Measurement and 3D-Visualization of Cell-Cycle Length Using Double Labelling with Two Thymidine Analogues Applied in Early Heart Development

Organ development is a complex spatial process in which local differences in cell proliferation rate play a key role. Understanding this role requires the measurement of the length of the cell cycle at every position of the three-dimensional (3D) structure. This measurement can be accomplished by exposing the developing embryo to two different thymidine analogues for two different durations immediately followed by tissue fixation. This paper presents a method and a dedicated computer program to measure the resulting labelling indices and subsequently calculate and visualize local cell cycle lengths within the 3D morphological context of a developing organ. By applying this method to the developing heart, we show a large difference in cell cycle lengths between the early heart tube and the adjacent mesenchyme of the pericardial wall. Later in development, a local increase in cell size was found to be associated with a decrease in cell cycle length in the region where the chamber myocardium starts to develop. The combined application of halogenated-thymidine double exposure and image processing enables the automated study of local cell cycle parameters in single specimens in a full 3D context. It can be applied in a wide range of research fields ranging from embryonic development to tissue regeneration and cancer research.


Derivation of the equation for T C
According to the equation given by Sanders and co-workers [1] the labelling fraction after CldU exposure is given by: which can be solved for T S : Similarly, the exposure to IdU results in the labelling fraction of: Substitution of Eq. [2] into Eq. [3] gives: which can be solved for T C : With Eq.
[6] it is easy to see that an incorporation lag (T L ) has no effect on observed T C , because such a lag affects both exposure times in the same way: which can be solved for T S .F D : The similar exposure to IdU results in the labelling fraction of: Substitution of Eq.
[3a] results in: which can be simplified to: Equation 5a shows that the observed T C of a population, i.e. the population doubling time, is the cell cycle length of the dividing cells multiplied by the growth fraction of the population.

Derivation of the equation for Ts
The equation given by Sanders and co-workers [1] states that the labelling index after exposure to CldU is given by: which, solved for T C reads like: Similarly the exposure to IdU results in the labelling fraction of: Substitution of Eq.
[9] then gives This can be rearranged to give the following equation for T S : Equation 11 can be simplified to: as was derived in Figure 1.
When the growth fraction (F D ), which is the fraction of cells that is dividing is constant, T S is derived as follows (the equations are in the same order as above): In Eq.
[10a] it is clear that F D disappears from the equation. Therefore, the growth fraction has no influence on the calculation of the S-phase length.

The bias due to the insertion a lag time (T L ) between injection and incorporation, on determined S-phase is equal to the incorporation lag. With the definition of T S in Eq.
11 and a lag phase T L , the real T S can be defined as which after re-arranged reads as: The first part on the right is the T S that will be observed because the presence of a lag phase is unknown, the second part simplifies to T L : Equation 14 shows that the observed S-phase length is too short when an incorporation lag is present. The length of this lag has to be added to obtain the real S-phase length.
The actual underestimation of the observed S-phase length would thus be equal to such an incorporation lag. The effect of this lag phase explains the discrepancy between our S-phase equation (11a) and those previously published [3,4]: by assuming a lag phase that is as long as the exposure time to the second label, these authors ignore the second exposure time and the S-phase length is thus overestimated by the length of this exposure time.

Division of labelled cells
When the exposure time to the first label (IdU) is longer than T G2 + T M , cells that were labelled during T S reach the end of T M and will divide. In that case, the fraction of labelled cells at the moment of fixation that was defined as F I , is also equal to the fraction of cells in S, G2 and M plus a fraction of cells that results from the cell division: and Eq. 3 for F I , F division (Eq. 16) can be re-written as Equation [19] shows that for exposure times (T I ) longer than the sum of T G2 and T M , an extra group of dividing cells is counted and added to F I . This will increase the