Emergent Lag Phase in Flux-Regulation Models of Bacterial Growth

Lag phase is observed in bacterial growth during a sudden change in conditions: growth is inhibited whilst cells adapt to the environment. Bi-phasic, or diauxic growth is commonly exhibited by many species. In the presence of two sugars, cells initially grow by consuming the preferred sugar then undergo a lag phase before resuming growth on the second. Biomass increase is characterised by a diauxic growth curve: exponential growth followed by a period of no growth before a second exponential growth. Recent literature lacks a complete dynamic description, artificially modelling lag phase and employing non-physical representations of precursor pools. Here, we formulate a rational mechanistic model based on flux-regulation/proteome partitioning with a finite precursor pool that reveals core mechanisms in a compact form. Unlike earlier systems, the characteristic dynamics emerge as part of the solution, including the lag phase. Focussing on growth of Escherichia coli on a glucose-lactose mixture we show results accurately reproduce experiments. We show that for a single strain of E. coli, diauxic growth leads to optimised biomass yields. However, intriguingly, for two competing strains diauxic growth is not always the best strategy. Our description can be generalised to model multiple different microorganisms and investigate competition between species/strains

Diauxie and co-utilization of carbon sources can coexist during bacterial growth in nutritionally complex environments

It is commonly thought that when multiple carbon sources are available, bacteria metabolize them either sequentially (diauxic growth) or simultaneously (co-utilization). However, this view is mainly based on analyses in relatively simple laboratory settings. Here we show that a heterotrophic marine bacterium, Pseudoalteromonas haloplanktis, can use both strategies simultaneously when multiple possible nutrients are provided in the same growth experiment. The order of nutrient uptake is partially determined by the biomass yield that can be achieved when the same compounds are provided as single carbon sources. Using transcriptomics and time-resolved intracellular 1H-13C NMR, we reveal specific pathways for utilization of various amino acids. Finally, theoretical modelling indicates that this metabolic phenotype, combining diauxie and co-utilization of substrates, is compatible with a tight regulation that allows the modulation of assimilatory pathways

Recent Advances in Single-Particle Tracking: Experiment and Analysis

This Special Issue of Entropy, titled “Recent Advances in Single-Particle Tracking: Experiment and Analysis”, contains a collection of 13 papers concerning different aspects of single-particle tracking, a popular experimental technique that has deeply penetrated molecular biology and statistical and chemical physics. Presenting original research, yet written in an accessible style, this collection will be useful for both newcomers to the field and more experienced researchers looking for some reference. Several papers are written by authorities in the field, and the topics cover aspects of experimental setups, analytical methods of tracking data analysis, a machine learning approach to data and, finally, some more general issues related to diffusion

Unifying metabolic networks, regulatory constraints, and resource allocation

Metabolic and gene regulatory networks are two classic models of systems biology. Biologically, gene regulatory networks are the control system of protein expression while metabolic networks, especially the genome-scale reconstructions consist of thousands of enzymatic reactions breaking down nutrients into precursors and energy to support the cellular survival. Metabolic-genetic networks, in addition, include the translational processes as an integrated model of classical metabolic networks and the gene expression machinery. Conversely, genetic regulation is also affected by the metabolic activities that provide feedbacks and precursors to the regulatory system. Thus, the two systems are highly interactive and depend on each other. Up to now, various efforts have been made to bridge the two network types. Yet, the dynamic integration of metabolic networks and genetic regulation remains a major challenge in computational systems biology. This PhD thesis is a contribution to mathematical modeling approaches for studying metabolic-regulatory systems. Inspired by regulatory flux balance analysis (rFBA), we first propose an analytic pipeline to explore the optimal solution space in rFBA. Then, our efforts focus on the dynamic combination of metabolic networks together with enzyme production costs and genetic regulation. For this purpose, we first explore the intuitive idea that incorporates Boolean regulatory rules while iterating resource balance analysis. However, with the iterative strategy, the gene expression states are only updated in discrete time steps. Furthermore, formalizing the metabolic-regulatory networks (MRNs) by hybrid automata provides a new mathematical framework that allows the quantitative integration of the metabolic-genetic network with the genetic regulation in a hybrid discrete-continuous system. For the application of this theoretical formalization, we develop a constraint-based approach regulatory dynamic enzyme-cost flux balance analysis (r-deFBA) as an optimal control strategy for the hybrid automata representing MRNs. This allows the prediction of optimal regulatory state transitions, dynamics of metabolism, and resource allocation capable of achieving a maximal biomass production over a time interval. Finally, this PhD project ends with a chapter on perspectives; we apply the theory of product automata to model the dynamics at population-level, integrating continuous metabolism and discrete regulatory states

Modelling of a bioelectrochemical system for metal-polluted wastewater treatment and sequential metal recovery

BACKGROUND This work develops a simplified mathematical model to predict the performance of a bioelectrochemical system (BES), first working as a microbial fuel cell (MFC) and then as a microbial electrolysis cell (MEC), for the recovery of dissolved metals (Fe, Cu, Sn, and Ni) from simulated industrial wastewater. Experimental data from a previous work were used as starting points for mathematical modelling. Wastewater was used as the catholyte and contained Cu2+ and Fe3+ (500 mg L−1) as well as Sn2+ and Ni2+ (50 mg L−1), while the anolyte was composed of sodium acetate. Two mixed microbial populations were considered in the anode compartment (electrogenic and non-electrogenic biomass). Dissolved metal ions were the electron acceptors in the electrogenic mechanism: Cu2+ and Fe3+ under MFC mode and then Fe2+, Ni2+, and Sn2+ under MEC mode. RESULTS The model predicted the organic substrate and microbial biomass (anode chamber) and Fe3+ and Cu2+ (cathode chamber) concentrations during MFC operation. Monod kinetic and stoichiometric parameters were calibrated, and it was observed that most of the organic substrate underwent a non-electrogenic mechanism. The generation of electric current until electron acceptors were removed was also predicted. Concentration profiles and first-rate constant values for the decreased Sn2+, Ni2+, and Fe2+ concentrations during the subsequent MEC operation were also obtained. The model was then used for simulations under different experimental conditions. CONCLUSION This work offers a single grey-box model proposal that is easy to implement, and it can be used as a practical tool for testing the removal of dissolved metals in BESs. © 2021 Society of Chemical Industry (SCI).ANTECEDENTES Este trabajo desarrolla un modelo matemático simplificado para predecir el desempeño de un sistema bioelectroquímico (BES), primero trabajando como celda de combustible microbiana (MFC) y luego como celda de electrólisis microbiana (MEC), para la recuperación de metales disueltos (Fe, Cu , Sn y Ni) de aguas residuales industriales simuladas. Los datos experimentales de un trabajo anterior se utilizaron como puntos de partida para el modelado matemático. Se utilizó agua residual como catolito y contenía Cu 2+ y Fe 3+ (500 mg L- 1 ), así como Sn 2+ y Ni 2+ (50 mg L- 1), mientras que el anolito estaba compuesto por acetato de sodio. Se consideraron dos poblaciones microbianas mixtas en el compartimiento del ánodo (biomasa electrogénica y no electrogénica). Los iones metálicos disueltos fueron los aceptores de electrones en el mecanismo electrogénico: Cu 2+ y Fe 3+ en modo MFC y luego Fe 2+ , Ni 2+ y Sn 2+ en modo MEC. RESULTADOS El modelo predijo el sustrato orgánico y la biomasa microbiana (cámara de ánodo) y las concentraciones de Fe 3+ y Cu 2+ (cámara de cátodo) durante la operación de MFC. Se calibraron los parámetros cinéticos y estequiométricos de Monod, y se observó que la mayor parte del sustrato orgánico sufrió un mecanismo no electrogénico. También se predijo la generación de corriente eléctrica hasta que se eliminaran los aceptores de electrones. También se obtuvieron perfiles de concentración y valores constantes de primer nivel para las concentraciones reducidas de Sn 2+ , Ni 2+ y Fe 2+ durante la operación MEC posterior. Luego, el modelo se utilizó para simulaciones en diferentes condiciones experimentales. CONCLUSIÓN Este trabajo ofrece una propuesta de modelo de caja gris única que es fácil de implementar y puede usarse como una herramienta práctica para probar la eliminación de metales disueltos en BES. © 2021 Sociedad de la Industria Química (SCI)

\u3cem\u3ePseudomonas aeruginosa\u3c/em\u3e reverse diauxie is a multidimensionl, optimized, resource utilization strategy

Pseudomonas aeruginosa is a globally-distributed bacterium often found in medical infections. The opportunistic pathogen uses a different, carbon catabolite repression (CCR) strategy than many, model microorganisms. It does not utilize a classic diauxie phenotype, nor does it follow common systems biology assumptions including preferential consumption of glucose with an ‘overflow’ metabolism. Despite these contradictions, P. aeruginosa is competitive in many, disparate environments underscoring knowledge gaps in microbial ecology and systems biology. Physiological, omics, and in silico analyses were used to quantify the P. aeruginosa CCR strategy known as ‘reverse diauxie’. An ecological basis of reverse diauxie was identified using a genome-scale, metabolic model interrogated with in vitro omics data. Reverse diauxie preference for lower energy, nonfermentable carbon sources, such as acetate or succinate over glucose, was predicted using a multidimensional strategy which minimized resource investment into central metabolism while completely oxidizing substrates. Application of a common, in silico optimization criterion, which maximizes growth rate, did not predict the reverse diauxie phenotypes. This study quantifies P. aeruginosa metabolic strategies foundational to its wide distribution and virulence including its potentially, mutualistic interactions with microorganisms found commonly in the environment and in medical infections

Modelling of biological systems using multidimensional population balances

Biological systems are intrinsically heterogeneous and, consequently, their mathematical descriptions should account for this heterogeneity as it often influences the dynamic behaviour of the individual cells. For example, in the cell cycle dependent production ofproteins, it is necessary to account for the distribution of the individual cells with respect to their position in the cell cycle as this has a strong influence on protein production. A second notable example is the formation of cancerous cells. In this case, the failure of regulatory mechanisms results in the transition of somatic cells to their cancerous state. Therefore, in developing the corresponding mathematical model, it is necessary to consider both the different states of the cells as well as their regulation. In this regard, the population balance equation is the ideal mathematical framework to capture cell population heterogeneity as it elegantly takes into account the distribution of cell populations with respect to their intracellular state together with the phenomena of cell birth, division, differentiation and recombination. Recent developments in solution algorithms together with the exponential increase in computational abilities now permit the efficient solution of one-dimensional population balance models which attribute the heterogeneity of cell populations to differences in the age or mass of individual cells. The inherent complexity of biological systems implies that the differentiation of cells based on a single characteristic alone may not be sufficient to capture the underlying biological phenomena. Therefore, current research is focussing on the development of multi-dimensional population balances that consider the differentiation of cells based on multiple characteristics, most notably, the state of cells with respect to key intracellular metabolites. However, conventional numerical techniques are inefficient for the solution of the formulated population balance models and this warrants the development of novel, tailor-made algorithms. This thesis presents one such solution algorithm and demonstrates its application to the study of several biological systems. The algorithm developed herein employs a finite-volume technique to convert the partial-differential equation comprising the population balance model into a set of ordinary differential equations. A two-tier technique based on the solution technique for inhomogeneous differential equations is then developed to solve the system of ordinary differential equations. This approach has two main advantages: (a) the decomposition technique considerably reduces the stiffness of the system of equations enabling more efficient solution, and (b) semianalytical solutions for the integrals employed in the modelling of cell division and differentiation can be obtained further reducing computation times. Further improvements in solution efficiency are obtained by the formulation of a two-level discretisation algorithm. In this approach, processes such as cell growth which are more sensitive to the discretisation are solved using a fine grid whereas less sensitive processes such as cell' division - which are usually more computationally expensive - are solved using a coarse grid at a higher level. Thus, further improvements are obtained in the efficiency of the technique. The solution algorithm is applied to various multi-dimensional population balance models of biological systems. The technique is first demonstrated on models of oscillatory dynamics in yeast glycolysis, cell-cycle related oscillations in eukaryotes, and circadian oscillations in crayfish. A model of cell division and proliferation control in eukaryotes is an example of a second class of problems where extracellular phenomena influence the behaviour of cells. As a third case for demonstration, a hybrid model of biopolymer accumulation in bacteria is formulated. In this case, cybernetic modelling principles are used to account for intracellular competitions while the population balance framework takes into consideration the heterogeneity of the cell population. Another important aspect in the formulation ofmulti-dimensional population balances is the development of the intracellular models themselves. While research in the biological sciences is permitting the formulation of detailed dynamic models of various bioprocesses, the accurate estimation of the kinetic parameters in these models can be difficult due to the unavailability of sufficient experimental data. This can result in considerable parametric uncertainty as is demonstrated on a simple cybernetic' model of biopolymer accumulation in bacteria. However, it is shown that, via the use of systems engineering tools, experiments can be designed that permit the accurate estimation of all model parameters even when measurements pertaining to all modelled quantities are unavailable.Imperial Users onl

The mathematical model of Schizosaccharomyces pombe : Batch and repeated batch simulations.

Mathematical models are playing an important part in the current developments in engineering, science and biotechnology. Within this field the most fashionable and representative organisms are the ones who are genetically and physiologically tractable. Since the fission yeast Schizosaccharomyces pombe plays a role model among them and its behaviour has medical, genetic and industrial links (related to cancer research, metabolic pathways and beer production), this makes it a particularly interesting organism for study. This dissertation presents the first physiological model ever developed for the yeast S. pombe. The model allows for the simulation and prediction of batch and repeated batch experiments which are an important engineering tool in terms of optimization of industrial processes improving yield in bioreactors by predicting precise values of harvest fraction (HF) and dilution cycle times (DCT). The model has been developed within the generic modelling framework of CelCyMUS (Cell Cycle Model University of Surrey). As part of the research being carried out CelCyMUS has been up-dated by introducing the new Fortran 95 features and utilities in order to exploit its powerful new features and to keep the generic model in pace with technological software advancements. The model is a one-dimensional age-based population balance for the fission yeast S. pombe. It includes the four typical phases (S, G2, M and G1) with the G2 phase divided into two phases (G2A, G2B) and two checkpoints that govern the movement of cells between G1 and S, and G2B and M phases. The transitions (movement of cells between phases) are determined by a probability function related to the consumption of glucose. The G2B-M transition is also dependent on cell size, but since individual growth of cells is related to the consumption of the carbon source (in this case glucose), cell size is dependent upon the amount of glucose consumed per cell. The model also includes a phase for cells facing starvation before going into a meiotic cycle, with some chance of coming back to the mitotic cycle, and a death phase that accounts for cells dying with no chance of recovering at all. Parameters in the S. pombe model have been gathered from experimental data in batch culture reported in literature. Data generated from this specific model have been compared with data from experiments (Fotuhi, 2002) in batch and repeated batch cultures of S. pombe following the behaviour of population balance, consumption of nutrients, and production of metabolites. The new code was tested by successftilly reproducing data from mm-321 hybridoma cell line, the first specific model of a cell line developed in CelCyMUS. As a new feature a model of mass transfer has been incorporated in the generic framework. This mass transfer module accounts for interactions of metabolites (oxygen and carbon dioxide) in the gas and liquid phase of bioreactors. The new S. pombe model was fitted to the experiments of Creanor (1992) on synchronised cultures where the consumption of oxygen was being measured. Such experiments identify two points (G2B and G1) where the rate of oxygen uptake increased in the cycle, doubling the consumption at the end of every cycle. With the model fitted to experimental results in synchronised cultures of S. pombe the model was then used to simulate desynchronised cultures. S. pombe was successfully tested when reproducing experimental data generated by Fotuhi (2002) in S.pombe for batch and repeated batch bioreactors. The S. pombe model was able to simulate cell number, oxygen and glucose consumption. Carbon dioxide and ATP production were predicted by the model however there was no experimental data to compare with. Now that the S. pombe model has been tested against experimental data it will be applied in a model-based observer strategy for the online control of bioreactors