Adaptive response and enlargement of dynamic range

Many membrane channels and receptors exhibit adaptive, or desensitized, response to a strong sustained input stimulus, often supported by protein activity-dependent inactivation. Adaptive response is thought to be related to various cellular functions such as homeostasis and enlargement of dynamic range by background compensation. Here we study the quantitative relation between adaptive response and background compensation within a modeling framework. We show that any particular type of adaptive response is neither sufficient nor necessary for adaptive enlargement of dynamic range. In particular a precise adaptive response, where system activity is maintained at a constant level at steady state, does not ensure a large dynamic range neither in input signal nor in system output. A general mechanism for input dynamic range enlargement can come about from the activity-dependent modulation of protein responsiveness by multiple biochemical modification, regardless of the type of adaptive response it induces. Therefore hierarchical biochemical processes such as methylation and phosphorylation are natural candidates to induce this property in signaling systems.Comment: Corrected typos, minor text revision

Exact asymptotic analysis for metapopulation dynamics on correlated dynamic landscapes

We compute the mean patch occupancy for a stochastic, spatially explicit patch-occupancy metapopulation model on a dynamic, correlated landscape, using a mathematically exact perturbation expansion about a mean-field limit that applies when dispersal range is large. Stochasticity in the metapopulation and landscape dynamics gives negative contributions to patch occupancy, the former being more important at high occupancy and the latter at low occupancy. Positive landscape correlations always benefit the metapopulation, but are only significant when the correlation length is comparable to, or smaller than, the dispersal range. Our analytical results allow us to consider the importance of spatial kernels in all generality. We find that the shape of the landscape correlation function is typically unimportant, and that the variance is overwhelmingly the most important property of the colonisation kernel. However, short-range singularities in either the colonisation kernel or landscape correlations can give rise to qualitatively different behaviour

Chemotactic response and adaptation dynamics in Escherichia coli

Adaptation of the chemotaxis sensory pathway of the bacterium Escherichia coli is integral for detecting chemicals over a wide range of background concentrations, ultimately allowing cells to swim towards sources of attractant and away from repellents. Its biochemical mechanism based on methylation and demethylation of chemoreceptors has long been known. Despite the importance of adaptation for cell memory and behavior, the dynamics of adaptation are difficult to reconcile with current models of precise adaptation. Here, we follow time courses of signaling in response to concentration step changes of attractant using in vivo fluorescence resonance energy transfer measurements. Specifically, we use a condensed representation of adaptation time courses for efficient evaluation of different adaptation models. To quantitatively explain the data, we finally develop a dynamic model for signaling and adaptation based on the attractant flow in the experiment, signaling by cooperative receptor complexes, and multiple layers of feedback regulation for adaptation. We experimentally confirm the predicted effects of changing the enzyme-expression level and bypassing the negative feedback for demethylation. Our data analysis suggests significant imprecision in adaptation for large additions. Furthermore, our model predicts highly regulated, ultrafast adaptation in response to removal of attractant, which may be useful for fast reorientation of the cell and noise reduction in adaptation.Comment: accepted for publication in PLoS Computational Biology; manuscript (19 pages, 5 figures) and supplementary information; added additional clarification on alternative adaptation models in supplementary informatio

Modeling a bacterial ecosystem through chemotaxis simulation of a single cell

International audienceWe present in this paper an artificial life ecosystem in which bacteria are evolved to perform chemotaxis. In this system, surviving bacteria have to overcome the problems of detecting resources (or sensing the environment), modulating their motion to generate a foraging behavior, and communicating with their kin to produce more sophisticated behaviors. A cell’s chemotactic pathway is modulated by a hybrid approach that uses an algebraic model for the receptor clusters activity, an ordinary differential equation for the adaptation dynamics, and a metabolic model that converts nutrients into biomass. The results show some analysis of the motion obtained from some bacteria and their effects on the evolved population behavior. The evolutionary process improves the bacteria’s ability to react to their environment, enhancing their growth and allowing them to better survive. As future work, we propose to investigate the effect of emergent bacterial communication as new species arise, and to explore the dynamics of colonies

Mathematical description of bacterial traveling pulses

The Keller-Segel system has been widely proposed as a model for bacterial waves driven by chemotactic processes. Current experiments on {\em E. coli} have shown precise structure of traveling pulses. We present here an alternative mathematical description of traveling pulses at a macroscopic scale. This modeling task is complemented with numerical simulations in accordance with the experimental observations. Our model is derived from an accurate kinetic description of the mesoscopic run-and-tumble process performed by bacteria. This model can account for recent experimental observations with {\em E. coli}. Qualitative agreements include the asymmetry of the pulse and transition in the collective behaviour (clustered motion versus dispersion). In addition we can capture quantitatively the main characteristics of the pulse such as the speed and the relative size of tails. This work opens several experimental and theoretical perspectives. Coefficients at the macroscopic level are derived from considerations at the cellular scale. For instance the stiffness of the signal integration process turns out to have a strong effect on collective motion. Furthermore the bottom-up scaling allows to perform preliminary mathematical analysis and write efficient numerical schemes. This model is intended as a predictive tool for the investigation of bacterial collective motion

Mathematical analysis of the Escherichia coli chemotaxis signalling pathway

We undertake a detailed mathematical analysis of a recent nonlinear ordinary differential equation (ODE) model describing the chemotactic signalling cascade within an {\it Escherichia coli} cell. The model includes a detailed description of the cell signalling cascade and an average approximation of the receptor activity. A steady-state stability analysis reveals the system exhibits one positive real steady-state which is shown to be asymptotically stable. Given the occurrence of a negative feedback between phosphorylated CheB (CheB-P) and the receptor state, we ask under what conditions, the system may exhibit oscillatory type behaviour. A detailed analysis of parameter space reveals that whilst variation in kinetic rate parameters within known biological limits is unlikely to lead to such behaviour, changes in the total concentration of the signalling proteins does. We postulate that experimentally observed overshoot behaviour can actually be described by damped oscillatory dynamics and consider the relationship between overshoot amplitude, total cell protein concentration and the magnitude of the external ligand stimulus. Model reductions of the full ODE model allow us to understand the link between phosphorylation events and the negative feedback between CheB-P and receptor methylation, as well as elucidate why some mathematical models exhibit overshoot and others do not. Our manuscript closes by discussing intercell variability of total protein concentration as means of ensuring the overall survival of a population as cells are subjected to different environments

Targeted cell imaging properties of a deep red luminescent iridium(III) complex conjugated with a c-Myc signal peptide

A nuclear localisation sequence (NLS) peptide, PAAKRVKLD, derived from the human c-Myc regulator gene, has been functionalised with a long wavelength (λex = 550 nm; λem = 677 nm) cyclometalated organometallic iridium(III) complex to give the conjugate Ir-CMYC. Confocal fluorescence microscopy studies on human fibroblast cells imaged after 18–24 h incubation show that Ir-CMYC concentrations of 80–100 μM promote good cell uptake and nuclear localisation, which was confirmed though co-localisation studies using Hoechst 33342. In comparison, a structurally related, photophysically analogous iridium(III) complex lacking the peptide sequence, Ir-PYR, showed very different biological behaviour, with no evidence of nuclear, lysosomal or autophagic vesicle localisation and significantly increased toxicity to the cells at concentrations >10 μM that induced mitochondrial dysfunction. Supporting UV-visible and circular dichroism spectroscopic studies show that Ir-PYR and Ir-CMYC display similarly low affinities for DNA (ca. 103 M−1), consistent with electrostatic binding. Therefore the translocation and nuclear uptake properties of Ir-CMYC are attributed to the presence of the PAAKRVKLD nuclear localisation sequence in this complex

Racemisation in chemistry and biology

The two enantiomers of a compound often have profoundly different biological properties and so their liability to racemisation in aqueous solutions is an important piece of information. We have reviewed the available data concerning the process of racemisation in vivo, in the presence biological molecules (e.g. racemase enzymes, serum albumin, cofactors and derivatives) and under purely chemical but aqueous conditions (acid, base and other aqueous systems). Mechanistic studies are described critically in light of reported kinetic data. The types of experimental measurement that can be used to effectively determine rate constants of racemisation in various conditions are discussed and the data they provide is summarised. The proposed origins of enzymatic racemisation are presented and suggest ways to promote the process that are different from processes taking place in bulk water. Experimental and computational studies that provide understanding and quantitative predictions of racemisation risk are also presented