The mean replication time of a locus expressed as a percentage of the time spent in S- phase is linked to the probability of replication on a random S-phase chromosome (fi). It is simply 1-p,, where 1 is equivalent to the end of S-phase (i.e. there comes at time at the end of S-phase when the entire genome has replicated and the probability of seeing a doublet at any locus must therefore be 1). 1-p, is also the probability that replication has not occurred (i.e. the proportion of singlet chromosomes). The proportion of chromosomes in an asynchronized experiment that have not replicated and the mean replication time expressed as a percentage of the time spent in S-phase are equivalent, see below.
Ideally, we want to observe the locus of interest on every chromosome within a cell population and, once the cells enter S-phase, use a stopwatch to time precisely when each locus becomes a doublet. In this way we would generate a distribution of actual replication times from which the mean could be read (Figure A. I).
No. of doublets
S-phase (minutes)
If, for example, replication always occurred at time t way through the S-phase then in the impossible stopwatch experiments, all replication times will equal t and the mean will equal t. If, on the other hand, the replication of a particular locus takes place at either tl with probability p or at t2 with probability I-p, see Figure A .2. Then, on average, the mean replication time will be p*tl + (I-p)*t2, hatched areas on Figure A.2. probability of replication I-p — 0 tl t2 I S-phase
Figure A .2 . Estimating the mean replication time.
Such stopwatch experiments are, of course, impossible. However, it would be possible to perform FISH experiments on synchronized cells, fractionated into different stages of S-phase by retro-synchrony. In this way we could generate a cumulative curve of the proportion of chromosomes on which a particular locus has replicated by a given time through S-phase. The steepest part of this curve would be equivalent to the highest part of the histogram in Figure A .I. We could read off the median replication time when 50% of the loci had been replicated (see Figure A .3, below).
p ro p o rtio n o f d oub lets
0.5
fractio n s o f S -phase
Figure A.3. T h e o re tic a l c u m u la tiv e cu rv e o f re p lic a tio n tim in g
H o w e v e r, the E B V -tran sfo rm ed B -cells u se d in the m ajor part o f this w o rk w ere
refractory to sy n ch ro n iz atio n , and thus these experim ents w ere also im p o ssib le .
S y n ch ro n iza tio n w as perfo rm ed by S elig et al in their original p ap e r (1 9 9 2 ). W e can
illustrate its im plications, using o u r idealized locus w hich alw ays rep licates at t. At any
tim e < t, no ch ro m o so m e have replicated. A t any tim e >t, all c h ro m o so m e s have
re p lic ated , this is illu stra te d in F ig u re A .4, below .
Proportion o f doublets
tim e in S-phase
Note that the area "over the curve" (in the hatched box in Fig A.4.) is equal to l*t . Hence, the area over the curve is equal to the mean replication time.
We can also look again at our example of replication taking place at either tl with probability p or at t2 with probability 1-p. From the hatched area on Figure A.5, we can see that the mean replication time is tl* l + (t2-tl)*(l-p), which simplifies to p*tl + (l-p)*t2, the same as the mean replication time in the impossible stopwatch experiments. Hence, the area over the curve is equal to the mean replication time.
probability of replication 1 P t2-tl 0 0 tl t2 1 S-phase (minutes) Figure A.5. Estimating the mean replication time from the cumulative curve.
We had to resort to asynchronous experiments. In asynchronous experiments, with probability x, a randomly chosen chromosome will be between 0 and x of the way through S-phase. Hence, with probability t, it will be at the some time between 0 and t (strictly speaking, less than t). Hence with probability t, it will not have replicated (see Figure A.4).
In our example in which a locus replicates at tl with probability p or at t2 with probability 1-p, we want to know how far into S-phase is a doublet at our locus of
interest. But since these are asynchronous experiments, we can not know this. Instead, we have to observe the locus on many S-phase chromosomes and estimate the mean probability of seeing a doublet.
With probability tl our locus of interest is between 0 and tl, in which case it will not have replicated (see Figure A.5). With probability (t2-tl) it will be between tl and t2, in which case it will have replicated with probability p. This probability is calculated from the number of doublets in the asynchronous experiments, see equation in section 3.5. In this case, the locus will not have replicated with probability 1-p. Thus the
probability that the locus on a randomly chosen chromosome will be a singlet is tl + (l-p)*(t2-tl), which again becomes p*tl + (l-p)*t2, the same as the mean replication time in the above experiments.
To reiterate, p is the probability of observing a doublet at a particular locus in a random sample of S-phase chromosomes, 1-p is the probability that replication of the locus has not occurred and equates to the mean replication time expressed as a percentage of the time spent in S-phase (i.e. the area above the curves in Figs A.4 & A.5). What this proportion means in terms of actual hours and minutes through S-phase, cannot be determined from our experiments. This would require knowledge of the approximate length of the S-phase, but to estimate this would require synchronization, which is not possible with this B-cell line.