title: Information transfer in signaling pathways: a study using coupled simulated and experimental data.
abstract: BACKGROUND
  The topology of signaling cascades has been studied in quite some detail. However, how information is processed exactly is still relatively unknown. Since quite diverse information has to be transported by one and the same signaling cascade (e.g. in case of different agonists), it is clear that the underlying mechanism is more complex than a simple binary switch which relies on the mere presence or absence of a particular species. Therefore, finding means to analyze the information transferred will help in deciphering how information is processed exactly in the cell. Using the information-theoretic measure transfer entropy, we studied the properties of information transfer in an example case, namely calcium signaling under different cellular conditions. Transfer entropy is an asymmetric and dynamic measure of the dependence of two (nonlinear) stochastic processes. We used calcium signaling since it is a well-studied example of complex cellular signaling. It has been suggested that specific information is encoded in the amplitude, frequency and waveform of the oscillatory Ca(2+)-signal.
  
  
  RESULTS
  We set up a computational framework to study information transfer, e.g. for calcium signaling at different levels of activation and different particle numbers in the system. We stochastically coupled simulated and experimentally measured calcium signals to simulated target proteins and used kernel density methods to estimate the transfer entropy from these bivariate time series. We found that, most of the time, the transfer entropy increases with increasing particle numbers. In systems with only few particles, faithful information transfer is hampered by random fluctuations. The transfer entropy also seems to be slightly correlated to the complexity (spiking, bursting or irregular oscillations) of the signal. Finally, we discuss a number of peculiarities of our approach in detail.
  
  
  CONCLUSIONS
  This study presents the first application of transfer entropy to biochemical signaling pathways. We could quantify the information transferred from simulated/experimentally measured calcium signals to a target enzyme under different cellular conditions. Our approach, comprising stochastic coupling and using the information-theoretic measure transfer entropy, could also be a valuable tool for the analysis of other signaling pathways.
authors.affiliation: Bioinformatics and Computational Biochemistry, EML Research, Schloss-Wolfsbrunnenweg 33, 69118 Heidelberg, Germany. juergen@pahle.de
authors.forename: Jürgen
authors.initials: J
authors.lastname: Pahle
authors.forename: Anne K
authors.initials: AK
authors.lastname: Green
authors.forename: C Jane
authors.initials: CJ
authors.lastname: Dixon
authors.forename: Ursula
authors.initials: U
authors.lastname: Kummer
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D016247:Information Storage and Retrieval / Q000379:methods*; D008954:Models, Biological; D015233:Models, Statistical; D011506:Proteins / Q000378:metabolism*; D015398:Signal Transduction / Q000502:physiology*; D013269:Stochastic Processes
chemical_list: D011506:Proteins