Feedback control architecture and the bacterial chemotaxis network.

PMCID: PMC3088647This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.Bacteria move towards favourable and away from toxic environments by changing their swimming pattern. This response is regulated by the chemotaxis signalling pathway, which has an important feature: it uses feedback to 'reset' (adapt) the bacterial sensing ability, which allows the bacteria to sense a range of background environmental changes. The role of this feedback has been studied extensively in the simple chemotaxis pathway of Escherichia coli. However it has been recently found that the majority of bacteria have multiple chemotaxis homologues of the E. coli proteins, resulting in more complex pathways. In this paper we investigate the configuration and role of feedback in Rhodobacter sphaeroides, a bacterium containing multiple homologues of the chemotaxis proteins found in E. coli. Multiple proteins could produce different possible feedback configurations, each having different chemotactic performance qualities and levels of robustness to variations and uncertainties in biological parameters and to intracellular noise. We develop four models corresponding to different feedback configurations. Using a series of carefully designed experiments we discriminate between these models and invalidate three of them. When these models are examined in terms of robustness to noise and parametric uncertainties, we find that the non-invalidated model is superior to the others. Moreover, it has a 'cascade control' feedback architecture which is used extensively in engineering to improve system performance, including robustness. Given that the majority of bacteria are known to have multiple chemotaxis pathways, in this paper we show that some feedback architectures allow them to have better performance than others. In particular, cascade control may be an important feature in achieving robust functionality in more complex signalling pathways and in improving their performance

Optimization of Time-Course Experiments for Kinetic Model Discrimination

Systems biology relies heavily on the construction of quantitative models of biochemical networks. These models must have predictive power to help unveiling the underlying molecular mechanisms of cellular physiology, but it is also paramount that they are consistent with the data resulting from key experiments. Often, it is possible to find several models that describe the data equally well, but provide significantly different quantitative predictions regarding particular variables of the network. In those cases, one is faced with a problem of model discrimination, the procedure of rejecting inappropriate models from a set of candidates in order to elect one as the best model to use for prediction

CALIBRATION PROCEDURES ON OBLIQUE CAMERA SETUPS

Beside the creation of virtual animated 3D City models, analysis for homeland security and city planning, the accurately determination of geometric features out of oblique imagery is an important task today. Due to the huge number of single images the reduction of control points force to make use of direct referencing devices. This causes a precise camera-calibration and additional adjustment procedures. This paper aims to show the workflow of the various calibration steps and will present examples of the calibration flight with the final 3D City model. In difference to most other software, the oblique cameras are used not as co-registered sensors in relation to the nadir one, all camera images enter the AT process as single pre-oriented data. This enables a better post calibration in order to detect variations in the single camera calibration and other mechanical effects. The shown sensor (Oblique Imager) is based o 5 Phase One cameras were the nadir one has 80 MPIX equipped with a 50 mm lens while the oblique ones capture images with 50 MPix using 80 mm lenses. The cameras are mounted robust inside a housing to protect this against physical and thermal deformations. The sensor head hosts also an IMU which is connected to a POS AV GNSS Receiver. The sensor is stabilized by a gyro-mount which creates floating Antenna –IMU lever arms. They had to be registered together with the Raw GNSS-IMU Data. The camera calibration procedure was performed based on a special calibration flight with 351 shoots of all 5 cameras and registered the GPS/IMU data. This specific mission was designed in two different altitudes with additional cross lines on each flying heights. The five images from each exposure positions have no overlaps but in the block there are many overlaps resulting in up to 200 measurements per points. On each photo there were in average 110 well distributed measured points which is a satisfying number for the camera calibration. In a first step with the help of the nadir camera and the GPS/IMU data, an initial orientation correction and radial correction were calculated. With this approach, the whole project was calculated and calibrated in one step. During the iteration process the radial and tangential parameters were switched on individually for the camera heads and after that the camera constants and principal point positions were checked and finally calibrated. Besides that, the bore side calibration can be performed either on basis of the nadir camera and their offsets, or independently for each camera without correlation to the others. This must be performed in a complete mission anyway to get stability between the single camera heads. Determining the lever arms of the nodal-points to the IMU centre needs more caution than for a single camera especially due to the strong tilt angle. Prepared all these previous steps, you get a highly accurate sensor that enables a fully automated data extraction with a rapid update of you existing data. Frequently monitoring urban dynamics is then possible in fully 3D environment

A boundary preserving numerical algorithm for the Wright-Fisher model with mutation

The Wright-Fisher model is an Itô stochastic differential equation that was originally introduced to model genetic drift within finite populations and has recently been used as an approximation to ion channel dynamics within cardiac and neuronal cells. While analytic solutions to this equation remain within the interval [0,1], current numerical methods are unable to preserve such boundaries in the approximation. We present a new numerical method that guarantees approximations to a form of Wright-Fisher model, which includes mutation, remain within [0,1] for all time with probability one. Strong convergence of the method is proved and numerical experiments suggest that this new scheme converges with strong order 1/2. Extending this method to a multidimensional case, numerical tests suggest that the algorithm still converges strongly with order 1/2. Finally, numerical solutions obtained using this new method are compared to those obtained using the Euler-Maruyama method where the Wiener increment is resampled to ensure solutions remain within [0,1]