Explain metabolic network modeling

6.5.3 · Biology › Systems Biology & Frontiers

Metabolic network KYA hota hai?

• Nodes = metabolites (jaise glucose, ATP, pyruvate).
• Edges/reactions = enzyme-catalysed conversions.
• Har reaction ka ek flux $v_j$ hota hai = jis rate par woh chalti hai (units: mmol · gDW⁻¹ · h⁻¹, "per gram dry weight per hour").

Stoichiometric matrix $S$ (pehle principles se)

Hum track karna chahte hain ki har reaction har metabolite ko kaise change karti hai.

Mass-balance equation ko scratch se derive karna.

Metabolite $i$ lo. Iski concentration $x_i$ isliye change hoti hai kyunki reactions use produce ya consume karti hain. Change ki rate, sab reactions ka sum hai (reaction $j$ $i$ mein kitna banata hai) × (kitni tezi se $j$ chalta hai):

$\frac{d{x}_i}{dt}={\sum }_{j=1}^n{S}_{ij}{v}_j$

Saare metabolites ko vector $\mathbf{x}$ mein aur saare fluxes ko $\mathbf{v}$ mein stack karo:

Steady-state assumption

Ye linear equations ka ek set hai. Kyunki usually reactions, metabolites se bahut zyada hoti hain ($n\gg m$), system underdetermined hai: infinitely many flux vectors $\mathbf{v}$ ise satisfy karte hain. Solutions ka woh set $S$ ka null space hai, jise flux cone kehte hain.

Flux Balance Analysis (FBA) — ek solution chunna

Hum $S\mathbf{v}=0$ ko uniquely solve nahi kar sakte, toh hum add karte hain:

1. Har flux par Bounds (thermodynamics/enzyme limits): ${\alpha }_j\le v_j\le {\beta }_j$. Irreversible reactions mein ${\alpha }_j=0$ hota hai.
2. Maximise karne ke liye ek objective, usually biomass reaction $v_{\text{biomass}}$ (ek pseudo-reaction jo precursors ko un ratios mein drain karti hai jo ek naya cell banane ke liye chahiye).

Linear program kyun? Saare constraints aur objective fluxes mein linear hain, isliye hum linear programming (LP) use karte hain, jo genome-scale models (thousands of reactions) ke liye bhi fast hai.

Worked example 1 — ek tiny 3-reaction network

Reactions:

• $v_1$: $\to A$ (A ka uptake)
• $v_2$: $A\to B$
• $v_3$: $B\to$ (biomass/export)

Metabolites $A,B$. $S$ banao:

$S=\left(\begin{array}{ccc}+1& -1& 0\\ 0& +1& -1\end{array}\right)$

Ye signs kyun? Row A: $v_1$ A banata hai ($+1$), $v_2$ A khaata hai ($-1$). Row B: $v_2$ B banata hai ($+1$), $v_3$ B khaata hai ($-1$).

Steady state $S\mathbf{v}=0$:

• Row A: $v_1-v_2=0\Rightarrow v_1=v_2$.
• Row B: $v_2-v_3=0\Rightarrow v_2=v_3$.

Ye step kyun? Steady state ka matlab hai ki har internal pool balanced hai, teen saare fluxes ko equal hone par majboor karta hai — ek linear pathway mein conservation of throughput ka classic example.

Agar uptake $v_1\le 10$ par capped hai aur hum $v_3$ maximise karte hain: answer $v_1=v_2=v_3=10$. Bottleneck intake hai.

Worked example 2 — ek branch point

$v_4$ add karo: $A\to C$ (competing branch). Ab biomass maximise karo jise sirf B chahiye (yaani $v_3$ maximise karo).

Row A balance: $v_1=v_2+v_4$.

• Kyun? A ab do reactions consume karti hain, toh iski production dono consumers ke sum ke barabar honi chahiye.

$v_3$ (=$v_2$) maximise karne ke liye, $v_4=0$ set karo taaki saara A, B ki taraf flow kare.

Ye step kyun? Side branch $v_4$ mein koi bhi flux substrate ko biomass route se chura leta hai. Optimiser seekhta hai ki wasteful branches band kar de — aise hi FBA predict karta hai ki ek objective ke under cell "kaunse pathways choose" karta hai.

Worked example 3 — knockout padhna

$v_2$ ke enzyme ko delete karo: $v_2=0$ set karo. Tab row B: $0-v_3=0\Rightarrow v_3=0$. Biomass = 0 → lethal knockout.

Ye step kyun? B ka eklauta producer hata dene par, B ban hi nahi sakta, toh downstream kuch bhi nahi chalta. Exactly aise hi FBA gene essentiality in silico predict karta hai.

Common mistakes (Steel-manned)

Flashcards

Connections

• Flux Balance Analysis
• Linear Programming
• Stoichiometry and Mass Conservation
• Genome-scale Metabolic Models (GEMs)
• Null Space and Linear Algebra
• Enzyme Kinetics (flux bounds ka source)
• Gene Essentiality and Knockout Screens
• Systems Biology & Frontiers

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