Escherichia coil growth dynamics: A three-pool biochemically based description

A three-pool growth model of an individual Escherichia coli cell is described herein. The model is based on a previously developed chemically structured complex single cell growth model. The reduction in model complexity and the identification of the essential modes of motion, over the time scale of growth, is achieved by temporal decomposition and analysis of hierarchy in relaxation times. The three-pool model faithfully simulates the changes in cell size, cell shape, cell macromolecular composition, DNA initiation and termination periods, and the dependence of cell growth under abiotic glucose limitation. The predictions made by the reduced model compare favorably with both the experimental data and those of the full single cell model (SCM) without any parameter adjustments. The three-pool model has very few significant parameters and has the potential to find immediate practical use in bioreactor design and process control strategies. The model development illustrates the use of modal analysis to yield reduced physiologically realistic dynamic model of complex microbial system such as E. coll.     

Large‐scale analysis of the dynamics of enzymes

Protein enzymes enable the cell to execute chemical reactions in short time by accelerating the rate of the reactions in a selective manner. The motions or dynamics of the enzymes are essential for their function. Comparison of the dynamics of a set of 1247 nonhomologous enzymes was performed. For each enzyme, the slowest modes of motion are calculated using the Gaussian network model (GNM) and they are globally aligned. Alignment is done using the dynamic programming algorithm of Needleman and Wunsch, commonly used for sequence alignment. Only 96 pairs of proteins were identified to have three similar GNM slow modes with 63 of them having a similar structure. The most frequent slowest mode of motion describes a two domains anticorrelated motion that characterizes at least 23% of the enzymes. Therefore, dynamics uniqueness cannot be accounted for by the slowest mode itself but rather by the combination of several slow modes. Different quaternary structure packing can restrain the motion of enzyme subunits differently and may serve as another mechanism that increases the dynamics uniqueness. Proteins 2013; 81:1910–1918. © 2013 Wiley Periodicals, Inc.     

Reducing complexity in metabolic networks: making metabolic meshes manageable

The dynamics of complex systems can be effectively analyzed by judicious use of intrinsic time constants. Order of magnitude estimation based on time constants has been used successfully to examine the dynamic behavior of complicated processes. The main goal of this paper is to introduce this approach to the analysis of complex metabolic systems. Time constants and dynamic modes of motion are defined within the context of well-established linear algebra. The order of magnitude estimation is then introduced into the systemic framework. The main goals of the analysis are: to provide improved understanding of biochemical dynamics and their physiological significance, and to yield reduced dynamic models that are physiologically realistic but tractable for practical use.     

The consistency of large concerted motions in proteins in molecular dynamics simulations.

A detailed investigation is presented into the effect of limited sampling time and small changes in the force field on molecular dynamics simulations of a protein. Thirteen independent simulations of the B1 IgG-binding domain of streptococcal protein G were performed, with small changes in the simulation parameters in each simulation. Parameters studied included temperature, bond constraints, cut-off radius for electrostatic interactions, and initial placement of hydrogen atoms. The essential dynamics technique was used to reveal dynamic differences between the simulations. Similar essential dynamics properties were found for all simulations, indicating that the large concerted motions found in the simulations are not particularly sensitive to small changes in the force field. A thorough investigation into the stability of the essential dynamics properties as derived from a molecular dynamics simulation of a few hundred picoseconds is provided. Although the definition of the essential modes of motion has not fully converged in these short simulations, the subspace in which these modes are confined is found to be reproducible.     

A small metabolic flux model to identify transient metabolic regulations in Saccharomyces cerevisiae

The understanding of dynamic metabolic regulations is important for physiological studies and strain characterization tasks. The present study combined transient experiments with online metabolic flux analysis (MFA) in order to quantify metabolic regulations, namely carbon catabolite repression of respiration and transient acetic-acid production, in Saccharomyces cerevisiae during aerobic growth on glucose. The aim was to investigate which additional information can be gained from using a small metabolic flux model to study transient growth provoked by shift-up and shift-down experiments, compared to online monitoring alone. The MFA model allowed us to propose new correlations between pathways of the central metabolism. A linear correlation between glycolytic flux and respiratory capacity holds for shift-down and shift-up experiments. This confirmed that respiratory functions were subjected to carbon catabolite repression and suggested that respiratory capacity is controlled by the glycolytic flux rather than the glucose influx. Furthermore, the model showed that control of repression of respiration by the glycolytic flux was a dynamic phenomenon. Co-factor balancing within the MFA model showed that transient acetic-acid production indicated a transient limitation in another part of the central metabolism but not in oxidative phosphorylation. However, at super-critical growth rates and when coupling of anabolism and catabolism is resumed, the limitation shifts to oxidative phosphorylation, with the consequence that ethanol is formed. The online application of small metabolic flux models to transient experiments enhanced the physiological insight into transient growth and opens up the use of transient experiments as an efficient tool to understand dynamic metabolic regulations.     

Dynamic modeling of the central carbon metabolism of Escherichia coli

Application of metabolic engineering principles to the rational design of microbial production processes crucially depends on the ability to describe quantitatively the systemic behavior of the central carbon metabolism to redirect carbon fluxes to the product-forming pathways. Despite the importance for several production processes, development of an essential dynamic model for central carbon metabolism of Escherichia coli has been severely hampered by the current lack of kinetic information on the dynamics of the metabolic reactions. Here we present the design and experimental validation of such a dynamic model, which, for the first time, links the sugar transport system (i.e., phosphotransferase system [PTS]) with the reactions of glycolysis and the pentose-phosphate pathway. Experimental observations of intracellular concentrations of metabolites and cometabolites at transient conditions are used to validate the structure of the model and to estimate the kinetic parameters. Further analysis of the detailed characteristics of the system offers the possibility of studying important questions regarding the stability and control of metabolic fluxes.     

Dynamic flux balance analysis of the metabolism of Saccharomyces cerevisiae during the shift from fully respirative or respirofermentative metabolic states to anaerobiosis

Dynamic flux balance analysis was utilized to simulate the metabolic behaviour of initially fully respirative and respirofermentative steady-state cultures of Saccharomyces?cerevisiae during sudden oxygen depletion. The hybrid model for the dynamic flux balance analysis included a stoichiometric genome-scale metabolic model as a static part and dynamic equations for the uptake of glucose and the cessation of respirative metabolism. The yeast consensus genome-scale metabolic model [Herrg?rd MJ et?al. (2008) Nat Biotechnol26, 1155-1160; Dobson PD et?al. (2010) BMC Syst Biol4, 145] was refined with respect to oxygen-dependent energy metabolism and further modified to reflect S.?cerevisiae anabolism in the absence of oxygen. Dynamic flux balance analysis captured well the essential features of the dynamic metabolic behaviour of S.?cerevisiae during adaptation to anaerobiosis. Modelling and simulation enabled the identification of short time-scale flux distribution dynamics under the transition to anaerobic metabolism, during which the specific growth rate was reduced, as well as longer time-scale process dynamics when the specific growth rate recovered. Expression of the metabolic genes was set into the context of the identified dynamics. Metabolic gene expression responses associated with the specific growth rate and with the cessation of respirative metabolism were distinguished.     

Predicting Essential Metabolic Genome Content of Niche-Specific Enterobacterial Human Pathogens during Simulation of Host Environments

Microorganisms have evolved to occupy certain environmental niches, and the metabolic genes essential for growth in these locations are retained in the genomes. Many microorganisms inhabit niches located in the human body, sometimes causing disease, and may retain genes essential for growth in locations such as the bloodstream and urinary tract, or growth during intracellular invasion of the hosts’ macrophage cells. Strains of Escherichia coli (E. coli) and Salmonella spp. are thought to have evolved over 100 million years from a common ancestor, and now cause disease in specific niches within humans. Here we have used a genome scale metabolic model representing the pangenome of E. coli which contains all metabolic reactions encoded by genes from 16 E. coli genomes, and have simulated environmental conditions found in the human bloodstream, urinary tract, and macrophage to determine essential metabolic genes needed for growth in each location. We compared the predicted essential genes for three E. coli strains and one Salmonella strain that cause disease in each host environment, and determined that essential gene retention could be accurately predicted using this approach. This project demonstrated that simulating human body environments such as the bloodstream can successfully lead to accurate computational predictions of essential/important genes.     

Capturing the essence of a metabolic network: A flux balance analysis approach

As genome-scale metabolic reconstructions emerge, tools to manage their size and complexity will be increasingly important. Flux balance analysis (FBA) is a constraint-based approach widely used to study the metabolic capabilities of cellular or subcellular systems. FBA problems are highly underdetermined and many different phenotypes can satisfy any set of constraints through which the metabolic system is represented.Two of the main concerns in FBA are exploring the space of solutions for a given metabolic network and finding a specific phenotype which is representative for a given task such as maximal growth rate. Here, we introduce a recursive algorithm suitable for overcoming both of these concerns. The method proposed is able to find the alternate optimal patterns of active reactions of an FBA problem and identify the minimal subnetwork able to perform a specific task as optimally as the whole.Our method represents an alternative to and an extension of other approaches conceived for exploring the space of solutions of an FBA problem. It may also be particularly helpful in defining a scaffold of reactions upon which to build up a dynamic model, when the important pathways of the system have not yet been well-defined.     

Solitary wave dynamics as a mechanism for explaining the internal motion during microtubule growth

Microtubules, which play many diverse and important roles in biological systems, are usually made up of 13 nearly axial protofilaments formed from individual tubulin molecules. In this paper, a nonlinear dynamic model has been developed to elucidate the mechanism of the internal motion occurring during the assembly of microtubules. The results derived from the model indicate that such internal motion is associated with a solitary wave, or kink, excited by the energy released from the hydrolysis of GTP ? GDP in microtubular solutions. As the kink moves forward, the individual tubulin molecules involved in the kink undergo motions that can be likened to the dislocation of atoms within the crystal lattice. Thus, the dynamic instability of microtubules may be characterized by a series of dislocation motions of the tubulin molecules. An energy estimate shows that a kink in the system possesses about 0.36–0.44 eV, which is quite close to but smaller than the 0.49 eV of energy released from the hydrolysis of GTP. Therefore, the relevant energy derived from our model is fully consistent with experimental observations; this finding also suggests that the hydrolysis energy may be responsible for exciting the solitary wave, or kink, leading to tubulin dislocation in microtubules. Our model, and its intrinsic properties, i.e., dynamic nonlinearity, thermodynamic irreversibility, as well as an energy input from a sustained source, implies that the growth of microtubules is a typical dissipative process and that their structure in vivo is typical of dissipative structures. © 1994 John Wiley & Sons, Inc.     

Flux analysis uncovers key role of functional redundancy in formaldehyde metabolism

Genome-scale analysis of predicted metabolic pathways has revealed the common occurrence of apparent redundancy for specific functional units, or metabolic modules. In many cases, mutation analysis does not resolve function, and instead, direct experimental analysis of metabolic flux under changing conditions is necessary. In order to use genome sequences to build models of cellular function, it is important to define function for such apparently redundant systems. Here we describe direct flux measurements to determine the role of redundancy in three modules involved in formaldehyde assimilation and dissimilation in a bacterium growing on methanol. A combination of deuterium and ¹⁴C labeling was used to measure the flux through each of the branches of metabolism for growth on methanol during transitions into and out of methylotrophy. The cells were found to differentially partition formaldehyde among the three modules depending on the flux of methanol into the cell. A dynamic mathematical model demonstrated that the kinetic constants of the enzymes involved are sufficient to account for this phenomenon. We demonstrate the role of redundancy in formaldehyde metabolism and have uncovered a new paradigm for coping with toxic, high-flux metabolic intermediates: a dynamic, interconnected metabolic loop.     

Time hierarchy, equilibrium and non-equilibrium in metabolic systems.

A metabolic system consists of cooperating biochemical reactions. The motion is described by differential equations in the metabolites. The right-hand sides of these equations are linear combinations of the velocities of the individual reactions. These velocities depend in a non-linear manner on the metabolite concentrations (according to the law of mass action). A characteristic "metabolic" time may be defined for the motion of the whole system. It scales the essential metabolic events whose evolution time is comparable to this metabolite time unit. The constituent reactions of the metabolic system have an individual characteristic time which need not coincide with the general metabolic time. The individual time characterises the approach to the individual equilibrium of the isolated undisturbed reaction. According to the ratio of these two time scales, a single reaction may be fast, or slow, or essential, as compared with the metabolic events. Characteristic time of a single reaction and its steady-state deviation from equilibrium are closely related. It can be shown that the relative deviation from equilibrium of a reaction within the metabolic network is of the same numerical order as the ratio between individual time to metabolic time. The interaction of many reactions with different characteristic times introduces a time hierarchy into the system. This can be made transparent by appropriate scaling and by linear transformation of the system. The subsystem of fast cooperating reactions (dehydrogenases, phosphotransferases) attains a state which is near to the individual equilibrium and reestablishes this state after perturbation. The equilibration is fast; an ultrarapid phase of cofactor equilibrium can be distinguished from the fast phase of substrate equilibrium (exchange of metabolic material between different pathways). During the slower metabolic phase these near-equilibria manifest themselves as stoichiometric linkage between unrelated metabolites. The latter cease to be independent variables and combine to metabolic pools. It can be strictly shown that the essential variables at the metabolic time scale are carrier pools and the degree of occupancy of these carriers by metabolic groups. Chemically different types of carrier pools may be functionally linked together by fast reactions. A consequence of such an arrangement of reactions are distance effects: Changes at one end of a metabolic map may be directly conveyed to other pathways via stoichiometric linkage brought about by fast equilibration of cofactor reactions.     

Quantifying Neurite Growth Mediated by Interactions among Secretory Vesicles, Microtubules, and Actin Networks

Neurite growth is a fundamental process of neuronal development, which requires both membrane expansions by exocytosis and cytoskeletal dynamics. However, the specific contribution of these processes has not been yet assessed quantitatively. To study and quantify the growth process, we construct a biophysical model in which we relate the overall neurite outgrowth rate to the vesicle dynamics. By considering the complex motion of vesicles in the cell soma, we demonstrate from biophysical consideration that the main step of finding the neurite initiation site relies mainly on a two-dimensional diffusion/sequestration/fusion at the cell surface and we obtain a novel formula for the flux of vesicles at the neurite base. In the absence of microtubules, we show that a nascent neurite initiated by vesicular delivery can only reach a small length. By adding the microtubule dynamics to the secretory pathway and using stochastic analysis and simulations, we study the complex dynamics of neurite growth. Within this model, depending on the coupling parameter between the microtubules and the neurite, we find different regimes of growth, which describe dendritic and axonal growth. To validate one aspect of our model, we demonstrate that the experimental flux of TI-VAMP but not Synaptobrevin 2 vesicles contributes to the neurite growth. We conclude that although vesicles can be generated randomly in the cell body, the search for the neurite position using the microtubule network and diffusion is quite fast. Furthermore, when the TI-VAMP vesicular flow is large enough, the interactions between the microtubule bundle and the neurite control the growth process. In addition, all of these processes intimately cooperate to mediate the various modes of neurite growth: the model predicts three different growing modes including, in addition to the stable axonal growth and the stochastic dendritic growth, a fast oscillatory regime. Finally our study demonstrates that cytoskeletal dynamics is necessary to generate long protrusion, while vesicular delivery alone can only generate small neurite.     

Description of the deformation of the left ventricle by a kinematic model.

A model of left ventricular (LV) kinematics is essential to identify the fundamental physiological modes of LV deformation during a complete cardiac cycle as observed from the motion of a finite number of markers embedded in the LV wall. Kinematics can be described by a number of modes of motion and deformation in succession. An obvious mode of LV deformation is the ejection of cavity volume while the wall thickens. In the more sophisticated model of LV kinematics developed here, seven time-dependent parameters were used to describe not only volume change but also torsion and shape changes throughout the cardiac cycle. Rigid-body motion required another six parameters. The kinematic model employed a deformation field that had no singularities within the myocardium, and all parameters describing the modes of deformation were dimensionless. Note that torsion, volume and symmetric shape changes all require the definition of a cardiac coordinate system, which has generally been related to the measured cardiac geometry by reference to approximate anatomical landmarks. However, in the present study the coordinate system was positioned objectively by a least-squares fit of the kinematic model to the measured motion of markers. Theoretically, at least five markers are needed to find a unique set of parameters.(ABSTRACT TRUNCATED AT 250 WORDS)     

Metabolic modeling of Saccharomyces cerevisiae using the optimal control of homeostasis: a cybernetic model definition

A model is presented to describe the observed behavior of microorganisms that aim at metabolic homeostasis while growing and adapting to their environment in an optimal way. The cellular metabolism is seen as a network with a multiple controller system with both feedback and feedforward control, i.e., a model based on a dynamic optimal metabolic control. The dynamic network consists of aggregated pathways, each having a control setpoint for the metabolic states at a given growth rate. This set of strategies of the cell forms a true cybernetic model with a minimal number of assumptions. The cellular strategies and constraints were derived from metabolic flux analysis using an identified, biochemically relevant, stoichiometry matrix derived from experimental data on the cellular composition of continuous cultures of Saccharomyces cerevisiae. Based on these data a cybernetic model was developed to study its dynamic behavior. The growth rate of the cell is determined by the structural compounds and fluxes of compounds related to central metabolism. In contrast to many other cybernetic models, the minimal model does not consist of any assumed internal kinetic parameters or interactions. This necessitates the use of a stepwise integration with an optimization of the fluxes at every time interval. Some examples of the behavior of this model are given with respect to steady states and pulse responses. This model is very suitable for describing semiquantitatively dynamics of global cellular metabolism and may form a useful framework for including structured and more detailed kinetic models.     

Determining important regulatory relations of amino acids from dynamic network analysis of plasma amino acids

The changes in the concentrations of plasma amino acids do not always follow the flow-based metabolic pathway network. We have previously shown that there is a control-based network structure among plasma amino acids besides the metabolic pathway map. Based on this network structure, in this study, we performed dynamic analysis using time-course data of the plasma samples of rats fed single essential amino acid deficient diet. Using S-system model (conceptual mathematical model represented by power-law formalism), we inferred the dynamic network structure which reproduces the actual time-courses within the error allowance of 13.17%. By performing sensitivity analysis, three of the most dominant relations in this network were selected; the control paths from leucine to valine, from methionine to threonine, and from leucine to isoleucine. This result is in good agreement with the biological knowledge regarding branched-chain amino acids, and suggests the biological importance of the effect from methionine to threonine.