Identifying sources of variation and the flow of information in biochemical networks

Abstract

To understand how cells control and exploit biochemical fluctuations, we must identify the sources of stochasticity, quantify their effects, and distinguish informative variation from confounding "noise." We present an analysis that allows fluctuations of biochemical networks to be decomposed into multiple components, gives conditions for the design of experimental reporters to measure all components, and provides a technique to predict the magnitude of these components from models. Further, we identify a particular component of variation that can be used to quantify the efficacy of information flow through a biochemical network. By applying our approach to osmosensing in yeast, we can predict the probability of the different osmotic conditions experienced by wildtype yeast and show that the majority of variation can be informational if we include variation generated in response to the cellular environment. Our results are fundamental to quantifying sources of variation and thus are a means to understand biological "design."analysis of variance | internal history | gene expression | signal transduction | intrinsic and extrinsic noise C ells must make decisions in fluctuating environments using stochastic biochemistry. Such effects create variation between isogenic cells, which despite sometimes being disadvantageous for individuals may be advantageous for populations (1). Although the random occurrence and timing of chemical reactions are the primary intracellular source, we do not know how much different biochemical processes contribute to the observed heterogeneity (2). It is neither clear how fluctuations in one cellular process will affect variation in another nor how an experimental assay could be designed to quantify this effect. Further, we cannot distinguish variation that is extraneous "noise" from that generated by the flow of information within and between biochemical networks. We will show that a general technique to decompose fluctuations into their constituent parts provides a solution to these problems.Previous work divided variation in gene expression in isogenic populations into two components (3, 4): intrinsic and extrinsic variation. Both components necessarily include a variety of biochemical processes yet dissecting the effects of these processes has previously not been possible. Intrinsic variation should be understood as the average "variability" in gene expression between two copies of the same gene under identical intracellular conditions (4); extrinsic variation is the additional variation generated by interaction with other stochastic systems in the cell and the cell's environment. Single-cell experiments established that stochasticity generated during gene expression can be substantial in both bacteria (3, 5) and eukaryotes (6, 7), but did not identify the biochemical processes that generate this variation, regardless of whether the variation is intrinsic or extrinsic. Decomposing Variation in Biochemical SystemsConsider a fluctuating molecular species in a biochemical system and let ...

Information transfer by leaky, heterogeneous, protein kinase signaling systems

“…We can explain almost all of the large increase in mutual information caused by negative feedback using the fidelity measure. It is given here by the dimensionless expression (28,29),…”

“…The components of the output variance used correspond to widespread measures for understanding biochemical systems (dynamic range, intrinsic variation, etc.). The fidelity is related to mutual information, because it sets a lower bound on mutual information equal to log(1 + fidelity) 1/2 when evaluated under the appropriate signal distribution (28).…”

“…To understand further how different sources of noise in the output affect information transfer, we make use of recently introduced methods for decomposing variation in the output of biochemical systems (28). The fidelity of signaling (29) is based on the output-signal relationships that play a prominent role in most cell signaling research, is computed by decomposing the output variance, and can be seen as a generalized signal-to-noise ratio.…”

“…We propose to quantify the effect of heterogeneity in network componentry by computing the increase in mutual information under the assumption that the levels of the variable components in each cell are monitored in addition to the outputs of the signaling network. Recent methods for decomposing variation in the output of biochemical systems (28,29) are used to provide additional insight into the effects of negative feedback and of different sources of noise that harm signaling. In our experimental study of ERK signaling, we examine the effect of cell-to-cell variation in expression levels of the ERK protein itself and show that the interplay between such variation, basal activity, and negative feedback is critical for the effectiveness of PK signaling.…”

Information processing in the adaptation of Saccharomyces cerevisiae to osmotic stress: an analysis of the phosphorelay system

“…But we also need to consider the distribution of the external variables as well. Bowsher and Swain (2012) used a concept related to that of mutual information, called ''informational fraction''. Similar to our output of the Arimoto-Blahut algorithm, they draw conclusions on how the pathway could potentially have evolved to adapt the cell to a certain scenario of environmental state distributions.…”