# Change in gene expression over time for different environments when each individual can only be sampled once?

A colleague has collected data on plant root gene expression. Gene expression is expected to change over time, and be dependent upon the environment that each plant is grown in (i.e fertilizer mix). Measuring gene expression kills the plant, so each plant can only be sampled once. My colleague has two groups (high vs low fertilizer) and plans to sample different plants at 3 time points (day 5, day 10 and day 15).

In the past when we've looked at plant growth we've measured height at intervals for each plant and then used a multilevel longitudinal model. But that seems to need multiple measurements for each individual which isn't possible here (we can only make one measurement per individual). So how would you go about analysing the results from this experiment? Or would you design it differently in the first place?

• Just to be clear, I'm mainly interested in the overall question of how to treat the data, rather than the intricacies of comparing gene -expression. He has other data on protein levels, length of roots etc that he'd also like to look at. – Andrew Apr 5 '12 at 7:48

## 1 Answer

One very straightforward way to do it would be: $Gene=\alpha+\beta_1Groups+\beta_2Time+\epsilon$

Since they are different plants, we can assume them to be independent unlike your earlier experiment which requires multilevel analysis. You can also add other variables like protein levels, etc in the model. Time may be treated as a dummy variable; but I think that really depends on your specific knowledge of the field which I have none.

• Thanks! I hadn't thought of doing it this simply. I suspect that the relationship with time is non-linear - so I guess I could fit a spline to the time variable? – Andrew Apr 12 '12 at 8:44
• If the relationship with time is non-linear, you can include time as a dummy variable instead as I have mentioned. It would then estimate a different coefficient for each time point. I'm pretty sure they have a more fancy name for this; but I just can't recall it now. – King Apr 12 '12 at 14:19