Abstract
Kullback–Leibler divergence (KLD) is a type of extended mutual entropy, which is used as a measure of information gain when transferring from a prior distribution to a posterior distribution. In this study, KLD is applied to the thermodynamic analysis of cell signal transduction cascade and serves an alternative to mutual entropy. When KLD is minimized, the divergence is given by the ratio of the prior selection probability of the signaling molecule to the posterior selection probability. Moreover, the information gain during the entire channel is shown to be adequately described by average KLD production rate. Thus, this approach provides a framework for the quantitative analysis of signal transduction. Moreover, the proposed approach can identify an effective cascade for a signaling network.
Highlights
Kullback–Leibler divergence (KLD) is a type of generalized entropy or information quantity.It was introduced by Solomon Kullback and Richard A
The proposed approach using Bayesian statistics [13,14], which is based on KLD, is expected to provide a novel theoretical framework [7]
We introduce a priori selection probability of signaling molecule for the analysis
Summary
Kullback–Leibler divergence (KLD) is a type of generalized entropy or information quantity. The authors reported analyses of biological signal transduction based on information thermodynamics In these studies, a theoretical framework was developed on Shannon entropy. Xm2 activates Xm3 in the same manner In this way, the signaling molecule at the (j − 1)-th step of cascade m, denoted as Xmj− 1 , induces the modification of Xmj into. Qmj , which represents the selection probability of inactive Xmj used in the j-th step in cascade m (forward direction), takes the form of the j-th molecule. Qmj *, which represents the selection probability of active Xmj *, is used in the −j-th step for cascade m (backward direction), as follows:. In the above equations,mjτ0 mj 0 represents the the duration corresponding to positive code length in which thethe active molecule.
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