1. Shrinking urchins: two-phase experiment Kathy Ruggiero k.ruggiero@auckland.ac.nz Proteomics and Biomedicine Group School of Biological Sciences Shrinking sea-urchins in a high CO 2 world: a two-phase experimental design Kathy Ruggiero 2 December 2009 Richard Jarrett CSIRO, Division of Mathematics, Informatics and Statistics

2. Shrinking urchins: two-phase experiment Kathy Ruggiero k.ruggiero@auckland.ac.nz Two experiments Walk with me… Phase 1 Experiment: Simulate a high CO 2 world Phase 2 Experiment: Measure gene expression

3. Shrinking urchins: two-phase experiment Kathy Ruggiero k.ruggiero@auckland.ac.nz Global warming’s evil twin Where does all the CO 2 go? Some CO 2 remains in the atmosphere Some is taken up by terrestrial plants And, some is absorbed by seawater CO 2 absorption Ocean pH “Ocean acidification”

4. Shrinking urchins: two-phase experiment Kathy Ruggiero k.ruggiero@auckland.ac.nz Effects of ocean acidification Air+ 500+ 1000+ 2000+ 5000+ 10000 CO 2 in ppm Molecular mechanisms? Abnormal morphology ↓ ability to build shells and skeletal structures Swimming, feeding and survival affected

5. Shrinking urchins: two-phase experiment Kathy Ruggiero k.ruggiero@auckland.ac.nz Parent-pair Where babies come from Phase 1 experiment http://weboflife.nasa.gov/images/urchin.jpg

6. Shrinking urchins: two-phase experiment Kathy Ruggiero k.ruggiero@auckland.ac.nz Different CO 2 worlds Phase 1 experiment http://uncw.edu/aquaculture/images/Larval-rearing-tanks.jpg Divide into 3 cultures Mid = 540 ppm High = 970 ppm Control = 300ppm (current level) 15 ºC Until 4-arm stage http://www.ceoe.udel.edu/Antarctica/pluticon.jpg

7. Shrinking urchins: two-phase experiment Kathy Ruggiero k.ruggiero@auckland.ac.nz …and warmer oceans Split into 5 subsamples Subjected to heat stress Phase 1 experiment

8. Shrinking urchins: two-phase experiment Kathy Ruggiero k.ruggiero@auckland.ac.nz Phase 1 experiment …and warmer oceans Split into 5 subsamples Subject to heat stress 11ºC15ºC 19ºC 21ºC24ºC

9. Shrinking urchins: two-phase experiment Kathy Ruggiero k.ruggiero@auckland.ac.nz Phase 1 experiment Control MidHigh Design summary x 4 60 samples

10. Shrinking urchins: two-phase experiment Kathy Ruggiero k.ruggiero@auckland.ac.nz Phase 2 experiment Measure gene expression Mid 11ºC High 15ºC

11. Shrinking urchins: two-phase experiment Kathy Ruggiero k.ruggiero@auckland.ac.nz Phase 2 experiment Measure gene expression Mid 11ºC High 15ºC

12. Shrinking urchins: two-phase experiment Kathy Ruggiero k.ruggiero@auckland.ac.nz Phase 2 experiment Measure gene expression Mid 11ºC High 15ºC

13. Shrinking urchins: two-phase experiment Kathy Ruggiero k.ruggiero@auckland.ac.nz Phase 2 experiment Measure gene expression Mid 11ºC High 15ºC

14. Shrinking urchins: two-phase experiment Kathy Ruggiero k.ruggiero@auckland.ac.nz The dilemma Control MidHigh How to pair 60 samples on 30 arrays? x 4 60 samples

15. Shrinking urchins: two-phase experiment Kathy Ruggiero k.ruggiero@auckland.ac.nz ANOVA table Sourced.f. Between Parent-pairs (PP)3 Between Cultures in PP8 Between Subsamples in Cultures in PP48 CO 2 2 Residual6 HST.CO 2 8 Residual36 HST4 Total (adj.)59 Phase 1 design Var Compts in EMS

16. Shrinking urchins: two-phase experiment Kathy Ruggiero k.ruggiero@auckland.ac.nz The challenge

17. Shrinking urchins: two-phase experiment Kathy Ruggiero k.ruggiero@auckland.ac.nz Design considerations at Phase 2 CO 2 x HST at Phase 1 –E–Estimated between subsamples within cultures within parent pairs –W–Want subsamples  arrays OOnly 2 samples per array SSo, in our dreams! “We are most interested in how the response to heat stress differs between CO 2 levels.”

18. Shrinking urchins: two-phase experiment Kathy Ruggiero k.ruggiero@auckland.ac.nz Design considerations at Phase 2 CO 2 x HST at Phase 1 –Estimated between subsamples within cultures within parent pairs –Want subsamples  arrays (as much as possible) –What if difference is between CO 2 levels?  CO 2 main effect confounded with arrays  Estimated with low precision  Only 6 d.f. (at most from Phase 1) to estimate Between Cultures Expected Mean Square “We are most interested in how the response to heat stress differs between CO 2 levels.”

19. Shrinking urchins: two-phase experiment Kathy Ruggiero k.ruggiero@auckland.ac.nz Heat stressed samples  Arrays Group arrays into 6 “sets” of 5 11 15 1921 24 11 19 2415 21 Loop 1Loop 2 1115192124 1519212411 15192124 1921241115 Set 1Set 2

20. Shrinking urchins: two-phase experiment Kathy Ruggiero k.ruggiero@auckland.ac.nz Heat stress samples  Arrays Group arrays into 6 “sets” of 5 11 15 1921 24 11 19 2415 21 Loop 1Loop 2 Balanced incomplete block design w.r.t. heat stress 1115192124 1519212411 15192124 1921241115

21. Shrinking urchins: two-phase experiment Kathy Ruggiero k.ruggiero@auckland.ac.nz 6 sets of 5 arrays Set of Arrays 1 2 3 4 5 6 Array 12345 Loop 1 Loop 2 Loop 1 Loop 2 Loop 1 Loop 2

22. Shrinking urchins: two-phase experiment Kathy Ruggiero k.ruggiero@auckland.ac.nz BIB design w.r.t. Parent-pair (PP) Set of Arrays 1 2 3 4 5 6 1115192124 1519212411 15192124 1921241115 1115192124 1519212411 15192124 1921241115 1115192124 1519212411 15192124 1921241115 Array 12345 PPCO 2 1 2 3 4 C C C C 2 4 1 3 M M M M 4 1 2 3 H H H H

23. Shrinking urchins: two-phase experiment Kathy Ruggiero k.ruggiero@auckland.ac.nz Parent-pairs (1 vs 2, 3 vs 4)20.667 Parent-pairs (1+2 vs 3+4)10.556 Between Arrays within Sets24 HST40.375 Within Arrays29 ANOVA table Between Sets5 Total (adj.)59 CO 2 2 Parent-pairs30.333 Sourced.f.EfficiencyVar Compts in EMS Error15 HST.CO 2 80.375 Error12 HST40.625 HST.CO 2 80.625 Dye10.111

24. Shrinking urchins: two-phase experiment Kathy Ruggiero k.ruggiero@auckland.ac.nz Design considerations at Phase 2 An alternative –Consider CO 2 at Phase 1 –Estimated between cultures within parent pairs –Want cultures  arrays (as much as possible) –Confound parent pair (PP) with arrays  Odd number of samples (15) per PP  Must co-hybridize some samples from different PP “We are most interested in how the response to heat stress differs between CO 2 levels.”

25. Shrinking urchins: two-phase experiment Kathy Ruggiero k.ruggiero@auckland.ac.nz Two designs Set of Arrays 1 2 3 4 5 6 1115192124 1519212411 15192124 1921241115 1115192124 1519212411 15192124 1921241115 1115192124 1519212411 15192124 1921241115 Array 12345 PPCO 2 Design 2 1C 1M 2M 2H 3H 3C 4C 4M 1M 3H 2H 4C PPCO 2 Design 1 1C 2C 3C 4C 2M 4M 1M 3M 4H 1H 2H 3H

26. Shrinking urchins: two-phase experiment Kathy Ruggiero k.ruggiero@auckland.ac.nz How do they compare? Efficiencies CO 2 1, but in top “stratum”? HST0.6250.428 - 0.594 CO 2.HST0.6250.307 - 0.428 EffectDesign 1Design 2 Not canonical efficiencies, but based on efficiencies of particular chosen contrasts.

27. Shrinking urchins: two-phase experiment Kathy Ruggiero k.ruggiero@auckland.ac.nz In closing… Consider Phase 1 design when designing Phase 2 experiment Construct EMS for each design How do things change if Arrays are considered a random effect? How do things change if we fit Cultures ignoring Arrays followed by Arrays eliminating cultures? How do we do this in LIMMA?

28. Shrinking urchins: two-phase experiment Kathy Ruggiero k.ruggiero@auckland.ac.nz Acknowledgements Dr Mary Sewell (University of Auckland) Prof Gretchen Hofmann (UC, Santa Barbara) Dr Anne Todgham (San Francisco State University)