The impact of nonlinear exposure risk relationships on seasonal time series data: modelling danish neonatal birth anthropometric data

Background Birth weight and length have seasonal fluctuations. Previous analyses of birth weight by latitude effects identified seemingly contradictory results, showing both 6 and 12 monthly periodicities in weight. The aims of this paper are twofold: (a) to explore seasonal patterns in a large, Danish Medical Birth Register, and (b) to explore models based on seasonal exposures and a non-linear exposure-risk relationship. Methods Birth weight and birth lengths on over 1.5 million Danish singleton, live births were examined for seasonality. We modelled seasonal patterns based on linear, U- and J-shaped exposure-risk relationships. We then added an extra layer of complexity by modelling weighted population-based exposure patterns. Results The Danish data showed clear seasonal fluctuations for both birth weight and birth length. A bimodal model best fits the data, however the amplitude of the 6 and 12 month peaks changed over time. In the modelling exercises, U- and J-shaped exposure-risk relationships generate time series with both 6 and 12 month periodicities. Changing the weightings of the population exposure risks result in unexpected properties. A J-shaped exposure-risk relationship with a diminishing population exposure over time fitted the observed seasonal pattern in the Danish birth weight data. Conclusion In keeping with many other studies, Danish birth anthropometric data show complex and shifting seasonal patterns. We speculate that annual periodicities with non-linear exposure-risk models may underlie these findings. Understanding the nature of seasonal fluctuations can help generate candidate exposures.

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.