Biomass Coefficients

[Bryan Bartley]

According to Orth 2010, the stoichiometric coefficients of the biomass reaction are scaled so that the flux through it is equal to the exponential growth rate of the organism.

Can anyone confirm for me what the units are for this scaling factor or the stoichiometric coefficients in the biomass reaction?

Thanks,

Bryan Bartley

Graduate Student

UW Bioengineering

[Ronan Fleming]

Hi Bryan,

in an FBA problem
max c'*v
s.t. S*v = b
lb <= v <= ub
where c is nonzero only in the column corresponding to the biomass
reaction, the unit of flux is set by ones choice for the scale of the
upper and lower bounds to net reaction flux, lb & ub, respectively.
This is because the mass balance constraints, S*v = b, are linear, so
they have no preferred scale.

Ronan

--
--
Mr. Ronan MT Fleming B.V.M.S. Dip. Math. Ph.D.
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Assistant Professor,
Dept. Biochemistry & Molecular Biology,
Faculty of Medicine,
University of Iceland,
&
Center for Systems Biology,
University of Iceland,
Sturlugata 8,
101 Reykjavik,
Iceland.
http://www.hi.is/~rfleming
http://systemsbiology.hi.is/
Ph: +354 618 6245
Skype: ronan.fleming
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[Bryan Bartley]

Hi Ronan,

Thanks for the reply.  If I understand you correctly, you are simply saying that the flux units are an arbitrary choice.  So let's say I take a model such as E. coli iJR904 which has been defined in flux units of mmol / g DW hr.  When I optimize this model, the optimal biomass flux is then reported in units of specific growth rate ( 1/hr ).  So there must be some kind of scaling / unit-conversion factor that is implicitly defined in the stoichiometric coefficients of the biomass reaction.  I would like to understand the details of this conversion better.

Cheers

Bryan

[J H]

If I can interject,

I think what you're missing is the relative growth rate, gDW(growth)/gDW(culture)/hr. The grams used in defining the flux units in mmol/gDW(culture)/hr aren't the same grams going into biomass(growth). The mass of the "unit" biomass is ideally (but not necessarily) a unit quantity such as 1ug, 1mg, 1g. If you don't have the published value, you can determine it based on the molar masses of biomass components and their stoichiometries in the biomass equation. Be wary of carbohydrates and other polymers, eg. models handling starch 6 vs 12 carbon type monomers.

[Bryan Bartley]

Dear JH

Thanks for the response.  Can you also give me your insight about the following?

My understanding also is that the biomass coefficients, molar masses of components, specific growth rate, AND component percentage of biomass are related.  

In particular, my conclusion was that you can calculate the component percentage of biomass from the biomass coefficients as follows:

Given a biomass reaction, where u is a stoich. coeff. and A, B, C are mets:

u1*A + u2*B + u3*C ->

Then component percentage of biomass  ( grams metabolite / grams cell dry weight ) can be calculated as follows:

%A  = u1 / ( u1 + u2 + u3 )

Can you confirm this conclusion?  It will really help dispel some confusion I've had for a long time.

Thanks!

Bryan

[J H]

No, you're looking at the mol% there. You need to multiply the stoichiometric coefficient for each species (in mol/whatever) by the relevant molar mass if you want to deal in mass. These probably aren't in your model, but you can extract them from the formulae if they're provided.

Good luck Bryan :)