Fig 1.
Schematic of the model used in this simulation.
(A) Each individual, which is a unit of selection, contains cells aligned in a one-dimensional space. These contained the same gene network. The state of each cell, given by the gene expression pattern, changes according to identical gene networks. There were 100 individuals in the evolving population in each generation. (B) Starting from the initial states, the gene expression patterns change according to the gene regulation network. After sufficient time, the expression of each cell reaches the terminal state, on or off. Cell type was determined according to the on/off patterns of the target genes. For the four target genes, there were 24 possible states, as shown in the figure. The fitness of an individual is determined by the number of different cell types in the terminal state. (In the figure, for instance, it is 6). (C) The selection procedure of species diverged from a common ancestor. The left chain represents the result of the first step of evolutionary simulation to select one species. Each circle represents the ancestor at each generation (although significantly abbreviated). As the second step, an ancestor at a certain generation was cloned, and additional evolutionary simulations were carried from the ancestor up to the same generations of the original (1000).
Fig 2.
Examples of the evolutionary simulation that showed hourglass-like developmental correlation.
(A) Two examples of gene expression dynamics of evolved GRNs (A1, A2). The color represents the cellular state, i.e., the expression (On/Off) pattern of four output genes. The vertical axis is the spatial index of cells and the horizontal axis is developmental time. Spatial pattern transitions were more frequent in the early developmental time, and a horizontal log plot was used to adequately depict them. This is consistent with experimental observations. Thereafter, the developmental time was plotted in logs. Following evolving 800 generations, the two GRNs evolved from a common ancestor of the 800th generation and then simulated further over 200 more generations, while suffering from different genetic changes, such that the two have diverged from the common ancestor. (B) The heat map of the similarity indicator, comparing the developmental dynamics of the two individuals given in A. The horizontal axis is the developmental time of the individual A1, and the vertical axis is that of A2. Both axes are on a logarithmic scale. Each point indicates the similarity of gene expression states between the two examples at specific time points. (As the timescale of development can be different between the two in general, the comparison at different time points is included.) The green line indicates the locations where the similarity indicator takes maximum for each developmental time step of individual A1 (horizontal axis). Note that the high similarity region is approximately 100–200 in either individual developmental time, which is neither the beginning nor the end of the developmental dynamics. (C) Projection of the similarity indicator on the green line in B against the developmental time of the first species (i.e., the horizontal axis in B).
Fig 3.
The similarity between two species that departed from a common ancestor at given earlier generations in the phylogenetic tree.
The similarity is computed as in Fig 1B and 1C, the average over pairs of individuals. The horizontal axis represents the developmental time of the original species, and the vertical axis represents the similarity between the spatial patterns of gene expression. The line color denotes how far the two species are, in comparison, branched in the left phylogenetic tree, diverged from the 800th generation A(blue), 500th generation B(green), and 200th generation C(red). The horizontal axis was plotted on a logarithmic scale. At the intermediate developmental time, the similarity indicator takes a maximum when the pair branched at the later stage (in this example the peak exists up to ~500, whereas including other examples, the peaks exist for the pairs branched at the recent 100–300 generations). Typically, the closer the phylogenetic pair of individuals, the more prominent the peak in the similarity indicator.
Fig 4.
The time course of the fraction of the expressed pleiotropic genes.
The pleiotropic genes are defined as those that are expressed for more than half of the developmental stages, whereas the stage was defined as splitting developmental time before reaching the stationary state into equal 12 spans, either by linear scale (the plot of purple (+) points) or by the logarithmic scale (the green (×) points). The fraction is obtained by averaging over 1000 individuals of different initial conditions, whereas the variance from the average was quite small. The area colored by blue indicates the typical range of developmental bottleneck (average ± standard deviation), which is given by comparison over other individuals diverted 200 generations earlier.
Fig 5.
The variance of gene expression patterns over 1000 clones, i.e., those generated from the same genotype but with different initial conditions.
The horizontal axis represents developmental time, and the vertical axis represents the total variance in gene expression over all cells, i.e., the summation of variance over cells, over genes, and over clones (see also Methods). As specific examples, the data of three different individuals are indicated by different colors. The blue stripe indicates the typical range of observed developmental bottlenecks (average ± standard deviation), as obtained by comparing individuals belonging to blue triangle A in the phylogenetic tree in Fig 3, which exhibits clear hourglass-like developmental correlations. Here, the initial conditions are chosen by adding Gaussian distribution noise with a variance σ = 0.1. (The details of the computation scheme are presented in the Methods section).
Fig 6.
Control of the developmental schedule by slow genes.
(A) Examples of spatial gene expression dynamics. The gray vertical line in each figure is the timescale of the genes whose expression changes are slowest (see C and Methods). The left upper corner is the expression dynamics of the slowest gene. (B) Time series of expression levels of all genes at cell index 32 in A. Different colors correspond to the expression levels of different genes. (C) Time scale of expression changes of each gene, which is plotted in order as a function of its rank in magnitude. Each circle denotes the average value of the timescale of genes over cells. Error bars are the standard deviation. (For the computation of the timescale of genes, see the Methods section). (D) Correlation between the timescale of the slowest gene and the timing of the bottleneck of the detected developmental hourglass. Magenta circles represent data from the individuals acquired through evolutionary simulation, whereas green squares and orange triangles represent data obtained by adopting a parametric change to the slowest gene in the original (blue dots). Green squares represent the cases in which the timescale of the slowest genes was changed to five times faster, and the orange triangles represent those changed with ⅕ times slower (See also [37] and S6 Fig for the heterochronic shift induced by manipulation of the slow gene).
Fig 7.
An example of evolved gene network and expression control by the slow gene.
Left: The essential structure of the gene network of the individual of Fig 2A-1. Nodes filled with color are marker genes to determine fitness. Each color corresponds to the code in Fig 2A, i.e., red, green, blue, and brightness (which is represented as gray). The node with the light blue circumference is the slow gene. The path from the slow gene to the gray marker gene is shown as thick arrows. Note that paths from the slow gene to other marker genes exist. The procedure to extract essential gene network structure is explained in the Methods section. Right: Example of gene expression control of the slow gene. Expression dynamics of the genes in the thick arrowed path on the left, namely 9 (top), 12 (middle), and 5 (bottom), are shown for the cellular index 35. In each of these subfigures, the horizontal dashed line indicates the gene expression threshold of the arrowhead gene, and the vertical dashed arrows indicate the developmental time when the gene expression dynamics and the arrowhead gene expression threshold crossed, which basically corresponds to the expression change in the arrowhead gene.
Table 1.
List of the parameters adopted in the simulation.