Dissertation Proposal - The University of Arizona Campus Repository

weighted average of the cell volume), and ∆ρC (the average difference in density between
cells and water), yielding,
4
3 3 4
∆M ≈ π ⎡(1 − s) r + sr ⎤ S ∆ρCN ≈ ū∆ CN
3 ⎣ ⎦ π ρ . Eq.4b
3
Colony radius R depends on the number of flagellated cells Nq, composed of GS
and/or S cells, and on the area between cells. I model flagellated cells as circles arrayed
on the sphere surface, A being a cell concentration term that corrects for the intercellular
surface area. Then,
Nq ≈
2
4π
R
⎡⎛ s ⎞
⎢⎜1− r
q
⎟
⎣⎝ ⎠
s
+ rS
q
⎤
⎥+
⎦
2 2
π π
A
. Eq.5a
For GS colonies s/q = 0 since s = 0 (e.g. Eudorina), for GS/S colonies s/q = s since q = 1
(e.g. Pleodorina), and for G/S colonies s/q = 1 since s = q (e.g. V. carteri). R is then,
1/2
2 2
S
1/2 1/2 (
1/2
) 1/2 1/2
1⎡⎛ s ⎞ s ⎤
1
R≈ ⎢⎜1− ⎟r
+ r + A⎥ q N ≈ ā + A q N
2⎣⎝ q⎠ q ⎦
2
, Eq.5b
where ā is the weighted average of the flagellated cell area. If I insert Eq. 4b and Eq. 5b
in Eq. 3,
V
up
⎛ 4 ⎞
⎜ qf −gπū∆ρ 3 ⎟
≈ ⎜
⎜3 πη ( ā + A) q ⎟
⎝ ⎠
C
1/2
N
1/2 1/2 ⎟ . Eq.6
Finally, I assume that the size rmax that a colony’s reproductive cell with palintomic
development has to reach to produce a colony of the same type is a function of the
number, initial size, and type of cells in that colony:
22