Generation of the replication profiles
The spatiotemporal organization of the DNA replication process can be visualized by means of replication profiles. A replication profile is the plot of the replication time as a function of the position in the chromosome. In a replication profile peaks correspond to origins of replication, and valleys correspond to termination zones. The earlier an origin fires, the taller is its respective peak within the profile. Shoulders along the lines connecting peaks and valleys can either result from timely collisions of a firing origin and an oncoming replication fork, or they could also be the result of change in the fork migration rate, or inefficient origins. The slope of the line connecting a peak and a valley gives the direction and rate of the fork migration.
The simulation of the chromosomal duplication has been performed, as described in “Materials and methods” with a fork rate value equal to 3 kb/min. Sixteen replication profiles were generated, one for each chromosome, in order to highlight the spatiotemporal organization of the simulated DNA replication. Figure 2 shows the replication profiles for chromosome II. The smooth curve is recalculated from the data provided by Raghuraman et al. 2001, as described in “Materials and methods”, and the straight curve shows the simulated profile. All essential features of the experimental profile were captured in the simulation.
However, we observed a deviation in the slope of the lines, representing the speed of the fork migration. The lines of the simulated curve are straight, for a constant migration rate is implemented, whereas the experimental curve is smooth with a varying slope, indicating different fork rates. Most simulated regions reflect experimental data with high accuracy and only few regions with lower accuracy. We found similar results for all 16 chromosomes (see electronic supplementary material, Fig. S1). As reported in the work of Raghuraman et al. 2001, the fork rates range from 0.5 to 11 kb/min with a mean of 2.9 kb/min. Changes (increase or decrease) in the value of the fork rate could lead to different results in the computed simulations, implying more precise results in some regions and less accuracy in other regions. In addition, it is likely that, for some inefficient origins, the direction of fork migration during DNA synthesis may change from one cell division to the next. Moreover, it has been shown in mammalian cells that the replication speed controls the choice of the initiation firing sites on the chromosome (Courbet et al. 2008). However, we aim at a simplifying parametrization for this still not well-defined process to create an accurate, yet comprehensive representation.
We model the chromosome duplication deterministically using the published data for locations and firing times of 454 origins of replication. Since only few data are available about origin firing efficiency (Yamashita et al. 1997), which is nonetheless known to be a key property of the origin activation, we included origin efficiencies in an implicit way. We regarded the efficiencies of a subset of all origins (454 out of 732 reported in the OriDB) as to be 100%, which is a strong assumption. However, an approximation of the replication with 454 origins that fire with an efficiency equal to 100% represents a single replication event in a cell with 732 origins that fire at about 60% average efficiency. Since the number of actively engaged origins per cell cycle has been reported to be roughly around 400 (Wyrick et al. 2001; Takeda and Dutta 2005), this approximation seems reasonable. Employing this approach, the model does not represent a single cell behavior per se (no intrinsic noise in efficiencies and firing times) but reflects the average of a cell population. In other words, the model stands for a likely replication event in the average single cell, because it has been parametrized with population averaged data.
Chromosome duplication in the clb5Δ mutant
The activation of the replication machinery has still to be highlighted in many of its regulatory events, but a relevant step is the phosphorylation of different substrates by the Cdk1–Clb5,6 kinase complex that induces the firing of the DNA replication origins (Bell and Dutta 2002; Takeda and Dutta 2005). In a recent work, we described the steps which lead to the firing of DNA replication origins with a simple probabilistic model that considers the availability of the Cdk1–Clb5,6 nuclear concentration as the main input (Barberis and Klipp 2007). This model provides an explanation for the replication status of specific mutants which influence the entry into S phase, pointing out the direct correlation between the Cdk1–Clb5 activity and the temporal activation of the replication origins (Barberis and Klipp 2007). In support of this, clb5Δ cells suffer a significant decrease in the firing efficiency of some origins, in particular for those classified as late-S phase origins (Donaldson et al. 1998). Clb6 activates instead the early replication origins (Donaldson et al. 1998).
In the work of McCune et al. 2008, the activation of the replication origins has been investigated, comparing the temporal program versus the disordered firing, analysing cells lacking the initiator factor of DNA replication Clb5. Therefore, we tested the model in the clb5Δ mutant. Operatively, we stopped origin firing at 1,645 s. The replication profile computed for the chromosome II in a clb5Δ mutant is reported in Fig. 3. We found that multiple zones suffer significant delays in replication, whilst others are unaffected. Interestingly, the delayed regions correspond to the so-called CLB5-dependent regions (CDRs) experimentally observed in the work of McCune et al. 2008. These regions match sequences of the genome which on average replicate late in S phase (Alvino et al. 2007; Raghuraman et al. 2001), and each of the late replication origins reported in the work of Donaldson et al. 1998 resides in CDR regions. The simulations of the clb5Δ mutant are reported in the electronic supplementary material, Fig. S2 (compare CDR regions with the experimental profiles in Fig. 4; McCune et al. 2008). In detail we found a perfect match for nine chromosomes (from I to VIII, and XI), a good fit in the majority of the sequence length for chromosomes IX, X and XIV, and a small or no match for chromosomes XII, XIII, XV and XVI.
This analysis is in agreement with the fact that the clb5Δ mutant only affects late origins, whereas the early origins fire normally. Therefore, the precise time at which origins stop to fire in absence of CLB5 is important. We use 1,645 s as the time point, after which there is no more origin activation, because it represents the mean value of the distribution of the experimentally determined origin activation times (see electronic supplementary material, Fig. S3). Thus, the origins are divided in an early half (Clb5-unaffected) and in a late half (Clb5-affected). However, it is likely that Clb5 activates every origin not at the same time at every cell cycle, but with a certain variation. Intrinsic noise will affect the time of the activation of the Clb5-dependent origins that will become more like a time span (of some seconds or minutes). Therefore, the considered value of 1,645 is an approximation, which for some chromosomes might be quite accurate, but for others it might not be. This affects the results we observed in the following way: the chromosomes containing more early origins will be less sensitive to CLB5 deletion, whereas the chromosomes with more late origins will be more sensitive.
The general agreement of the replication kinetics between wild type and clb5Δ in the computed and experimental profiles supports the temporal program of the origin activation in budding yeast, as predicted (McCune et al. 2008).
Impact of origin deletion on DNA replication
Saccharomyces cerevisiae has well-defined, site-specific origins, many of which are efficient and fire as many as 90% of S phases (Fangman and Brewer 1991; Newlon et al. 1991). These characteristics lead to nearly homogeneous replication kinetics (Raghuraman et al. 2001). Despite the fact that DNA replication in budding yeast seems to follow a temporal program of origin activation, it has been reported that there is a stochastic component which can influence the process (Czajkowsky et al. 2008; McCune et al. 2008). In fact, the activation of some origins in the CDR regions, more closely fits a disordered, stochastic firing. They show no peak time of firing or are activated over a broad distribution of activation times in different cells in the population (McCune et al. 2008). In addition, it has been reported that variants of a stochastic firing model are compatible with a temporal staggered initiation of the replication origins in fission yeast (Lygeros et al. 2008; Rhind 2006).
In order to investigate the impact of change in the origin activation pattern on the replication dynamics, replication kinetics for all chromosomes have been computed repeatedly (30 times) with reduced sets of considered origins. The subsets are composed by random deletion of 50% of the original origins. This accounts for the change in environmental conditions (i.e. stress condition, checkpoint activation) or inefficient firing, which could reduce the global origin firing efficiency from 60 to 30%. Comparison of the replication kinetics for chromosome II exhibited under wild type (Fig. 4, left) and perturbed (Fig. 4, right) conditions shows that a 50% deletion of replication origins yields a prolonged chromosomal replication time. However, we do not observe fundamental alterations in the general shape of the replication kinetics, which indicates that conditional change leading to a 50% efficiency reduction of origin firing does not change the replication dynamics of the chromosomal duplication.
Moreover, we found that for most chromosomes the replication kinetics seem to show a remarkable resistance to origin reduction (see electronic supplementary material, Figs. S4, S5). The chromosomal duplication initiates within a short timeframe, which is consistent throughout the replication process, and only disperses towards replication termination. Concerning retardation, we found that 50% of origin deletion leads on average to a circa 12 min delay in duplication completion for chromosome II. The remaining chromosome kinetics show similar results (see electronic supplementary material, Figs. S4, S5). The outcome of the random perturbation of the system shows that the replication process is robust against firing failure or efficiency variation, and suggests that the replication kinetics displayed by a cell can be widely independent from the temporal program of the origin activation.
Simulating a stepwise loss of origin function
Despite the contribution that multiple origins per chromosome may make to efficient genome duplication in S. cerevisiae, it is widely accepted that there are many more replication origins than needed for the timely replication during the S phase (Bielinsky 2003). In fact, several origins on chromosome III can be deleted without substantially affecting the ability to faithfully inherit this chromosome during cell division (Dershowitz and Newlon 1993; Dershowitz et al. 2007).
To further understand the relationship between origin activation and replication time, we simulated the chromosomal replication with a decreasing number of active origins and monitored the change of the replication time. In the previous simulations we have observed that during perturbation of the system, the replication kinetics for the chromosomes are very similar, even though they are replicated with different sets of origins. Therefore, we ignored which specific selections of origins were used in the simulations and thus studied the relationship between the number of activated origins and the replication time directly. To this purpose, we used the same chromosomal location for origins and the same firing times, only the activated origins change randomly. The model predicts how the replication time of the average replication event would change, if a certain percentage of the origins were to be defective, deleted or inefficient. It is difficult to investigate the direct effect of activated origins and replication time in living systems, because the deletion of the origins often leads to the activation of adjacent usually inefficient/dormant origins. This mechanism ensures to the cell the successful chromosomal replication. Therefore, a systematic computational study is useful to highlight the relationship between a controlled quantity of active origins and the replication time.
Mean replication times for descending percentages of active origins (from 90 to 10%) have been computed for all chromosomes. The origin sets have been reduced stepwise (10%) and randomly selected. The simulations for every fraction of remaining origins were repeated 10,000 times. Mean and standard deviation for every fraction of remaining origins are displayed for every chromosome (Fig. 5; electronic supplementary material, Fig. S6). The average delay for 50% remaining origins is summarized in Table 1. The calculations for the chromosome II show that, with a decreasing percentage of remaining origins, the mean replication time increases, as well as the standard deviation (Fig. 5a). This is the case for all chromosomes, although the intensity of the increase differs amongst the chromosomes. Interestingly, the experimentally assessed duplication times can be obtained using only a certain subset of activated origins, and the subsets are different for every chromosome and composed randomly. An example is reported for chromosome XVI (Fig. 5b). The experimental replication time, derived from Raghuraman et al. 2001, is indicated as a dashed line. The simulation shows that chromosome XVI duplication could be achieved, in the experimentally measured time, with subsets of only 50–60% randomly selected origins (Fig. 5b; Table 1), as indicated by the intersection of dashed line and solid curve. This percentage differs for every chromosome, and for some chromosomes the replication can only be simulated in the appropriate time with 100% of the origins, e.g. for chromosome II (Fig. 5a; Table 1). Furthermore, it is important to consider that inaccuracies within the experimental replication times (see “Materials and methods” for details) affect the estimates of origin subsets in a way that, where the experimental times should be smaller, the estimated subsets should be larger.
Table 1 Average delay in chromosomal duplication time, under 50% origin deletion condition, calculated after 10,000 simulations of DNA replication
The simulations nicely mirror the robustness of the replication process against perturbations in origin firing, as a result of loss of the origin function or change in the total efficiency. Using a systems study, we highlight the relationship between origin activation and replication time in the average cell population in budding yeast. The reduction in origin firing up to, e.g. 50% in chromosome II can be compensated within the system resulting in a delay of about 12 min in replication completion (Figs. 4, 5). This is the case obviously only if no other late/dormant origins fire. A similar effect can be observed for the remaining chromosomes (Table 1). The average delay in chromosomal duplication increases with the size of the chromosomes (Fig. 6a), and decreases with an increasing origin density on the chromosomes (Fig. 6b). The origin density is the ratio between the number of origins on a chromosome and the chromosome size.