Amphibian Segmentation Clock Models Suggest How Large Genome and Cell Sizes Slow Developmental Rate

Abstract

Evolutionary increases in genome size, cell volume, and nuclear volume have been observed across the tree of life, with positive correlations documented between all three traits. Developmental tempo slows as genomes, nuclei, and cells increase in size, yet the driving mechanisms are poorly understood. To bridge this gap, we use a mathematical model of the somitogenesis clock to link slowed developmental tempo with changes in intra-cellular gene expression kinetics induced by increasing genome size and nuclear volume. We adapt a well-known somitogenesis clock model to two model amphibian species that vary 10-fold in genome size: Xenopus laevis (3.1 Gb) and Ambystoma mexicanum (32 Gb). Based on simulations and backed by analytical derivations, we identify parameter changes originating from increased genome and nuclear size that slow gene expression kinetics. We simulate biological scenarios for which these parameter changes mathematically recapitulate slowed gene expression in A. mexicanum relative to X. laevis, and we consider scenarios for which additional alterations in gene product stability and chromatin packing are necessary. Results suggest that slowed degradation rates as well as changes induced by increasing nuclear volume and intron length, which remain relatively unexplored, are significant drivers of slowed developmental tempo.

Fig. 1

Resulting periods of gene expression given for each species- and diffusion-specific model. Each combination of protein half-life and total delay time corresponds to a period shown in the colorbar to the right of each model plot. Dark purple areas are non-oscillatory; stars show where the known species-specific rates of somite segmentation are found on the colorbar, and the corresponding regions are outlined in dashed lines. Results for: (A) X. laevis model when normal diffusion is assumed/Brownian Motion is modeled; (B) X. laevis model when obstructed diffusion is assumed/fractional Brownian Motion is modeled; (C) A. mexicanum model when normal diffusion is assumed/Brownian Motion is modeled; and (D) A. mexicanum model when obstructed diffusion is assumed/fractional Brownian Motion is modeled.

Fig. 2

Resulting periods of gene expression for A. mexicanum models: (A), (C), and (E) normal diffusion/Brownian Motion; (B), (D), and (F) obstructed diffusion/fractional Brownian Motion. mRNA half-life is held constant at: (A) and (B) diffusion-specific estimates for mRNA export delay; (C) and (D) half of estimated mRNA export delays; (E) and (F) a quarter of estimated mRNA export delays. ^∗Note: Color of star/outline is chosen for contrast and has no additional meaning.

Fig. 3

Nuclear export estimates under normal and obstructed diffusion across a range of radii that captures estimates for X. laevis and A. mexicanum PSM nuclei (shown by the red dashed lines). An initial position at the nuclear center is assumed. Trajectories are scaled such that a radius of 3 µm corresponds to a mean export time of ∼3.36 min (shown by the red arrow) to match the reported export time of her1 (hes7) in zebrafish (Hoyle and Ish-Horowicz 2013). Analytical results for the normal diffusion case are also shown. ^∗Note: There is a limit to how closely 3 µm can be scaled with ∼3.36 min. As a result, obstructed diffusion mean export times start off slightly faster than normal diffusion when radius r < 3.5 µm, but this is not necessarily biologically meaningful, and mean export times are quick to converge back to expectations.