Cell lineage transport: a mechanism for molecular gradient formation

Marta Ibañes^1,a, Yasuhiko Kawakami¹, Diego Rasskin-Gutman^1,a & Juan Carlos Izpisúa Belmonte^1,2

^aPresent address: Department Estructura i Constituents de la Matèria, University of Barcelona, Diagonal 647, Barcelona 08028, Spain

^aPresent address: Institute Cavanilles for Biodiversity and Evolutionary Biology, University of Valencia, Apartado Postal 22085, 46071 Valencia, Spain

Article highlights

Synopsis

Gradients of secreted proteins have been repeatedly observed during embryonic development in a variety of multicellular organisms. By eliciting different responses according to concentration thresholds, gradients of secreted molecules (morphogens) have been proposed as a morphogenetic mechanism that can pattern the early embryo (Wolpert, 1969; Driever and Nusslein-Volhard, 1988a; Gurdon and Bourillot, 2001; Lawrence, 2001). Commonly, morphogen gradient formation dynamics involves molecular transport mechanisms such as passive diffusion or active transport through vesicles, among others. Moreover, several data point towards the importance of cell-driven molecular transport mechanisms for gradient formation during morphogenesis (Zhu and Scott, 2004). Specifically, it has been shown that an mRNA gradient can be formed through the mRNA decay in tissues with polarized growth (Dubrulle and Pourquié, 2004). However, a full characterization, involving mathematical analyses and further experimental evidence of the dynamics of gradient formation based on cellular transport processes, is missing. Specifically, the implications of cell division and cell growth dynamics in the formation and shaping of gradients of non-secreted proteins and mRNAs have not been studied yet.

In order to address these issues, we have used an in silico approach that characterizes a basic scenario for the formation of gradients of mRNAs and non-secreted proteins in growing tissues. In addition, we have exemplified such gradient formation through novel data on a graded expression of the homeobox transcription factor Hoxd13 in the developing vertebrate limb.

We have proposed a mathematical model in which cells divide and grow, diluting and transporting their molecular content, a mechanism we termed 'cell lineage transport.' In the model, only some of the dividing cells, located at one end of the growing tissue, transcribe the mRNA, whereas protein translation occurs in all cells containing mRNA. In addition, cells divide and grow forming an elongated distribution of cell descendants along the same spatial axis.

Our computational and analytical results indicate that mRNA gradients driven by cell lineage transport can be formed, which in turn always create gradients of non-secreted proteins (Figure 2A–C). In addition, we find that gradients of non-secreted proteins can be formed in the absence of graded distributions of mRNA (Figure 2A). Our results show that longer cell cycles elicit steeper gradients (Figure 2C), whereas longer molecular half-lives make gradients shallower (Figure 2A and B).

Figure 2

mRNA and protein gradients driven by cell lineage transport. Numerical gradients are represented by symbols (squares for mRNAs and circles for proteins). Lines are the continuous analytical profiles (Materials and methods). (A) mRNA and protein gradients for three different mRNA half-lives, H_p=0.7 h and Cc=1 h (gray, H_m=0.001 h). For very unstable mRNAs, a protein, but not an mRNA, gradient can be formed (red, H_m=0.3 h). For intermediate mRNA half-lives, mRNA and protein gradients are shaped by both the molecular decay and the dilution process (blue, H_m=2000 h). For very stable mRNAs, clonal dilution forms mRNA gradients. (B) mRNA and protein gradients in logarithmic scales for very unstable proteins (H_p=0.001 h). These protein gradients exhibit the same spatial decay as the mRNA, with very small protein amounts. Parameter values are H_m=2000 h and Cc=1 h. (C) mRNA and protein gradients for decreasing durations of the cell cycle: (blue) Cc=5 h, (red) Cc=1 h, (gray) Cc=0.2 h, for H_m=0.5 h and H_p=0.8 h. Gradients become steeper for slower cell cycles. In panels A–C, parameter values are N=10, m₀=2, b=1 and =1/2 and numerical gradients are averaged over 10³ simulations with stochastic cell cycles (Supplementary information). (D) (Orange) Spatial extent of the DoT (L^I=Nl) and (blue) spatial domain over which the (squares) mRNA gradient decays 10-fold (L₁₀^m). Cells are denoted by circles (encircled in orange inside the DoT and in gray outside it). Exonic and intronic probes can be used to detect the spatial region where the gradient spans and the DoT, respectively.

Full figure and legend (217K)Figures & Tables index

All these gradients can be characterized by two overlapping, but distinct in size, spatial domains (Figure 2D). The large domain is the spatial region over which the gradient is formed. The small domain is the region where cells transcribe mRNA. Importantly, these two domains can be detected experimentally, through the exonic/protein and intronic spatial expressions, respectively (Dubrulle and Pourquié, 2004). Our model indicates that the differences in size between the exonic and intronic domains of expression are controlled by the ratio between the mRNA half-life and the duration of cell cycle.

Our results support that the molecular turnover becomes essential in forming a gradient when cell proliferation occurs only in a pool of mRNA transcribing cells, as previously reported (Gaunt et al, 2003; Dubrulle and Pourquié, 2004). On the other hand, when all cells proliferate, as in cell lineage gradients, clonal dilution alone can create gradients of very stable molecules. Through our theoretical analysis, we have uncovered that these diverse tissue dynamics elicit gradients with distinct profiles and thus different properties. Cell lineage gradients are characterized by power-law decays, whereas gradients formed by molecular degradation in non-proliferating cells exhibit an exponential profile. Nonlinear growth and clonal dilution in cell lineage gradients make their spatial extension less sensitive to alterations in the duration of the cell cycle, but at the expense of more variable timing in gradient formation.

To find an example of an mRNA gradient formed by clonal dilution, we focused on the early stages of development of the chick limb, as it is characterized by the outgrowth and elongation of the initial limb bud through evenly proliferating cells (Hornbruch and Wolpert, 1970; Sun et al, 2002). Moreover, cell tracing experiments have shown that the spatial distribution of descendants of cells located distally at early stages form an elongated shape along the proximo-distal axis and correlates with the dynamical expression of Hoxd13 (Vargesson et al, 1997). We have found that Hoxd13 exonic expression spans more proximally than its intronic expression, which is located at the most distal end (Figure 6A). Quantitative PCR and fluorescent in situ hybridization confirm the graded expression of Hoxd13 along the proximo-distal axis (Figure 6B and C). Altogether, our results indicate that Hoxd13 expression in the chick limb bud is graded, suggesting, at the same time, that cell lineage transport is the mechanism driving such gradient formation.

Figure 6

Gradient of Hoxd13 mRNA in the chick limb bud. (A) Whole-mount in situ hybridization of (Ex) exonic and (In) intronic expression domains in the forelimb at stage 26. Panels are at the same magnification. Lines compare the length of the exonic and intronic expression domains. (B) qPCR for mRNA Hoxd13 in (p) proximal, (m) medial and (d) distal regions in logarithmic scale. The relative amount has been normalized to the value at the distal region. The bottom picture depicts the three spatial regions over the limb bud. Arrows denote the wrist and elbow. (C, left) Fluorescent in situ hybridization section of Hoxd13. The signal has been analyzed along the proximo-distal axis at different antero-posterior positions (represented by lines). (C, middle) Average fluorescent signal along the proximo-distal axis at (green) posterior, (blue) medial and (orange) anterior positions. (C, right) Total average fluorescent signal along the proximo-distal axis. The inset depicts the average gradient over longer distances.

Full figure and legend (307K)Figures & Tables index

One of the interesting features of the cell lineage transport mechanism resides in its ability for generating gradients of non-secreted molecules, such as receptors, transcription factors and second messengers (mRNA, microRNA, etc.), indicating that not only secreted proteins, but also non-secreted proteins, should be the focus of studying biologically relevant graded molecular distributions. In addition, cell lineage transport could also participate in the formation of gradients of secreted proteins. As gradients driven by cell lineage transport are formed as tissue grows, linking the timing of mitotic divisions with the steepness of the gradient, cell lineage transport gradients might represent a mechanism that coordinates the dynamics of patterning and growth.

MORE ARTICLES LIKE THIS

These links to content published by NPG are automatically generated.