Is this a proper use of mixed modeling? I admit I'm fairly new  at statistical modeling and so I'm not confident in the method I am using.
Using LC-MS/MS, I am monitoring the degree of post-translational modification of specific peptides by a given enzyme over time. The reaction conditions have the peptides in solution with the enzyme for varying reaction times. I should note, the peptide sequences are different and thus provide different substrate specificity. Additionally, within the time scale of this experiments, enzyme kinetics are accelerating over time.
For the study, I took 5 replicate measurements of for each peptide at each reaction time.
Edit: I am primarily interested in the effect on reaction time on area, but each peptide will have a contribution as well. I total I have 32 peptides with 5 reaction times. The modification variable is how many times we see a given modification on a specific peptide.
The dataset ends up looking like this (truncated for brevity):

I believe I it would make sense to use a mixed-effects model, but I’m having trouble defining my fixed vs. random effects, or whether this is the correct model to use in the first place.
So far I’ve tried the following.
Area ~ Peptide + ( Peptide | Reaction Time ))
Any suggestions, feedback, or simply pointing me in the right direction would be MUCH appreciated!
 A: The model you are thinking about:
Area ~ Peptide + ( Peptide | Reaction_Time )

doesn't really make sense. The primary interest is in the association of reaction times with Area, so reaction times should be a fixed effect. On the other hand, there are 32 Peptides, so fitting this as a fixed effect would involve a lot of estimates. Presumably we can also think of these 32 peptides as a sample from a wider population of peptides, and since there are repeated measures within each peptide, these three arguments favour treating peptide as the grouping factor. So the following model would make more sense:
Area ~ Reaction_Time + ( Reaction_Time | Peptide  )

This will estimate a global (fixed) intercept, being the estimated Area when Reaction_Time is zero, and a fixed effect for Reaction_Time which will be interpreted as the average linear slope - that is the estimated difference in Area for a 1 unit change in Reaction_Time. It will fit random intercepts for Peptide so that each Peptide has it's own intercept, and random slopes for Reaction_Time so that each Peptide has it's own slope for Reaction_Time. The random effects in most software will be assumed to follow a normal distribution, and an estimate of the correlation between the slopes and intercepts will also usually be estimated by default.
