Novel descriptive and model based statistical approaches in immunology and signal transduction

Abstract

Biological systems are usually complex nonlinear systems of which we only have a limited understanding. Here we show three different aspects of investigating such systems. We present a method to extract detailed knowledge from typical biological trajectory data, which have randomness as a main characteristic. The migration of immune cells, such as leukocytes, are a key example of our study. The application of our methodology leads to the discovery of novel random walk behaviour of leukocyte migration. Furthermore we use the gathered knowledge to construct the under- lying mathematical model that captures the behaviour of leukocytes, or more precisely macrophages and neutrophils, under acute injury. Any model of a biological system has little predictive power if it is not compared to collected data. We present a pipeline of how complex spatio- temporal trajectory data can be used to calibrate our model of leukocyte migration. The pipeline employs approximate methods in a Bayesian framework. Using the same approach we are able to learn additional information about the underlying signalling network, which is not directly apparent in the cell migration data. While these two methods can be seen as data processing and analysis, we show in the last part of this work how to assess the information content of experiments. The choice of an experiment with the highest information content out of a set of possible experiments leads us to the problem of optimal experimental design. We develop and implement an algorithm for simulation based Bayesian experimental design in order to learn parameters of a given model. We validate our algorithm with the help of toy examples and apply it to examples in immunology (Hes1 transcription regulation) and signal transduction (growth factor induced MAPK pathway).