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What Makes the Lac-Pathway Switch: Identifying the Fluctuations That Trigger Phenotype Switching in Gene Regulatory Systems

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What Makes the Lac-Pathway Switch: Identifying the Fluctuations That Trigger Phenotype Switching in Gene Regulatory Systems What makes the lac-pathway switch: identifying the fluctuations that trigger phenotype switching in gene regulatory systems Prasanna M. Bhogale1y, Robin A. Sorg2y, Jan-Willem Veening2∗, Johannes Berg1∗ 1University of Cologne, Institute for Theoretical Physics, Z¨ulpicherStraße 77, 50937 K¨oln,Germany 2Molecular Genetics Group, Groningen Biomolecular Sciences and Biotechnology Institute, Centre for Synthetic Biology, University of Groningen, Nijenborgh 7, 9747 AG, Groningen, The Netherlands y these authors contributed equally ∗ correspondence to [email protected] and [email protected]. Multistable gene regulatory systems sustain different levels of gene expression under identical external conditions. Such multistability is used to encode phenotypic states in processes including nutrient uptake and persistence in bacteria, fate selection in viral infection, cell cycle control, and development. Stochastic switching between different phenotypes can occur as the result of random fluctuations in molecular copy numbers of mRNA and proteins arising in transcription, translation, transport, and binding. However, which component of a pathway triggers such a transition is gen- erally not known. By linking single-cell experiments on the lactose-uptake pathway in E. coli to molecular simulations, we devise a general method to pinpoint the particular fluctuation driving phenotype switching and apply this method to the transition between the uninduced and induced states of the lac genes. We find that the transition to the induced state is not caused only by the single event of lac-repressor unbinding, but depends crucially on the time period over which the repressor remains unbound from the lac-operon. We confirm this notion in strains with a high expression level of the repressor (leading to shorter periods over which the lac-operon remains un- bound), which show a reduced switching rate. Our techniques apply to multi-stable gene regulatory systems in general and allow to identify the molecular mechanisms behind stochastic transitions in gene regulatory circuits. Introduction pathway in Bacillus subtilis. The comK -pathway enables B. subtilis to take up new genetic material, which may offer fitness advantages [22]. Maamar et al. increased Multistable gene regulatory systems use specific mech- the transcription rate of comK and simultaneously de- anisms like feedback to stabilize expression patterns creased its translation rate. Average protein levels were defining different phenotypic states [1{8]. However, no left unaffected, but fluctuations around this mean due to natural system is strictly multistable since it will not per- the random timing of mRNA production were reduced. sist in any one of its states indefinitely. Instead, the life- Maamar et al. observed a decrease in the switching rate times of stable states are finite, with random fluctuations between the states with low levels of ComK and high causing transitions between different states. In gene reg- levels of ComK, showing that mRNA-fluctuations affect ulatory systems the copy numbers of mRNA molecules, the switching rate. But are these the only rate-limiting proteins, and ligands fluctuate over time due to the ran- fluctuations in the system? Repeating this procedure for dom timing of transcription, translation, transport, and all components in a pathway is cumbersome for small binding [9{16]. These fluctuations can trigger a switch pathways and infeasible for larger pathways. Moreover, from one phenotype to another [17{21]. However, when arXiv:1312.6209v2 [q-bio.MN] 12 Sep 2014 transitions could be driven by fluctuations in ligand num- all components of a multistable system fluctuate, what bers, protein conformations or binding state, which are are the fluctuations causing the transition? In other even harder to control in experiments. words, what are the rate-limiting fluctuations? Such rate-limiting fluctuations are difficult to identify If rate-limiting fluctuations are hard to identify experi- experimentally, because it is hard to monitor and con- mentally, they cannot be identified purely on the basis of trol variation in molecular copy numbers inside a cell. regulatory network models and computer simulations ei- In an ideal scenario, one would take a multistable sys- ther. Any model describes a restricted number of molec- tem and reduce the amplitude of fluctuations of each of ular species and replaces the rest with effective reaction its components in turn. If reducing the fluctuations of a rates. The formulation of a model thus already consti- particular component affects the switching rate between tutes an a priori assumption on the relevant constituents. different states, then one can consider fluctuations in that Being rare events, transitions between stable states are component rate-limiting to the transition. This strat- strongly influenced by the molecular details. Two mod- egy has been implemented experimentally by Maamar els can thus exhibit the same bistable expression pat- et al. [17] for a single component of a bistable signaling terns as a function of external parameters, e.g. hysteresis 2 tury [23, 24], and most kinetic rates have been mea- sured [25{30], and the parameter space over which the system is bistable has been explored [1]. Despite a large body of experimental [1, 13, 19, 31] and compu- tational studies [32{34], there is no consensus on the transition mechanism. Experimentally, a key observa- tion was made by Choi et al. [19], who find that the lac- repressor tetramer is released just before the transition to the induced state. But is this single-molecule event alone driving the transition, or are there other fluctuations in- volved? A study by Robert et al. [31] shows that cellular concentrations of the repressor affect the switching be- havior of the lac-pathway, suggesting that rebinding of the repressor to the operator might play a role. In this paper, we use single cell analysis to determine switching rates from the uninduced to the induced state of the lac-system. We set up a detailed mechanistic FIG. 1: Feedback in the lactose-uptake pathway. Three model of the lac-system and propose a simple scheme genes under common regulatory control constitute the lactose- to reduce fluctuations in the constituents of the lac- uptake pathway: lacZ encodes the enzyme to break down lactose, lacY encodes a permease (importer of lactose, shown pathway in silico and identify the fluctuations driving in green), which actively imports lactose from the environ- the transitions between states. Our method to pinpoint ment (here: the non-metabolizable lactose-analogue TMG, rate-limiting fluctuations is general and can be applied blue wedge), and lacA encodes a transacetylase. Bistability to any system whose kinetic rates are sufficiently well is achieved by a positive feedback-loop; the imported TMG known. acts as an inducer of the lac genes by increasing the unbinding rate of LacI tetramers (red) from the so-called operator bind- ing sites in the lac-regulatory region. LacI tetramers inhibit Materials and methods the expression of the lac genes. As a result, the induced state shown on the right, with the lac genes expressed, is stable if the permease imports enough inducers to deactivate the re- Determining phenotypic switching rates. To as- pressors. The uninduced state shown on the left can also be sess expression of the lac genes at the single-cell level stable, since in the absence of lac-expression, the repressors we used flow cytometry on a population of E. coli strain prevent expression of the lac genes by binding to the regula- CH458, which contains a gfp-cat cassette inserted down- tory region and forming a DNA loop. However, this regula- tory circuit is built from stochastic components and can be stream of the lac-operon [35] (see SI section 1 for de- interrupted by random fluctuations of the number of mRNA, tails). The switching rate from the uninduced state to proteins, inducer, repressors, or the binding state of repres- the induced state is the number of cells per unit time sors to DNA. These fluctuations lead to transitions between which switch from low numbers of lac-proteins to a state the induced and uninduced states. with high number of lac-proteins. To determine the rate of switching to the induced state, we start with a pop- ulation of uninduced cells and fit the fraction of cells in the uninduced state at subsequent times to an exponen- plots [1], yet differ markedly in the mechanisms and rates tial decay. Examples are shown in Figure 2 and Figure of switching between states. Indeed the rate-limiting fluc- S3. Switching rates are determined at different external tuation is thought to differ drastically across pathways: inducer concentrations, resulting in a rate curve of the mRNA fluctuations in the comK -pathway [17], fluctu- switching rate against inducer concentration (see Figure ations in initial pump numbers in the arabinose-uptake 4). The reverse transition from the induced to the unin- pathway [18], and gene activity bursts in the λ-phage duced state is slow by comparison and, on the timescales lysogeny [21]. Hence, transitions between stable states of our experiment, few cells switch back from the induced can act as a sensitive probe into molecular details of a to the uninduced state. pathway. Experimental conditions. We used the non- The best-studied example of a multistable regulatory metabolizable thio-methylgalactoside (TMG) as an in- system is the lactose-uptake pathway in Escherichia coli, ducer. M9 minimal salts supplemented with thiamine, exhibiting bistable expression of the genes lacZ, lacY, MgSO4, CaCl2, and casamino acids were chosen as lacA. Due to a positive feedback loop, both the induced growth medium for the CH458 strain used in our exper- state (high expression levels of the lac-genes) and the iments. We used succinate instead of glucose as carbon uninduced state (low expression levels of the lac-genes) source to reduce catabolite repression yet maintain suffi- can be stable, see Fig. 1.
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