1. The Sustaining and Depriving Effects of Diffusion on Migratory Salmon Prepared by: Nick Breninger

2. Life Cycle: The Beginning  Three main phases of development follow the fertilization of the egg:  First phase is cell formation and division  Second phase is embryo development  Third phase is organ formation  Individual organs and body parts become distinct, the heart begins to beat, and blood vessels form over the yolk.

3.  From 60-120 days after fertilization, the embryo has developed a backbone, fins, and gills, and is ready to hatch from the egg.  The most crucial factor in assuring that this development progresses properly is the availability of oxygen to the embryo within the egg.  Placement of the eggs by the parents on the river bottom is extremely location dependent, as well as construction dependent for an adequate source of oxygen.

4. Salmon Redd  To lay her eggs (roe), the female salmon builds a spawning nest called a “redd”. She builds the redd by using her tail (caudal fin) to create a low- pressure zone, lifting gravel to be swept downstream, and excavating a shallow depression.

5. Salmon Redd  Once the male salmon deposits his milt (sperm) on the eggs, the female disrupts the upstream edge of the shallow depression lightly covering the eggs in small pebbles.

6. Aqua Engineers  The design and placement of the “redd” ensures the eggs receive the oxygen from the aerated current while not being exposed and swept downstream.  While it is up to the female to place the eggs in a location enabling their exposure to oxygen, it is up to the diffusion of oxygen into the eggs for proper embryotic development  In this case, the diffusion is driven by the higher concentration of oxygen in the water as compared to the lower concentration in the egg.

7. Diffusion of oxygen into a salmon egg  The scenario examined can be modeled: The amount of oxygen entering the spherical shell of radius r equals the amount of oxygen leaving a smaller differential spherical shell of radius thus becoming available to the egg. With the salmon eggs not exposed to the current, it is assumed to be a steady state scenario, and a shell mass balance may formulate the diffusion:,

8.  The shell mass balance can be simplified by dividing by the surface area, A, and the change in the radius,, defining the differential element, and taking the limit as approaches zero, which yields: A=  The molar flux of oxygen can be found using the expression: (1) It can be assumed the rate at which the egg is using oxygen is equivalent to the rate at which oxygen is being diffused into the surface of the egg. The following relation is used: (2)

9.  Substituting equation 2 into equation 1 and solving for the molar flux yields: Multiplying both sides of the molar flux equation by satisfying equation 2, and isolating the terms on each side separates the unknown relationship between the mole fraction of oxygen relative to the radius ( ) and prepares the application of the integral: (2) Employing boundary conditions, the egg may be simplified by being surrounded only by free oxygen. This means at a distance r from the center of the egg (surface of the egg), the mole fraction of oxygen is assumed to be zero where it is immediately used by the egg. It shall also be assumed at a distance infinity from the center of the egg the mole fraction of oxygen is one, having not yet had a chance to diffuse:

10.  Evaluating the integral:  Simplifying: Using the fact that an average salmon eggs measures 6-9mm in diameter, along with the fact that salmon thrive in an environment with an oxygen concentration between 5 and 15 ppm, assumptions can be made to find the amount of oxygen entering the egg, and thus the amount of oxygen being used by the egg.

11. Life Cycle: Juvenile  Once the diffusion of oxygen into the egg becomes insufficient enough for the growing embryo, they release a hatching enzyme, digesting the egg membrane allowing them to break through the cell membrane.  Once hatched from the egg, the tiny salmon are referred to as “alevin”, deriving nourishment from their yolk sac for several weeks.  The sac shrinks as the alevin develop teeth, eyes, a digestive system and a respiration system allowing use of their gills.  Until they are able to use their gills, diffusion of oxygen into their ellipsoid yolk sacs, as well as their bodies, represents their primary source of oxygen.

12. Life Cycle: The Migration  Once their yolk sac is completely absorbed they begin feeding. They are now referred to as “fry”, remaining in freshwater from just a few days to two years depending on species, before they migrate to the ocean.  Once they begin their migration toward the ocean they experience a physiological change enabling the fish to live in salt water while not absorbing the salt into their blood. This is called “smolting”.  Salmon are hypertonic in nature, meaning they naturally have a higher solute concentration than the surrounding water.  Because the freshwater is so low in salinity, the smolt experience a constant diffusion driven loss of NaCl from their bodies.

13. Battling Diffusion  In order to maintain their homeostasis, the smolt pump NaCl from the freshwater into their blood stream as the water flows over their gills.  It is possible to model how much NaCl they need to be pumping into their blood using mass transfer equations:  Examining the cross section of the salmon body Simplified as diffusion from a basic ellipse, Using the same technique as diffusion into the salmon egg, with a different surface area, the shell mass balance is simplified as: (3)

14.  Since there is only diffusion from their bodies, the molar flux of NaCl from their bodies is simplified as: Multiplying both sides of the equation by satisfying yields: Since two radii define the ellipse, and assuming NaCl will be diffusing from the smaller radius before the larger one, the integral is with respect to the smaller radius. The flux of NaCl will be evaluated from to some distance infinity. The mole fraction of NaCl will be evaluated from some value A, representing the mole fraction inside the body of the salmon, to zero, some distance infinity outside the body:

15.  Which can be simplified as:  By making assumptions of the molar flux of NaCl from the salmon body as well as the mole fraction at the surface of the salmon body, the amount of salt leaving per unit time can be found.

16. Into the Ocean  While reaching progressively saltier water approaching the ocean, the “smolt” begin drinking the water and their kidneys begin to produce a concentrated, low volume urine, holding water and excreting NaCl ions, preserving their homestasis.  Once fully acclimated, the salmon smolt move out into the ocean where they exhibit a remarkable adaptation.  The secret lies in the operation of their gills.

17. Gill Function  Salmon have epithelial cells in their gills where they produce an enzyme that hydrolyzes adenosine triphosphate (ATP)  ATP is a molecule that stores the energy needed to do just about everything  Once the ATP is hydrolyzed, it is decomposed into adenosine diphosphate (ADP) when a bond holding the phosphate group in ATP is broken, which releases energy:

18.  Salmon will use this released energy to pump the NaCl in the water against its concentration gradient.  Energy is used to actively transport NaCl out of the salmon’s blood and into the water flowing over the gills.  Between the changing function of their kidneys and the function of their gills, salmon are able to maintain their homeostasis in both fresh and saltwater.  The stage of their life in the open ocean accounts for their weight gain where they undergo extensive migrations from one to five years.  It is believed when they are ready to return to their home stream to spawn they rely on earth’s magnetic field to guide them.