Question

The Fick equation is used to describe the embryonic gas exchange. Provide the equation and describe each of its components. Describe how oxygen consumption rate (V̇o₂) and oxygen conductance (GO₂) increase throughout amphibian development. How do these changes influence PO₂ inside the egg?

Answer 1

Fink equation: Embryonic Gas exchange

Fick's law determines the movement of these particles. In this equation, p is the diffusion coefficient; A is cross-sectional area of membrane; C1 and C2 are the concentration of the solute on either side of the membrane; and d is the thickness of the membrane. Other particles diffuse across membranes through specific carriers, by a process called facilitated diffusion. C. In active transport, carrier proteins use cellular energy to move molecules against an electrochemical gradient.

Small, neutrally charged particles, such as oxygen and carbon dioxide, pass directly through the lipid bilayer. Fick's first law of diffusion can be used to calculate the net amount of molecules transferred, or net flux. Charged or large particles cannot pass through the lipid bilayer easily; therefore diffusion either does not occur or progresses at a slow rate. Proteins embedded in the lipid bilayer can increase the rate of diffusion by creating an aqueous channel for these particles to travel, or by shuttling molecules across the bilayer. Hormones often regulate whether channels are “open” or “closed.” In carrier-mediated diffusion, both the numbers of carriers and the concentration difference of the solute may limit rate of diffusion across the membrane.

Ambhibian development:

The jelly capsule of amphibian eggs is an impediment to O2 diffusion to the embryo. This effect can be evaluated with a diffusion equation that relates the rate of O2 uptake (Vo2), Krogh's coefficient of diffusion in jelly (Ko2), the geometry of the capsule which is characterized by its inner and outer radii (r. and ro), and the O2 partial pressure difference across the capsule (ΔPo2). Data for Ko2 are presented to enable calculation of the O2 conductance (Go2) of the capsule from its dimensions. As Vo2 increases during embryonic development, Go2 also increases by swelling of the capsule due to osmotic absorption of water into the perivitelline space; thus, changes in ΔPo2 are minimized. The changes in Go2 appear inexorably linked to the embryonic stage, and cannot be modified during development to adapt to high O2 demand or low ambient Po2. ΔPo2 is very sensitive to changes in ri, but less sensitive to ro. Consequently, failure to absorb enough water into the perivitelline space can result in severe hypoxia, but the existence of a thick jelly coat or boundary layer need not. A preliminary interspecific comparison indicates that Go2 is matched to Vo2 such that the average ΔPo2 near hatching is about 6 kPa. Nevertheless Vo2 may become limited by diffusion through the capsule in late development, and added hypoxia can stimulate hatching. Low availability of O2 to embryos within egg masses is caused mainly by O2 consumption by other eggs in the mass rather than by the existence of jelly. In fact, the jelly aids gas exchange in egg masses by reducing the population density of embryos. Natural selection has resulted in diverse modes of oviposition that avoid the limitations that the egg mass places on O2 delivery to the embryos.