Metabolic networks Guest lecture by Dr. Carlotta Martelli 26_10_2007

(... ) coa + nad + pyr --> accoa + co2 + nadh g1p + h2o --> glc-D + pi 2pg h2o + pep g3p + nad +pi 13dpg + h + nadh fdp dhap + g3p fdp + h2o --> f6p + pi f6p dha + g3p adpglc --> adp + glycogen + h atp + g1p + h --> adpglc + ppi glycogen + pi --> g1p atp + glc-D --> adp + g6p + h 2pg 3pg atp + f6p --> adp + fdp + h g6p f6p 3pg + atp 13dpg + adp atp + h2o + pyr --> amp + (2) h + pep + pi adp + h + pep --> atp + pyr dhap g3p (... ) biochemistry thermodynamics

Thermodynamics range of flux feasibility Si≥0 Biochemistry network definition a i m b i m

It' s a dynamic system !

Optimization principles! ● Realistic mathematical models turn to be very expensive: – Detailed rate equations – Reliable rate equations ● Understanding the evolutionary layout: – Adaptation – Selection

Stationary state: Flux Balance Analysis convex polytope

Define of objective function Z : biomass production Maximize (or min.) Z, subject to constraints: Linear Z = Linear Programming technics (Simplex Algorithm)

1) Many other possible target functions exist!! It depends on your problem.

2) Be carefull with optimization! Not all the organisms live in your optimal state

reactions metabolites Von Neumann model

Problem definition growth: maximize  subject to the linear constraints:

FBA vs VN ● Stationary state condition ● Mass balance ● Local optimization ● Evolving system ● No mass balance ● Global optimization  =1 n=N/P  * ? FBA

 n=N/P  * ?  Min-over ( better than backtraking! ) Random initial {S i }

Random vs Real metabolic networks 1) Optimal growth rate 2) Number of solutions

Conserved pools of metabolites

Random E.coli

VN FBA EXP