Shrinking urchins: two-phase experiment Kathy Ruggiero 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

Shrinking urchins: two-phase experiment Kathy Ruggiero Two experiments Walk with me… Phase 1 Experiment: Simulate a high CO 2 world Phase 2 Experiment: Measure gene expression

Shrinking urchins: two-phase experiment Kathy Ruggiero 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”

Shrinking urchins: two-phase experiment Kathy Ruggiero Effects of ocean acidification Air CO 2 in ppm Molecular mechanisms? Abnormal morphology ↓ ability to build shells and skeletal structures Swimming, feeding and survival affected

Shrinking urchins: two-phase experiment Kathy Ruggiero Parent-pair Where babies come from Phase 1 experiment

Shrinking urchins: two-phase experiment Kathy Ruggiero Different CO 2 worlds Phase 1 experiment Divide into 3 cultures Mid = 540 ppm High = 970 ppm Control = 300ppm (current level) 15 ºC Until 4-arm stage

Shrinking urchins: two-phase experiment Kathy Ruggiero …and warmer oceans Split into 5 subsamples Subjected to heat stress Phase 1 experiment

Shrinking urchins: two-phase experiment Kathy Ruggiero Phase 1 experiment …and warmer oceans Split into 5 subsamples Subject to heat stress 11ºC15ºC 19ºC 21ºC24ºC

Shrinking urchins: two-phase experiment Kathy Ruggiero Phase 1 experiment Control MidHigh Design summary x 4 60 samples

Shrinking urchins: two-phase experiment Kathy Ruggiero Phase 2 experiment Measure gene expression Mid 11ºC High 15ºC

Shrinking urchins: two-phase experiment Kathy Ruggiero Phase 2 experiment Measure gene expression Mid 11ºC High 15ºC

Shrinking urchins: two-phase experiment Kathy Ruggiero Phase 2 experiment Measure gene expression Mid 11ºC High 15ºC

Shrinking urchins: two-phase experiment Kathy Ruggiero Phase 2 experiment Measure gene expression Mid 11ºC High 15ºC

Shrinking urchins: two-phase experiment Kathy Ruggiero The dilemma Control MidHigh How to pair 60 samples on 30 arrays? x 4 60 samples

Shrinking urchins: two-phase experiment Kathy Ruggiero 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

Shrinking urchins: two-phase experiment Kathy Ruggiero The challenge

Shrinking urchins: two-phase experiment Kathy Ruggiero 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.”

Shrinking urchins: two-phase experiment Kathy Ruggiero 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.”

Shrinking urchins: two-phase experiment Kathy Ruggiero Heat stressed samples  Arrays Group arrays into 6 “sets” of Loop 1Loop Set 1Set 2

Shrinking urchins: two-phase experiment Kathy Ruggiero Heat stress samples  Arrays Group arrays into 6 “sets” of Loop 1Loop 2 Balanced incomplete block design w.r.t. heat stress

Shrinking urchins: two-phase experiment Kathy Ruggiero 6 sets of 5 arrays Set of Arrays Array Loop 1 Loop 2 Loop 1 Loop 2 Loop 1 Loop 2

Shrinking urchins: two-phase experiment Kathy Ruggiero BIB design w.r.t. Parent-pair (PP) Set of Arrays Array PPCO C C C C M M M M H H H H

Shrinking urchins: two-phase experiment Kathy Ruggiero Parent-pairs (1 vs 2, 3 vs 4) Parent-pairs (1+2 vs 3+4) Between Arrays within Sets24 HST Within Arrays29 ANOVA table Between Sets5 Total (adj.)59 CO 2 2 Parent-pairs Sourced.f.EfficiencyVar Compts in EMS Error15 HST.CO Error12 HST HST.CO Dye10.111

Shrinking urchins: two-phase experiment Kathy Ruggiero 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.”

Shrinking urchins: two-phase experiment Kathy Ruggiero Two designs Set of Arrays Array 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

Shrinking urchins: two-phase experiment Kathy Ruggiero How do they compare? Efficiencies CO 2 1, but in top “stratum”? HST CO 2.HST EffectDesign 1Design 2 Not canonical efficiencies, but based on efficiencies of particular chosen contrasts.

Shrinking urchins: two-phase experiment Kathy Ruggiero 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?

Shrinking urchins: two-phase experiment Kathy Ruggiero Acknowledgements Dr Mary Sewell (University of Auckland) Prof Gretchen Hofmann (UC, Santa Barbara) Dr Anne Todgham (San Francisco State University)