Perfect and near perfect adaptation in a model of bacterial chemotaxis

The signaling apparatus mediating bacterial chemotaxis can adapt to a wide range of persistent external stimuli. In many cases, the bacterial activity returns to its pre-stimulus level exactly and this "perfect adaptability" is robust against variations in various chemotaxis protein concentrations. We model the bacterial chemotaxis signaling pathway, from ligand binding to CheY phosphorylation. By solving the steady-state equations of the model analytically, we derive a full set of conditions for the system to achieve perfect adaptation. The conditions related to the phosphorylation part of the pathway are discovered for the first time, while other conditions are generalization of the ones found in previous works. Sensitivity of the perfect adaptation is evaluated by perturbing these conditions. We find that, even in the absence of some of the perfect adaptation conditions, adaptation can be achieved with near perfect precision as a result of the separation of scales in both chemotaxis protein concentrations and reaction rates, or specific properties of the receptor distribution in different methylation states. Since near perfect adaptation can be found in much larger regions of the parameter space than that defined by the perfect adaptation conditions, their existence is essential to understand robustness in bacterial chemotaxis.Comment: 16 pages, 9 figure

Dynamic receptor team formation can explain the high signal transduction gain in E. coli

Evolution has provided many organisms with sophisticated sensory systems that enable them to respond to signals in their environment. The response frequently involves alteration in the pattern of movement, such as the chemokinesis of the bacterium Escherichia coli, which swims by rotating its flagella. When rotated counterclockwise (CCW) the flagella coalesce into a propulsive bundle, producing a relatively straight ``run'', and when rotated clockwise (CW) they fly apart, resulting in a ``tumble'' which reorients the cell with little translocation. A stochastic process generates the runs and tumbles, and in a chemoeffector gradient runs that carry the cell in a favorable direction are extended. The overall structure of the signal transduction pathways is well-characterized in E. coli, but important details are still not understood. Only recently has a source of gain in the signal transduction network been identified experimentally, and here we present a mathematical model based on dynamic assembly of receptor teams that can explain this observation.Comment: Accepted for publication in the Biophysical Journa

Modeling of negative autoregulated genetic networks in single cells

We discuss recent developments in the modeling of negative autoregulated genetic networks. In particular, we consider the temporal evolution of the population of mRNA and proteins in simple networks using rate equations. In the limit of low copy numbers, fluctuation effects become significant and more adequate modeling is then achieved using the master equation formalism. The analogy between regulatory gene networks and chemical reaction networks on dust grains in the interstellar medium is discussed. The analysis and simulation of complex reaction networks are also considered.Comment: 15 pages, 4 figures. Published in Gen

Relationship between cellular response and behavioral variability in bacterial chemotaxis

Bacterial chemotaxis in Escherichia coli is a canonical system for the study of signal transduction. A remarkable feature of this system is the coexistence of precise adaptation in population with large fluctuating cellular behavior in single cells (Korobkova et al. 2004, Nature, 428, 574). Using a stochastic model, we found that the large behavioral variability experimentally observed in non-stimulated cells is a direct consequence of the architecture of this adaptive system. Reversible covalent modification cycles, in which methylation and demethylation reactions antagonistically regulate the activity of receptor-kinase complexes, operate outside the region of first-order kinetics. As a result, the receptor-kinase that governs cellular behavior exhibits a sigmoidal activation curve. This curve simultaneously amplifies the inherent stochastic fluctuations in the system and lengthens the relaxation time in response to stimulus. Because stochastic fluctuations cause large behavioral variability and the relaxation time governs the average duration of runs in response to small stimuli, cells with the greatest fluctuating behavior also display the largest chemotactic response. Finally, Large-scale simulations of digital bacteria suggest that the chemotaxis network is tuned to simultaneously optimize the random spread of cells in absence of nutrients and the cellular response to gradients of attractant.Comment: 15 pages, 4 figures, Supporting information available here http://cluzel.uchicago.edu/data/emonet/arxiv_070531_supp.pd

Understanding the link between single cell and population scale responses of Escherichia coli in differing ligand gradients

We formulate an agent-based population model of Escherichia coli cells which incorporates a description of the chemotaxis signalling cascade at the single cell scale. The model is used to gain insight into the link between the signalling cascade dynamics and the overall population response to differing chemoattractant gradients. Firstly, we consider how the observed variation in total (phosphorylated and unphosphorylated) signalling protein concentration affects the ability of cells to accumulate in differing chemoattractant gradients. Results reveal that a variation in total cell protein concentration between cells may be a mechanism for the survival of cell colonies across a wide range of differing environments. We then study the response of cells in the presence of two different chemoattractants.In doing so we demonstrate that the population scale response depends not on the absolute concentration of each chemoattractant but on the sensitivity of the chemoreceptors to their respective concentrations. Our results show the clear link between single cell features and the overall environment in which cells reside

The challenge of evaluating pain and a pre-incisional local anesthetic block

Background. Our objective was to test the effectiveness of a local anesthetic line block administered before surgery in reducing postoperative pain scores in dogs undergoing ovariohysterectomy (OVHX).Methods. This study is a prospective, randomized, blinded, clinical trial involving 59 healthy female dogs. An algometric pressure-measuring device was used to determine nociceptive threshold, and compared to three subjective pain scales. Group L/B received a line block of lidocaine (4 mg/kg) and bupivacaine (1 mg/kg) subcutaneously in the area of the incision site and saline subcutaneously as premedication; group L/BM (positive control) received a similar block and morphine (0.5 mg/kg) subcutaneously for premedication; and group SS (negative control) received a saline line block and saline premedication. Criteria for rescue analgesia were defined before the study. Dogs were assessed prior to surgery, at extubation (time 0) and at 2, 4, 6, 8 and 24 h post-recovery. The data were analyzed with one-way ANOVA, and a Split Plot Repeated Measures ANOVA with one grouping factor and one repeat factor (time). P < 0.05 was considered statistically significant.Results. Approximately 33% of dogs required rescue analgesia at some point during the study, with no significant difference between groups. There was no significant difference between treatment groups with any assessment method.Conclusions. As there were no statistically significant differences between positive and negative controls, the outcome of this technique cannot be proven

Treatment of Septic arthritis of the coxofemoral joint in 12 foals

Objective: To describe the clinical signs, surgical treatment, and outcome of septic arthritis of the coxofemoral joint in foals. Study Design: Retrospective clinical study. Sample Population: Foals (n = 12) with confirmed sepsis of the coxofemoral joint. Methods: Lameness was localized to the coxofemoral joint based on physical examination. Sepsis was confirmed by cytological analysis of synovial fluid obtained under ultrasonographic guidance, during general anesthesia or standing sedation. Intra-articular analgesia was used as an adjunct diagnostic modality in 2 foals. Surgical lavage of the affected joint was performed via arthroscopy or needle lavage, with repeated lavage performed in 7 foals. Results: Synovial fluid contained 4.4 to 173 × 109/L white blood cells (WBCs), and 38-63 g/L total protein. Cultures were positive in 10/12 foals. Isolated organisms included Salmonella spp., Streptococcus spp., Rhodococcus spp., Enterococcus spp., Escherichia spp., Staphylococcus spp., Acinetobacter spp., Methicillin-resistant Staphylococcus aureus and Bacillus spp. Ten foals were discharged from hospital (83%). One of these was euthanized 15 days later due to chronic intestinal salmonellosis and renal failure, and 9 foals survived with no residual lameness detected 1 year after discharge from hospital. Conclusions: Sepsis of the coxofermoral joint can be effectively treated with a combination of arthroscopic lavage and the use of systemic and local antimicrobials

Overview of mathematical approaches used to model bacterial chemotaxis I: the single cell

Mathematical modeling of bacterial chemotaxis systems has been influential and insightful in helping to understand experimental observations. We provide here a comprehensive overview of the range of mathematical approaches used for modeling, within a single bacterium, chemotactic processes caused by changes to external gradients in its environment. Specific areas of the bacterial system which have been studied and modeled are discussed in detail, including the modeling of adaptation in response to attractant gradients, the intracellular phosphorylation cascade, membrane receptor clustering, and spatial modeling of intracellular protein signal transduction. The importance of producing robust models that address adaptation, gain, and sensitivity are also discussed. This review highlights that while mathematical modeling has aided in understanding bacterial chemotaxis on the individual cell scale and guiding experimental design, no single model succeeds in robustly describing all of the basic elements of the cell. We conclude by discussing the importance of this and the future of modeling in this area