Modeling of bacterial growth; formulation and evaluation of a structured model

Growth Dynamics of Bacterial Populations in a Two-Compartment Biofilm Bioreactor Designed for Continuous Surfactin Biosynthesis

Biofilm bioreactors are promising systems for continuous biosurfactant production since they provide process stability through cell immobilization and avoid foam formation. In this work, a two-compartment biofilm bioreactor was designed consisting of a stirred tank reactor and a trickle-bed reactor containing a structured metal packing for biofilm formation. A strong and poor biofilm forming B. subtilis 168 strain due to restored exopolysaccharides (EPS) production or not were cultivated in the system to study the growth behavior of the planktonic and biofilm population for the establishment of a growth model. A high dilution rate was used in order to promote biofilm formation on the packing and wash out unwanted planktonic cells. Biofilm development kinetics on the packing were assessed through a total organic carbon mass balance. The EPS⁺ strain showed a significantly improved performance in terms of adhesion capacity and surfactin production. The mean surfactin productivity of the EPS⁺ strain was about 37% higher during the continuous cultivation compared to the EPS^- strain. The substrate consumption together with the planktonic cell and biofilm development were properly predicted by the model (α = 0.05). The results show the efficiency of the biofilm bioreactor for continuous surfactin production using an EPS producing strain.

Thermodynamic Limits and Optimality of Microbial Growth

Understanding microbial growth with the use of mathematical models has a long history that dates back to the pioneering work of Jacques Monod in the 1940s. Monod’s famous growth law expressed microbial growth rate as a simple function of the limiting nutrient concentration. However, to explain growth laws from underlying principles is extremely challenging. In the second half of the 20th century, numerous experimental approaches aimed at precisely measuring heat production during microbial growth to determine the entropy balance in a growing cell and to quantify the exported entropy. This has led to the development of thermodynamic theories of microbial growth, which have generated fundamental understanding and identified the principal limitations of the growth process. Although these approaches ignored metabolic details and instead considered microbial metabolism as a black box, modern theories heavily rely on genomic resources to describe and model metabolism in great detail to explain microbial growth. Interestingly, however, thermodynamic constraints are often included in modern modeling approaches only in a rather superficial fashion, and it appears that recent modeling approaches and classical theories are rather disconnected fields. To stimulate a closer interaction between these fields, we here review various theoretical approaches that aim at describing microbial growth based on thermodynamics and outline the resulting thermodynamic limits and optimality principles. We start with classical black box models of cellular growth, and continue with recent metabolic modeling approaches that include thermodynamics, before we place these models in the context of fundamental considerations based on non-equilibrium statistical mechanics. We conclude by identifying conceptual overlaps between the fields and suggest how the various types of theories and models can be integrated. We outline how concepts from one approach may help to inform or constrain another, and we demonstrate how genome-scale models can be used to infer key black box parameters, such as the energy of formation or the degree of reduction of biomass. Such integration will allow understanding to what extent microbes can be viewed as thermodynamic machines, and how close they operate to theoretical optima.

Population dynamics of a Salmonella lytic phage and its host: implications of the host bacterial growth rate in modelling

The prevalence and impact of bacteriophages in the ecology of bacterial communities coupled with their ability to control pathogens turn essential to understand and predict the dynamics between phage and bacteria populations. To achieve this knowledge it is essential to develop mathematical models able to explain and simulate the population dynamics of phage and bacteria. We have developed an unstructured mathematical model using delay-differential equations to predict the interactions between a broad-host-range Salmonella phage and its pathogenic host. The model takes into consideration the main biological parameters that rule phage-bacteria interactions likewise the adsorption rate, latent period, burst size, bacterial growth rate, and substrate uptake rate, among others. The experimental validation of the model was performed with data from phage-interaction studies in a 5 L bioreactor. The key and innovative aspect of the model was the introduction of variations in the latent period and adsorption rate values that are considered as constants in previous developed models. By modelling the latent period as a normal distribution of values and the adsorption rate as a function of the bacterial growth rate it was possible to accurately predict the behaviour of the phage-bacteria population. The model was shown to predict simulated data with a good agreement with the experimental observations and explains how a lytic phage and its host bacteria are able to coexist.

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.

Structured modeling of a microbial system: II. Experimental verification of a structured lactic acid fermentation model

A two-compartment model for the lactic acid fermentation with Streptococcus cremoris is experimentally verified. The seven parameters of the model are determined using steady-state chemostat data at varying values of dilution rate, D, but with a constant feed concentration, s(f), of a single carbohydrate source (glucose, lactose, or galactose), and a constant feed concentration of s(Nf) of the N source. Steady-state measurements of the RNA content at different exit concentrations, s, of the carbohydrate are included to calculate kinetic parameters that determine the cell composition for varying operating conditions. The model is tested using data from a large set of steady-state and non-steady-state experiments: batch fermentations and step and pulse experiments in a chemostat. Both qualitatively and quantitatively the major features of the model are confirmed: the external substrates enter into intracellular high-energy building blocks, and lactic acid is formed as a by-product of these reactions. Cell growth depends on the fraction of active components (X(A)) of the cell and is not accompanied by lactic acid production. Possible model modifications are discussed, primarily to obtain a better description of lactic acid fermentation at nongrowth conditions.

Development of bioreaction engineering

In addition to summarizing the early investigations in bioreaction engineering, the present short review covers the development of the field in the last 50 years. A brief overview of the progress of the fundamentals is presented in the first part of this article and the key issues of bioreaction engineering are advanced in its second part.

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

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

Microbial growth dynamics on the basis of individual budgets

The popular theories for microbial dynamics by Monod, Pirt and Droop are shown to be special cases of a model for individual budgets, in which growth and maintenance are on the expense of reserve materials. The dynamics of reserve materials is a first order process with a relaxation time proportional to cell length; maintenance is proportional to cell volume, and uptake, which depends hyperbolically on substrate density, is proportional to cell volume as well. Because of the latter, population dynamics depends on the behaviour of the individuals in a simple way, such that the cell volume distribution has no quantitative effect. When uptake is proportional to the surface area of the cell, which is realistic from a physical point of view, the relation between the individual level and the population one becomes more complicated and the cell size and shape distribution affects population dynamics. It is shown how the changing shape of rods modifies uptake and, consequently, growth. The concept of energy conductance, defined as the ratio of the maximum surface area specific uptake and the volume specific energy reserve has been introduced in the analysis of microbial dynamics. The first tentative results indicate that the value for E. coli is close to the mean value for a wide variety of animals. Properties of the model for cell suspension at constant substrate densities are analyzed and tested against a variety of experimental data from the literature on both the individual and the population level.

A structured model for immobilized cell kinetics

An intrinsic, structured model has been formulated to describe the kinetics of viable (living) cells immobilized within porous supports. Predictions of steady-state internal biomass concentration distributions, biocatalyst substrate profiles, and immobilized cell growth and leakage from the support are in qualitative agreement with the literature. Simulation studies indicate that carrier pore structure is a particularly important design variable to be optimized.