Enzymatic & Biological Recycling: Depolymerisation Kinetics & PETase/MHETase Biocatalysis

Conventional chemical recycling (pyrolysis) requires high temperatures ($> 400^\circ$C) and is energy-intensive. Enzymatic recycling (biocatalysis) operates under mild conditions ($30 - 70^\circ$C) in water, selectively depolymerizing specific polymers like PET without breaking down other materials in mixed waste. Companies like Carbios in Europe and research setups in India are scaling up PETase enzymes to recycle packaging and textiles into virgin-quality monomers. Understanding enzyme kinetics, reaction mechanisms, and bioreactor design is crucial for circular economy engineers.

• Explain the biocatalytic mechanism of PETase and MHETase in cleaving ester bonds.
• Apply the Michaelis-Menten kinetic model to calculate enzyme affinity ($K_m$) and maximum reaction velocity ($V_{max}$).
• Analyze how crystallinity, Tg, and particle surface area of PET influence enzymatic hydrolysis rates.
• Compare enzymatic recycling with mechanical and pyrolysis recycling in terms of environmental impact.
• Reference international standards for testing biological recycling.

3.1 Biocatalytic Pathway: PETase & MHETase

The discovery of Ideonella sakaiensis in 2016 revealed two key enzymes that digest PET:

1. PETase (PET hydrolase): Cleaves the PET chain ester bonds, releasing soluble oligomers, primarily MHET (mono-(2-hydroxyethyl) terephthalate), along with small amounts of BHET and terephthalic acid (TPA).
2. MHETase: Specifically hydrolyzes MHET into the final monomers: TPA and Ethylene Glycol (EG). These monomers can be recovered and repolymerized into virgin PET.

3.2 Michaelis-Menten Kinetics for Enzymatic Hydrolysis

The rate of enzymatic depolymerisation ($v$) as a function of substrate concentration $[S]$ follows Michaelis-Menten kinetics:

Where:

• $V_{max}$: Maximum reaction velocity at enzyme saturation ($V_{max} = k_{cat} [E]_0$).
• $K_m$: Michaelis constant (substrate concentration at which the velocity is $1/2 V_{max}$; measures enzyme-substrate affinity).
• $[S]$: Concentration of reactive ester sites on the polymer surface.

3.3 Influence of Polymer Crystallinity

Enzymes are large proteins ($\approx 30$ kDa) that cannot diffuse into the crystalline region of PET. They only access the mobile amorphous regions. Therefore:

• Amorphous PET (quenched, crystallinity $< 5\%$): High rate of enzymatic degradation.
• Semi-Crystalline PET (bottles, crystallinity $30\% - 40\%$): Extremely slow degradation. Prior to enzymatic treatment, the PET must be heated above $T_g$ and mechanically micronised (micronised flakes) to disrupt crystals and increase surface area.

Problem: A kinetic study of an engineered PETase enzyme is conducted on micronised amorphous PET. The enzyme concentration is held constant. The initial rates of monomer release ($v$) at different substrate (reactive ester site) concentrations $[S]$ are measured:

• At $[S] = 2.0$ mM: $v = 12.5$ $\mu$mol/(L·min)
• At $[S] = 10.0$ mM: $v = 31.25$ $\mu$mol/(L·min) (close to saturation) Assuming the reaction follows Michaelis-Menten kinetics, calculate:

1. The Michaelis constant ($K_m$) of the PETase.
2. The maximum reaction velocity ($V_{max}$).

Solution: Using the Michaelis-Menten equation:

Set up a system of two equations:

1. $12.5 = \frac{2 V_{max}}{K_m + 2} \Rightarrow 12.5 K_m + 25 = 2 V_{max} \Rightarrow V_{max} = 6.25 K_m + 12.5$
2. $31.25 = \frac{10 V_{max}}{K_m + 10} \Rightarrow 31.25 K_m + 312.5 = 10 V_{max}$

Substitute $V_{max}$ from (1) into (2):

Now solve for $V_{max}$:

Interpretation: The enzyme has a Michaelis constant $K_m = 6.0$ mM and a maximum turnover velocity $V_{max} = 50.0$ $\mu$mol/(L·min). To optimize industrial bioreactor throughput, the reactor substrate loading should be kept well above $K_m$ (e.g., $[S] \ge 30.0$ mM) to operate near maximum velocity.

Indian biotechnology research institutes (such as CSIR-NCL in Pune and IIT Bombay) are engineering thermo-tolerant PETase variants. Standard PETase degrades at temperatures above 50°C, but industrial reactors need to run at 65–70°C (near the $T_g$ of PET) to soften the polymer chains and accelerate enzymatic cleavage.

• PETase: Hydrolase enzyme that cleaves PET ester bonds, producing MHET.
• MHETase: Enzyme that converts MHET into monomers TPA and EG.
• Michaelis-Menten: Kinetic model relating reaction rate to substrate concentration.
• $K_m$ (Michaelis Constant): Substrate concentration at half-maximum velocity; lower values show higher affinity.
• Micronisation: Mechanical grinding to reduce particle size, increasing surface area for enzymatic attack.

1. ISO 14851 — Determination of ultimate aerobic biodegradability in aqueous medium
2. Academic protocols for enzyme activity assays on synthetic polyesters

1. Draw the active site catalytic triad (typically Ser-His-Asp) of PETase, showing how nucleophilic attack cleaves the ester bond.
2. Explain why the enzymatic degradation rate of PET drops to near zero when the crystallinity exceeds $40\%$. How does thermal pre-treatment solve this?
3. Derive the Lineweaver-Burk double reciprocal plot equation from the Michaelis-Menten model. Explain how to extract $K_m$ and $V_{max}$ from the intercept values.