Biophysics of information processing in gene regulation

When cells respond to changes in the environment by regulating the expression levels of their genes, we often draw parallels between these biological processes and engineered information processing systems. One can go beyond this qualitative analogy by analyzing information processing in biochemical hardware using Shannons information theory. Gene regulation is then viewed as a transmission channel operating under restrictive constraints set by intracellular noise. While the properties of gene expression noise have been carefully quantified in the last decade, its functional impact remains unclear. To address this, we propose to develop a predictive theory of genetic regulatory circuits, grounded at the interface of biophysics and information theory. The basic intuition is that some regulatory networksboth in terms of their interaction topology as well as the numbers on the arrowswill make best use of their limited resources to achieve reliable regulation despite noise in gene expression. These optimal networks can be derived from first principles and compared to data. Such an ab initio prediction approach is clearly different from the traditional modeling approaches in systems biology, where a postulated mathematical model is fitted to a particular dataset. If successful, a real prediction of a regulatory network, which so far has not been achieved for any regulatory system, would show that even complex biological functions can be derived from appropriately formulated fundamental principles, and are thus likely not just an evolutionary historical contingency. Moreover, we would also be provided with a compelling functional answer for why a particular network is observed in nature, thus going beyond a mathematical summary of how a network might work, as provided by model fits. Specifically, we propose the following: First, we will derive and analyze optimal small genetic regulatory networks that maximize information transmission under resource and noise constraints, in a biophysically realistic setup that can be connected to data. We will consider networks with arbitrary interactions (including feedback loops), coupled networks that can collectively respond to spatial input signals, and networks that operate in or out of steady state. Second, we will examine whether optimal regulatory interactions can evolve in known promoter/ enhancer architectures on typical speciation timescales. We will use a thermodynamic model of gene regulation to construct a genotype-phenotype-fitness map and (in the low mutation limit) compute the evolutionary rates for the emergence of regulatory functions, selecting either for the optimal regulatory function or high information transmission directly. Third, we will formulate (and possibly extend) our theory for a particular experimental system whose properties enable us to put the theory to a quantitative test. We will predict the network structure and spatial expression profiles of gap genes in Drosophila melanogaster, and compare them to high-quality quantitative data of our collaborator, Thomas Gregor.

Our primary goal was to theoretically predict how gene regulatory networks should function and evolve, and to compare the predictions to known regulatory networks. The key idea is that such networks transmit information which can be mathematically optimized, much as car traffic in the city can be optimized by smartly positioning traffic lights and building new roads. We promised to: (i) study how information flow is organized in small networks; (ii) study, in biophysically realistic models, how networks evolve by mutational changes in the genetic regulatory sequences on the DNA; (iii) predict a concrete regulatory network ab initio and compare these predictions to measurements of gene expression in early fruit fly development. We delivered on these promises as follows: (i) In a simple theoretical model that mimics fly development we understood how gene-gene interactions combine with chemical inputs to create complex spatial gene expression patterns (Hillenbrand et al, 2016). We showed that network complexity is limited by the limited precision of chemical reactions that underlie regulation (Friedlander et al, 2016). We showed how information flows can be estimated from single-cell dynamical measurements (Cepeda et al, 2018) and applied this in collaboration with experimentalists at University of Edinburgh to yeast stress signaling network (Granados et al, 2018). (ii) For the first time we created a biophysically realistic model of how gene regulatory proteins interact with the DNA and how both regulatory sequences on the DNA and the proteins themselves evolve to specialize their function (Friedlander, Prizak et al, 2017). In comparison with previous work, we now understand the detailed pathways and timescales by which regulation evolves through gene duplication. (iii) We finished two major papers (Petkova et al, 2019, Zagorski et al, 2017) in collaboration with experimental colleagues to show that gene regulatory networks in development of the fruit fly and the vertebrate neural tube are optimized by evolution along the lines that our information theory predicts. This was a necessary condition for our plan to derive such networks ab initio. We recently succeeded also in this prediction the first time any regulatory network has been derived theoretically and presented our results at the EMBL conference (March 2019); we will write these results up in 2019 in a major publication. Additionally, we completed several other projects, which resulted in visible papers relating to gene regulation that had strong synergies with this grant. This grant also forms a direct basis for roughly half of our planned efforts over the next 5 years, as well as a Human Frontiers Science Program grant that we acquired in 2018 to follow up directions (i) and (ii) on consequences of regulatory crosstalk. With the publication of all outstanding items from (iii), I would assess our work on both theoretical projects and theory-experiment collaborations as successful.