Quantitative assessment of regulation in metabolic systems

We show how metabolic regulation as commonly understood in biochemistry can be described in terms of metabolic control analysis. The steady-state values of the variables of metabolic systems (fluxes and concentrations) are determined by a set of parameters. Some of these parameters are concentrations that are set by the environment of the system; they can act as external regulators by communicating changes in the environment to the metabolic system. How effectively a system is regulated depends both on the degree to which the activity of the regulatory enzyme with which a regulator interacts directly can be altered by the regulator (its regulability) and on the ability of the regulatory enzyme to transmit the changes to the rest of the system (its regulatory capacity). The regulatory response of a system also depends on its internal organisation around key variable metabolites that act as internal regulators. The regulatory performance of the system can be judged in terms of how sensitivity the fluxes respond to the external stimulus and to what degree homeostasis in the concentrations of the internal regulators is maintained. We show how, on the level of both external and internal regulation, regulability can be quantified in terms of an elasticity coefficient and regulatory capacity in terms of a control coefficient. Metabolic regulation can therefore be described in terms of metabolic control analysis. The combined response relationship of control analysis relates regulability and regulatory capacity and allows quantification of the regulatory importance of the various interactions of regulators with enzymes in the system. On this basis we propose a quantitative terminology and analysis of metabolic regulation that shows what we should measure experimentally and how we should interpret the results. Analysis and numerical simulation of a simple model system serves to demonstrate our treatment.     

Condition-dependent cell volume and concentration of Escherichia coli to facilitate data conversion for systems biology modeling

Systems biology modeling typically requires quantitative experimental data such as intracellular concentrations or copy numbers per cell. In order to convert population-averaging omics measurement data to intracellular concentrations or cellular copy numbers, the total cell volume and number of cells in a sample need to be known. Unfortunately, even for the often studied model bacterium Escherichia coli this information is hardly available and furthermore, certain measures (e.g. cell volume) are also dependent on the growth condition. In this work, we have determined these basic data for E. coli cells when grown in 22 different conditions so that respective data conversions can be done correctly. First, we determine growth-rate dependent cell volumes. Second, we show that in a 1 ml E. coli sample at an optical density (600 nm) of 1 the total cell volume is around 3.6 μl for all conditions tested. Third, we demonstrate that the cell number in a sample can be determined on the basis of the sample's optical density and the cells' growth rate. The data presented will allow for conversion of E. coli measurement data normalized to optical density into volumetric cellular concentrations and copy numbers per cell--two important parameters for systems biology model development.     

Dynamical Allocation of Cellular Resources as an Optimal Control Problem: Novel Insights into Microbial Growth Strategies

Microbial physiology exhibits growth laws that relate the macromolecular composition of the cell to the growth rate. Recent work has shown that these empirical regularities can be derived from coarse-grained models of resource allocation. While these studies focus on steady-state growth, such conditions are rarely found in natural habitats, where microorganisms are continually challenged by environmental fluctuations. The aim of this paper is to extend the study of microbial growth strategies to dynamical environments, using a self-replicator model. We formulate dynamical growth maximization as an optimal control problem that can be solved using Pontryagin’s Maximum Principle. We compare this theoretical gold standard with different possible implementations of growth control in bacterial cells. We find that simple control strategies enabling growth-rate maximization at steady state are suboptimal for transitions from one growth regime to another, for example when shifting bacterial cells to a medium supporting a higher growth rate. A near-optimal control strategy in dynamical conditions is shown to require information on several, rather than a single physiological variable. Interestingly, this strategy has structural analogies with the regulation of ribosomal protein synthesis by ppGpp in the enterobacterium Escherichia coli. It involves sensing a mismatch between precursor and ribosome concentrations, as well as the adjustment of ribosome synthesis in a switch-like manner. Our results show how the capability of regulatory systems to integrate information about several physiological variables is critical for optimizing growth in a changing environment.     

Integral rein control in physiology II: a general model

We generalize the principle of integral rein control to include other systems which partition in such a way that the equilibrium values of some variables are not dependent on the equations governing those variables. Instead, they are determined by the dynamics of other, "regulator" variables. We improve our earlier model for the control of glucose by insulin and glucagon by relaxing the condition necessary for it to operate. The two hormones do not have to be inhibited in the same way; they need only respond to the same combination of their concentrations. We also present a model for the control of ionized calcium by PTH and calcitonin and suggest that the role of chromogranin A may be to stabilize an otherwise unstable system.     

The YebC family protein PA0964 negatively regulates the Pseudomonas aeruginosa quinolone signal system and pyocyanin production

Bacterial pathogenicity is often manifested by the expression of various cell-associated and secreted virulence factors, such as exoenzymes, protease, and toxins. In Pseudomonas aeruginosa, the expression of virulence genes is coordinately controlled by the global regulatory quorum-sensing systems, which includes the las and rhl systems as well as the Pseudomonas quinolone signal (PQS) system. Phenazine compounds are among the virulence factors under the control of both the rhl and PQS systems. In this study, regulation of the phzA1B1C1D1E1 (phzA1) operon, which is involved in phenazine synthesis, was investigated. In an initial study of inducing conditions, we observed that phzA1 was induced by subinhibitory concentrations of tetracycline. Screening of 13,000 mutants revealed 32 genes that altered phzA1 expression in the presence of subinhibitory tetracycline concentrations. Among them, the gene PA0964, designated pmpR (pqsR-mediated PQS regulator), has been identified as a novel regulator of the PQS system. It belongs to a large group of widespread conserved hypothetical proteins with unknown function, the YebC protein family (Pfam family DUF28). It negatively regulates the quorum-sensing response regulator pqsR of the PQS system by binding at its promoter region. Alongside phzA1 expression and phenazine and pyocyanin production, a set of virulence factors genes controlled by both rhl and the PQS were shown to be modulated by PmpR. Swarming motility and biofilm formation were also significantly affected. The results added another layer of regulation in the rather complex quorum-sensing systems in P. aeruginosa and demonstrated a clear functional clue for the YebC family proteins.     

Bridging the gap: linking molecular simulations and systemic descriptions of cellular compartments

Metabolic processes in biological cells are commonly either characterized at the level of individual enzymes and metabolites or at the network level. Often these two paradigms are considered as mutually exclusive because concepts from neither side are suited to describe the complete range of scales. Additionally, when modeling metabolic or regulatory cellular systems, often a large fraction of the required kinetic parameters are unknown. This even applies to such simple and extensively studied systems like the photosynthetic apparatus of purple bacteria. Using the chromatophore vesicles of Rhodobacter sphaeroides as a model system, we show that a consistent kinetic model emerges when fitting the dynamics of a molecular stochastic simulation to a set of time dependent experiments even though about two thirds of the kinetic parameters in this system are not known from experiment. Those kinetic parameters that were previously known all came out in the expected range. The simulation model was built from independent protein units composed of elementary reactions processing single metabolites. This pools-and-proteins approach naturally compiles the wealth of available molecular biological data into a systemic model and can easily be extended to describe other systems by adding new protein or nucleic acid types. The automated parameter optimization, performed with an evolutionary algorithm, reveals the sensitivity of the model to the value of each parameter and the relative importances of the experiments used. Such an analysis identifies the crucial system parameters and guides the setup of new experiments that would add most knowledge for a systemic understanding of cellular compartments. The successful combination of the molecular model and the systemic parametrization presented here on the example of the simple machinery for bacterial photosynthesis shows that it is actually possible to combine molecular and systemic modeling. This framework can now straightforwardly be applied to other currently less well characterized but biologically more relevant systems.     

Metabolic setpoint control mechanisms in different physiological systems at rest and during exercise

Using a number of different homeostatic control mechanisms in the brain and peripheral physiological systems, metabolic activity is continuously regulated at rest and during exercise to prevent catastrophic system failure. Essential for the function of these regulatory processes are baseline “setpoint” levels of metabolic function, which can be used to calculate the level of response required for the maintenance of system homeostasis after system perturbation, and to which the perturbed metabolic activity levels are returned to at the end of the regulatory process. How these setpoint levels of all the different metabolic variables in the different peripheral physiological systems are created and maintained, and why they are similar in different individuals, has not been well explained. In this article, putative system regulators of metabolic setpoint levels are described. These include that: (i) innate setpoint values are stored in a certain region of the central nervous system, such as the hypothalamus; (ii) setpoint values are created and maintained as a response to continuous external perturbations, such as gravity or “zeitgebers”, (iii) setpoint values are created and maintained by complex system dynamical activity in the different peripheral systems, where setpoint levels are regulated by the ongoing feedback control activity between different peripheral variables; (iv) human anatomical and biomechanical constraints contribute to the creation and maintenance of metabolic setpoints values; or (v) a combination of all these four different mechanisms occurs. Exercise training and disease processes can affect these metabolic setpoint values, but the setpoint values are returned to pre-training or pre-disease levels if the training stimulus is removed or if the disease process is cured. Further work is required to determine what the ultimate system regulator of metabolic setpoint values is, why some setpoint values are more stringently protected by homeostatic regulatory mechanisms than others, and the role of conscious decision making processes in determining the regulation of metabolic setpoint values.