Abstract
Inferring the directionality of interactions between cellular processes is a major challenge in systems biology. Time-lagged correlations allow to discriminate between alternative models, but they still rely on assumed underlying interactions. Here, we use the transfer entropy (TE), an information-theoretic quantity that quantifies the directional influence between fluctuating variables in a model-free way. We present a theoretical approach to compute the transfer entropy, even when the noise has an extrinsic component or in the presence of feedback. We re-analyze the experimental data from Kiviet et al. (2014) where fluctuations in gene expression of metabolic enzymes and growth rate have been measured in single cells of E. coli. We confirm the formerly detected modes between growth and gene expression, while prescribing more stringent conditions on the structure of noise sources. We furthermore point out practical requirements in terms of length of time series and sampling time which must be satisfied in order to infer optimally transfer entropy from times series of fluctuations.
Highlights
Quantifying information exchange between variables is a general goal in many studies of biological systems because the complexity of such systems prohibits mechanistic bottom-up approaches
In order to benchmark our inference method and perform a rigorous test in a controlled setting, we first applied it on times series generated by a simple model for which the transfer entropy and the information flow can be computed analytically
The estimates decrease as k is increased from 1 to 5, and one can reasonably expect that the theoretical value of TV!Y computed in Ref. [16] and given by Eq (21) in the section on Methods would be reached in the limit k ! 1
Summary
Quantifying information exchange between variables is a general goal in many studies of biological systems because the complexity of such systems prohibits mechanistic bottom-up approaches. Several statistical methods have been proposed to exploit either the specific dependence of the covariances between input and output variables with respect to a perturbation applied to the network [1], or the information contained in 3-point correlations [2]. These methods are potentially well suited for datasets obtained from destructive measurements, such as RNA sequencing or immunohistochemistry. Time-delayed cross-correlations between gene expression fluctuations have been shown to discriminate between several mechanistic models of well characterized genetic networks [3] Such methods become difficult to interpret in the presence of feedback
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