic modeling frameworks and derive generalized governing dynamic equations for optimal and cybernetic models. We finally illustrate the influence of various constraints in the cybernetic modeling framework on the optimal growth behavior of microorganisms by solving several dynamic optimization problems using genetic algorithms.

Fed-batch strategies using butyrate for high cell density cultivation of Pseudomonas putida and its use as a biocatalyst

A mathematically based fed-batch bioprocess demonstrated the suitability of using a relatively cheap and renewable substrate (butyric acid) for Pseudomonas putida CA-3 high cell density cultivation. Butyric acid fine-tuned addition is critical to extend the fermentation run and avoid oxygen consumption while maximising the biomass volumetric productivity. A conservative submaximal growth rate (μ of 0.25 h(-1)) achieved 71.3 g L(-1) of biomass after 42 h of fed-batch growth. When a more ambitious feed rate was supplied in order to match a μ of 0.35 h(-1), the volumetric productivity was increased to 2.0 g L(-1) h(-1), corresponding to a run of 25 h and 50 g L(-1) of biomass. Both results represent the highest biomass and the best biomass volumetric productivity with butyrate as a sole carbon source. However, medium chain length polyhydroxyalkanoate (mcl-PHA) accumulation with butyrate grown cells is low (4 %). To achieve a higher mcl-PHA volumetric productivity, decanoate was supplied to butyrate grown cells. This strategy resulted in a PHA volumetric productivity of 4.57 g L(-1) h(-1) in the PHA production phase and 1.63 g L(-1) h(-1)over the lifetime of the fermentation, with a maximum mcl-PHA accumulation of 65 % of the cell dry weight.

Application of statistical techniques for elucidating flow cytometric data of batch and fed-batch cultures

The objective of this work is to develop structured, segregated stochastic models for bioprocesses using time-series flow cytometric (FC) data. To this end, mammalian CHO cells were grown in both batch and fed-batch cultures, and their viable cell numbers (VCDs), monoclonal antibody (MAb), cell cycle phases, mitochondria membrane potential/mitochondria mass, Golgi apparatus, and endoplasmic reticulum (ER) were analyzed. For the fed-batch mode, soy hydrolysate was introduced at 24-H intervals. The cytometric data were analyzed for early indicators of growth and productivity by multiple linear regression analysis, which involved taking into account multicollinearity diagnostics, Durbin-Watson statistics, and Houston tests to determine and refine statistically significant correlations between categorical variables (FC parameters) and response variables (yield parameters). The results indicate that the percentage of G1 cells and ER was significantly correlated with VCD and MAb in the case of batch culture, whereas for fed-batch culture, the percentage of G2 cells and ER was correlated significantly. There was a significant difference between cells in the batch and fed-batch cultures in their ER content, suggesting that the increase in protein synthesis as reflected by the ER content and consequent increase in growth rate and MAb productivity both can be monitored at the cellular level by FC analysis of ER content.

Real-time estimation of biomass and specific growth rate in physiologically variable recombinant fed-batch processes

The real-time measurement of biomass has been addressed since many years. The quantification of biomass in the induction phase of a recombinant bioprocess is not straight forward, since biological burden, caused by protein expression, can have a significant impact on the cell morphology and physiology. This variability potentially leads to poor generalization of the biomass estimation, hence is a very important issue in the dynamic field of process development with frequently changing processes and producer lines. We want to present a method to quantify “biomass” in real-time which avoids off-line sampling and the need for representative training data sets. This generally applicable soft-sensor, based on first principles, was used for the quantification of biomass in induced recombinant fed-batch processes. Results were compared with “state of the art” methods to estimate the biomass concentration and the specific growth rate µ. Gross errors such as wrong stoichiometric assumptions or sensor failure were detected automatically. This method allows for variable model coefficients such as yields in contrast to other process models, hence does not require prior experiments. It can be easily adapted to a different growth stoichiometry; hence the method provides good generalization, also for induced culture mode. This approach estimates the biomass (or anabolic bioconversion) in induced fed-batch cultures in real-time and provides this key variable for process development for control purposes.

Parametric sensitivity of stoichiometric flux balance models applied to wild-type Escherichia coli metabolism

Stoichiometrically based flux balance models provide a method to quantify the metabolic pathway fluxes within a living cell. Predictions of flux balance models are expected to have applications in pathway engineering as well as in bioprocess design and control. These models utilize optimality principles applied to metabolic pathway stoichiometry along with the metabolic requirements for growth to determine the flux distribution in a metabolic network. A flux balance model has been developed for Escherichia coli W3110 using five experimentally determined strain-specific parameters. In this report, we determine the sensitivity of the predictions of the flux balance model to these five strain-specific parameters. Model predictions are shown to be sensitive to the two parameters describing metabolic capacity, while they are relatively insensitive to the three parameters that describe the metabolic requirements for growth. Thus, when stoichiometrically based models are formulated for additional strains one needs to measure the metabolic capacity (maximum rates of nutrient and oxygen utilization) accurately. Determination of metabolic capacity from batch experiments is relatively easy to perform. On the other hand, the harder to determine maintenance parameters need not be as accurately determined. (c) 1995 John Wiley & Sons, Inc.

Unilineage model of hematopoiesis predicts self-renewal of stem and progenitor cells based on ex vivo growth data

Stem cell models are used to describe the function of several tissues. We present unilineage kinetic description of stem cell models and their application to the analysis of ex vivo hematopoietic cell expansion data. This model has the capability to simulate the total cell number and the number of cells at each stage of differentiation over time as a function of the stem cell self-renewal probability, the growth rate of each subpopulation, and the mature cell death rate. The model predicts experimental observations in perfusion-based hematopoietic bioreactor systems. To obtain net cell expansion ex vivo, the model simulations show that the stem cell self-renewal probability must exceed one-half, thus resulting in net expansion of the stem cell population. Experimental data on long-term culture-initiating cells (LTC-IC) confirm this prediction and the probability of self-renewal is estimated to be 0.62 to 0.73. This self-renewal probability, along with the death rate, define a relationship in which the apparent overall growth rate is less than the compartmental growth rate. Finally, the model predicts that cells beyond the stem cell stage of differentiation must self-renew to achieve the level of expansion within the time frame observed in experimental systems. (c) 1996 John Wiley & Sons, Inc.

Structured morphological modeling as a framework for rational strain design of Streptomyces species

Successful application of a computational model for rational design of industrial Streptomyces exploitation requires a better understanding of the relationship between morphology—dictated by microbial growth, branching, fragmentation and adhesion—and product formation. Here we review the state-of-the-art in modeling of growth and product formation by filamentous microorganisms and expand on existing models by combining a morphological and structural approach to realistically model and visualize a three-dimensional pellet. The objective is to provide a framework to study the effect of morphology and structure on natural product and enzyme formation and yield. Growth and development of the pellet occur via the processes of apical extension, branching and cross-wall formation. Oxygen is taken to be the limiting component, with the oxygen concentration at the tips regulating growth kinetics and the oxygen profile within the pellet affecting the probability of branching. Biological information regarding the processes of differentiation and branching in liquid cultures of the model organism Streptomyces coelicolor has been implemented. The model can be extended based on information gained in fermentation trials for different production strains, with the aim to provide a test drive for the fermentation process and to pre-assess the effect of different variables on productivity. This should aid in improving Streptomyces as a production platform in industrial biotechnology.

Systems analysis of microbial adaptations to simultaneous stresses

Microbes live in multi-factorial environments and have evolved under a variety of concurrent stresses including resource scarcity. Their metabolic organization is a reflection of their evolutionary histories and, in spite of decades of research, there is still a need for improved theoretical tools to explain fundamental aspects of microbial physiology. Using ecological and economic concepts, this chapter explores a resource-ratio based theory to elucidate microbial strategies for extracting and channeling mass and energy. The theory assumes cellular fitness is maximized by allocating scarce resources in appropriate proportions to multiple stress responses. Presented case studies deconstruct metabolic networks into a complete set of minimal biochemical pathways known as elementary flux modes. An economic analysis of the elementary flux modes tabulates enzyme atomic synthesis requirements from amino acid sequences and pathway operating costs from catabolic efficiencies, permitting characterization of inherent tradeoffs between resource investment and phenotype. A set of elementary flux modes with competitive tradeoffs properties can be mathematically projected onto experimental fluxomics datasets to decompose measured phenotypes into metabolic adaptations, interpreted as cellular responses proportional to the experienced culturing stresses. The resource-ratio based method describes the experimental phenotypes with greater accuracy than other contemporary approaches and further analysis suggests the results are both statistically and biologically significant. The insight into metabolic network design principles including tradeoffs associated with concurrent stress adaptation provides a foundation for interpreting physiology as well as for rational control and engineering of medically, environmentally, and industrially relevant microbes.

A biochemically structured model for ethanol fermentation by Kluyveromyces marxianus: A batch fermentation and kinetic study

Anaerobic batch fermentations of ricotta cheese whey (i.e. containing lactose) were performed under different operating conditions. Ethanol concentrations of ca. 22g L(-1) were found from whey containing ca. 44g L(-1) lactose, which corresponded to up to 95% of the theoretical ethanol yield within 15h. The experimental data could be explained by means of a simple knowledge-driven biochemically structured model that was built on bioenergetics principles applied to the metabolic pathways through which lactose is converted into major products. Use of the model showed that the observed concentrations of ethanol, lactose, biomass and glycerol during batch fermentation could be described within a ca. 6% deviation, as could the yield coefficients for biomass and ethanol produced on lactose. The model structure confirmed that the thermodynamics considerations on the stoichiometry of the system constrain the metabolic coefficients within a physically meaningful range thereby providing valuable and reliable insight into fermentation processes.

Matrix notation for efficient development of first-principles models within PAT applications: integrated modeling of antibiotic production with Streptomyces coelicolor

A matrix notation coupled to macroscopic principles is introduced as a means to develop first- principles models in an efficient and structured way within PAT applications. The notation was evaluated for developing an integrated biological, chemical (pH modeling) and physical (gas-liquid exchange) model for describing antibiotic production with Streptomyces coelicolor in batch fermentations. The model provided statistically adequate fits to all the monitored macroscopic biological, chemical and physical data of the process, except the phosphate uptake dynamics. This phosphate discrepancy is hypothesized to result from the internal storage of phosphate as polyphosphate prior to the exponential growth phase. The antibiotic production was associated with the stationary phase and its kinetics was adequately described using a modified Luedeking-Piret equation. Further, the maintenance was best described by employing a combination of Pirt and Herbert models, a result that was supported by a model-based hypothesis testing. Overall the process knowledge currently incorporated in the model is believed to be useful both for process optimization purposes and for further testing of hypotheses aiming at improving the mechanistic understanding of antibiotic production with S. coelicolor. Last but not least, the matrix notation is believed to be a promising supporting tool for efficient development and communication of complex dynamic models within a PAT framework.

Modeling of enzyme production kinetics

Models of single cells, cell populations, and cultures can be most useful in organizing information in a comprehensive system description, as well as in optimizing and controlling actual production operations. Models discussed in this article are of various degrees of biological structure and mathematical complexity. The models are developed based on the biomass formation, substrate consumption, and product formation. the potentials asn the limitations of all the models have been reported. The parameter estimation by different methods has been discussed in this communication. These parameters will be helpful to explore the areas where future-modeling studies may be especially valuable.

Growth kinetics and Pho84 phosphate transporter activity of Saccharomyces cerevisiae under phosphate-limited conditions

The effect of phosphate (P ( i )) concentration on the growth behavior of Saccharomyces cerevisiae strain CEN.PK113-5D in phosphate-limited batch and chemostat cultures was studied. The range of dilution rates used in the present study was 0.08-0.45 h(-1). The batch growth of yeast cells followed Monod relationship, but growth of the cells in phosphate-limited chemostat showed change in growth kinetics with increasing dilution rates. The difference in growth kinetics of the yeast cells in phosphate-limited chemostat for dilution rates below and above approximately 0.2 h(-1) has been discussed in terms of the batch growth kinetic data and the change in the metabolic activity of the yeast cells. Immunological detection of a C-terminally myc epitope-tagged Pho84 fusion protein indicated derepressive expression of the Pho84 high-affinity P ( i ) transporter in the entire range of dilution rates employed in this study. Phosphate transport activity mediated by Pho84 transporter was highest at very low dilution rates, i.e. 0.08-0.1 h(-1), corresponding to conditions in which the amount of synthesized Pho84 was at its maximum.

Analysis of growth of Lactobacillus plantarum WCFS1 on a complex medium using a genome-scale metabolic model

A genome-scale metabolic model of the lactic acid bacterium Lactobacillus plantarum WCFS1 was constructed based on genomic content and experimental data. The complete model includes 721 genes, 643 reactions, and 531 metabolites. Different stoichiometric modeling techniques were used for interpretation of complex fermentation data, as L. plantarum is adapted to nutrient-rich environments and only grows in media supplemented with vitamins and amino acids. (i) Based on experimental input and output fluxes, maximal ATP production was estimated and related to growth rate. (ii) Optimization of ATP production further identified amino acid catabolic pathways that were not previously associated with free-energy metabolism. (iii) Genome-scale elementary flux mode analysis identified 28 potential futile cycles. (iv) Flux variability analysis supplemented the elementary mode analysis in identifying parallel pathways, e.g. pathways with identical end products but different co-factor usage. Strongly increased flexibility in the metabolic network was observed when strict coupling between catabolic ATP production and anabolic consumption was relaxed. These results illustrate how a genome-scale metabolic model and associated constraint-based modeling techniques can be used to analyze the physiology of growth on a complex medium rather than a minimal salts medium. However, optimization of biomass formation using the Flux Balance Analysis approach, reported to successfully predict growth rate and by product formation in Escherichia coli and Saccharomyces cerevisiae, predicted too high biomass yields that were incompatible with the observed lactate production. The reason is that this approach assumes optimal efficiency of substrate to biomass conversion, and can therefore not predict the metabolically inefficient lactate formation.

Modelling strategies for the industrial exploitation of lactic acid bacteria

Lactic acid bacteria (LAB) have a long tradition of use in the food industry, and the number and diversity of their applications has increased considerably over the years. Traditionally, process optimization for these applications involved both strain selection and trial and error. More recently, metabolic engineering has emerged as a discipline that focuses on the rational improvement of industrially useful strains. In the post-genomic era, metabolic engineering increasingly benefits from systems biology, an approach that combines mathematical modelling techniques with functional-genomics data to build models for biological interpretation and--ultimately--prediction. In this review, the industrial applications of LAB are mapped onto available global, genome-scale metabolic modelling techniques to evaluate the extent to which functional genomics and systems biology can live up to their industrial promise.

Kinetics of lactose fermentation using a recombinantSaccharomyces cerevisiae strain

This work presents a multi-route, non-structural kinetic model for interpretation of ethanol fermentation of lactose using a recombinant flocculent Saccharomyces cerevisiae strain expressing both the LAC4 (coding for beta-galactosidase) and LAC12 (coding for lactose permease) genes of Kluyveromyces lactis. In this model, the values of different metabolic pathways are calculated applying a modified Monod equation rate in which the growth rate is proportional to the concentration of a key enzyme controlling the single metabolic pathway. In this study, three main metabolic routes for S. cerevisiae are considered: oxidation of lactose, reduction of lactose (producing ethanol), and oxidation of ethanol. The main bioprocess variables determined experimentally were lactose, ethanol, biomass, and dissolved oxygen concentrations. Parameters of the proposed kinetic model were established by fitting the experimental data obtained in a small lab-scale fermentor with the initial lactose concentrations ranging from 5 g/dm3 to 50 g/dm3. A very good agreement between experimental data and simulated profiles of the main variables (lactose, ethanol, biomass, and dissolved oxygen concentrations) was achieved.

Synthesizing cellular intelligence and artificial intelligence for bioprocesses

Microbial processes operated under realistic conditions are difficult to describe by mechanistic models, thereby limiting their optimization and control. Responses of living cells to their environment suggest that they possess some "innate intelligence". Such responses have been modeled by a cybernetic approach. Furthermore, the overall behavior of a bioreactor containing a population of cells may be described and controlled through artificial intelligence methods. Therefore, it seems logical to combine cybernetic models with artificial intelligence to evolve an integrated intelligence-based strategy that is physiologically more faithful than the current approaches. This possibility is discussed, together with practical considerations favoring a hybrid approach that includes some mathematical modeling.