Shadow Price and New Cobra Version

[Bushra Saeed Dohai]

Dear all,

I am using two models for same organism but one is wild type and other one is mutant, so I am doing analysis using flux balance analysis by getting the fluxes of the reactions and shadow prices of metabolites which is in COBRA Toolbox is the FBASolution.x and FBASolution.y, respectively. I have the following problems:

1. When using the old COBRA Version 2.0.5 I got different shadow prices than that when I am using the New COBRA version !! and the differences are only in signs (negative to positive). Is the new version has that much effect and what is the interpretation of that?.

2. As far as I know is that shadow price is representative of exchange reaction, however reduced cost (FBASolution.w) is a representative for internal reaction. Am I correct?. 

I highly appreciate if someone could answer the above questions. Thanks

 

Sincerely,

Bushra Dohai Modelling Engineer and Research Technologist   Laboratory of Algal, Systems, and Synthetic Biology Centre for Science and Engineering Saadiyat Island Campus Center  C1 Building, ERB, Office No. RL5 D2 NYU Abu Dhabi, United Arab Emirates Office Tel: +971 2 628 5144, P.O. Box 129188 http://lassb.abudhabi.nyu.edu/index.php

[Andres Mauricio Pinzon Velasco]

Dear Bushra,

Some solvers report positive shadow prices (gplk), perhaps this is your situation?

Now, regarding your second question remember that:

Shadow prices refer to metabolite flux, and reduced costs refer to reactions. So RC are the derivatives of the objective function with respect to a reaction

 and SP re the derivatives of the objective function with respect to flux of a metabolite. At the end these values tell you, for instances, how much the change of a given metabolite (SP) / reaction (RC) will affect the objective.

Regards,

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[Bushra Saeed Dohai]

Thanks Dr. Pinzon, yes i am using the glpk solver but in both Cobra versions old and new, so i didn't change the solver. New COBRA version gave me positive values but old version gave me negative values? So i think something related to the updates.

Now regarding second question negative shadow price indicates a limiting metabolite, positive SP indicates excess metabolite, and zero SP is for secreted metabolite , that is my understanding, is it the same indications for reduced cost? . Also if I have two SPs and both e.g were negative but had different values say one is -10 and other is -20 , how to interpretate  that? . Thanks

[Ronan M.T. Fleming]

Dear All
Some time ago I  checked to make sure that the solver signs were consistent.
Regards
Ronan

Git clone

[Bushra Saeed Dohai]

Dear Dr.Ronan,

Thanks for your reply. It is not about inconsistent solver, i am using the same solver in both versions but I am getting different sign? . 

 Sincerely,

Bushra Dohai Modelling Engineer and Research Technologist   Laboratory of Algal, Systems, and Synthetic Biology Centre for Science and Engineering Saadiyat Island Campus Center  C1 Building, ERB, Office No. RL5 D2 NYU Abu Dhabi, United Arab Emirates Office Tel: +971 2 628 5144, P.O. Box 129188 http://lassb.abudhabi.nyu.edu/index.php

[Andres Mauricio Pinzon Velasco]

Dear Bushra,

The interpretation could be the following: the metabolites with a zero shadow price do not have an effect over the objective function and are thus secreted. On the other hand, metabolites showing  a negative shadow price have an effect (increase) the objective function and are thus not secreted. 

Hope it helps.

Regards,

[Bushra Saeed Dohai]

Thanks Dr.Andres,

I understood your interpretation, but what would be with the reduced cost?, from my reading I got confused between shadow price and reduced cost, I think they are so closed, any clarification? . thanks

 Sincerely,

Bushra Dohai Modelling Engineer and Research Technologist   Laboratory of Algal, Systems, and Synthetic Biology Centre for Science and Engineering Saadiyat Island Campus Center  C1 Building, ERB, Office No. RL5 D2 NYU Abu Dhabi, United Arab Emirates Office Tel: +971 2 628 5144, P.O. Box 129188 http://lassb.abudhabi.nyu.edu/index.php

[Andres Mauricio Pinzon Velasco]

Hi,

RC s associated to the reaction, SP to metabolites.

Best,

[Ronan M.T. Fleming]

Hi Bushra,

the sign of a dual variable is firstly a convention and secondly to be biologically interpreted. Different mathematical textbooks/solvers/cobra papers/cobra books use different signs. Some time ago, I checked and made sure that solveCobraLP was always returning dual variables with the same convention in sign independent of the solver being used. If you want to check what sign is being used, I suggest that you take your FBA problem

min c'v

st. Sv=0 : y

l <= v <= u : w

Where

y = solution.dual = dual vector corresponding to steady state (equality) constraints

w = solution.rcost = dual vector corresponding to lower and upper bound (inequality) constraints

then slightly relax either one of the steady state or one of the upper/lower bounds (corresponding to a nonzero y_i or w_j) then see how the resulting value of c'v changes compared to when you don't do any relaxation. This should tell you the meaning of the signs.

Regards,

Ronan

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[Ashlin James Poruthoor]

Dear Teachers,

I'm a student who have recently  started using COBRA for FBA calculations. I would like to know more about the interpretations of x,y,w and f. Could you suggest and articles or research papers that I can look forward to.

Thank you all.

Ashlin James P

[Ronan M.T. Fleming]

http://www.nature.com/nbt/journal/v28/n3/abs/nbt.1614.html

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[Ashlin James Poruthoor]

Dear Dir,

Thank you for the article but I'm afraid I have read this article before and I got a good idea about the FBA but can you suggest more specific articles or others on reduced costs and shadow price and their interpretations based on their signs. I apologize for any inconvenience.

Thank you

[Ronan M.T. Fleming]

Hi Ashlin,

see Chapter 18: Optimisation, a lecture on this is here:

http://systemsbiology.ucsd.edu/Publications/Books/SB1-2LectureSlides

Regards,

Ronan

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