9 | Metabolic engineering strategies II

Question 1

What are the 4 steps of the OptStrain approach?

Answer 1

1. Build universal reaction database
2. Compute max theoretical product yield
3. Identify stoichiometrically pathways that minimize non-native functionalities
4. Integrate pathway into host and optimize further via OptKnock

Question 2

How is the universal database created in step 1 of the OptStrain approach?

Answer 2

• Based on KEGG (or BioCyc, MetRxn, RetroRules)
• Unbalanced reactions are removed
• databases include native + non-native reactions (global library of metabolism).

Question 3

What is the set 𝑅 in optStrain?

Answer 3

• set of biologically plausible input metabolites that are allowed to enter the system
• ie, external nutrients/ feed compounds organism can take up from environment.
• set is defined by user, not derived automatically based on proximity to product
• Known substrates for wild-type or engineered strains
• Eg glucose, glycerol, acetate, lactate, methanol, pyruvate, succinate…..

Question 4

What is the LP used in step 2 of OptStrain, to calculate maximum theoretical yield?

Answer 4

max MW_P ∑ S_Pj · v_j

Subject to:

Mass balance for i ∉ R: ∑ S_ij v_j ≥ 0
Total substrate uptake: ∑_{i ∈ R} MW_i ∑ S_ij v_j = -1

Question 5

Consider the LP for step 2 of Optstrain
max MW_P ∑ S_Pj · v_j
Subject to:
Mass balance for i ∉ R: ∑ S_ij v_j ≥ 0
Total substrate uptake: ∑_{i ∈ R} MW_i ∑ S_ij v_j = -1
Explain the objective function.

Answer 5

MW_P denotes the molecular weight of the product of interest.
The objective maximises the sum of all reaction fluxes producing minus those consuming the target metabolite, weighted by the stoichiometric coefficient of the target metabolite in these reactions.
→ So you’re maximizing the total mass of product P generated via all reactions.

Question 6

Consider the LP for step 2 of Optstrain
max MW_P ∑ S_Pj · v_j
Subject to:
Mass balance for i ∉ R: ∑ S_ij v_j ≥ 0
Total substrate uptake: ∑_{i ∈ R} MW_i ∑ S_ij v_j = -1
Explain the constraints.

Answer 6

• 1st constraint (mass balance for non-substrates) ensures only allowed substrates are taken up. All other metabolites can only be secreted.
• 2nd constraint sets total substrate uptake to exactly 1 unit of mass, i.e., a standardized input → scales the results to a total substrate uptake flux of one unit of mass

Question 7

In OptStrain, why do we fix substrate uptake to 1 in theoretical yield calculation?

Answer 7

• To normalize yield values
• Ensures results are comparable across substrates

Question 8

How does OptStrain model handle identification of stoichiometrically balanced pathway(s) that minimizes the number of non-native functionalities in Step 3?

Answer 8

Formulate a MILP approach:
We introduce binary variable 𝑦_𝑖 for each non-native reaction 𝑖 (heterologous functionalities):
* 𝑦_𝑖 = 1, active reaction
* 𝑦_𝑖 = 0, inactive (blocked)
Switching a reaction on/off can then be achieved by adding the capacity constraint:
* 𝑣_𝑗^𝑚𝑖𝑛𝑦<sun>𝑗</sub> ≤ 𝑣_𝑗 ≤ 𝑣_𝑗^𝑚𝑎𝑥𝑦<sun>𝑗</sub>
The objective function is:
* Minimizes ∑ y_j for all non-native reactions
Yield:
* MW_P ∑ S_Pj v_j >= 𝑌𝑖𝑒𝑙𝑑^{𝑡𝑎𝑟𝑔𝑒𝑡}
* ensures that the product yield meets the maximum theoretical yield, 𝑌𝑖𝑒𝑙𝑑^{𝑡𝑎𝑟𝑔𝑒𝑡}, calculated in Step 2</sun></sun>

Question 9

What is step 3 in OptStrain?

Answer 9

Identification of stoichiometrically balanced pathway(s) that minimizes the number of non-native functionalities
Using:
* binary variables & matching capacity constraints
* constraint for at least the yield determined in step 2
* integer cuts to get alternative solutions which have both the same maximum yield and minimum non-native reactions.

Question 10

Consider step 3 of OptStrain: Identification of stoichiometrically balanced pathway(s) that minimizes the number of non-native functionalities. How could we identify alternative solutions, ensuring both optimality criteria of maximum yield and minimum non-native reactions?

Answer 10

This is achieved by iteratively solving the same MILP problem augmented with additional constraints called integer cuts
Integer cut constraints exclude from consideration previously found solutions

Question 11

What do integer cuts do in OptStrain? Give an example for how they are implemented.

Answer 11

This process helps explore multiple minimal non-native pathways that achieve the same yield, ie prevent reuse of the same y_j combinations as a solution.
Example. a previous solution includes reactions 1, 2, and 3.
We introduce an integer cut constraint 𝑦₁ + 𝑦₂ + 𝑦₃ ≤ 2

Question 12

What kind of reactions does OptStrain insert into the host?

Answer 12

• Non-native (heterologous) reactions
• Stoichiometrically balanced
• Selected to maximize product yield

Question 13

What is the goal of OptStrain Step 4?

Answer 13

• Add best combination of non-native genes to host
• Use OptKnock on augmented model to further optimize chemical production

Question 14

Give an example of application of OptStrain in E Coli to determine the most suitable substrate to maximise a product.

Answer 14

• Step 1: Universal database obtained by combining KEGG with reactions from methylotroph Methylobacterium extroquens AM1 → ~3000 reactions balanced for C, O, H, N, S, P
• Different substrate choices- Pentose and hexose sugars- Acetate, lactate, malate, glycerol, pyruvate, succinate, methanol
• Step 2 – maximizing yield of hydrogen production
• Result: methanol gave highest hydrogen yield.

Question 15

Fluxes are considered to be down-/up-regulated if they are sufficiently smaller / larger than a given ______ flux.
This is achieved by consideration of a parameter 𝐶, or ______ ______ ______, which quantifies the ______ which have to be overcome to deem a reaction changed.
𝐶 takes values ______ . The higher the value of 𝐶, the ______ the requirement imposed on the reaction to be regulated

Answer 15

Fluxes are considered to be down-/up-regulated if they are sufficiently smaller / larger than a given steady-state flux.
This is achieved by consideration of a parameter 𝐶, or regulation strength parameter, which quantifies the thresholds which have to be overcome to deem a reaction changed.
𝐶 takes values between 0 and 1. The higher the value of 𝐶, the stronger the requirement imposed on the reaction to be regulated

Question 16

What is the goal of OptReg?

Answer 16

• To improve product yield using gene expression control
• Allows knockouts, up- and down-regulation
• Formulated as a MILP

Question 17

Draw and annotate the ranges of flux values relevant in OptReg

Answer 17

• 𝑣⁰_𝑗,𝐿 and 𝑣⁰_𝑗,𝑈 denote the allowed fluxes at steady state - determined by FVA with constraints on known fluxes in WT (= operational range?)
• 𝑣_𝑗^min and 𝑣_𝑗^max denote the feasible range, determined in FBA
• 𝐶, regulation strength parameter

see:
https://drive.google.com/file/d/1k0yV31EVAJScJBm4HnCozvfinhXW0wvs/view?usp=drive_link

Question 18

What is the flux range constraint for downregulation in optReg? Deduce the range for downregulation from this.

Answer 18

Constraint: v_j^min ≤ v_j ≤ (v_j,L⁰ · (1 − C) + v_j^min · C) · (1 − y_j^d) + v_j^max,d · y_j^d

→ make y_j^d = 0 to get range: between 𝑣_𝑗^min and 𝑣⁰_𝑗,𝐿(1 - C) + 𝑣_𝑗^minC

Question 19

What is the flux range constraint for upregulation in optReg? Deduce the range for upregulation from this.

Answer 19

(CHECK!)
Constraint:
(𝑣⁰_𝑗,U(1 - C) + 𝑣_𝑗^maxC)(1 - y_j^u) + 𝑣_𝑗^miny_j^u ≤ 𝑣_𝑗 ≤ 𝑣_𝑗^max

→ make y_j^u = 0 to get range: between 𝑣⁰_𝑗,U(1 - C) + 𝑣_𝑗^maxC
and 𝑣_𝑗^max

Question 20

How is a knockout modeled in OptReg?

Answer 20

Constraint: v_j^min,k · y_j^k ≤ v_j ≤ v_j^max,k · y_j^k
If y_i^ko = 0 → knocked out!

Question 21

What regulatory actions are allowed in OptReg?

Answer 21

For every reaction, there are 3 binary variables:
* Knockout: y_j^k = 0 → v_j = 0
* Down-regulation: y_j^d = 0 → v_j ≤ some limit
* Up-regulation: y_j^u = 0→ v_j ≥ some limit

Question 22

How many regulatory interventions can be applied to one reaction in OptReg? What is the relevant constraint?

Answer 22

At most one
Constraint: (1 - y_j^k) + (1 - y_j^d) + (1 - y_j^u) ≤ 1

Question 23

How are the total number of manipulations constrained in OptReg?

Answer 23

∑_j(1 − y_j^k) ≤ K
∑_j(1 − y_j^d) ≤ D
∑_j(1 − y_j^u) ≤ U
Or: 
∑_j(1 − y_j^k) + (1 − y_j^d) + (1 − y_j^u) ≤ L

Question 24

What type of linear program is optReg? How to solve it?

Answer 24

Bilevel program

Transformed by KKT conditions and Duality (similar to optKnock)

Question 25

What is the objective function in OptReg?

Answer 25

Maximize v_product

Question 26

How is reversibility dealt with in optReg?

Answer 26

KO: both fwd, bwd reactions both knocked-out → make two corresponding variables same up/downregulated: either forward or backward reaction only → sum of two variables >= 1