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

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

Robust Signal Processing in Living Cells

Cellular signaling networks have evolved an astonishing ability to function reliably and with high fidelity in uncertain environments. A crucial prerequisite for the high precision exhibited by many signaling circuits is their ability to keep the concentrations of active signaling compounds within tightly defined bounds, despite strong stochastic fluctuations in copy numbers and other detrimental influences. Based on a simple mathematical formalism, we identify topological organizing principles that facilitate such robust control of intracellular concentrations in the face of multifarious perturbations. Our framework allows us to judge whether a multiple-input-multiple-output reaction network is robust against large perturbations of network parameters and enables the predictive design of perfectly robust synthetic network architectures. Utilizing the Escherichia coli chemotaxis pathway as a hallmark example, we provide experimental evidence that our framework indeed allows us to unravel the topological organization of robust signaling. We demonstrate that the specific organization of the pathway allows the system to maintain global concentration robustness of the diffusible response regulator CheY with respect to several dominant perturbations. Our framework provides a counterpoint to the hypothesis that cellular function relies on an extensive machinery to fine-tune or control intracellular parameters. Rather, we suggest that for a large class of perturbations, there exists an appropriate topology that renders the network output invariant to the respective perturbations

Voronoi Tessellation Captures Very Early Clustering of Single Primary Cells as Induced by Interactions in Nascent Biofilms

Biofilms dominate microbial life in numerous aquatic ecosystems, and in engineered and medical systems, as well. The formation of biofilms is initiated by single primary cells colonizing surfaces from the bulk liquid. The next steps from primary cells towards the first cell clusters as the initial step of biofilm formation remain relatively poorly studied. Clonal growth and random migration of primary cells are traditionally considered as the dominant processes leading to organized microcolonies in laboratory grown monocultures. Using Voronoi tessellation, we show that the spatial distribution of primary cells colonizing initially sterile surfaces from natural streamwater community deviates from uniform randomness already during the very early colonisation. The deviation from uniform randomness increased with colonisation — despite the absence of cell reproduction — and was even more pronounced when the flow of water above biofilms was multidirectional and shear stress elevated. We propose a simple mechanistic model that captures interactions, such as cell-to-cell signalling or chemical surface conditioning, to simulate the observed distribution patterns. Model predictions match empirical observations reasonably well, highlighting the role of biotic interactions even already during very early biofilm formation despite few and distant cells. The transition from single primary cells to clustering accelerated by biotic interactions rather than by reproduction may be particularly advantageous in harsh environments — the rule rather than the exception outside the laboratory

Sleeping sickness and its relationship with development and biodiversity conservation in the Luangwa valley, Zambia

The Luangwa Valley has a long historical association with Human African trypanosomiasis (HAT) and is a recognised geographical focus of this disease. It is also internationally acclaimed for its high biodiversity and contains many valuable habitats. Local inhabitants of the valley have developed sustainable land use systems in co-existence with wildlife over centuries, based on non-livestock keeping practices largely due to the threat from African Animal Trypanosomiasis. Historical epidemics of human sleeping sickness have influenced how and where communities have settled and have had a profound impact on development in the Valley. Historical attempts to control trypanosomiasis have also had a negative impact on conservation of biodiversity. Centralised control over wildlife utilisation has marginalised local communities from managing the wildlife resource. To some extent this has been reversed by the implementation of community based natural resource management programmes in the latter half of the 20th century and the Luangwa Valley provides some of the earliest examples of such programmes. More recently, there has been significant uncontrolled migration of people into the mid-Luangwa Valley driven by pressure on resources in the eastern plateau region, encouragement from local chiefs and economic development in the tourist centre of Mfuwe. This has brought changing land-use patterns, most notably agricultural development through livestock keeping and cotton production. These changes threaten to alter the endemically stable patterns of HAT transmission and could have significant impacts on ecosystem health and ecosystem services. In this paper we review the history of HAT in the context of conservation and development and consider the impacts current changes may have on this complex social-ecological system. We conclude that improved understanding is required to identify specific circumstances where win-win trade-offs can be achieved between the conservation of biodiversity and the reduction of disease in the human population.Ecosystem Services for Poverty Alleviation (ESPA

Dependence of Bacterial Chemotaxis on Gradient Shape and Adaptation Rate

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

Characterisation of the Wildlife Reservoir Community for Human and Animal Trypanosomiasis in the Luangwa Valley, Zambia

Animal and human trypanosomiasis are constraints to both animal and human health in Sub-Saharan Africa, but there is little recent evidence as to how these parasites circulate in natural hosts in natural ecosystems. A cross-sectional survey of trypanosome prevalence in 418 wildlife hosts was conducted in the Luangwa Valley, Zambia, from 2005 to 2007. The overall prevalence in all species was 13.9%. Infection was significantly more likely to be detected in waterbuck, lion, greater kudu and bushbuck, with a clear pattern apparent of the most important hosts for each trypanosome species. Human infective Trypanosoma brucei rhodesiense parasites were identified for the first time in African buffalo and T. brucei s.l. in leopard. Variation in infection is demonstrated at species level rather than at family or sub-family level. A number of significant risk factors are shown to interact to influence infection rates in wildlife including taxonomy, habitat and blood meal preference. Trypanosoma parasites circulate within a wide and diverse host community in this bio-diverse ecosystem. Consistent land use patterns over the last century have resulted in epidemiological stability, but this may be threatened by the recent influx of people and domesticated livestock into the mid-Luangwa Valley

Long-term changes in lowland calcareous grassland plots using Tephroseris integrifolia subsp. integrifolia as an indicator species

We investigated the changes to calcareous grassland plots within protected sites, and whether Tephroseris integrifolia subsp. integrifolia can act as a useful indicator species for re-visitation studies within vegetation predicted to remain relatively stable. Twenty-two plots located across lowland England and all formerly containing T. integrifolia were re-surveyed following the methodology used in the original survey undertaken in the 1960s. Pseudo-turnover and between-observer bias were minimised by sampling replicate quadrats at each fixed plot using a single surveyor and at a similar time of year as the original survey. Qualitative details concerning grazing management were obtained for all sites. In contrast to other long-term re-visitation studies, all our study plots were intact and retained diverse, herb-rich vegetation, demonstrating the value of site protection. However, there were clear shifts in vegetation composition, most notably where T. integrifolia was absent, as shown by an increase in Ellenberg fertility and moisture signifying nutrient enrichment, and a decrease in the cover of low-growing, light-demanding specialists, with a change likely to be associated predominantly with grazing management. Whereas in the mid-20th century the greatest threat to calcareous grassland was habitat loss, undergrazing or temporary neglect now appears to pose the principal threat. Distinctive species such as T. integrifolia with marked sensitivity to habitat change provide a potentially useful tool for rapid assessment and monitoring of site quality. Focusing monitoring on such species allows non-expert observers to recognise the early stages of habitat degradation, providing, in effect, a “health check” on individual sites and groups of sites