Pahle Jürgen, Green Anne K, Dixon C Jane, Kummer Ursula
Bioinformatics and Computational Biochemistry, EML Research, Schloss-Wolfsbrunnenweg 33, 69118 Heidelberg, Germany.
BMC Bioinformatics. 2008 Mar 4;9:139. doi: 10.1186/1471-2105-9-139.
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.
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.
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.
信号级联的拓扑结构已得到相当详细的研究。然而，信息究竟是如何被处理的仍相对未知。由于同一信号级联必须传输相当多样的信息（例如在不同激动剂的情况下），很明显其潜在机制比依赖于特定物质的单纯存在或不存在的简单二元开关更为复杂。因此，找到分析所传递信息的方法将有助于解读细胞中信息究竟是如何被处理的。我们使用信息论测度转移熵，在一个示例案例中研究了信息传递的特性，即不同细胞条件下的钙信号传导。转移熵是两个（非线性）随机过程依赖性的不对称且动态的测度。我们使用钙信号传导，因为它是复杂细胞信号传导中一个经过充分研究的示例。有人提出特定信息编码在振荡性Ca(2+)信号的幅度、频率和波形中。
我们建立了一个计算框架来研究信息传递，例如针对不同激活水平和系统中不同粒子数的钙信号传导。我们将模拟的和实验测量的钙信号随机耦合到模拟的靶蛋白，并使用核密度方法从这些二元时间序列估计转移熵。我们发现，在大多数情况下，转移熵随着粒子数的增加而增加。在粒子数很少的系统中，随机波动会阻碍可靠的信息传递。转移熵似乎也与信号的复杂性（尖峰、爆发或不规则振荡）略有相关。最后，我们详细讨论了我们方法的一些独特之处。
本研究首次将转移熵应用于生化信号通路。我们能够量化在不同细胞条件下从模拟/实验测量的钙信号传递到靶酶的信息。我们的方法，包括随机耦合和使用信息论测度转移熵，也可能是分析其他信号通路的有价值工具。
