A Bayesian model predicts the response of axons to molecular gradients

Axon guidance by molecular gradients plays a crucial role in wiring up the nervous system. However, the mechanisms axons use to detect gradients are largely unknown. We first develop a Bayesian “ideal observer” analysis of gradient detection by axons, based on the hypothesis that a principal constraint on gradient detection is intrinsic receptor binding noise. Second, from this model, we derive an equation predicting how the degree of response of an axon to a gradient should vary with gradient steepness and absolute concentration. Third, we confirm this prediction quantitatively by performing the first systematic experimental analysis of how axonal response varies with both these quantities. These experiments demonstrate a degree of sensitivity much higher than previously reported for any chemotacting system. Together, these results reveal both the quantitative constraints that must be satisfied for effective axonal guidance and the computational principles that may be used by the underlying signal transduction pathways, and allow predictions for the degree of response of axons to gradients in a wide variety of in vivo and in vitro settings.

Stochastic analysis of the VEGF receptor response curve

Recently, an analysis of the response curve of the vascular endothelial growth factor (VEGF) receptor and its application to cancer therapy was described in [T. Alarcón, and K. Page, J. R. Soc. Lond. Interface 4, 283–304 (2007)]. The analysis is significantly extended here by demonstrating that an alternative computational strategy, namely the Krylov FSP algorithm for the direct solution of the chemical master equation, is feasible for the study of the receptor model. The new method allows us to further investigate the hypothesis of symmetry in the stochastic fluctuations of the response. Also, by augmenting the original model with a single reversible reaction we formulate a plausible mechanism capable of realizing a bimodal response, which is reported experimentally but which is not exhibited by the original model. The significance of these findings for mechanisms of tumour resistance to antiangiogenic therapy is discussed.

Frequency response function based structural damage detection using artificial neural networks

Damage detection in structures has become increasingly important in recent years. While a number of damage detection and localization methods have been proposed, few attempts have been made to explore the structure damage with frequency response functions (FRFs). This paper illustrates the damage identification and condition assessment of a beam structure using a new frequency response functions (FRFs) based damage index and Artificial Neural Networks (ANNs). In practice, usage of all available FRF data as an input to artificial neural networks makes the training and convergence impossible. Therefore one of the data reduction techniques Principal Component Analysis (PCA) is introduced in the algorithm. In the proposed procedure, a large set of FRFs are divided into sub-sets in order to find the damage indices for different frequency points of different damage scenarios. The basic idea of this method is to establish features of damaged structure using FRFs from different measurement points of different sub-sets of intact structure. Then using these features, damage indices of different damage cases of the structure are identified after reconstructing of available FRF data using PCA. The obtained damage indices corresponding to different damage locations and severities are introduced as input variable to developed artificial neural networks. Finally, the effectiveness of the proposed method is illustrated and validated by using the finite element modal of a beam structure. The illustrated results show that the PCA based damage index is suitable and effective for structural damage detection and condition assessment of building structures.