19BIO201

Intelligence in Biological Systems - 3

Flux Balance Analysis

Intelligence in Biological Systems - 3

Aadharsh Aadhithya - CB.EN.U4AIE20001
Anirudh Edpuganti - CB.EN.U4AIE20005

Madhav Kishor - CB.EN.U4AIE20033

Onteddu Chaitanya Reddy - CB.EN.U4AIE20045
Pillalamarri Akshaya - CB.EN.U4AIE20049

Team-1

Flux Balance Analysis

\vdots

Flux Balance Analysis

-1

-2

r_1

r_2

r_3

Flux Balance Analysis

\vec{v} = \begin{bmatrix} v_1 \\ v_2 \\ v_3 \end{bmatrix}

S = \begin{bmatrix} -1 & 0 & 1 \\ -1 & 0 & 0 \\ 1 & 0 & 0 \\ 0 & -1 & -1 \\ 0 & -1 & 0 \\ 0 & 1 & -2 \\ \end{bmatrix}

Flux Balance Analysis

Rate of production and consumption of a metabolite is equal at steady state. There fore, we can write, for the net system,

S\cdot \vec{v} = 0

Flux Balance Analysis

S\cdot \vec{v} = 0

This is an Undertermined System! 😞

Flux Balance Analysis

S\cdot \vec{v} = 0

\underset{Sv=0 \,\, a \leq v \leq b }{maximize} \,\, c^Tv

Flux Balance Analysis

S\cdot \vec{v} = 0

\underset{Sv=0 \,\, a \leq v \leq b }{maximize} \,\, c^Tv

c^T = [0\,\, 1\,\, 0]

If we want to maximise v2, then c would be

Flux Balance Analysis

S\cdot \vec{v} = 0

\underset{Sv=0 \,\, a \leq v \leq b }{max} \,\, c^Tv

The solution to this problem is unique. But the flux distribution is not unique.

IBS3_A4