1. BT8118 – Adv. Topics in Systems Biology
Prof. Eivind Almaas
Dept. of Biotechnology, NTNU

2. In and Out of Null Stoichiometric matrix: S = [-1 -1 2]
– x1 – x2 + 2 x3 = 0
Normal vector to plane:
[-1, -1, 2]T /√6
Possible null space (2-D) orthonormal basis vectors:
y1 = [1,1,1]T /√3
y2 = [-1,1,0]T /√2
Corresponding projection matrix:
P = [ y1 y2 ] : Rn-mRn
PT = [ y1T
y2T ]
F = PT P : Rn  Rn y2 y1

3. Hit-and-run method Algorithm:
Find random starting point in null space (red)
Pick random direction
Move in random direction until boundary is hit.
Specular reflection from boundary
After k reflections, randomize direction
Store coordinates every time distance d is traversed since last sample point.
Why not Monte Carlo sampling? …

4. Non-optimal flux organization in E. coli
Sample 300-dimensional null space
Average over 50,000 sample points
Each individual sample point also has power-law flux distribution
E. Almaas et al, Nature 427, 839 (2004).

5. How do you explain the power law?
Hint: Think geometry…

6. Using linear programming
SUCC: Succinate uptake
GLU : Glutamate uptake
Central Metabolism,
Emmerling et. al, J Bacteriol 184, 152 (2002)
E. Almaas et al Nature 427, 839 (2004).

7. Power law robust feature
Simulate varying conditions by randomization of input substrate:
Out of 89 substrates, make X% available.
Find optimal flux state.
Repeat.
Flux distribution still follows power law.
Large variations localized to high-flux reactions.

8. Flux Balance Analysis
(FBA)

9. Stoichiometric matrix
FBA in a nutshell R1 R2 R3 R4 R5 R6 T1 T2 T3 M1 M2 M3 M4 M5
M1ext
M5ext
M3ext … RN
S11
S21
S12
S22
….. V1 V2
...
= 0
Stoichiometric matrix
Flux vector
FBA is a constraint based approach to model cellular metabolism on a systems level
Internal Flux Constraints
Exchange Flux Constraints
Maximize objective function 9

10. Modeling of knockouts

11. Biologically inspired cellular objectives

12. Model of flux rerouting
WT = black
zwf mutant = red
zwf pnt mutant = blue
What are your thoughts when seeing flux values presented like this?

13. COBRA Toolbox
interlude

14. Reconstruction revisited

15. Thiele & Palsson, Nature Protcols, 5:95 (2010)

16. Network evaluation

17. Gap analysis

18. Summary