Metabolic Networks

Exercises

Prof. Patrick E. Meyer

FBA script

library(boot)
FBA(S, C, c, w, maxi)

S stoichiometric matrix
C upper bounds vector for fluxes
c lower bounds vector for fluxes
w weights vector for the fluxes to optimize
maxi boolean to maximize (T) or minimize (F)

Exercise 1

\[v_1:IN \rightleftharpoons CoA\] \[v_2:CoA \rightleftharpoons ATP\] \[v_3:CoA \rightleftharpoons Fruc6P\] \[v_4:ATP \rightleftharpoons OUT\] \[v_5:Fruc6P \rightleftharpoons OUT\]

maximize for ATP (flux between 0 and 1)?

best to maximize v2 or v4 or v2+v4?
and max v2 but min v4 (storing ATP)?
what if 10% of Fruc6P needed to survive?
what if two ways to produce ATP (but one more costly)?

Exercise 2 : citric acid cycle (Krebs)

\[v_1:IN \rightleftharpoons H_2O\] \[v_2:IN \rightleftharpoons CoA\] \[v_3:H_2O \rightleftharpoons Citrate\] \[v_4:CoA \rightleftharpoons Citrate\] \[v_5:Citrate \rightleftharpoons NAD^+\]

\[v_6:Citrate \rightleftharpoons NADH\] \[v_7:NAD^+ \rightleftharpoons CO_2\] \[v_8:NAD^+ \rightleftharpoons NADH\] \[v_9:NADH \rightleftharpoons OUT\] \[v_{10}:CO_2 \rightleftharpoons OUT\]

Maximize NADH with flux constrained between 0 and 1 (what changes if \(v4:CoA \rightleftharpoons 2Citrate\) ?)

Exam Question (2020)

Let us assume we are able to fine tune the flux of each of the five following reactions between 0 and 1 (for example through under- or over-expression of its corresponding enzyme).
What would be the optimal flux setting for each of these following reactions if our end goal is to maximize S4 production?

Exam Question: Reactions

R1:S1->S4
R2:S1->S2+S3
R3:S2+S3+S4->OUT
R4:IN->S1+S3
R5:IN->S1+S2+S4

WARNING: for encoding decimal number, round to 2 digits after the dot (e.g. 0.666666, 0.1 and 1 should be encoded respectively as 0.67, 0.1 and 1).
v1:[A] v2:[B] v3:[C] v4:[D] v5:[E]