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Organisms must acquire and use environmental information to guide their behaviors. However, it is unclear whether and how information quantitatively limits behavioral performance. Here, we relate information to behavioral performance in Escherichia coli chemotaxis. First, we derive a theoretical limit for the maximum achievable gradient-climbing speed given a cells information acquisition rate. Next, we measure cells gradient-climbing speeds and the rate of information acquisition by the chemotaxis pathway. We find that E. coli make behavioral decisions with much less than the 1 bit required to determine whether they are swimming up-gradient. However, they use this information efficiently, performing near the theoretical limit. Thus, information can limit organisms performance, and sensory-motor pathways may have evolved to efficiently use information from the environment.
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Bacteria have remarkably robust cell shape control mechanisms. For example, cell diameter only varies by a few percent across a population. MreB is necessary for establishment and maintenance of rod shape although the mechanism of shape control remains unknown. We perturbed MreB in two complimentary ways to produce steady-state cell diameters over a wide range, from 790+/-30 nm to 1700+/-20 nm. To determine which properties of MreB are important for diameter control, we correlated structural characteristics of fluorescently-tagged MreB polymers with cell diameter by simultaneously analyzing 3-dimensional images of MreB and cell shape. Our results indicate that the pitch angle of MreB inversely correlates with cell diameter. Other correlations are not found to be significant. These results demonstrate that the physical properties of MreB filaments are important for shape control and support a model in which MreB dictates cell diameter and organizes cell wall growth to produce a chiral cell wall.
We present a mathematical model of glucose-lactose diauxic growth in Escherichia coli including both the postive and negative regulation mechanisms of the lactose operon as well as the inducer exclusion. To validate this model, we first calculated the time evolution of beta-galactosidase for only the lactose nutrient and compared the numerical results with experimental data. Second, we compared the calculated cell biomass of the glucose-lactose diauxic growth with the experimental optical density of the diauxic growth for a particular E. coli MG 1655. For both cases, the numerical calculations from this model are in good agreement with these two experiments data. The diauxic growth pattern of a wild type E. coli was also investigated.
Adherent cells exert traction forces on to their environment, which allows them to migrate, to maintain tissue integrity, and to form complex multicellular structures. This traction can be measured in a perturbation-free manner with traction force microscopy (TFM). In TFM, traction is usually calculated via the solution of a linear system, which is complicated by undersampled input data, acquisition noise, and large condition numbers for some methods. Therefore, standard TFM algorithms either employ data filtering or regularization. However, these approaches require a manual selection of filter- or regularization parameters and consequently exhibit a substantial degree of subjectiveness. This shortcoming is particularly serious when cells in different conditions are to be compared because optimal noise suppression needs to be adapted for every situation, which invariably results in systematic errors. Here, we systematically test the performance of new methods from computer vision and Bayesian inference for solving the inverse problem in TFM. We compare two classical schemes, L1- and L2-regularization, with three previously untested schemes, namely Elastic Net regularization, Proximal Gradient Lasso, and Proximal Gradient Elastic Net. Overall, we find that Elastic Net regularization, which combines L1 and L2 regularization, outperforms all other methods with regard to accuracy of traction reconstruction. Next, we develop two methods, Bayesian L2 regularization and Advanced Bayesian L2 regularization, for automatic, optimal L2 regularization. Using artificial data and experimental data, we show that these methods enable robust reconstruction of traction without requiring a difficult selection of regularization parameters specifically for each data set. Thus, Bayesian methods can mitigate the considerable uncertainty inherent in comparing cellular traction forces.
Two distinct mechanisms for filtering noise in an input signal are identified in a class of adaptive sensory networks. We find that the high frequency noise is filtered by the output degradation process through time-averaging; while the low frequency noise is damped by adaptation through negative feedback. Both filtering processes themselves introduce intrinsic noises, which are found to be unfiltered and can thus amount to a significant internal noise floor even without signaling. These results are applied to E. coli chemotaxis. We show unambiguously that the molecular mechanism for the Berg-Purcell time-averaging scheme is the dephosphorylation of the response regulator CheY-P, not the receptor adaptation process as previously suggested. The high frequency noise due to the stochastic ligand binding-unbinding events and the random ligand molecule diffusion is averaged by the CheY-P dephosphorylation process to a negligible level in E.coli. We identify a previously unstudied noise source caused by the random motion of the cell in a ligand gradient. We show that this random walk induced signal noise has a divergent low frequency component, which is only rendered finite by the receptor adaptation process. For gradients within the E. coli sensing range, this dominant external noise can be comparable to the significant intrinsic noise in the system. The dependence of the response and its fluctuations on the key time scales of the system are studied systematically. We show that the chemotaxis pathway may have evolved to optimize gradient sensing, strong response, and noise control in different time scales
All living cells need to coordinate DNA replication with growth and division to generate cell cycles that are stable in time. The bacterium Escherichia coli initiates replication at a volume per origin that on average is independent of the growth rate. It also adds an on average constant volume per origin between successive initiation events, independent of the initiation size. Yet, a molecular model that can explain these observations has been lacking. Here, we develop a mathematical model of DNA replication initiation in E. coli that is consistent with a wealth of experimental data. We first show that the previously proposed initiator titration model, which is based on the accumulation of the initiator protein DnaA on chromosomal titration sites, is not consistent with the experimental data. We then present a model that is based on an ultra-sensitive switch between an inactive form of DnaA and an active form that induces replication initiation. Our model shows that at low growth rates the switch is predominantly controlled by activation of DnaA via lipids and deactivation via the chromosomal site datA, while at high growth rates DARS2 and RIDA become essential. Crucially, in our mean-field model DNA replication is initiated at a constant volume per origin, qualifying our model as a sizer. Yet, we show that in a stochastic version of the same model the inevitable fluctuations in the components that control the DnaA activation switch naturally give rise to the experimentally observed adder correlations.
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