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Ratio-based sensing of two transcription factors regulates the transit to cell 1 differentiation 2

Cell state transitions depend on transcription factors to effect mRNA expression changes. 32 Although certain transitions are directed by change in absolute concentration of single 33 transcription factors, transitions in animal cells frequently require combinations of multiple 34 factors. To investigate how cells sense and respond to concentration changes of concurrently 35 expressed factors, we quantified the expression dynamics of the Drosophila transcription 36 factor activator-repressor pair Pnt and Yan during photoreceptor differentiation. Progenitor cells 37 maintain a constant ratio of Pnt-to-Yan despite extensive cell-to-cell variation in absolute protein 38 concentrations. A rapid and sustained increase in the ratio accompanies each progenitor cell as it 39 transitions to a photoreceptor state. Perturbations disrupting the ratio result in gains or losses of 40 these transitions. We used biophysical modeling to illustrate how a ratiometric system can 41 produce differential transcription factor binding necessary to drive transitions. Reliance on 42 relative rather than absolute concentration as the control variable may allow ratiometric systems 43 to function more robustly under conditions of component variability.

In this study, we investigated how poised P cells sense and respond to changes in abundance of 92 Pnt and Yan proteins by measuring the expression dynamics of these two transcription factors in 93 thousands of individual nuclei during P to R cell state transitions. We find that P to R cell state 94 transitions are marked by a change in the relative ratio of the Pnt and Yan proteins. P cells maintain during the second peak ( Figure 1C,H). All young R cells at these transition windows displayed a 158 25-50% increase in Pnt levels, which decayed as these cells matured over time. Yan showed the 159 opposite dynamical behavior during R cell differentiation; young R cells exhibited lower Yan 160 protein levels compared to concurrent P cells ( Figure 1G,I). Yan levels rapidly decayed in 161 maturing R cells, reaching a basal level that was at least two-fold lower than that in concurrent P 162 cells. To summarize, pulses of the activator Pnt and the repressor Yan coincide with two windows 163 of P to R cell state transitions. Within these windows, a respective increase and decrease in Pnt 164 and Yan protein levels accompany the transitions. 165 166 P to R state transitions are robust to variation in Pnt and Yan protein levels. 167 We previously found that P to R state transitions are robust to systematic perturbation of absolute 168 Yan protein levels (22, 31). Could cell state transitions be similarly robust to changes in Pnt protein 169 levels? To answer this question, we decreased Pnt protein levels by reducing the pnt gene copy 170 number from two (wildtype) to one. As expected, having a single copy of the pnt gene resulted in 171 a ~ 50% reduction in Pnt protein levels compared to levels measured in animals with two copies 172 ( Figure 2A,C). Pnt levels were not only reduced in P cells, but when R cells differentiated from 173 single-copy pnt P cells, there was a corresponding reduction in the maximal amplitude of Pnt levels 174 reached by these cells (Figure 2A,C). Notably, P to R state transitions were robust to this 175 significant reduction in Pnt protein levels, and eyes developed with a wildtype pattern and 176 morphology ( Figure S3). 177 178 Unexpectedly, when we measured Yan levels in P cells in these single-copy pnt eyes, we found 179 that Yan protein levels were significantly reduced, despite these cells still having two copies of the 180 yan gene ( Figure 2B,D). This suggests a role for Pnt in positively regulating Yan expression, and 181 perhaps a mechanism of coordinated regulation of Pnt and Yan abundance. The qualitatively 182 parallel behaviors of Pnt and Yan in this experiment prompted us to quantitatively assess the extent 183 to which Pnt and Yan levels are coordinated within individual nuclei. To do this, we calculated the 184 Pnt-to-Yan ratio in individual P cells at each P-to-R transition point and compared the results 185 between populations with one vs. two copies of the pnt gene. Consistent across the different 186 transition points, the Pnt-to-Yan ratios in single copy pnt P cells were remarkably similar to the 187 ratios in two-copy pnt P cells ( Figure 2E). 188

A reset in the Pnt-to-Yan ratio coincides with P to R cell state transitions. 190
Given that the robustness of cell state transitions to systematic variation in pnt gene copy number 191 was accompanied by a stabilized Pnt-to-Yan ratio in P cells, we wondered if the ratio might act as 192 a control parameter regulating the transitions from P to R states. Consistent with this possibility, 193 the average Pnt-to-Yan ratio in P cells remained dynamically stable about a fixed value over time 194 ( Figure 3A). Greater cell-to-cell fluctuations in the ratio coincided with the specific times when 195 Pnt and Yan levels peaked ( Figures 3A and 1D,E). 196 197 We next asked whether the Pnt-to-Yan ratio was also invariant in R cells over time. We first 198 examined the ratio in R7 cells along their differentiation trajectory. Strikingly, the average Pnt-to-199 Yan ratio was higher in young R7 cells relative to their concurrent P cells ( Figure 3A, note log 200 scale of y-axis). The ratio rose and then gradually fell as R7 cell differentiation progressed over 201 time, but always remained at higher values than that of concurrent P cells. Examination of the Pnt-202 to-Yan ratio dynamics in all other R cell types revealed a similar and consistent rapid increase as 203 R cells differentiated from the P cell pool, followed by a gradual decline to a new steady value that 204 was higher than that of concurrent P cells ( Figure S4). 205

206
The stable Pnt-to-Yan ratio in P cells rapidly shifts to a new, higher ratio value as P cells transition 207 to become R cells, and subsequently stabilizes at that higher value in the R cells. This observation 208 prompted us to hypothesize that the ratio becomes destabilized during state transitions and then 209 re-set as cells stabilize their states. If so, then cell-to-cell heterogeneity of this ratio should rise 210 during the time-windows for state transitions, and then subside as cell states are resolved. We used 211 our established method (31) to quantify cell-to-cell heterogeneity of Pnt levels, Yan levels, and the 212 ratio along each P to R differentiation trajectory ( Figure S5). We found increased heterogeneity in 213 the ratio, as quantified by the coefficient of variation, coincided with the time windows in which 214 subsets of P cells differentiated to R cells. The enhanced heterogeneity persisted in young R cells 215 and diminished as they matured. 216 217 We next focused on how ratio values are distributed in young R vs. concurrent P cells at the time 218 windows of cell state transitions. Interestingly, we found that there was a substantial overlap in 219 ratio values between young R cells and concurrent P cells in these time windows. Nevertheless, 220 the Pnt-to-Yan ratios of most young R cells were greater than the median ratio for the concurrent 221 P cells ( Figure 3B-F). This resulted in a significantly higher average ratio in all young R cell types 222 relative to their concurrent P cell neighbors ( Figure 3G, P<0.001, KS 2-sample test). Together 223 these measurements reveal that a subset of P cells transiently elevate their Pnt-to-Yan ratio at the 224 P-to-R state decision points, but that only young R cells maintain the elevated ratio as they mature. 225 226 Controlled perturbations of the Pnt-to-Yan ratio bias P cells towards or against R state 227

transitions. 228
If the Pnt-to-Yan ratio is a control variable that triggers P to R state transitions, then tuning up or 229 down the proportion of P cells that stably elevate the ratio should correspondingly change the 230 proportion of cells that transition to R states. As a first test of this hypothesis, we altered the RTK 231 signaling circuitry to artificially induce a ratio increase in a larger number of P cells at specific cell 232 By overriding the endogenous RTK circuitry, this perturbation should increase Pnt protein 237 abundance ( Figure 4A). As predicted, sev>Ras V12 dramatically increased the amplitude and 238 duration of the second peak of Pnt expression in P cells, which coincides with the second wave of 239 R cell differentiation events ( Figure 4B). Yan protein levels were weakly reduced in P cells during 240 this time window ( Figure 4D). The result was a sustained elevation in the Pnt-to-Yan ratio in a 241 larger number of P cells at the transition window and continuing thereafter ( Figure 4C). sev>Ras V12 242 expression also resulted in supernumerary R cells that had comparable ratios to neighboring R7 243 cells ( Figure 4E). These ectopic R cells were typically found flanking the R7 cell of each 244 ommatidium ( Figure S7A,B). Thus, forcing P cells to have an elevated Pnt-to-Yan ratio results in 245 too many P cells becoming R cells, consistent with the ratio being a key control variable that 246 regulates P to R state transitions. 247

248
To further test this hypothesis, we performed the converse experiment by preventing the Pnt-to-249 Yan ratio from increasing in P cells during transition windows. We used the same sev 250 enhancer/promoter to drive expression of a constitutively active form of Yan, Yan Act , which results 251 in accumulation of the repressor protein in the nuclei of R3/4 and R7 cells ( Figure 5A) (22, 39)). 252 As expected, R8, R2/R5 and R1/R6 state transitions appeared normal and exhibited normal ratio 253 dynamics ( Figures 5E and S8A-D,G,H). There was a mild increase in Yan levels and a delayed 254 increase in the Pnt-to-Yan ratio in young R3/R4 cells ( Figures S8E,F). As these cells matured, 255 their ratios reached a steady state value that was comparable to wildtype R3/4 cells. 256

257
In contrast, the sev>Yan ACT perturbation resulted in a large reduction in the total number of R7 258 cells ( Figure 5B-E). The few cells that could be plausibly identified as R7s were mostly young R7 259 cells. These young R7 cells had diminished Pnt-to-Yan ratios that were comparable to the ratio in 260 concurrent P cells ( Figure 5C,D). Comparison of Yan and Pnt expression confirmed that the 261 reduced ratio in these young R7 cells was driven primarily by increased Yan levels ( Figure S9 Above a certain activator-to-repressor ratio, cells will transition to a new state, while below that 331 threshold, they will remain in the initial state, regardless of the absolute transcription factor 332 concentrations ( Figures 6D,E). In this way, small changes in the relative ratio of Pnt-to-Yan would 333 Our study has quantitatively analyzed in vivo a series of cell state transitions that are controlled by 339 the abundance ratio between an activator transcription factor and a repressor transcription factor. 340 In this multicellular developing system, cells in the progenitor pool (P cells) maintain a 341 dynamically constant Pnt-to-Yan ratio necessary to sustain the undifferentiated state. RTK 342 signaling changes the ratio set-point and produces a sustained increase in the ratio, at the same time as it is driving a P cell's transition to differentiation. In this way the relative ratio would 344 directly control the makeup of transcription factor complexes on target genes required for R cell 345 fates, with low Pnt-to-Yan ratios favoring transcriptional repression of target genes and high ratios 346 favoring their transcriptional activation. We support this description with in vivo experiments in 347 which we show that the changes in ratio associated with correct cell differentiation can take place 348 at different absolute concentrations of the transcription factors. Indeed, our experiments 349 demonstrate that the Pnt/Yan system is able to maintain a fixed ratio and to make correct transitions 350 over at least a four-fold range of activator and repressor abundance. 351 352 Several features of the Pnt/Yan system may reflect general requirements for any ratiometric-based 353 control mechanisms. First, the regulators must be co-expressed, compete for the same molecular 354 partners and exert opposite effects on them. In eye cells, Pnt and Yan compete for the same DNA 355 binding sites to respectively activate and repress target gene transcription. Second, distinct states 356 must be mechanistically associated with specific ratio values. In our case, a lower activator-to-357 repressor ratio connects repressor-dominated DNA occupancy to maintenance of the progenitor 358 state, while a higher ratio couples activator-dominated occupancy to differentiation. Third, to 359 induce a new state, the initial ratio set-point point must be changed. In our system, the initial set 360 point in P cells is buffered by a compensatory mechanism that keeps the ratio dynamically stable. 361 During the transit to differentiation, RTK signaling increases the ratio, most likely by differentially 362 regulating the synthesis and degradation of Pnt and Yan through a combination of transcriptional 363 and posttranscriptional mechanisms (44). To override the progenitor state ratio set point, signaling 364 must induce changes that are different either in kind and/or in magnitude from those that set the 365 initial ratio. Fourth, for a system to be controlled by molecular ratios rather than by absolute 366 concentrations, its output must rely on the probability of binding of the two transcription factors 367 to common DNA sites or partners, which is dictated by their relative concentrations. Finally, 368 incorporating cooperativity can make a ratiometric system tunable and sensitive to small changes 369 in the ratio. 370

371
In silico modeling of a Pnt/Yan-like system suggests that stabilizing interactions between repressor 372 molecules bound to adjacent DNA sites could sensitize enhancer occupancy to the relative 373 abundance of the competing transcription factors. Indeed, prior work has shown that DNA-bound Yan monomers enhance recruitment of Yan to adjacent binding sites through stabilizing protein-375 protein interactions (19, 40). As shown in our model, such cooperativity makes the system 376 sensitive to small but sustained relative changes, leading to non-linear (ultrasensitive and 377 threshold-like) changes in site occupancy that can drive a state transition. These general ratiometric 378 system features could be readily incorporated into transcriptional networks with more than two 379 regulators and more generally could provide robust regulation to a broad spectrum of biological 380 processes that require precise combinatorial interactions between competing regulatory factors. 381

382
An unexpected discovery in our experiments is the ability of the Pnt/Yan system to maintain a 383 fixed ratio and to make correct transitions over at least a four-fold range of activator concentration. 384 This predicts a stabilizing mechanism that monitors the relative ratio of Pnt and Yan and takes 385 corrective action when the ratio deviates from a specified reference value. The molecular nature 386 of the stabilizing mechanism in P cells and the means by which it is modified so that R cells can Empirically, the replicate number of three eye discs provided reproducible composite dynamics. 463 No outlier eye discs were found for any experimental condition, so all samples were pooled, 464 temporally aligned and included in the analysis. The sample size was not pre-computed before 465 data collection. 466 467 Nuclear segmentation was performed using either H2Av-mRFP (Figures 1, 3, 4 The model presented in Figures 6 and S11 expands upon the work of (43). The model is based on 552 a single cis-regulatory element consisting of n adjacent binding sites, each of which may be 553 designated as ETS or non-ETS. Each binding site may exist in one of three binding states; bound 554 by a single copy of Yan, bound by a single copy of Pnt, or unbound. Thermodynamic potentials 555 were assigned to each binding state using two parameters for each transcription factor. The 556 parameter αX defines the free energy of transcription factor X binding to an ETS site, 557 while βX defines the free energy of binding to a non-ETS site. A unique configuration of binding 558 states for all n binding sites constitutes a single microstate, k. The thermodynamic potential of 559 each microstate was taken to be the sum of thermodynamic potentials for each of its constituent 560 binding sites. For each microstate, the stabilizing effect of polymerization was incorporated via a 561 third parameter, γX, that defines the free energy of SAM-SAM binding between a pair of similar 562 transcription factors bound to adjacent sites. The net result is a total thermodynamic 563 potential, ΔGk, for each microstate. An example enumeration of all possible microstates for an 564 element consisting of one ETS site preceding two non-ETS sites is provided in Figure S11B