BT8118 – Adv. Topics in Systems Biology

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Presentation transcript:

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

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

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? …

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).

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

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).

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.

Flux Balance Analysis (FBA)

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

Modeling of knockouts

Biologically inspired cellular objectives

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

COBRA Toolbox interlude

Reconstruction revisited

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

Network evaluation

Gap analysis

Summary