Duality, thermodynamics, and the linear programming problem in constraint-based models of metabolism

It is shown that the dual to the linear programming problem that arises in constraint-based models of metabolism can be given a thermodynamic interpretation in which the shadow prices are chemical potential analogues, and the objective is to minimise free energy consumption given a free energy drain corresponding to growth. The interpretation is distinct from conventional non-equilibrium thermodynamics, although it does satisfy a minimum entropy production principle. It can be used to motivate extensions of constraint-based modelling, for example to microbial ecosystems.Comment: 4 pages, 2 figures, 1 table, RevTeX 4, final accepted versio

Noise-driven oscillations in microbial population dynamics

Microbial populations in the natural environment are likely to experience growth conditions very different from those of a typical laboratory xperiment. In particular, removal rates of biomass and substrate are unlikely to be balanced under realistic environmental conditions. Here, we consider a single population growing on a substrate under conditions where the removal rates of substrate and biomass are not necessarily equal. For a large population, with deterministic growth dynamics, our model predicts that this system can show transient (damped) oscillations. For a small population, demographic noise causes these oscillations to be sustained indefinitely. These oscillations arise when the dynamics of changes in biomass are faster than the dynamics of the substrate, for example, due to a high microbial death rate and/or low substrate flow rates. We show that the same mechanism can produce sustained stochastic oscillations in a two-species, nutrient-cycling microbial ecosystem. Our results suggest that oscillatory population dynamics may be a common feature of small microbial populations in the natural environment, even in the absence of complex interspecies interactions.Comment: 25 pages, 11 figure

Improving the batch-to-batch reproducibility in microbial cultures during recombinant protein production by guiding the process along a predefined total biomass profile

In industry Escherichia coli is the preferred host system for the heterologous biosynthesis of therapeutic proteins that do not need posttranslational modifications. In this report, the development of a robust high-cell-density fed-batch procedure for the efficient production of a therapeutic hormone is described. The strategy is to guide the process along a predefined profile of the total biomass that was derived from a given specific growth rate profile. This profile might have been built upon experience or derived from numerical process optimization. A surprisingly simple adaptive procedure correcting for deviations from the desired path was developed. In this way the batch-to-batch reproducibility can be drastically improved as compared to the process control strategies typically applied in industry. This applies not only to the biomass but, as the results clearly show, to the product titer also

Microbial Maintenance: A Critical Review on Its Quantification

Microbial maintenance is an important concept in microbiology. Its quantification, however, is a subject of continuous debate, which seems to be caused by (1) its definition, which includes nongrowth components other than maintenance; (2) the existence of partly overlapping concepts; (3) the evolution of variables as constants; and (4) the neglect of cell death in microbial dynamics. The two historically most important parameters describing maintenance, the specific maintenance rate and the maintenance coefficient, are based on partly different nongrowth components. There is thus no constant relation between these parameters and previous equations on this subject are wrong. In addition, the partial overlap between these parameters does not allow the use of a simple combination of these parameters. This also applies for combinations of a threshold concentration with one of the other estimates of maintenance. Maintenance estimates should ideally explicitly describe each nongrowth component. A conceptual model is introduced that describes their relative importance and reconciles the various concepts and definitions. The sensitivity of maintenance on underlying components was analyzed and indicated that overall maintenance depends nonlinearly on relative death rates, relative growth rates, growth yield, and endogenous metabolism. This quantitative sensitivity analysis explains the felt need to develop growth-dependent adaptations of existing maintenance parameters, and indicates the importance of distinguishing the various nongrowth components. Future experiments should verify the sensitivity of maintenance components under cellular and environmental conditions

Maximum Photosynthetic Yield of Green Microalgae in Photobioreactors

The biomass yield on light energy of Dunaliella tertiolecta and Chlorella sorokiniana was investigated in a 1.25- and 2.15-cm light path panel photobioreactor at constant ingoing photon flux density (930 µmol photons m−2 s−1). At the optimal combination of biomass density and dilution rate, equal biomass yields on light energy were observed for both light paths for both microalgae. The observed biomass yield on light energy appeared to be based on a constant intrinsic biomass yield and a constant maintenance energy requirement per gram biomass. Using the model of Pirt (New Phytol 102:3–37, 1986), a biomass yield on light energy of 0.78 and 0.75 g mol photons−1 and a maintenance requirement of 0.0133 and 0.0068 mol photons g−1 h−1 were found for D. tertiolecta and C. sorokiniana, respectively. The observed yield decreases steeply at low light supply rates, and according to this model, this is related to the increase of the amount of useable light energy diverted to biomass maintenance. With this study, we demonstrated that the observed biomass yield on light in short light path bioreactors at high biomass densities decreases because maintenance requirements are relatively high at these conditions. All our experimental data for the two strains tested could be described by the physiological models of Pirt (New Phytol 102:3–37, 1986). Consequently, for the design of a photobioreactor, we should maintain a relatively high specific light supply rate. A process with high biomass densities and high yields at high light intensities can only be obtained in short light path photobioreactors

Resource limitation drives spatial organization in microbial groups.

Dense microbial groups such as bacterial biofilms commonly contain a diversity of cell types that define their functioning. However, we have a limited understanding of what maintains, or purges, this diversity. Theory suggests that resource levels are key to understanding diversity and the spatial arrangement of genotypes in microbial groups, but we need empirical tests. Here we use theory and experiments to study the effects of nutrient level on spatio-genetic structuring and diversity in bacterial colonies. Well-fed colonies maintain larger well-mixed areas, but they also expand more rapidly compared with poorly-fed ones. Given enough space to expand, therefore, well-fed colonies lose diversity and separate in space over a similar timescale to poorly fed ones. In sum, as long as there is some degree of nutrient limitation, we observe the emergence of structured communities. We conclude that resource-driven structuring is central to understanding both pattern and process in diverse microbial communities

Differences in Cell Division Rates Drive the Evolution of Terminal Differentiation in Microbes

Multicellular differentiated organisms are composed of cells that begin by developing from a single pluripotent germ cell. In many organisms, a proportion of cells differentiate into specialized somatic cells. Whether these cells lose their pluripotency or are able to reverse their differentiated state has important consequences. Reversibly differentiated cells can potentially regenerate parts of an organism and allow reproduction through fragmentation. In many organisms, however, somatic differentiation is terminal, thereby restricting the developmental paths to reproduction. The reason why terminal differentiation is a common developmental strategy remains unexplored. To understand the conditions that affect the evolution of terminal versus reversible differentiation, we developed a computational model inspired by differentiating cyanobacteria. We simulated the evolution of a population of two cell types –nitrogen fixing or photosynthetic– that exchange resources. The traits that control differentiation rates between cell types are allowed to evolve in the model. Although the topology of cell interactions and differentiation costs play a role in the evolution of terminal and reversible differentiation, the most important factor is the difference in division rates between cell types. Faster dividing cells always evolve to become the germ line. Our results explain why most multicellular differentiated cyanobacteria have terminally differentiated cells, while some have reversibly differentiated cells. We further observed that symbioses involving two cooperating lineages can evolve under conditions where aggregate size, connectivity, and differentiation costs are high. This may explain why plants engage in symbiotic interactions with diazotrophic bacteria

Phosphate feeding to permit growth while maintaining secondary product synthesis

Maintaining high metabolic activities for extended periods by feeding small amounts of the growth limiting nutrient was examined for the production of cycloheximide by Streptomyces griseus . Batch studies indicated that increased initial phosphate levels led to increased cell concentrations, stimulated glucose utilization, and over a limited range (<0.6 g/l KH 2 PO 4 ) did not adversely affect cycloheximide production rates. Semi-continuous phosphate feeding was observed to permit limited cell growth, and to enhance metabolic activities (i. e. glucose utilization). The effect of semi-continuous phosphate feeding on antibiotic production depended on the feed rate, with high feed rates suppressing production.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46756/1/253_2004_Article_BF00451634.pd