Experimental design for RNA-seq time-course with the same start and end points but different treatments

Question

[James Ashmore]

I have RNA-seq data for a time-course experiment which consists of the same starting and end points but two different conditions: https://postimg.cc/DW0RzJf1

I am unsure how to correctly model the data to answer the following questions:

1. Identify differential genes between each time-point within each condition
2. Identify differential genes between conditions within each time-point

To answer each question respectively I thought about doing the following:

1. Subset the data by condition and identify differential genes separately using a formula such as: ~ Time.
2. Remove the start and end points entirely and model the data using a simple formula such as: ~ Time + Treat)

Would this be an appropriate design? I'm concerned about subsetting the data too much because it will affect the estimation of variance e.t.c

[russhh]

The final endpoint confuses me a bit; otherwise the design seems a straight ~ Time * Treat. Why do the two different treatments fork back into the same endpoint?

[James Ashmore]

It’s a bit of a specific example but the time-course is for iPS reprogramming - the treatment gets to the end-point faster than the control. The end-point is around 15 days from the beginning.