Simulation of cellular behavior on multiple scales requires models that are sufficiently detailed to capture central intracellular processes but at the same time enable the simulation of entire cell populations in a computationally cheap way. In this paper we present RapidCell, a hybrid model of chemotactic Escherichia coli that combines the Monod-Wyman-Changeux signal processing by mixed chemoreceptor clusters, the adaptation dynamics described by ordinary differential equations, and a detailed model of cell tumbling. Our model dramatically reduces computational costs and allows the highly efficient simulation of E. coli chemotaxis. We use the model to investigate chemotaxis in different gradients, and suggest a new, constant-activity type of gradient to systematically study chemotactic behavior of virtual bacteria. Using the unique properties of this gradient, we show that optimal chemotaxis is observed in a narrow range of CheA kinase activity, where concentration of the response regulator CheY-P falls into the operating range of flagellar motors. Our simulations also confirm that the CheB phosphorylation feedback improves chemotactic efficiency by shifting the average CheY-P concentration to fit the motor operating range. Our results suggest that in liquid media the variability in adaptation times among cells may be evolutionary favorable to ensure coexistence of subpopulations that will be optimally tactic in different gradients. However, in a porous medium (agar) such variability appears to be less important, because agar structure poses mainly negative selection against subpopulations with low levels of adaptation enzymes. RapidCell is available from the authors upon request.

Signal processing in bacterial chemotaxis relies on large sensory complexes consisting of thousands of protein molecules. These clusters create a scaffold that increases the efficiency of pathway reactions and amplifies and integrates chemotactic signals. The cluster core in Escherichia coli comprises a ternary complex composed of receptors, kinase CheA, and adaptor protein CheW. All other chemotaxis proteins localize to clusters by binding either directly to receptors or to CheA. Here, we used fluorescence recovery after photobleaching (FRAP) to investigate the turnover of chemotaxis proteins at the cluster and their mobility in the cytoplasm. We found that cluster exchange kinetics were proteinspecific and took place on several characteristic time scales that correspond to excitation, adaptation, and cell division, respectively. We further applied analytical and numerical data fitting to analyze intracellular protein diffusion and to estimate the rate constants of cluster equilibration in vivo. Our results indicate that the rates of protein turnover at the cluster have evolved to ensure optimal performance of the chemotaxis pathway.T he relatively simple chemotaxis signaling pathway in Escherichia coli, with analogues of its components-receptors, kinase, phosphatase, and adaptation system-common to many other networks, is an ideal model system for studying general principles of signal transduction (1-3). In E. coli, allosteric interactions among receptors in chemosensory arrays or clusters (Fig. 1), where receptors of different ligand specificities are intermixed (4, 5), integrate and amplify chemotactic stimuli. The networked receptors regulate the autophosphorylation activity of an associated kinase, CheA, which in turn controls the phosphorylation state of a small response regulator protein, CheY, to modulate the cell's flagellar motors. The signaling pathway also includes CheZ, a phosphatase of CheY-P. Excitatory signaling is rapid: changes in CheY phosphorylation level upon repellent or attractant stimulation take place in several hundreds of milliseconds (6-9).In addition, the pathway includes an adaptation system, comprising methyltransferase CheR and methylesterase CheB, that adjusts the activity and sensitivity of the sensory complex by methylating and demethylating receptors. The adaptation system uses feedback from receptor and kinase activity to return CheY phosphorylation to a preset level even in the presence of high levels of chemoeffectors. The time course of the adaptation process depends on stimulus strength (10, 11), varying from several seconds for weak stimuli to several minutes for strong stimuli.Most of the reaction rates and binding constants for chemotaxis proteins have been measured in vitro, and the average intracellular protein concentrations under standard growth conditions were determined (12,13). This abundance of biochemical data has inspired multiple attempts at detailed kinetic analysis of the chemotaxis pathway (9, 13-17), making it the most thoroughly modeled signaling pathw...

Ethylene oxide synthesis has been chosen as a benchmark case to evaluate the performance of a microreaction system in comparison to an existing industrial process. This reaction was selected because microreaction technology provides equipment with very good mass-and heat-transfer conditions, which avoids hot spots inside the reactor channels that are known problems for the partial oxidation of ethylene. Furthermore, because the microstructured reactors are inherently safe with respect to explosions, gas compositions within the explosion limits are attainable and can be handled safely. For example, 15% ethylene in pure oxygen, which is in the middle of the explosive regime and far away from typical compositions for industrial processes, could be used. Space time yields of 0.14-0.78 tons h -1 m -3 calculated on the basis of the channel volume, in comparison to the values of 0.13-0.26 tons h -1 m -3 for an industrial reactor calculated on the basis of the reactor volume, have been achieved by using the microreactor.

Evolutionary selection for robustness of signaling output in the face of stochastic variations in protein expression may explain the organization of bacterial chemotaxis genes.

Advanced experimental techniques in chemistry and physics provide increasing access to detailed deterministic mass action models for chemical reaction kinetics. Especially in complex technical or biochemical systems the huge amount of species and reaction pathways involved in a detailed modeling approach call for efficient methods of model reduction. These should be automatic and based on a firm mathematical analysis of the ordinary differential equations underlying the chemical kinetics in deterministic models. A main purpose of model reduction is to enable accurate numerical simulations of even high dimensional and spatially extended reaction systems. The latter include physical transport mechanisms and are modeled by partial differential equations. Their numerical solution for hundreds or thousands of species within a reasonable time will exceed computer capacities available now and in a foreseeable future. The central idea of model reduction is to replace the high dimensional dynamics by a low dimensional approximation with an appropriate degree of accuracy. Here I present a global approach to model reduction based on the concept of minimal entropy production and its numerical implementation. For given values of a single species concentration in a chemical system all other species concentrations are computed under the assumption that the system is as close as possible to its attractor, the thermodynamic equilibrium, in the sense that all modes of thermodynamic forces are maximally relaxed except the one, which drives the remaining system dynamics. This relaxation is expressed in terms of minimal entropy production for single reaction steps along phase space trajectories.