Reduced Costs and Shadow Prices

[Daniel F. Hernandez]

Hello, could someone interpret what the reduced cost field (w) returned by optimizeCbModel means?

Also, is there a way to associate the Shadow Prices to the specific flux rate bounds that are limiting?

Thank you kindly,

Daniel

[Ben]

Hi Daniel -

Have you learned more about this in the past couple years? I ask because I'm trying to figure out the answer to your first question.

If I have a maximum reduced cost of 2.07 (found by max(sln.w)), which is associated with reaction # 1259 (found with find(sln.w == max(sln.w))), and a minimum of -0.1627 for reaction 2984, how would I interpret those in relation to a sln.f of 0.1010?

Here's how I'm going about it at the moment.

I think that one of those should be the reaction that is the limiting factor for this particular optimum...

To examine that possibility, I look at the constraints on those reactions, and consider relaxing them:

constrainedModel.ub(1259) %1.1742
constrainedModel.lb(1259) % 0

(reaction 2984 is constrained to 0 flux).

testModel = constrainedModel;
testModel.ub = 1000;
optimizeCbModel(testModel) %f = 0.1010

- so relaxing that constraint didn't change the objective value. But perhaps there are others that are nearby?

sln.w(find(sln.w > 2.07)) % turns out there are 4 that are about that big! I'll relax them all...

testModel.ub([1247 1249 1259 1261]) = 1000

sln2 = optimizeCbModel(testModel) %f = 0.1010 (still!)

And find(sln2.w > 2.07) still finds the same 4 reactions - [1247 1249 1259 1261].

In this case, they're all associated with biosynthesis of cardiolipin, so I suspect that the limitation is imposed by the coefficient on the biomass definition in this model, not because of any of these reactions...

Does that seem like a reasonable approach to the problem? Do you (or does anyone else) have suggestions on reduced cost/Shadow Price analysis and interpretation?

Thanks!
Ben

[Ines Thiele]

By definition the reduced cost is negative. So you are searching for the smallest number(s) in w.

The reduced cost indicates how much the objective value where to increase (in your case by 0.1627) if you were to increase the flux through the associated reaction (her: 2984) by one unit.

Good place to read more details about this are B Palsson's books.

Best Ines

Sent from my iPad

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[Ben]

Thanks, Ines. Always good to go back and review the fundamentals!

-b

[Bushra Dohai]

Dear Dr.Thiele,

As you mentioned here that reduced cost is negative, in my model I am getting positive reduced cost? What is the interpretation of positive, negative, and zero reduced cost? . I went through Dr.Palsson's Book, it mentioned that zero reduced cost means " that the flux through the corresponding reaction does not change the objective function", and nothing stated about positive or negative reduced cost. Also what is the differences then between shadow price and reduced cost?? from metabolic point of view? . THanks