Oxygen profiles in egg masses predicted from a diffusion–reaction model

Abstract

We developed a novel diffusion-reaction model to describe spatial and temporal changes in oxygen concentrations in gelatinous egg masses containing live, respiring embryos. We used the model in two ways. First, we constructed artificial egg masses of known metabolic density using embryos of the Antarctic sea urchin Sterechnius neumayeri, measured radial oxygen profiles at two temperatures, and compared our measurements to simulated radial oxygen profiles generated by the model. We parameterized the model by measuring the radius of the artificial masses, metabolic densities (=embryo metabolic rate x embryo density) and oxygen diffusion coefficients at both ambient (-1.5 degrees C) or slightly warmer (+1.5-2 degrees C) temperatures. Simulated and measured radial oxygen profiles were similar, indicating that the model captured the major biological features determining oxygen distributions. Second, we used the model to analyze sources of error in step-change experiments for determining oxygen diffusion coefficients (D), and to determine the suitability of simpler, analytical equations for estimating D. Our analysis indicated that embryo metabolism can lead to large (several-fold) overestimates of D if the analytical equation is fitted to step-down-traces of central oxygen concentration (i.e. external oxygen concentration stepped from some high value to zero). However, good estimates of D were obtained from step-up-traces. We used these findings to estimate D in egg masses of three species of nudibranch molluscs: two Antarctic species (Tritonia challengeriana and Tritoniella belli; -1.5 and +2 degrees C) and one temperate Pacific species (Tritonia diomedea; 12 and 22 degrees C). D for all three species was approximately 8 x 10(-6) cm(2) s(-1), and there was no detectable effect of temperature on estimated D. For the Antarctic species, D in egg masses was 70-90% of its value in seawater of similar temperature.