Dissertation Proposal - The University of Arizona Campus Repository

More documents

Recommendations

Info

conditions), daughter colonies “choose” to continue growing inside the mother colony and hatch as larger colonies the next day, but, if colonies are placed in unfavorable conditions, daughter colonies hatch in search of a better place for growth. C - Using the Measurements in the Model to Determine the Physical Limits of the Spherical Design I now insert back into the model the experimentally measured and calculated parameters. The major result yielded by the analysis of the data is that the average swimming force per motile cell decreases with colony size, or f ∝ N -0.21 ā 0.51 (Section B). Although the average contribution of each flagellated cell to the total swimming force decreases as colony size increases, this force increases as flagellated cell size increases (ā). If I insert this relation in Eq. 6, and assume that A = 0: 1/2 ⎛ 0.29 ū∆ρC N ⎞ ⎜ ( ) π 1/2 1/2 1 4 Vup ≈ x Nq −g 6πη ⎝ 3 ā q ⎠ ⎟, Eq. 8a where x is the normalization constant of the inserted relationship. Based on the same assumptions and parameters used when previously analyzing the model, Figure 6A shows that the size constraint on motility is higher than what I concluded when analyzing the model. Furthermore, if I take the intercellular surface area, A, into account, colonies with increased intercellular space area have a higher constraint on motility due to the increase in drag (e.g., V. gigas). Colonies with larger flagellated cells have a higher flagellar force (f), but not enough to compensate the increase in mass (∆M; Section B). Only the decrease in ∆ρC due to the lower density of large germ cells may ease this constraint (Appendix B). 42
I now compute a physical limit on colony size assuming colonies need to be buoyant. If I insert the scaling relations for Nqf, ∆M, and R from the SLR analysis (Table 4) in Eq. 3, I get the swimming speed Vup solely as a function of N: 1 0.32 0.61 Vup= ( fCr N −g∆MCr N ) Eq. 8b 6πηR Cr where fCr, ∆MCr, and RCr are the C. reinhardtii measured and calculated values used as normalization constants. The flagellar force f in C. reinhardtii is two to three orders of magnitude higher than the negative gravitational force (f ~ 10 -7 dyn, g∆M ~ 10 -9 dyn), but as N increases, g∆M increases proportionally more than Nqf, making the colonies sink at a threshold size (Figure 6B). If colonies at least need to be buoyant, from Figure 6B I can infer that there is a size limit for the Volvocalean colony design (N ~ 2 17 ). Figure 6. Applying the measurement results to the model: A- The major result yielded by the analysis is inserted in Eq. 6 (f ∝ N -0.21 ā 0.51 ; Eq. 8A) to get Vup (cm/sec) as a function of number of cell divisions (Log 2 N) for different s. The same values in Figure 3 are used for ∆ρC, rin, rSin, and rS ; x = 10 -3.03 . B- The physical limit on colony size assuming colonies need to be buoyant. Scaling relations for Nqf, ∆M, and R from the SLR analysis (Table 4) are inserted in Eq. 3 to get the swimming speed Vup (cm/sec) solely as a function of N (Log 2 N; Eq. 8B). fCr = 2.410 -7 dyn, ∆MCr = 1.01 10 -11 grams, and RCr = 0.00035 cm. 43
Page 1 and 2: A HYDRODYNAMICS APPROACH TO THE EVO
Page 3 and 4: STATEMENT BY AUTHOR This dissertati
Page 5 and 6: TABLE OF CONTENTS - Continued IV -
Page 7 and 8: LIST OF TABLES Table 1, Development
Page 9 and 10: eproductive cell ratio must increas
Page 11 and 12: and fecundity (e.g. higher number o
Page 13 and 14: To summarize, as volvocalean coloni
Page 15 and 16: differentiation, e.g., Gonium and E
Page 17 and 18: for up to 5 cell divisions (e.g., t
Page 19 and 20: III - CELLULAR DIFFERENTIATION AND
Page 21 and 22: In GS and GS/S colonies, q = 1 sinc
Page 23 and 24: N ≈ 4 π r 3 3 max 4 3 3 π[(1
Page 25 and 26: in higher proportions of somatic ce
Page 27 and 28: To investigate the assumptions used
Page 29 and 30: EXPERIMENTAL METHODS Species and Mu
Page 31 and 32: Colonies were sampled from the sync
Page 33 and 34: Data Analysis To perform a size-dep
Page 35 and 36: Figure 4. The change in size and sw
Page 37 and 38: Figure 5. Allometric analysis: R,
Page 39 and 40: Log R, Vsed, and Vup versus Log N u
Page 41: colonies develop, larger cells have
Page 45 and 46: Table 5. Models selected from the M
Page 47 and 48: IV - CELLULAR DIFFERENTIATION AND F
Page 49 and 50: y the flagellar beating of somatic
Page 51 and 52: light period and germ cells continu
Page 53 and 54: medium treatments (total of four).
Page 55 and 56: the still and bubbling medium exper
Page 57 and 58: entrained fluorescent flow-marking
Page 59 and 60: arrangement of flagellar motors on
Page 61 and 62: confirming the hypothesis that coll
Page 63 and 64: concurrently benefits nutrient upta
Page 65 and 66: and in colony radius) decrease the
Page 67 and 68: APPENDIX A: VELOCITIES AND SIZES. T
Page 69 and 70: Vc 600 5 22 193 15.6 12 114 20.0 12
Page 71 and 72: APPENDIX B: COMPLEMENTARY ANALYSIS
Page 73 and 74: Induced Hatching Experiments In a s
Page 75 and 76: Size and Flagellar Length I measure
Page 77 and 78: APPENDIX C: ANALYSIS OF R AND ∆M
Page 79 and 80: REFERENCES Angeler, D. G., M. Schag
Page 81: (Volvocales). Biologia 58:425-431.

Dissertation Proposal - The University of Arizona Campus Repository

Create successful ePaper yourself

Delete template?

Save as template?