Overview of mathematical approaches used to model bacterial chemotaxis II: bacterial populations

We review the application of mathematical modeling to understanding the behavior of populations of chemotactic bacteria. The application of continuum mathematical models, in particular generalized Keller–Segel models, is discussed along with attempts to incorporate the microscale (individual) behavior on the macroscale, modeling the interaction between different species of bacteria, the interaction of bacteria with their environment, and methods used to obtain experimentally verified parameter values. We allude briefly to the role of modeling pattern formation in understanding collective behavior within bacterial populations. Various aspects of each model are discussed and areas for possible future research are postulated

C-ME: A 3D Community-Based, Real-Time Collaboration Tool for Scientific Research and Training

The need for effective collaboration tools is growing as multidisciplinary proteome-wide projects and distributed research teams become more common. The resulting data is often quite disparate, stored in separate locations, and not contextually related. Collaborative Molecular Modeling Environment (C-ME) is an interactive community-based collaboration system that allows researchers to organize information, visualize data on a two-dimensional (2-D) or three-dimensional (3-D) basis, and share and manage that information with collaborators in real time. C-ME stores the information in industry-standard databases that are immediately accessible by appropriate permission within the computer network directory service or anonymously across the internet through the C-ME application or through a web browser. The system addresses two important aspects of collaboration: context and information management. C-ME allows a researcher to use a 3-D atomic structure model or a 2-D image as a contextual basis on which to attach and share annotations to specific atoms or molecules or to specific regions of a 2-D image. These annotations provide additional information about the atomic structure or image data that can then be evaluated, amended or added to by other project members

Bacterial Chemotaxis in an Optical Trap

An optical trapping technique is implemented to investigate the chemotactic behavior of a marine bacterial strain Vibrio alginolyticus. The technique takes the advantage that the bacterium has only a single polar flagellum, which can rotate either in the counter-clock-wise or clock-wise direction. The two rotation states of the motor can be readily and instantaneously resolved in the optical trap, allowing the flagellar motor switching rate to be measured under different chemical stimulations. In this paper the focus will be on the bacterial response to an impulsive change of chemoattractant serine. Despite different propulsion apparati and motility patterns, cells of V. alginolyticus apparently use a similar response as Escherichia coli to regulate their chemotactic behavior. Specifically, we found that the switching rate of the bacterial motor exhibits a biphasic behavior, showing a fast initial response followed by a slow relaxation to the steady-state switching rate . The measured can be mimicked by a model that has been recently proposed for chemotaxis in E. coli. The similarity in the response to the brief chemical stimulation in these two different bacteria is striking, suggesting that the biphasic response may be evolutionarily conserved. This study also demonstrated that optical tweezers can be a useful tool for chemotaxis studies and should be applicable to other polarly flagellated bacteria

Quantitative Modeling of Escherichia coli Chemotactic Motion in Environments Varying in Space and Time

Escherichia coli chemotactic motion in spatiotemporally varying environments is studied by using a computational model based on a coarse-grained description of the intracellular signaling pathway dynamics. We find that the cell's chemotaxis drift velocity vd is a constant in an exponential attractant concentration gradient [L]∝exp(Gx). vd depends linearly on the exponential gradient G before it saturates when G is larger than a critical value GC. We find that GC is determined by the intracellular adaptation rate kR with a simple scaling law: . The linear dependence of vd on G = d(ln[L])/dx directly demonstrates E. coli's ability in sensing the derivative of the logarithmic attractant concentration. The existence of the limiting gradient GC and its scaling with kR are explained by the underlying intracellular adaptation dynamics and the flagellar motor response characteristics. For individual cells, we find that the overall average run length in an exponential gradient is longer than that in a homogeneous environment, which is caused by the constant kinase activity shift (decrease). The forward runs (up the gradient) are longer than the backward runs, as expected; and depending on the exact gradient, the (shorter) backward runs can be comparable to runs in a spatially homogeneous environment, consistent with previous experiments. In (spatial) ligand gradients that also vary in time, the chemotaxis motion is damped as the frequency ω of the time-varying spatial gradient becomes faster than a critical value ωc, which is controlled by the cell's chemotaxis adaptation rate kR. Finally, our model, with no adjustable parameters, agrees quantitatively with the classical capillary assay experiments where the attractant concentration changes both in space and time. Our model can thus be used to study E. coli chemotaxis behavior in arbitrary spatiotemporally varying environments. Further experiments are suggested to test some of the model predictions

Computational Model of the Insect Pheromone Transduction Cascade

A biophysical model of receptor potential generation in the male moth olfactory receptor neuron is presented. It takes into account all pre-effector processes—the translocation of pheromone molecules from air to sensillum lymph, their deactivation and interaction with the receptors, and the G-protein and effector enzyme activation—and focuses on the main post-effector processes. These processes involve the production and degradation of second messengers (IP3 and DAG), the opening and closing of a series of ionic channels (IP3-gated Ca2+ channel, DAG-gated cationic channel, Ca2+-gated Cl− channel, and Ca2+- and voltage-gated K+ channel), and Ca2+ extrusion mechanisms. The whole network is regulated by modulators (protein kinase C and Ca2+-calmodulin) that exert feedback inhibition on the effector and channels. The evolution in time of these linked chemical species and currents and the resulting membrane potentials in response to single pulse stimulation of various intensities were simulated. The unknown parameter values were fitted by comparison to the amplitude and temporal characteristics (rising and falling times) of the experimentally measured receptor potential at various pheromone doses. The model obtained captures the main features of the dose–response curves: the wide dynamic range of six decades with the same amplitudes as the experimental data, the short rising time, and the long falling time. It also reproduces the second messenger kinetics. It suggests that the two main types of depolarizing ionic channels play different roles at low and high pheromone concentrations; the DAG-gated cationic channel plays the major role for depolarization at low concentrations, and the Ca2+-gated Cl− channel plays the major role for depolarization at middle and high concentrations. Several testable predictions are proposed, and future developments are discussed

Towards A Rich-Context Participatory Cyberenvironment

To enable and support innovative research in science and engineering, the next generation Cyberinfrastructure must be able to support collaboration across disciplines and conceptual contexts. At NCSA, we are building Cyberenvironments which support ???architecture of participation??? where user-driven innovation is empowered. In this paper, we will first describe the Cyberenvironment and Web 2.0/Where 2.0 concepts, and present our definition of a participatory Cyberenvironment and the roles of contexts for building such Cyberinfrastructure. We then present our arguments of the importance of supporting the full range of social, geospatial, causal and conceptual contexts. We will describe the foundation work that we have built so far, the CyberCollaboratory (a collaborative portal) and Tupelo (a semantic content repository), and then provide the vision for the path towards a rich context participatory Cyberenvironment with potential impact on scientific communities such as distributed environment observatory networks.published or submitted for publicationis peer reviewe