Epigenetic memory independent of symmetric histone inheritance

Heterochromatic gene silencing is an important form of gene regulation that usually requires specific histone modifications. A popular model posits that inheritance of modified histones, especially in the form of H3-H4 tetramers, underlies inheritance of heterochromatin. Because H3-H4 tetramers are randomly distributed between daughter chromatids during DNA replication, rare occurrences of asymmetric tetramer inheritance within a heterochromatic domain would have the potential to destabilize heterochromatin. This model makes a prediction that shorter heterochromatic domains would experience unbalanced tetramer inheritance more frequently, and thereby be less stable. In contrast to this prediction, we found that shortening a heterochromatic domain in Saccharomyces had no impact on the strength of silencing nor its heritability. Additionally, we found that replisome mutations that disrupt inheritance of H3-H4 tetramers had only minor effects on heterochromatin stability. These findings suggest that histones carry little or no memory of the heterochromatin state through DNA replication.

mutations that disrupt inheritance of H3-H4 tetramers had only minor effects on heterochromatin stability. These findings suggest that histones carry little or no memory of the heterochromatin state through DNA replication.

Introduction
A central question in biology is how cells with identical genotypes can exhibit different, heritable phenotypes. By definition, these phenotypes are determined by information that is epigenetic, or "above the genome." Just as genetic inheritance requires faithful replication of DNA, epigenetic inheritance requires replication of information that is transmitted to both daughter cells during division. Faithful transmission of epigenetic information is crucial for multiple heterochromatin-based processes such as X-chromosome inactivation in mammals and cold-induced gene silencing in Arabidopsis. In these cases and others, the epigenetic inheritance of heterochromatin indicates that some components of heterochromatin must behave as heritable units. Surprisingly, the identity of this epigenetic information remains unclear and heavily debated.
The histone subunits of nucleosomes, especially histones H3 and H4, are modified by a variety of covalent modifications that are integral to heterochromatin function. During DNA replication, nucleosomes are partially disrupted and marked parental H3-H4 tetramers are locally inherited to daughter chromatids. As these 2006). In contrast, one study in A. thaliana found that a chromatin domain containing only three H3K27me3-marked nucleosomes is inherited more frequently than would be predicted if random segregation of tetramers caused loss events (Yang et al. 2017).
However, no study to our knowledge has systematically tested this prediction.
To test directly whether inheritance of a chromatin state is affected by chromatin-domain size, we focused on the heterochromatin domains at the HMR and HML loci in S. cerevisiae. These loci contain copies of mating-type genes that are silenced by the activity of Sir proteins. Specifically, the E and I silencers flanking HMR and HML are occupied by the DNA-binding proteins Rap1, Abf1, and ORC, that collectively recruit Sir proteins; Sir1 is present only at silencers, whereas Sir2/3/4 complexes bind to silencers and spread across the locus in a process that requires deacetylation of H4K16 (Rusché et al. 2002;Thurtle & Rine 2014). Notably, DNA methylation and RNA interference do not exist in S. cerevisiae.
Under normal conditions, HMR and HML are constitutively silenced. Rare and transient loss-of-silencing events can be measured by a sensitive assay that uses the cre recombinase under control of the HMLa2 promoter to convert transient transcriptional events into permanent, heritable changes in fluorescence phenotypes (Dodson & Rine 2015). In contrast, deletion of SIR1 causes genetically identical cells to be in either of two states at HMR and HML: either fully silenced or fully expressed transcriptional states are mitotically heritable and cells switch between states at a low frequency. This study addresses three questions regarding the inheritance of heterochromatin in Saccharomyces: 1) Does the size of a silenced domain determine the fidelity of inheritance? 2) Does removal of Sir1, a protein that facilitates recruitment of silencing machinery to silencers, uncover an effect of chromatin domain size on heritability of transcriptional states? 3) Do replisome components that facilitate symmetric inheritance of parental H3-H4 tetramers also promote inheritance of transcriptional states?

Results
Local inheritance of nucleosomes and their locus-specific modifications are thought to facilitate inheritance of chromatin states. According to this view, if parental H3-H4 tetramers were randomly partitioned between the two daughter chromatids during replication, one would expect a chromatin state to be lost if, by chance, one of the daughter chromatids failed to receive enough parental H3-H4 tetramers to support the propagation of that state. By this model, the number of nucleosomes in the chromatin domain would influence the fidelity of chromatin-state inheritance.

Nucleosome number did not determine the rate of silencing loss
To test if nucleosome number affected the stable inheritance of a chromatin state, we used the Cre-Reported Altered States of Heterochromatin (CRASH) assay (Dodson & Rine 2015) ( Figure 1A). In this assay, cre replaces the a2 coding sequence in HMRa, and a lox cassette containing fluorescent reporters separated by loxP sites is located on a separate chromosome. Though HMRa is transcriptionally repressed, rare loss-of-silencing events cause transient expression of cre. These events lead to excision of RFP from the lox cassette, and a switch from RFP to GFP expression.
Because this change is heritable, loss-of-silencing events during colony growth lead to formation of sectors of cells expressing GFP, appearing green on an otherwise red background. The number of sectors in a colony reflects the frequency at which HMRa transiently loses silencing: more sectors indicate less stable silencing.
HMRa::cre contained fifteen well-positioned nucleosomes between the E and I silencers (Figure 1-figure supplement 1). To change nucleosome number within the locus, we deleted DNA corresponding to different sets of nucleosomes ( Figure 1B).
Notably, removing DNA corresponding to different combinations of nucleosomes allowed us to discern whether any effects on silencing stability were due to nucleosome number or to removal of specific DNA sequences. These deletions did not affect the local positions of the remaining nucleosomes as measured by MNase-Seq (Figure 1-figure supplement 1).
At the limit of models by which nucleosomes transmit memory of transcriptional states, inheritance of a single parental H3-H4 tetramer to a daughter chromatid would be sufficient to template the silenced state. The expected loss-ofsilencing rate would thereby reflect the frequency at which a chromatid inherits no marked parental H3-H4 tetramers due to random segregation of these tetramers during replication. This rate would increase exponentially with shorter chromatin domains as the probability of inheriting at least one parental tetramer decreases ( Figure 1C). Additionally, if inheritance of two or more parental H3-H4 tetramers were necessary to template the silenced state, the expected loss-of-silencing rate would be even higher. Full-length HMRa::cre (Strain N14) experiences a loss-of-silencing event in approximately 0.1% of cell divisions (Dodson & Rine 2015). The silencing-loss rate predicted by random segregation of H3-H4 tetramers would be approximately 1% of cell divisions in the smallest version of HMRa::cre tested (Strain N7). Therefore, if this model were correct, we would expect to see increased sectoring rates in strains with shorter versions of HMRa::cre. Surprisingly, decreasing nucleosome number at HMRa::cre led to a slight decrease in silencing loss as measured by sector frequency ( Figure 1D).
To provide an independent measurement of the silencing-loss rate, we also measured fluorescence profiles of single cells. Cells that have recently lost silencing of cre at HMRa contain both RFP and GFP due to GFP expression and the persistence of RFP prior to its degradation and dilution. Using flow cytometry to measure the frequency of cells that contain both RFP and GFP, we confirmed that nucleosome number did not strongly affect silencing-loss rates, and that reduction of nucleosomes might have a slight stabilizing effect on silencing ( Figure 1E). Thus, the size of HMRa::cre did not dramatically influence inheritance of the silenced state, in contrast to the expectation from models in which H3-H4 tetramers carry memory of chromatin states through cell divisions. Additionally, we found that changing nucleosome number at HMLa::cre led to a small increase in silencing loss, and that these effects were not due strictly to domain size ( Figure 1-figure supplements 2-4).
Since studies at HMLa are potentially complicated by its proximity to a telomere, which is also bound by Sir proteins, further studies were performed only at HMRa.  (Dodson & Rine 2015). HMRa::cre contains the E and I silencers, the a1 gene, and a cre transgene. Transient loss of silencing at HMRa::cre causes Cre-mediated recombination of loxP sites in a RFP-GFP cassette. This process creates a permanent, heritable switch from RFP to GFP expression. (B) Diagram of nucleosomes in HMRa::cre. Fourteen nucleosomes were present in full-length HMRa::cre, which we term Strain N14 (JRY11471).
Combinations of nucleosomal DNA were deleted to change the size of HMRa::cre; the smallest size was seven nucleosomes (Strain N7) (JRY11540). Nucleosome positions were determined by MNaseseq as shown in Figure 1- Nucleosome number did not affect transmission of epigenetic states in sir1∆.
The silencers flanking HMRa are bound by three different proteins that collaborate to recruit Sir proteins (Rusché et al. 2003). One possibility for the apparent insensitivity of silencing inheritance to nucleosome number was that the constant recruitment of Sir proteins to these sites was efficient enough to mask a contribution of histone inheritance to inheritance of chromatin states. In this scenario, silencers would be capable of recruiting enough Sir proteins to keep the locus silenced during DNA replication, regardless of histone segregation patterns. Sir1 binds to silencers, and deletion of SIR1 partially disrupts silencer activity, as measured by defects in silencing establishment and silencing heritability (Pillus & Rine 1989;Dodson & Rine 2015). We therefore tested if parental H3-H4 tetramer inheritance contributed to transmission of the silenced state when silencer-based recruitment of Sir proteins was impaired by the HMRa::GFP could be used to measure the efficiency of epigenetic inheritance in sir1∆, similarly to previous studies (E. Y. Xu et al. 2006). For simplicity, we named this the FLuorescent Analysis of Metastable Expression (FLAME) assay.
To test the prediction that chromatin domain size affects silencing heritability with the FLAME assay, we removed DNA corresponding to sets of nucleosomes in the their descendants as they divided, we found that nucleosome number did not affect the frequency of silencing loss ( Figure 2D). Because the expressed state is also heritable, with occasional switches to the silenced state, we also asked if the heritability of the expressed state was influenced by the number of nucleosomes in the locus. The frequency of silencing establishment was similar between strains with different numbers of nucleosomes at HMRa::GFP ( Figure 2E). Therefore, even in a background with defective silencer activity, chromatin-domain size did not strongly influence silencing dynamics. These findings argued against models in which parental H3-H4 tetramers and their modifications are required for the epigenetic inheritance of gene expression states in Saccharomyces.

Replisome defects affected epigenetic inheritance
An orthogonal approach to test the role of histones in carrying epigenetic memory would be to consistently bias parental H3-H4 tetramer inheritance to one daughter chromatid, leaving the other daughter chromatid with fewer parental H3-H4 tetramers. Recent reports demonstrate conserved roles of two replisome components, Dpb3 and Mcm2, in producing a more symmetric distribution of parental H3-H4 tetramers between the leading and lagging strands. Specifically, dpb3∆ causes biased parental H3-H4 tetramer inheritance to the lagging strand (Yu et al. 2018) and a set of point mutations in MCM2 (mcm2-3A) causes biased parental H3-H4 tetramer inheritance to the leading strand (Petryk et al. 2018;Gan et al. 2018).
A complementary study that was able to observe local inheritance of histone H4 in a small chromatin domain, though was unable to distinguish leading versus lagging strand biases, found that local histone H4 inheritance was moderately reduced in both the dpb3∆ and mcm2-3A single mutants, and severely reduced in the dpb3∆ mcm2-3A double mutant (Schlissel & Rine, in press). Together, these studies demonstrate that Dpb3 and Mcm2 are necessary for efficient inheritance of parental H3-H4 tetramers to both daughter chromatids during DNA replication.
If parental H3-H4 tetramer inheritance contributes to transmission of chromatin states, we would predict more loss-of-silencing events in strains with defects in tetramer inheritance. To test this idea, we measured silencing loss in replisome mutants using the CRASH assay ( Figure 3A). The dpb3∆ and mcm2-3A single mutants exhibited higher silencing-loss rates, consistent with previous studies done at HML (Yu et al. 2018;Gan et al. 2018), and the dpb3∆ mcm2-3A double mutant lost silencing more frequently than either single mutant. Similar results were obtained by using flow cytometry to measure silencing-loss rates ( Figure 3B). These data were consistent with a model in which inheritance of parental H3-H4 tetramers could contribute to inheritance of the silenced state at HMR. However, the data were also compatible with the possibility that heterochromatin assembled in such mutants was simply unstable for reasons independent of defects in its inheritance. independent cultures). ANOVA and Tukey tests were used to test statistical significance. ANOVA and Tukey tests were used to test statistical significance. DPB3 MCM2 was significantly different than dpb3∆ MCM2 and DPB3 mcm2-3A (p < 0.05 each), and dpb3∆ mcm2-3A was significantly different than dpb3∆ MCM2 and DPB3 mcm2-3A (p < 0.05 each). It is possible that parental H3-H4 tetramer inheritance affects both transient loss-of-silencing events, as detected by the CRASH assay, and heritability of epigenetic states. Testing this possibility was important because the currently unidentified epigenetic information that determines expression states in sir1∆ is transmitted locally at HML and HMR, respectively, rather than being transmitted in trans from processes elsewhere in the cell (E. Y. Xu et al. 2006). If parental H3-H4 tetramers were the crucial local factors that transmitted this information, we would predict that disrupted tetramer inheritance would cause more loss-of-silencing events in sir1∆. To test this, we generated replisome mutant strains in combination with sir1∆ in the FLAME assay and evaluated the inheritance of transcriptional states using Fluorescence-Activated Cell Sorting (FACS) and live-cell microscopy.
Populations of dpb3∆, mcm2-3A, and dpb3∆ mcm2-3A mutants all showed a mix of cells that were silenced or expressed at HMRa::GFP; all three mutant strains also showed a higher frequency of expressed cells than wildtype (Figure 4-figure supplement 1, Table 1). Because silencing-loss rates and silencing-establishment rates both affect the frequency of cells in which HMR is silenced or expressed, one or both of these rates were presumably different in replisome mutants. To measure these rates, we used FACS to sort cells from each strain into two separate populations of HMR-silenced and HMR-expressed cells ( Figure 4A). By monitoring the rate at which the initial sorted all-silenced population shifted back to a mixed population of silenced and expressed cells ( Figure 4B, Figure 4-figure supplement 2), we observed that dpb3∆ and mcm2-3A had a higher loss-of-silencing rate than wildtype ( Figure   4C). The dpb3∆ mcm2-3A double mutant had a higher loss rate than the single mutants. Similar loss trends were observed using time-lapse fluorescence microscopy ( Figure 4D), albeit with overall higher loss rates than those seen with FACS sorting.
Together, these data suggested that faithful inheritance of parental H3-H4 tetramers helped transmit the silenced state of HMR. However, we also noted that the vast majority of silenced cells still faithfully transmitted the silenced state in the replisome mutant backgrounds.
We also asked if replisome mutants had differences in the frequency of silencing-establishment events. Curiously, any strain containing dpb3∆ had an

Variations in nucleosome number in replisome mutant backgrounds
Though the rate of silencing loss increased in replisome mutant backgrounds, the large majority of silenced cells still faithfully transmitted the silenced state through cell divisions. Indeed, though dpb3∆ and mcm2-3A single mutants exhibit asymmetric parental H3-H4 tetramer inheritance (Yu et al. 2018;Petryk et al. 2018), it is likely that this asymmetry is not complete and some parental H3-H4 tetramers are still stochastically transmitted to each daughter chromatid during DNA replication.
Similarly, the dpb3∆ mcm2-3A double mutant exhibits residual local inheritance of histone H4 (Schlissel & Rine, in press). We reasoned that, if a daughter chromatid consistently inherits fewer parental H3-H4 tetramers and thereby loses the silenced state more frequently, an additional reduction in the size of a chromatin domain would cause that daughter chromatid to inherit even fewer marked parental H3-H4 tetramers and experience loss-of-silencing events even more frequently. Therefore, if parental H3-H4 tetramers carry epigenetic memory, we would expect loci with fewer nucleosomes to exhibit more loss-of-silencing events in replisome mutant backgrounds. To test his idea, we used the FLAME assay on nucleosome-number mutants in dpb3∆ and dpb3∆ mcm2-3A strains ( Figure 5A, figure 5-figure supplement 1). There was no clear correlation between silencing-loss rates and nucleosome number in these sensitized backgrounds ( Figure 5B). Establishment-ofsilencing rates were also not strongly affected, though there was a slight increase in the establishment rate with fewer nucleosomes in dpb3∆ mcm2-3A ( Figure 5C). Therefore, even when parental H3-H4 tetramer inheritance was disrupted and the number of parental H3-H4 tetramers available for inheritance at HMR was decreased, cells faithfully transmitted epigenetic transcriptional states. (JRY11478) are identical to those in Figure 2D,E and shown here for convenience. Error bars represent 95% confidence intervals.

Discussion
Heterochromatin is frequently characterized by specific histone modifications bound by silencing proteins; these components are critical to mechanisms of silencing and have long been considered as mediators of epigenetic inheritance. A popular model is that modified H3-H4 tetramers are heritable units of epigenetic information that are randomly segregated between daughter chromatids during DNA replication (Ramachandran & Henikoff 2015). Models founded on random segregation of parental Specifically, induced silencer excision from HMR causes rapid loss of silencing in arrested cells (Cheng & Gartenberg 2000). Studies at other loci in S. cerevisiae and Drosophila show that removal of silencers permits maintenance of silencing in arrested cells, but causes loss of silencing once the same cells subsequently complete one or two rounds of DNA replication (Holmes & Broach 1996;Laprell et al. 2017). Therefore, the presence of modified histones is not sufficient for silencing maintenance or heritability, depending on the example under consideration. Indeed, given that silencers are constantly recruiting Sir proteins to these loci, any role of H3-H4 tetramers in transmission of epigenetic information might be hard to detect.
We considered the possibility that silencer activity masks an underlying contribution of H3-H4 tetramer inheritance to silencing inheritance. However, the weakened silencer activity in sir1∆ mutants did not reveal a sensitivity of silencing inheritance to the size of the silenced domain at HMR. Importantly, epigenetic states of HML and HMR in sir1∆ are a property of the locus rather than the cell, demonstrating that factors that determine these epigenetic states are inherited locally at HML and HMR respectively (E. Y. Xu et al. 2006). Similar studies of an epigenetically-inherited heterochromatin state in Arabidopsis also demonstrate that the relevant epigenetic information is carried in cis (Berry et al. 2015 (Dodd et al. 2007). This model also predicts that random segregation of parental H3-H4 tetramers would lead to loss-of-chromatinstate events, and that decreasing chromatin domain size would also decrease the heritability of both the expressed and silenced states. However, we found that shorter versions of HMR did not strongly affect inheritance of the expressed state of HMR.
Alternatively, if parental H3-H4 tetramers carry memory of the expressed state, mutations that disrupt parental H3-H4 tetramer inheritance would be expected to increase the rate of silencing establishment. Curiously, dpb3∆ exhibited a ~3-fold increase in the rate of silencing establishment and mcm2-3A had no observable effect. These data may suggest that parental tetramer inheritance facilitates heritability of the expressed state, though such an explanation could not account for the mcm2-3A phenotype. Alternatively, these data may suggest that inheritance of the expressed state is influenced by a function of Dpb3p that is separate from its role in tetramer inheritance. It is also important to note that dpb3∆ but not mcm2-3A led to elevated levels of GFP expression when HMRa::GFP was fully expressed. This finding is paradoxical, as one would expect elevated transcription to inhibit silencing establishment, rather than facilitate it. However, recruitment of the transcriptional activator Ppr1 to HMR causes both increased transcription in expressed cells and an increased establishment rate in sir1∆ (E. Y. Xu et al. 2006).
Together, our results suggested that the fidelity of H3-H4 tetramer inheritance has minimal consequences for heritability of the silenced state and may affect heritability of the expressed state in some contexts. These findings raised doubts regarding the model in which histones are significant carriers of epigenetic memory in S. cerevisiae. As such, future studies that continue to examine histone-based memory models will be complemented by studies on other possible mechanisms of transcriptional memory.

Yeast strains
The strains and oligonucleotides used in this study are listed in Supplementary   Files 1 and 2 To delete DNA corresponding to nucleosomes at HMRα and HMLα, CRISPR/Cas9 was employed as previously described (Lee et al. 2015). Each deletion or repair fwd/rev primer set contained two partially overlapping primers that were amplified by PCR prior to use. The HMR-E-proximal sgRNA was used to induce Cas9 cutting between the HMR-E silencer and cre, and N14 to N12 deletion fwd/rev was used to delete DNA corresponding to two nucleosomes in this region. This sgRNA and oligo set was also used to convert sN12 to sN10 in the FLAME strain background.
The HMR-I-proximal sgRNA, which cuts between the HMR-I silencer and cre, was used with N14 to N10 deletion fwd/rev (to convert N14 to N10, and sN12 to sN8) or with N14 to N9 (to convert N14 to N9 Application Suite X (LAS X) imaging software. At least ten colonies were imaged per genotype.

Live-cell imaging
Cells were grown to saturation in CSM (Sunrise Science Products) at 30°C overnight. These cells were then back-diluted in 5 ml CSM and grown to mid-log phase over 6 hours. 500µl was transferred to a microfuge tube and sonicated at 20% For time-lapse microscopy (i.e. Figure 2D), samples were kept at 30°C and humidified with a P-Set 2000 Heated Incubation Insert (PeCon, Erbach, Germany).
Time-lapse experiments involved brightfield and fluorescence imaging of 16 different fields per sample, and images were taken every 10 minutes for 10 hours. Subsequent analysis of cell divisions was done in ImageJ (NIH, Bethesda, MD). To measure epigenetic switching rates in the FLAME assay, cell divisions and switching events were manually counted and the counter was blind to the genotype (single-blind study). This counting was performed only on cells that could be clearly distinguished from each other. If a mother and daughter cell pair switched simultaneously, we counted this as one switching event that probably appeared as two events due to the lag time in yEGFP expression or degradation.

Flow cytometry
To measure fluorescence intensities per cell in the CRASH and FLAME assays, a BD LSR Fortessa cell analyzer (BD Biosciences, San Jose, CA) with a FITC filter (for GFP) and a PE-TexasRed filter (for RFP) was used. Subsequent analysis was performed with FlowJo software.
For quantification of silencing-loss rates in the CRASH assay ( Figure 1E  For calculating the frequency of silenced and expressed cells at equilibrium in the FLAME assay, cells were first streaked out to generate single colonies. Three colonies per genotype were added to CSM media in a 96-well plate and grown to saturation overnight. These samples were then serially back-diluted in CSM media in 96-well plates and grown at 30°C. After twelve hours, the serial dilutions had a range of cell densities; the dilution that was closest to ~1 O.D. was again back-diluted in CSM media and grown at 30°C for another 12 hours. At this point, wells close to ~1 O.D. contained cells that had been growing at log-phase for approximately 24 hours.
These cells were analyzed by flow cytometry. Because three populations were analyzed per genotype, the most representative profiles of silenced and expressed cells were used for figures. We considered these populations as biological replicates.
To calculate GFP expression levels in expressed cells in the FLAME assay, cells were streaked out for single colonies and three colonies per genotype were grown overnight in CSM + 5 mM Nicotinamide (NAM) (Sigma-Aldrich, St. Louis, MO). These samples were then back-diluted in CSM + 5 mM NAM and grown at 30°C for 12 hours. Samples at ~1 O.D. were analyzed by flow cytometry. For Figure 2 Supplemental Figure 3, the most representative profiles of the three profiles generated per strain were shown. For Figure 4 Supplemental Figure 3, the geometric mean intensity of GFP per cell (excluding cells that formed a smaller, artifactual peak at a lower GFP intensity) was calculated for each population using FlowJo software.
Independent cultures were considered as biological replicates.
FACS was utilized in the FLAME assay to calculate switching rates between epigenetic states in  Figure 4B and 4E. Because the initial sorting event required ~20 minutes per sample, the time of initial sorting (t = 0 hrs) was different between samples; this made the time points between samples slightly staggered as seen in Figure 4B and 4E. Because cells were divided into subpopulations after the initial sorting, these subpopulations were considered as technical replicates.

Switching rate calculation from cell sorting
The following equations were used to model the dynamics of switching rates between epigenetic states in sir1∆. We considered the balance of GFP+ and GFP- The nls() function in R was used to provide a nonlinear least squares estimate of the unknown variables %& and %(( for each genotype, and 95% confidence intervals for estimates. With this approach, each genotype had an estimated %& and %(( from sorting silenced cells and an estimated %& and %(( from sorting expressed cells. Since sorting silenced cells subsequently allowed for observation of more loss-of-silencing events, the %& rates from those data were considered more accurate and used in Figure 4C. Similarly, the %(( rates calculated from sorting expressed cells were used in Figure 4F.
Because each population of sorted cells was evenly divided into three subpopulations, each genotype has three calculated values for the percent of GFP+ cells at each given time point after sorting. The nonlinear least squares estimate was made by drawing a best fit line through all data points for a given genotype, effectively combining the values of all subpopulations. The quality of the fit was calculated using the confint2() function and represented as 95% confidence intervals for %& values in Figure 4C and %(( values in Figure 4F. An alternative approach involved drawing a best fit line for each individual subpopulation to give three %& values and three %(( values for each genotype and averaging these values to get a single %& value and %(( value for each genotype, with error bars representing a standard deviation. Though we also performed this latter analysis method, we favor the former analysis method because it incorporates how well the data fit the nonlinear least squares estimate. Notably, both analysis methods gave similar %& and %(( values.
The generation time of DPB3 MCM2 (JRY11471) was 1.96 hours in CSM media at 30°C. To convert %& and %(( as rates per hour to rates per generation, we multiplied these variables by the generation time. Similar generation times were observed for all replisome mutants.

MNase-seq
Cells were grown to saturation overnight in 5 mL CSM at 30°C. The following day, these cells were back-diluted to ~0.1 O.D. in 50 ml CSM and grown at 30°C for 5 hours. Cells were then centrifuged and washed twice in 500 µl SKC buffer (1.2 M Sorbitol, 100 mM KH 2 PO 4 , 0.5 mM CaCl 2 , 7 mM b-mercaptoethanol) and then resuspended in 100 µl SKC buffer. Cells were incubated at 37°C for 15 minutes, then 30 µl of 1mg/mL Zymolyase-100T (MP Biomedicals, LLC, Solon, OH) was added for a final concentration of 0.23 mg/ml Zymolyase-100T and incubated at 37°C for 15 minutes. All subsequent steps were performed on ice. Once spheroplasting was complete, cells were spun at 3k RPM for 3 minutes at 4°C. Cells were washed twice in 500 µl SPC buffer (1 M Sorbitol, 20 mM PIPES pH 6.3, 0.1 mM CaCl 2 , with Roche cOmplete protease inhibitors (Sigma)) and spun at 2k RPM for 3 minutes at 4°C between washes. Cells were resuspended in 250 µl SPC buffer, and this solution was gently mixed with 250 µl freshly prepared Ficoll buffer (9% Ficoll, 20 mM PIPES pH 6.3, 0.5 mM CaCl 2 ) to lyse the cell membranes.
Nuclei were then pelleted by centrifugation at 10k RPM for 20 minutes at 4°C.
Nuclei were washed twice in 500 µl SPC and spun at 8k RPM for 3 minutes at 4°C between washes. Washed nuclei were subsequently resuspended in 250 µl SPC and CaCl 2 was added to a final concentration of 2mM CaCl 2 . Nuclei were incubated for 5 minutes at 37°C, then 20 units of Worthington MNase was added (Worthington Biochemical Corporation, Lakewood, NJ). Nuclei were incubated for 15 minutes at 37°C. MNase activity was quenched by addition of EDTA to a final concentration of 10 mM EDTA. Nuclei were centrifuged at 3.7k RPM for 5 minutes at 4°C. The nucleosome-containing supernatant was subsequently removed and DNA and RNA were purified using a Qiagen spin column. RNase A (Sigma) was added to a final concentration of 1 mg/ml RNase A and incubated for 2 hours at 37°C. DNA was then purified using a Qiagen spin column. MNase libraries were constructed with NEBnextUltra II library preparation kit (New England Biolabs, Ipswich, MA) and sequenced on an Illumina HiSeq4000 (Illumina, San Diego, CA) as 100 bp paired-end reads.
Reads were mapped to the Saccharomyces cerevisiae S288C genome (GenBank accession number GCA_000146045.2) using Bowtie2 (Langmead and Salzberg, 2012). Mapped reads between 140 bp and 180 bp in length were used in all further analysis to ensure mononucleosome resolution. The midpoint for each read was calculated and midpoints were stacked in a histogram. Finally, a 25 bp rolling mean was used to smooth out the resulting nucleosome peaks. All sequences and processed data files have been deposited in the NCBI Gene Expression Omnibus archive under accession number GSE136897.   Samples were taken at different time-points and analyzed by flow cytometry. These data correspond to experiments shown in Figure 4B and 4E. At least 700 cells were analyzed for each time-point.  mcm2-3A (JRY11590) were grown at log phase for 12 hours in 5 mM Nicotinamide (NAM) and

Figure Supplements
HMRa::GFP expression was measured with flow cytometry. The geometric mean intensity of GFP for each strain was calculated using FlowJo software. Data are means ± SD (n = 3 independent cultures).

Separate Files
Video 1: Time-lapse video of inheritance of epigenetic states in the FLAME assay.
HMRa::GFP sir1∆ (JRY11478) cells were grown to log-phase in liquid media and subsequently imaged by time-lapse microscopy. A loss-of-silencing event is visible near the center of the field of view at 4 hrs, and an establishment-of-silencing event is visible near the upper-left corner at 5 hrs.