Figure 1.
Space-time representation of the replication kinetics.
The left-hand side shows the original (solid lines) and new synthesized (dashed lines) DNA while replications forks (triangles) are moving. In this example, the forks originate from two origins (circles) that are initiated at times and
. The forks move at a constant speed until they coalesce with another fork (diamond at
) or reach the ends of the molecule of length
(around
and
). The right-hand side presents the space-time replication fraction
, where
is the position along the genome, of the same replication cycle. Orange and blue areas represent unreplicated (
) and replicated DNA (
), respectively.
Figure 2.
used to produce the results presented in Fig. 3. The left-hand side is a density plot of the initiation rate, while the right-hand side shows
at various time points. (For clarity, each curve is offset by
/kb/sec from the previous one.) The initiation pattern is composed of two Gaussian initiation zones at 200 and 800 kb. The first, or “early,”zone is constant throughout time, while the second, more efficient, “late” zone is turned on at 5000 sec.
Figure 3.
Comparison between one simulated replication cycle (a), 1000 simulation cycles (b), and our rate-equation solution (c).
In graph (I), the color scale goes from 0 (orange) to 1 (blue); in graphs (II) and (III), it goes from 0 (white) to 0.01/kb (black); in graphs (IV) and (V), it goes from 0 (white) to 1.5/kb/sec (black). In all cases, we used the initiation function
presented in Fig. 2 and the fork velocity
kb/sec. The genome size is 1000 kb, with periodic boundary conditions. Column I compares the replication fraction
in the three cases. The dashed lines in b–I and c–I show the 10%, 50% and 90% contour curves. Columns II and III present the fork densities
. Fork densities are expressed in forks/kb in (b) and (c) while trajectories only are shown for the single cell cycle in (a). Columns IV and V present the space-time probability density functions of observing an initiation,
, or a coalescence,
, respectively. Part (a) shows where and when initiations and coalescences from one cycle occurred while parts (b) and (c) represent probability densities in 1/kb/sec.
Figure 4.
Replication starting and ending times density functions,
and
, for our model system. Symbols were obtained from simulations, while solid lines were calculated from the solution of our rate-equations.
Figure 5.
(a) Example of a replication space-time profile and the corresponding SMARD labeling procedure. As before, blue sections indicate replicated DNA while orange sections represent unreplicated DNA. Circles denote fired origins, while diamonds indicate coalescences of replication forks. Periodic boundary conditions were used (circular genome). The dashed line at time sec indicates the end of the first labeling period (red) and the beginning of the second (green) one. Arrows indicates the fork propagation directions at the labeling transition time. The labeling timeline on the right side and the solid line on the space-time profile illustrate the labeling process to produce the molecule example presented in (b). (b) Example of a molecule extracted from the simulation presented in (a). Red sections were replicated during the red pulse (before
sec), while green sections were replicated later. To obtain a two-color molecule, the label transition time must occur after the first initiation and before the last coalescence.
Figure 6.
Simulation of SMARD experiment with comparison to rate-equation estimates.
(a) Labeled molecules collected from simulations of the SMARD procedure, using the model system of Fig. 2 . Each line corresponds to a molecule as the example presented in Fig. 5 b. Molecules were organized according to their red-label content. Only molecules that were fully substituted with fluorescent nucleotides were considered for the analysis. (b) Red-green content of the molecules from (a) as a function of the position
along the genome (circles). A value of one (zero) means that all the molecules are red (green) labeled at a given position. The solid line was calculated using our rate equations for
(see Eq. 23). Red-green content was determined by averaging over 5 kb bins; for clarity, only one value in ten is shown. (c) Left- and right-moving fork densities
observed in the molecules presented in (a) as a function of the position
along the genome (triangles). The fork density is defined as the number of forks per unit length at a given position (using 50 kb bins, 10 times larger than the simulation bin size). The solid line is derived from the rate equations for
(see Eq. 24). Gray arrows in background show the locations of initiation zones (i.e., from left to right, the intersections of increasing right-moving fork densities with decreasing left-moving fork densities). (d) Autocorrelation function of average red-green content, computed from the pool of molecules presented in (a). Since we used periodic boundary conditions, the maximum displacement is
.
Figure 7.
SMARD analysis of DNA replication in mouse bone marrow pro-B cells.
The left side presents the data collected from four fragments covering a Mb region in normal cells. The right side shows data obtained from clone cells where the genome sequence was rearranged (65 kb was deleted from the genome). ÊThe deletion is located between the two dashed lines on the left side graphs. Only the equivalent of fragments 3 and 4 from normal cells was studied in the clonal population. Symbols represent experimental data while solid lines refer to the solution of our rate-equation system. (a) Red-green content
obtained from Eqs. 18 (symbols) and 23 (solid lines). (b, c) Left- and right-moving fork densities
given by Eqs. 19 (symbols) and 24 (solid lines). (d) Best fit result for the initiation rate
(solid lines) and boundary fork injection rates (symbols) used to solve our rate-equations. The best-fit fork velocities we obtained were
kb/sec and
kb/sec for normal and clonal cell populations, respectively. Errors bars in (a, b, c) were obtained from simulations of the best-fit replication scenario.