A variable fork rate affects timing of origin firing and S phase dynamics in Saccharomyces cerevisiae

Journal of Biotechnology 168 (2013) 174–184

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Journal of Biotechnology journal homepage: www.elsevier.com/locate/jbiotec

A variable fork rate affects timing of origin firing and S phase dynamics in Saccharomyces cerevisiae Adriana Supady a,1 , Edda Klipp a , Matteo Barberis a,b,∗ a

Institute for Biology, Theoretical Biophysics, Humboldt University Berlin, Invalidenstraˇe 42, 10115 Berlin, Germany Synthetic Systems Biology and Nuclear Organization, Swammerdam Institute for Life Sciences, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands b

a r t i c l e

i n f o

Article history: Received 21 December 2012 Received in revised form 23 May 2013 Accepted 27 June 2013 Available online 9 July 2013 Keywords: DNA replication Origin firing Replication timing Replication fork rate Firing efficiency Budding yeast

a b s t r a c t Activation (in the following referred to as firing) of replication origins is a continuous and irreversible process regulated by availability of DNA replication molecules and cyclin-dependent kinase activities, which are often altered in human cancers. The temporal, progressive origin firing throughout S phase appears as a characteristic replication profile, and computational models have been developed to describe this process. Although evidence from yeast to human indicates that a range of replication fork rates is observed experimentally in order to complete a timely S phase, those models incorporate velocities that are uniform across the genome. Taking advantage of the availability of replication profiles, chromosomal position and replication timing, here we investigated how fork rate may affect origin firing in budding yeast. Our analysis suggested that patterns of origin firing can be observed from a modulation of the fork rate that strongly correlates with origin density. Replication profiles of chromosomes with a low origin density were fitted with a variable fork rate, whereas for the ones with a high origin density a constant fork rate was appropriate. This indeed supports the previously reported correlation between inter-origin distance and fork rate changes. Intriguingly, the calculated correlation between fork rate and timing of origin firing allowed the estimation of firing efficiencies for the replication origins. This approach correctly retrieved origin efficiencies previously determined for chromosome VI and provided testable prediction for other chromosomal origins. Our results gain deeper insights into the temporal coordination of genome duplication, indicating that control of the replication fork rate is required for the timely origin firing during S phase. © 2013 Elsevier B.V. All rights reserved.

1. Introduction S phase is a critical stage in cell cycle progression where genome duplication has to occur exactly once, without errors, to avoid chromosomal defects that can lead to genomic instability (Machida et al., 2005). This process is realized by firing of multiple chromosomal locations called replication origins (Méchali, 2010), and in the budding yeast genome over 700 potential origin sites have been identified and mapped by genome-wide studies and deepsequencing technologies (Siow et al., 2012 and references therein). Replication origins are determined and prepared to fire by the binding of initiator proteins that are assembled into pre-replicative

∗ Corresponding author at: Synthetic Systems Biology and Nuclear Organization, Swammerdam Institute for Life Sciences, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands. Tel.: +31 20 525 8686; fax: +31 20 525 7934. E-mail address: [email protected] (M. Barberis). 1 Present address: Fritz Haber Institute of the Max Planck Society, Theory Department, Faradayweg 4-6, 14195 Berlin, Germany. 0168-1656/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jbiotec.2013.06.022

complexes, pre-RCs (Bell and Dutta, 2002; DePamphilis, 2005; Sclafani and Holzen, 2007; Takeda and Dutta, 2005), and their phosphorylation by cyclin-dependent kinases (Cdk/cyclin) sets the correct timing of S phase progression (Araki, 2010a,b; Labib, 2010; Sacco et al., 2012; Tanaka and Araki, 2010). Strikingly, Cdk/cyclin complexes synchronize origin firing with cell cycle progression by determining the efficiency of origin firing (Donaldson et al., 1998; Duncker et al., 1999; Katsuno et al., 2009; Krasinska et al., 2008; McCune et al., 2008; Nakanishi et al., 2010; Thomson et al., 2010). Deregulation (inactivation or alteration in the total amount) of components involved in the control of S phase entrance, such as the pre-replication complex (pre-RC), e.g. proteins forming ORC and MCM complexes, leads to inappropriate firing in the number of origins, resulting in a premature or retarded genome duplication. These abnormalities are the underlying cause of genomic instability and strongly associated to human cancers (Blow and Gillespie, 2008; Hook et al., 2007; Lau et al., 2007; Schär, 2001; Sidorova and Breeden, 2003; Stoeber et al., 2001; Tlsty et al., 1995; Williams and Stoeber, 2012). In budding yeast, genomic stability is compromised when deterioration in the performance of genome duplication

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or in its surveillance mechanisms occurs (Kolodner et al., 2002). Cdk1 activity plays a role in genome duplication (Enserink et al., 2009): Cdk1/cyclin complexes modulate the replication timing of early and late origin firing (Donaldson et al., 1998; Jackson et al., 2006; McCune et al., 2008; Raghuraman and Brewer, 2010; Schwob and Nasmyth, 1993), and the inhibitor Sic1 (Barberis, 2012a,b and references therein) counteracts their activities to set the kinase threshold for DNA replication, thereby the correct timing of origin firing throughout S phase (Barberis et al., 2007, 2011, 2012; Barberis and Klipp, 2007). In absence of Sic1, DNA replication initiates from few origins, the distance between replicons is 1.5 times longer than wild type and cells accumulate gross chromosomal rearrangement, indication of increased genome instability (Caburet et al., 2002; Lengronne and Schwob, 2002; Nugroho and Mendenhall, 1994). This clearly shows that origin density is crucial for genome integrity and determines S phase dynamics (Bielinsky, 2003), and suggests that either fewer origins could fire with a wild type efficiency, or the firing efficiency could be preserved but the rate of fork progression would decrease. Replication origins fire at characteristic times (Raghuraman et al., 2001; Yabuki et al., 2002) but exhibit variable frequency of firing in different cell cycles (i.e. efficiency), some firing in almost every cell cycle while others rarely used (Czajkowsky et al., 2008; Friedman et al., 1996, 1997; Raghuraman et al., 2001; Shirahige et al., 1993; Yamashita et al., 1997). As a result, the rate of DNA replication is not uniform throughout the genome, with an average speed of about 3 kb/min (Raghuraman et al., 2001; Rivin and Fangman, 1980; Yabuki et al., 2002). In recent years, deterministic (Barberis et al., 2010a; Brümmer et al., 2010; Gidvani et al., 2012; Spiesser et al., 2009) and stochastic (Barberis et al., 2010b; de Moura et al., 2010; Hyrien and Goldar, 2010; Luo et al., 2010; Retkute et al., 2011, 2012; Yang et al., 2010) models of spatiotemporal activation of replication origins have been developed. Although a few contributions seem to suggest that regulation of origin firing might occur through modulation of the replication fork rate for a timely S phase (Azvolinsky et al., 2009 and references therein), modeling and experimental efforts neglected this aspect by considering the fork speed to be uniform throughout the yeast genome (de Moura et al., 2010; Sekedat et al., 2010; Spiesser et al., 2009; Yang et al., 2010). Indeed, it has been observed that large variations in replication fork rates occur along the yeast genome (Ferguson et al., 1991; Raghuraman et al., 2001; Yabuki et al., 2002), that a significant increase in the fork rate during S phase is observed in mammalian cells (Gauthier et al., 2012; Housman and Huberman, 1975; Painter and Schaefer, 1971; Scott et al., 1997; Takebayashi et al., 2005), and that a gradual and increasing density of fired replication origins occurs in the course of S phase (Farkash-Amar and Simon, 2010; Goldar et al., 2009; Guilbaud et al., 2011; Herrick et al., 2000; Hyrien and Goldar, 2010; Ma et al., 2012; Rhind et al., 2010). Taking into account this observed variability, a modeling approach representing not homogeneous fork progression rates has been developed to analyse mice cells (Gauthier et al., 2012). Moreover, we have observed that in the budding yeast genome many DNA regions with significant fork rate changes do not show uniform spatial distribution and are clustered on distinct chromosomal locations (Spiesser et al., 2010). It is therefore a challenge to investigate in this organism how fork rate changes may affect efficiency of origin firing for a timely S phase. 2. Materials and methods 2.1. Origins of replication A total of 206 replication origins identified by the Heavy:Light (HL) timing study (Raghuraman et al., 2001) were considered for the analyses. These origins are annotated in the OriDB database

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(Siow et al., 2012) with a definite replication timing and correspond univocally to peaks in the replication profiles (Raghuraman et al., 2001). Moreover, 96 valleys which are generated from replication forks departing from two origins traveling in opposite direction were identified. 2.2. Model implementation A deterministic model of DNA replication was implemented in the programming language Matlab 7.10.0 (The Mathworks Inc.). The input file of the model is specific for each chromosome, and it contains (i) chromosomal location and firing times collected in the OriDB database for each replication origin considered in the study, i.e. only origins with available replication timing determined according to the HL study, and (ii) value of constant or variable fork rate used to reproduce the replication profiles (see below). If the fork rate value is constant, only this value is listed in the input file. If a variable fork rate is implemented, lower and upper boundaries of the range are specified, and an equation is added to ensure a linear dependency between firing times and fork rate. Fork rate progression was then implemented as follows. A local fork rate is assigned to each replication origin and represented by the slope of a line drawn bidirectionally starting from this origin. For all origins considered, the program verifies whether origins that are passively replicated are present along these lines and, if this does occur, their corresponding lines are deleted. The lines terminate only if they meet each other traveling from opposite directions or reach beginning/end of a chromosome. The program stops when the whole length of each chromosome is replicated. 2.3. Model parameters From the experimental replication profiles (Raghuraman et al., 2001), the following parameters were derived or computed: length of chromosomes, duration of replication, origin density and percentage of symmetric peaks (Table 1). The duration of replication is the timing intercurring between the replication of first and last base pairs in a given chromosome, whereas origin density is calculated by dividing the number of replication origins by the length of each chromosome. In this calculation, only distinct origins, i.e. with a distance between them of at least 2.5 kb, were considered. The percentage of symmetric peaks was calculated from the values of fork rates traveling in opposite directions (see below). Peaks were considered to be symmetric if fork rate values showed a difference <25%. Regions of low density (Raghuraman et al., 2001) were not included in the calculation. Replication profiles obtained from raw data together with the smoothed curves obtained transforming raw data by using the technique of Fourier convolution smoothing (FCS) (Raghuraman et al., 2001, Supplementary material, part II: Secondary Data Analysis) have been compared (see Supplementary Fig. 1). The smoothening does not change the overall dynamic of the replication profiles, thus resulting in a not biased data analysis. 2.4. Fork rate determination To calculate fork rate values, experimental replication profiles were scanned to identify peaks (defined as chromosomal regions with a minimum replication timing that increases bidirectionally for a length of at least 7.5 kb) and valleys (defined as chromosomal regions with a maximum replication timing that decreases bidirectionally for a length of at least 7.5 kb). Fork rate values were calculated from the slopes of 2.5 kb fragments departing from peaks and valleys, excluding the near-to-minimum (closer than 2.5 kb) and near-to-maximum (closer than 2.5 kb) regions to avoid errors of smoothing the curves. Only peaks that identify univocally known

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Table 1 Model parameters derived or computed from experimental replication profiles. Chromosome

Length (kb)

Duration of replication (s)

Origin density

Symmetric peaks (%)

I II III IV V VI VII VIII IX X XI XII XIII XIV XV XVI

228.91 809.08 313.17 1522.14 568.47 269.14 1081.72 556.72 437.76 743.27 662.59 1062.72 923.38 780.40 1079.26 940.72

2010.07 1877.12 2254.35 2322.28 1498.25 2222.11 1250.29 1536.85 1673.39 1675.77 1122.78 1527.20 2015.10 1259.57 1455.82 1159.87

0.0393 0.0396 0.0447 0.0322 0.0299 0.0334 0.0370 0.0431 0.0411 0.0350 0.0362 0.0414 0.0325 0.0333 0.0324 0.0457

33.33 30.77 37.50 32.26 33.33 60.00 36.84 36.36 0.00 42.86 53.85 11.11 38.89 50.00 33.33 31.58

origins with a defined replication timing, i.e. not different in location on the chromosome for more than 5.5 kb, and valleys that are generated from two forks traveling in opposite directions, i.e. emanating from two origins with defined replication timing, were included in the analysis. 2.5. Fitting of replication profiles The fitting of experimental replication profiles (Raghuraman et al., 2001) was performed according to the procedure shown in Supplementary Fig. 2. The best constant or variable fork rate values were fitted separately for each chromosome. For the search of appropriate ranges, a variable fork rate was modeled as a function of the replication timing assuming a linear dependency between firing times and fork rate for each origin. First, a global search was performed in order to narrow down the solution space (Step 1). We allowed the first origin to fire with an initial (start) fork rate value within the range 0.5–4 kb/min, and the last origin to fire with a final (end) fork rate value within the range 3–11 kb/min. These ranges were then sampled for every 0.5 kb steps along the chromosomes, and the residual sum of square between simulation and experimental data (RSS) was calculated for each combination of start and end fork rate values. The combination resulting in the lowest RSS was chosen as a starting point to retrieve precise fork rate values (Step 2). Thus, for the local optimization, the ranges were refined accordingly and sampled for every 0.1 kb steps in order to further minimize the RSS (Step 3). The procedure led to the identification of the best range of variable fork rates fitting each chromosome (Step 4). A similar procedure was used to fit the replication profiles with the best constant fork rate, with only one value fitted at each step. In order to avoid overfitting of the model, a fitting with a variable fork rate was accepted only if the RSS value was decreased for at least 20% as compared to a fitting with a constant fork rate; otherwise, a constant value was considered to be optimal. 2.6. Prediction of firing efficiencies for chromosomal replication origins A correlation between firing times and fork rate for the origins considered in the study was calculated, and chromosomes showing a high correlation were then selected to derive the efficiency of firing for each confirmed origin. From the experimental replication profiles, the first observed replicated fragment is observed not before 10 min from the beginning of S phase, and the last fragments are replicated slightly after 50 min (Raghuraman et al., 2001). Thus, we considered that an origin with 100% efficiency (maximum efficiency we assumed) would fire after 10 min (600 s) from the

beginning of S phase, and an origin with 20% efficiency (minimum efficiency we assumed) would fire after 50 min (3000 s). The range was chosen based on the temporal evolution of the replication process. Therefore, we calculated the firing efficiency with a formula that assumes a linear relationship between firing efficiency and replication timing (in s), where: efficency = −

1 × tfiring + 120 30

3. Results and discussion 3.1. Leftward and rightward replication fork rates are correlated and show high variability Genome duplication proceeds bidirectionally from each firing origin, generating two replication forks traveling in opposite directions along the DNA (Brewer and Fangman, 1988). Moreover, replication has been inferred to progress asymmetrically from certain origins resulting in replication profiles with fork rates not uniform throughout the budding yeast genome (Raghuraman et al., 2001). In this respect, analyses conducted in this organism have revealed an apparent contradiction: an asynchronous departure of the two forks from an origin in addition to differences in the replication fork rate was envisioned (Santamaría et al., 2000), however the fork speed measured for 67 replication origins showed a significant correlation between sister forks (Natsume and Tanaka, 2010). Fork rate changes may influence origin firing, and we hypothesized that a combination of slow fork rates emanating from early origins and fast fork rates departing from late origins would reproduce adequately replication profiles (Fig. 1). The slope of replication profiles is taken as a measure of the fork rate, and the replication timing depends not only on the overall fork rate but also on the local proportion of rightward and leftward fork rates (de Moura et al., 2010; Guilbaud et al., 2011). Therefore, we have calculated right and left slopes emanating from each peak and valley in the replication profiles for the 16 yeast chromosomes (Fig. 2). This analysis includes: (i) 206 peaks identifying univocally replication origins for which the replication timing is available according to the HL study (Raghuraman et al., 2001; Siow et al., 2012) (Fig. 2A) and (ii) 96 valleys which are undoubtedly generated from two replication forks traveling in opposite directions (Fig. 2B). The significant positive correlation of individual outgoing (Fig. 2A) and incoming (Fig. 2B) leftward and rightward fork rates indicate that they move bidirectionally at a similar rate, however the high dispersion of data in the scatter diagram suggests that they are not identical. Studies performed in human cells have also shown a similar change in leftward and rightward rates measured for the

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fast fork rates at late firing times would be required for a timely S phase. Origin firing occurs through modulation of the fork rate (Azvolinsky et al., 2009 and references therein), and in mammalian cells changes in the fork rate have been shown to positively correlate with origin spacing (inter-origin distance), i.e. when the distance between two origins increases, fork rates emanating from those origins also increase, and vice versa (Anglana et al., 2003; Conti et al., 2007; Courbet et al., 2008). To elucidate this relationship in budding yeast, average incoming fork rates were calculated and plotted versus the inter-origin distance (Fig. 2D). A tendency for a positive correlation between the two parameters is observed, although with a less extent as compared to mammalian cells (Conti et al., 2007), indicating that density of replication origins influences fork rate progression. In agreement with our finding, it has been previously shown that in budding yeast fork sizes get smaller as S phase progresses (Koren et al., 2010), which predicts an increasing replication fork rate. Altogether, these evidence indeed corroborate the fact that density of firing replication origins affect S phase dynamics (Bielinsky, 2003).

3.2. Fork rate changes and origin density affects accuracy of origin firing

Fig. 1. Fork rate changes influence origin firing. (A) Replication profile indicates firing of DNA replication origins in time as a function of their chromosomal location. Peaks correspond to genomic regions where early origins fire, and two replication forks emanating from a fired origin (white stars) proceed bidirectionally with a rate proportional to the slope of the peak, i.e. steeper the slope, lower the fork rate. When two forks traveling from opposite directions meet, a valley is generated, corresponding to a late replicated region. If the fork rate is high and constant along the chromosome – so that some origins are passively replicated (black star) – the replication is fast but the temporal profile of origin firing will be not correctly reproduced. The length of the tick black line on the y-axes (time) represents the total time of replication for a specific chromosome, i.e. shorter the line, shorter the replication time. (B) If the fork rate is slow and all origins are expected to be activated, they will indeed fire but the overall replication time will be substantially extended (longer tick black line as compared to panel A). (C) If the rate of forks emanating from early origins is slower than the rate of forks departing from origins activated later, a high reproducibility of replication profiles would be expected, with a characteristic timing expected for a timely S phase.

majority of replication fork pairs (Conti et al., 2007), although previously in vitro data indicated that the two forks departing from an origin showed highly heterogeneous rates which can differ for each individual fork (Marheineke et al., 2005). Interestingly, the average outgoing fork rates calculated from the replication origins considered in the study progressively increase with the timing at which origins are replicated (Fig. 2C), supporting our hypothesis that a combination of slow fork rates at early firing times and

As we and others observed, fork rates are not uniform throughout the budding yeast genome, with an average speed of about 3 kb/min (Raghuraman et al., 2001; Rivin and Fangman, 1980; Yabuki et al., 2002). By implementing this constant fork rate, we have recently fit the experimental replication profiles (Raghuraman et al., 2001) in a deterministic model of DNA replication (Spiesser et al., 2009). The recalculated profiles matched the experimental ones for half of the chromosomes, although some of them present areas with a poor fitting; however, significant differences were observed for the other chromosomes (Spiesser et al., 2009). As previously hypothesized, whereas the slope of the recalculated profiles is constant due to the constant fork rate implemented, the experimental curve is smooth with a varying slope. This may reflect a change in the fork rate throughout the genome (Barberis et al., 2010a; Hyrien and Goldar, 2010; Spiesser et al., 2009), and the implementation of a dynamic fork rate function could increase the accuracy of the model. To test this hypothesis, we expanded the deterministic model of DNA replication implementing a fitting procedure such that each chromosome was fitted with a variable or a constant fork rate, the latter considering the determined value of 3 kb/min or a chromosome-specific constant value which fitted best the replication profiles. Replication origins with a replication timing determined according to the HL study (Raghuraman et al., 2001) were considered for the 16 yeast chromosomes. In Fig. 3 and Supplementary Fig. 3 the procedure is shown for chromosome VI, where either a constant (1.7 kb/min) or a variable (range 1.2–2.8) fork rate was applied to fit the experimental replication profile. For this chromosome, the implementation of a variable fork rate fitted best the replication profile, although the constant value of 1.7 kb/min also showed a very good agreement. Although replication profiles are population averages, thus imprecision is expected during the fitting procedure, all chromosomes with the exception of chromosome IX showed a very good match between calculated and experimental replication profiles (see Supplementary Fig. 4). In detail, half of the chromosomes (I, IV, V, VI, XI, XIII, XIV and XV) was fitted best with a variable fork rate, whereas the other half (II, III, VII, VIII, IX, X, XII and XVI) with a constant fork rate. For chromosomes that were fitted with a variable fork rate, an additional analysis was performed in order to verify that fitted ranges were not random but chromosome-specific (see Supplementary Fig. 5).

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Fig. 2. Leftward and rightward fork rates are correlated along the yeast genome. (A) For each peak, right outgoing fork rates are plotted versus left outgoing fork rates (R = 0.44; p < 10−10 , N = 206, 203 plotted). The gray area includes all points for which the difference between the value of left and right fork rates is <20%, and red dots represent the origins identified for chromosome VI. (B) For each valley, right incoming fork rates are plotted versus left incoming fork rates (R = 0.78; p < 10−19 ; N = 96, 95 plotted). (C) The average outgoing fork rate for each peak is plotted versus the replication timing of the corresponding origin (R = 0.25; p < 10−3 , N = 206). (D) The average incoming fork rate for each valley is plotted versus the corresponding inter-origin distance (R = 0.12; p = 0.243; N = 96, 95 plotted). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)

Fig. 3. Fork rate changes affect accuracy of origin firing. A constant or variable fork rate was implemented to fit the calculated replication profile for chromosome VI to the experimental one (Raghuraman et al., 2001). The experimental profile (black line) with marked centromere (black square) and a low-density region (gray bar) are shown. A constant or a variable fork rate were applied to fit the experimental replication profile, and overlapping of calculated and experimental replication profiles are shown: constant fork rate of 3 kb/min (blue line), chromosome-specific constant fork rate of 1.7 kb/min (green line), and variable fork rate (red line) with the first and last origins firing with fork rates of 1.2 and 2.8 kb/min, respectively. Fork rate values for the intermediate origins were calculated with an increasing linear function of the firing timing. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)

This differential behavior was further investigated by plotting these values versus the density of replication origins for each chromosome and, strikingly, an interesting feature was observed: chromosomes with a low origin density replicated the DNA with a variable fork rate, whereas chromosomes with a higher origin density were described with a constant fork rate (Fig. 4). Only two chromosomes, I and X, did not follow this trend. This result indicates that, if two replication origins are in a close vicinity (high density), the fork rates traveling from one to the other would be generally low and at a constant value; on the other side, if the distance between the two origins increases, a higher speed would be required in order to maintain the temporal window of the S phase. This is in agreement with the positive correlation observed between changes in fork rate and origin spacing (Anglana et al., 2003; Conti et al., 2007; Courbet et al., 2008). Moreover, our result supports a model in which the rate of replication fork progression is inversely related to the number of active replication forks, which is determined by the level of origin firing. In fact, replication forks has been shown to proceed more rapidly in cells where fork numbers are reduced, whereas a slower

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Fig. 4. Origin density affects fork rate changes. Fork rate values were systematically calculated to fit the 16 yeast chromosomes and, for each chromosome, the best constant or variable fork rate value was identified as reported in Section 2. The fork rate values derived from the fitting procedure were then plotted versus the origin density for each chromosome. The small panel within the figure represents a blow-up of a region with high origin density (0.032–0.034).

fork progression was observed due to an excess of replication forks (Zhong et al., 2013). Altogether, this evidence suggests that chromosome-specific modulation of the fork rate affects DNA replication dynamics. Various scenarios may be envisioned to explain the reported evidence. Chromatin structure is correlated with replication timing. Chromatin-binding proteins, e.g. transcription factors, and chromatin-modifying enzymes, e.g. histone deacetylases, influence efficiency and timing of origin firing (Knott et al., 2009, 2012; Vogelauer et al., 2002). These evidence suggest that firing of replication origins along the genome may be regulated by spatial modification of the chromatin status, which in turn influences the speed at which DNA is replicated. In budding yeast, three polymerases have a specialized role in the replication process (Hiraga et al., 2005; Pavlov and Shcherbakova, 2010), and a variable rate at which their function is exploited may occur. It is at present not known whether the replication rate differs among polymerases, or each polymerase modulates its speed along the genome during the replication process. Interestingly, metabolic genes involved in catabolic and anabolic reactions have been found near early and late replication origins, respectively (Spiesser and Klipp, 2010), suggesting their possible, yet unknown, differential activation in the course of S phase.

3.3. Interplay between fork rate, replication timing and origin density for an efficient origin firing As we have observed, fork rate changes appear to influence the timing at which replication origins fire. Thus, the correlation between these two parameters may be relevant to coordinate the progressive origin firing throughout S phase. Although no chromosomes display a negative correlation, coefficient values differ significantly among them. We found that this correlation decreases with the chromosome length (Fig. 5A) and a similar trend is observed for the origin density (Fig. 5B), with at a slightly less extent for short chromosomes. This evidence suggests that the correlation between fork rate and replication timing is a property of genome duplication, and that a precise modulation of the fork rate may occur during the replication process.

The overall data presented suggest that origin density influences changes in fork rate, which in turn impacts origin firing. This conclusion derives from the systematic analysis of replication profiles, which represent the average behavior of individual origins over a cell population: a peak in a replication profile indicates that an origin fires at a specific chromosomal location, but it does not say whether it fires in every cell in the population (Raghuraman and Brewer, 2010; Rhind et al., 2010). This is because the replication timing may be heterogeneous at the single cell level, thus leading to a different firing efficiency for replication origins, some firing in almost every cell cycle while others in less than 10% of the cells (Friedman et al., 1997; Raghuraman et al., 2001; Shirahige et al., 1993; Yamashita et al., 1997). Moreover, origins that have a higher firing probability are likely to fire in early S phase, whereas origins with a low firing probability are unlikely to fire in early S phase. Hence, the firing time of an origin determines its pattern of replication and firing efficiency (Luo et al., 2010). In order to capture the relationship between these parameters (fork rate, replication timing and firing efficiency), we have first calculated the correlation between average fork rate and replication timing and, subsequently, derived the firing efficiency based on this correlation. Correlation coefficients were calculated for replication origins identified by Heavy:Light (HL) and Copy Number (CN) (Yabuki et al., 2002) methods, for which replication timing is available (Siow et al., 2012). A tornado plot was generated to visualize this correlation, and chromosomes with a coefficient >0.5 were indicated as black bars (Fig. 5C). The analysis showed that short chromosomes generally tend to a high correlation as compared to long chromosomes: six short chromosomes out of eight (I, III, V, VI, IX and X) exhibit a correlation >0.5 in both HL and CN studies, whereas the remaining two chromosomes (VIII and XI) exhibit a correlation >0.5 only in the CN study. In the next step, we focused on the six short chromosomes and calculated the efficiency for the replication origins fired within each chromosome, as reported in Materials and methods. In Table 2 firing efficiencies for confirmed origins of chromosome VI are reported, with the known, experimentally determined (Friedman et al., 1997; Yamashita et al., 1997) and predicted values. Our deterministic model was able to derive successfully the efficiency values for five out of seven origins for which firing efficiencies are known

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Fig. 5. Correlation between fork rate and replication timing is a property of genome duplication. For each chromosome, a correlation between the average fork rate departing from origins in the experimental replication profiles (see Fig. 2C) and their replication timing was calculated. (A) Correlation coefficients were plotted versus the length of each chromosome. Chromosomes with low and high origin density are indicated with light and dark gray squares, respectively. (B) Correlation coefficients were plotted versus the origin density of each chromosome. Short and long chromosomes are indicated with light and dark gray squares, respectively. (C) Correlation coefficients were calculated for replication origins identified in both Heavy:Light (HL) and Copy Number (CN) studies. Black bars correspond to chromosomes characterized by a correlation coefficient >0.5 (dotted lines individuate this threshold) between average fork rate and replication timing for both studies.

(601/602, 603, 605, 606 and 607). For the origins 603.5 and 604, the predicted values did not match the experimental ones. In this case, their close vicinity on the chromosome suggests that, if a competition between them occurs for a firing event (analyzed below), their firing efficiencies would be potentially different in each cell

cycle. In addition, a prediction was made for the origins 600.3 and 600.4, which most probably represent a unique firing event. Overall, the accuracy of the firing efficiencies was substantially increased as compared to a recent study where values were estimated by a stochastic model of DNA replication (Luo et al., 2010). Considering

Table 2 Efficiencies (%) for replication origins of chromosome VI. Experimentally determined (Friedman et al., 1997; Yamashita et al., 1997) and predicted efficiencies are reported. Genomic location

Name

Firing time (s)

Efficiency (%) (Yamashita)

VI–19 VI–20 VI–33 VI–69 VI–119 VI–128 VI–136 VI–168 VI–199 VI–236

600.3 600.4 601/602 603 603.5 604 605 606 607 –

2622 2622 2544 2172 1290 1290 1524 1116 768 2232

– – 40 58 55 5 72 82 88 –

Efficiency (%) (Friedman) – – 32 67 50 – 27 74 >85 –

Predicted efficiency (%) 32.6 32.6 35.2 47.6 77 77 69.2 82.8 94.4 45.6

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Fig. 6. Firing of adjacent replication origins. A region of chromosome VI (black line) with three adjacent origins (603.5, 604 and 605) is shown. The fitting (gray line) is performed by assuming that at least one of the three origins fires, which results in seven possible scenarios: only one origin fires (A–C), two out of three origins fire (D–F) or all three origins fire (G). Starting from the firing efficiencies determined experimentally (Yamashita et al., 1997), the probability of occurrence for each scenario was calculated and then combined into a mean replication profile that fits best the experimental one (H).

the positive outcome of our method, testable predictions of firing efficiencies were derived for confirmed origins with known replication timing of short chromosomes previously selected (I, III, V, IX and X) (Supplementary Table 1). With the help of recent developments of highly powerful DNA combing techniques, these prediction can now be experimentally tested for their consistency. 3.4. Estimation of efficiency for adjacent replication origins Although the deterministic model provided a good match between experimental and calculated firing efficiencies for chromosome VI, the estimation for replication origins 603.5 and 604 was largely inaccurate. We have proposed that, being in the close vicinity on the chromosome, the competition between them for a firing event may lead to an uncertainty in the resulting firing efficiencies. The firing efficiency indicates the probability of each origin to fire in a cell population; however it does not provide the information about how many of them are competent to fire. In this context, competence is defined as the percentage of cells in which an origin is biochemically competent to fire (Raghuraman and Brewer, 2010). Thus, this would mean that efficiency and competence of origin firing may have a different value. For ‘single’, origins, i.e. not surrounded by adjacent origins, similar percentage of efficiency and competence are expected. Contrarily, for multiple origins located in a close vicinity on the chromosome, efficiency values may be not comparable with competence values due to the possible competition between them. This could lead to a not accurate prediction of firing efficiencies, as it seems to be the case for the origins 603.5 and 604 on chromosome VI. As shown in Table 2, in this chromosome firing efficiencies for replication origins are available (Friedman

et al., 1997; Yamashita et al., 1997), but competence values remain still unknown. As aforementioned, efficiency and competence would be similar for ‘single’ origins in chromosome VI; however, three adjacent origins are observed in a definite chromosomal region, where competition between them can occur. The measured firing efficiencies of the origins 603.5, 604 and 605 are 55%, 5% and 72%, respectively (Yamashita et al., 1997), but our prediction matched the experimental value only for the origin 605 (69.2%). Therefore, in order to provide a rationale explanation for the values observed for origins 603.5 and 604, we developed an approach to retrieve competence values from experimental efficiencies. To this purpose, seven different scenarios where one or multiple origins fire together were considered and, according to these cases, an equation system was formulated and solved (see Supplementary Text for details). Starting from the firing efficiencies determined experimentally (Yamashita et al., 1997), the calculated probability of occurrence for each scenario were calculated and then combined into a mean replication profile that fits best the experimental one (Fig. 6). We assumed that, if two origins are competent to fire simultaneously but only one fires, each of them would have the same probability to be the one that fires. Similarly, if three origins are competent to fire, each of them would have about 33% probability to fire. In order to solve the problem of competition between origins and to find out how the values of competence are related, we investigated further the scenarios with only one origin firing. By developing a subsequent equation system (see Supplementary Text for details), and discarding complex and negative solutions, we obtained the following competence values: origin 603.5 = 73.4%,

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origin 604 = 3.8% and origin 605 = 99.9%. Comparing these values to the firing efficiency we predicted for these origins (see Table 2), a few observations can be done. First, the value of efficiency we calculated for origin 603.5 (77%) corresponds to the competence value retrieved (73.4%), suggesting that the competition with the neighbor origins 604 and 605 may decrease this value to the experimental observed of 55%. Furthermore, the value of efficiency we calculated for origin 604 (77%) was inaccurate; the value we now retrieved in fact indicates a poor competence of firing (3.8%), which is indeed observed experimentally (5%). Finally, the competence value we retrieved for origin 605 (99.9%) indicates a high probability of firing; however, the competition with the adjacent origins 603.5 and 604 leads to a lower firing efficiency measured experimentally (72%), which was indeed correctly predicted from our study (69.2%). 3.5. Comparison with existing models of DNA replication dynamics The counter part of the work we presented here is the analysis of Yang et al. (2010). The authors proposed an analytical model of DNA replication that is based on a probabilistic firing of the replication origins. The results of their model support the hypothesis that origin timing is not governed by a temporal program but is rather a consequence of a stochastic manner of origin firing, as envisioned earlier (Spiesser et al., 2009; Barberis et al., 2010b). It should be noticed that the proposed model of Yang and colleagues can describe not only the stochastic mode of origin firing but can be also converted to a deterministic model that allows modeling of different scenarios. Both constant and variable fork rates were implemented in the model; however, as both of them allowed a good fit of the data, the results were presented considering a constant fork rate. The authors have extracted the distributions of the firing time for the replication origins reported in the work of McCune et al. (2008), and used them further to calculate the firing efficiencies. One of the main findings of this work is that the variation in firing time increases with the increasing average time of firing. To explain this finding authors provide a further multiple-initiator model and suggest that the MCM complex is a good candidate as initiator of the firing process. The aspect of deriving intrinsic origin properties from experimental data was extended further in the work of Baker et al. (2012). In this paper, the authors present how to calculate the firing rate at a given locus directly from the spatiotemporal data, without the necessity to use a model. The approaches described in the aforementioned papers are successful to reproduce the experimental data and address a quite few questions at the same time, e.g. where and when the replication initiates, and in which mode it progresses. The main difference between these contributions and the work here presented is that neither the distribution of the firing time nor the variation in the location of firing sites are included in the computational model. Our approach is purely deterministic and based exclusively on the experimental data, with the focus to investigate the dynamics of the progression of DNA replication, i.e. the emerging value of the fork rate among different chromosomes and among different origins within each chromosome. One of the assumptions of our model that has been chosen to reproduce the experimental data (replication profiles) is that the competence of an origin that fires decreases with the time of firing. Strikingly, this is consistent with one of the outcomes of the model presented by Yang et al. (2010). Altogether, these findings suggest that our deterministic model is able to correctly retrieve the firing efficiency of a definite set of replication origins and provide testable prediction for other firing origins. In addition, our approach can derive the competence of origin firing for adjacent origins, providing a rationale explanation for

the resulting, not obvious, efficiency values that may be observed experimentally. Therefore, our model could be suitable for further and more accurate investigation of the temporal origin firing in budding yeast, in particular as soon as additional values of origin efficiencies become available. 4. Conclusion In budding yeast, the opposite activities of Cdk1/cyclin kinase complexes and their inhibitor Sic1 determine the correct timing of firing of replication origins. Alterations in this temporal coordination result in an inappropriate firing of the origin number, therefore leading to genome instability. Replication origins fire at characteristic times, but their firing probability varies, resulting in a DNA replication rate that is not uniform throughout the genome. Large variations in replication fork rates occur along the yeast genome; however no attempts have been reported so far to provide a rationale explanation for this observation. In the present study, we developed a deterministic model of DNA replication to investigate how fork rate changes may affect the observed efficiency of origin firing for a timely S phase. Our findings support a scenario where modulation of the fork rate affects the timing of origin firing during S phase. Moreover, we provide evidence for the interplay between fork rate, timing of origin firing and origin density for efficient origin firing, estimating firing efficiencies for a wide range of replication origins that can be testable experimentally. Therefore, our approach could be suitable for further investigation of DNA replication dynamics in eukaryotes, investigating the altered genomic stability observed in a wide range of cell cycle mutations. Author’s contribution MB conceived and designed the computational study. AS performed the computational analysis. AS, EK and MB analyzed data. MB wrote the manuscript. All authors have read and approved the final article. Acknowledgments We are grateful to Wolfram Liebermeister for the help with the implementation of Matlab scripts. This work was supported by grants from the European Commission ENFIN (contract number LSHG-CT-2005-518254) and UNICELLSYS (contract number HEALTH-2007-201142). The funding sources had no involvement in preparation and writing of the article, study design, collection, analysis and interpretation of data. Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.jbiotec. 2013.06.022. References Anglana, M., Apiou, F., Bensimon, A., Debatisse, M., 2003. Dynamics of DNA replication in mammalian somatic cells: nucleotide pool modulates origin choice and interorigin spacing. Cell 114, 385–394. Araki, H., 2010a. Regulatory mechanism of the initiation step of DNA replication by CDK in budding yeast. Biochimica et Biophysica Acta 1804, 520–523. Araki, H., 2010b. Cyclin-dependent kinase-dependent initiation of chromosomal DNA replication. Current Opinion in Cell Biology 22, 766–771. Azvolinsky, A., Giresi, P.G., Lieb, J.D., Zakian, V.A., 2009. Highly transcribed RNA polymerase II genes are impediments to replication fork progression in Saccharomyces cerevisiae. Molecular Cell 34, 722–734. Baker, A., Audit, B., Yang, S.C., Bechhoefer, J., Arneodo, A., 2012. Inferring where and when replication initiates from genome-wide replication timing data. Physical Review Letters 108, 268101.

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