# Finding total concentration of enzymes

Sorry if my question is very basic for biology majors because I am not. I am trying to build a mathematical model of a particular pathway using systems of differential equations and in order to reduce the number of parameters, I need to know the total concentration of multiple enzymes. How are enzyme concentrations usually reported in the literature so I can google it? Also, this does not seem to me to be a straightforward measurement for professional biologists, so how are enzyme concentrations actually measured or approximated? Thanks in advance!

I am interested in the following pathway:

• I wonder whether you could clarify whether your equations deal with concentration in term of physical amount of enzyme (mg/ml) or (functional) activity (enzyme units per ml). The reason I ask is the latter is what I would think determines the operation of the pathway. But perhaps I misunderstand what your mathematics is modelling. Presumably you are trying to quantify the effect following some stimulus — can you elaborate. Oh, and in what tissue in what organism do you wish the concentrations? – David Jul 24 '20 at 11:40
• @David: I am interested in the physical amount of enzyme, because I intend to use an oversimplified relational equation: $E_T=E_f + ES$ where $E_T$, $E_f$, and $ES$ stands for total enzyme (physical) concentration, "free"-enzyme, and enzyme-substrate complex, respectively. I think this would be a way to approximate a model of inhibition where $S$ is an inhibitor of the enzyme $E$, since the inhibitor would "eat up" the amount of free-enzymes. Ideally, I am interested in human fibroblast or endothelial cells. However, if data is too scarce for human cells, then mice would be fine. – TheLast Cipher Jul 24 '20 at 16:15
• @David: Also, by functional enzyme, did you mean an active enzyme? – TheLast Cipher Jul 24 '20 at 16:16
• Yes. I was trying to use layman's terms (not very helpful). I'll think about your approach and see if I have anything useful to contribute. – David Jul 24 '20 at 16:47

Hi again TheLast Cipher,

Enzymes in a cell are usually semi-quantified by the: Western Blot technique.

But there are lesser known techniques.

E.g. For a Western Blot the unit of measurement is the color intensity of the enzyme band on the blot membrane.

If I were you I would look for journal articles covering your pathway of interest.

Covers the electron transport chain (Co-enzyme Q10)

If you can get through the pay-wall & read their results and you will find:

"Western blot analysis of membrane protein isolated from keratinocytes derived from one young and old donor. A representative picture out of five experiments is displayed."

Also they used and I quote:

"Arbitrary Units"

Maybe you could comment on which pathway and I can find some assisting material.

• Thank you very much, Andrew! I've uploaded an oversimplified version of the pathway as a rough sketch of what I am working on. So there are kinases in between the interactions and I'm interested in their concentrations (e.g. PIP2, PRAS40, TSC2, Rheb-GDP, Rheb-GTP, as found on figure 3 of pubmed.ncbi.nlm.nih.gov/28069808). – TheLast Cipher Jul 23 '20 at 10:27
• Your attachment is unfortunately RNA concentrations. I'll see what I can find. – Andrew Jul 23 '20 at 10:44

The BioNumbers site (https://bionumbers.hms.harvard.edu/search.aspx) is often useful for these types of questions, if you're interested in an order of magnitude. However, if you want precise concentration ratios (i.e. something like "is there twice as much Ras as ERK, or more like half as much"), you are unlikely to get a definitive answer.

These may be cell type-dependent and even vary from cell to cell due to noise. You probably want to simulate your network with a variety of absolute concentration, and then the most interesting behaviors are those that are reasonably robust to the exact numbers used (results that depend on, e.g., having almost exactly the same number of molecules of Ras as ERK are likely irrelevant as they would be too "brittle" inside a living cell). Once you find out what the necessary limits are for a given behavior that you find interesting, you could think about checking whether values reported by the literature indeed tend to fall within those bounds.

• Hey, thank you very much for this. This looks like a great resource! – TheLast Cipher Aug 10 '20 at 4:48