Optimizing information flow in small genetic networks

Abstract

In order to survive, reproduce, and (in multicellular organisms) differentiate, cells must control the concentrations of the myriad different proteins that are encoded in the genome. The precision of this control is limited by the inevitable randomness of individual molecular events. Here we explore how cells can maximize their control power in the presence of these physical limits; formally, we solve the theoretical problem of maximizing the information transferred from inputs to outputs when the number of available molecules is held fixed. We start with the simplest version of the problem, in which a single transcription factor protein controls the readout of one or more genes by binding to DNA. We further simplify by assuming that this regulatory network operates in steady state, that the noise is small relative to the available dynamic range, and that the target genes do not interact. Even in this simple limit, we find a surprisingly rich set of optimal solutions. Importantly, for each locally optimal regulatory network, all parameters are determined once the physical constraints on the number of available molecules are specified. Although we are solving an oversimplified version of the problem facing real cells, we see parallels between the structure of these optimal solutions and the behavior of actual genetic regulatory networks. Subsequent papers will discuss more complete versions of the problem.

Extending the dynamic range of transcription factor action by translational regulation

“…As a second step, we need to understand theoretically how the various features of the systemsthe architecture of signal transmission, the noise levels, the distribution of input signalscontribute to determining information transmission. In qualitative terms, the noise levels set a limit to information flow given a fixed maximum signal level, and thus understanding information transmission is intimately connected to the question of how the cell can maximize the information conveyed by a limited number of molecules produced and transported stochastically [14][15][16][17][18][19][20][21][22][23][24]; completing the circle, this problem is directly analogous to the "efficient coding" problem in neural systems [25]. As emphasized in Ref.…”

“…As described more fully in Refs. [8,[15][16][17][18][19], we can think of the regulatory mechanism as propagating information from c to g, and this information transmission is a measure of the control power achieved by the system.…”

“…We can think of transcriptional regulation as a mechanism for sensing the concentration of TFs, connecting the analysis of "input noise" to the broader problem of limits on biochemical signaling and sensing [28][29][30][31][32][33][34][35][36][37], first studied in the context of bacterial chemotaxis [2]. Changing the shape of input-output relations, both through cooperativity and through feedback, changes the balance between input and output noise, thus rendering the optimization of information flow a well-posed problem even with very simple physical constraints on the total mean number of molecules [16][17][18].…”

“…Several averaging strategies that make transcriptional regulation more reliable have been identified: there is averaging over time as molecules accumulate [2,28,[31][32][33][34], averaging over expression levels of multiple genes that are regulated by the same TF [16,17,38,39], and averaging over space as molecules diffuse between neighboring cells or nuclei, e.g., in a developing embryo [19,[40][41][42][43] or organoid [44]. In the (typical) case where one TF targets multiple genes, there is a regime where information transmission is optimized by complete redundancy in the response of these targets, and another regime in which the concentrations for activation or repression of the targets are staggered so as to "tile" the dynamic range of inputs [16,17]. But, even as we consider networks with increasing numbers of targets, the theoretically optimal strategy is to insert the additional genes into the high-concentration end of the input range and to avoid the lower part of the dynamic range altogether.…”

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

“…This famous theory (with its long history in engineering) was successfully integrated in neuro-biology already several years ago, where it has since become a standard tool to study neuronal information processing (Borst and Theunissen 1999). Due to the stochastic nature of transcriptional processes, information theoretical concepts have also been extensively used to study information flow in gene expression (Tkačik et al 2009;Walczak et al 2010;Tkačik et al 2012), drawing in addition the parallel to positional information (Tkacik et al 2008;Dubuis et al 2013). With all that recent research in mind, it seems immediately appealing to also study biochemical signaling processes within the same framework.…”