SynPETic

Best Model

Models and computer simulations can help us understand the function and operation of BioBrick Parts and Devices. Simulation and modeling are critical engineering skills that can contribute to project design or provide a better understanding of the modeled process. These processes are even more useful and/or informative when real-world data are included in the model. This award is for teams who build a model of their system and use it to inform system design or simulate expected behavior before, or in conjunction with, experiments in the wetlab.

Visit the Special Prizes page for more information.

Overview

Mathematical models and computer simulations provide a great way to describe the function and operation of Parts and Devices. Synthetic Biology is an engineering discipline, and part of engineering is simulation and modeling to determine the behavior of your design before you build it. Designing and simulating can be iterated many times in a computer before moving to the lab.

Five Models of Enzymatic PET Degradation

Every simulation reviewed here tracks the same chemistry — PET broken down by PETase, its intermediate cleaved by MHETase into terephthalic acid (TPA) and ethylene glycol (EG) — but each encodes a different mathematical assumption about how fast that happens. This section lays out the governing equations side by side, and is deliberately candid about which of these six simulations have real problems.

1. Saturable (Michaelis–Menten) kinetics · Simulation X · baseline

The baseline model treats both enzymes as classic single-substrate catalysts. Reaction velocity saturates as substrate becomes abundant, because enzyme active sites are the limiting resource:

$$ v_{\text{PETase}} = \frac{V_{\max}^{P}\,S}{K_m^{P} + S}, \qquad v_{\text{MHETase}} = \frac{V_{\max}^{M}\,[\text{MHET}]}{K_m^{M} + [\text{MHET}]} $$ $$ V_{\max}^{P} = 2.5\,[\text{PETase}], \quad K_m^{P} = 150 \qquad\qquad V_{\max}^{M} = 4.0\,[\text{MHETase}], \quad K_m^{M} = 50 $$

Crystalline PET is harder to attack than amorphous PET, so velocity is split by phase and the crystalline fraction is damped exponentially by a crystallinity index $x = S_{\text{cryst}}/S$:

$$ v_{\text{amorph}} = v_{\text{PETase}}\cdot\frac{S_a}{S}, \qquad v_{\text{cryst}} = v_{\text{PETase}}\cdot\frac{S_c}{S}\cdot e^{-2.5x} $$

Temperature enters through an Arrhenius term centered on a 30°C optimum, with an extra penalty past 55°C:

$$ f(T) = \exp\!\left[\frac{E_a}{R}\left(\frac{1}{T_{\text{opt}}}-\frac{1}{T}\right)\right] \times \begin{cases} 1 & T \le 55^{\circ}\text{C} \\ e^{-0.3(T-55)} & T > 55^{\circ}\text{C} \end{cases} $$

MHET cleavage splits into TPA and EG at a fixed, mass-conserving ratio (molar composition of MHET): $ \Delta\text{TPA} = 0.73\,v_{\text{MHETase}}, \; \Delta\text{EG} = 0.27\,v_{\text{MHETase}} $. Time is advanced in discrete ticks (an explicit Euler-style update), not continuous integration.

2. Linearized kinetics — and a broken mass balance · Simulation Y · variant

Same skeleton as X, but every saturating term is replaced with a first-order approximation — valid only when $S \ll K_m$, which is not the regime this simulation actually runs in:

$$ v_{\text{PETase}} = k_P\,[\text{PETase}]\cdot S, \qquad v_{\text{MHETase}} = k_M\,[\text{MHETase}] \quad (k_P = 0.015,\; k_M = 0.4) $$

Notice $v_{\text{MHETase}}$ here has no dependence on $[\text{MHET}]$ at all — cleavage proceeds at a constant rate even as the MHET pool empties. Temperature is reduced to a three-step function instead of a continuous curve:

$$ f(T) = \begin{cases} 1.0 & T = 30^{\circ}\text{C} \\ 0.9 & 30 < T \le 50^{\circ}\text{C} \\ 0.5 & T > 50^{\circ}\text{C} \end{cases} \qquad\text{and crystallinity hindrance is removed: } e^{-2.5x} \to 1 $$

Mass balance failure. The stoichiometric split is coded as $ \Delta\text{TPA} = 1.00\,v_{\text{MHETase}}, \; \Delta\text{EG} = 1.00\,v_{\text{MHETase}} $ — both products get the full cleaved amount instead of a 0.73/0.27 partition. Running this model for 50 ticks inflates total system mass from 1000 mg to 1196 mg: $ \sum(\text{PET, MHET, TPA, EG}) $ is not conserved, i.e. $ \tfrac{d}{dt}\big[S + \text{MHET} + \text{TPA} + \text{EG}\big] \neq 0 $ when it should be.

3. Cooperative (Hill) kinetics with a sharper thermal cliff · Simulation Z · variant

Here PETase activity is modeled as cooperative rather than simple Michaelis–Menten, using a Hill coefficient $n = 1.8$ — velocity rises more sigmoidally with substrate concentration:

$$ v_{\text{PETase}} = \frac{V_{\max}^{P}\,S^{\,n}}{\big(K_m^{P}\big)^{n} + S^{\,n}}, \qquad n = 1.8,\;\; V_{\max}^{P} = 3.5\,[\text{PETase}],\;\; K_m^{P} = 200 $$

MHETase kinetics stay Michaelis–Menten (identical to X). What changes most is thermal behavior: instead of X's gentle penalty above 55°C, Z applies a much steeper denaturation cliff starting ten degrees earlier:

$$ f(T) = \underbrace{\exp\!\left[\frac{E_a}{R}\left(\frac{1}{T_{\text{opt}}}-\frac{1}{T}\right)\right]}_{\text{Arrhenius term, same as X}} \times \begin{cases} 1 & T \le 45^{\circ}\text{C} \\ e^{-0.8(T-45)} & T > 45^{\circ}\text{C} \end{cases} $$

Crystallinity hindrance is also linearized rather than exponential: $ e^{-2.5x} \to 1 - 0.95x $. Stoichiometry reverts to the correct 0.73/0.27 TPA/EG split, so unlike Y, Z conserves mass.

4. Continuous-time ODE integration · alternate_simulation.html

Rather than stepping forward in discrete ticks, this model expresses the same PET→MHET→TPA pathway as a coupled system of ordinary differential equations and integrates it continuously with an explicit Runge–Kutta solver (scipy.integrate.solve_ivp, RK45):

$$ \frac{d[\text{PET}]}{dt} = -\,0.15\,k_1\,\frac{[\text{PET}]}{[\text{PET}]+20} $$ $$ \frac{d[\text{MHET}]}{dt} = 0.15\,k_1\,\frac{[\text{PET}]}{[\text{PET}]+20} \;-\; 0.25\,k_2\,\frac{[\text{MHET}]}{[\text{MHET}]+10} $$ $$ \frac{d[\text{TPA}]}{dt} = 0.25\,k_2\,\frac{[\text{MHET}]}{[\text{MHET}]+10} $$

Here $k_1, k_2$ (PETase/MHETase expression levels) are the free parameters a user drags on sliders; the interface also perturbs each by a small $\delta$ and re-integrates to show a live finite-difference sensitivity, $ \partial Y/\partial k_i \approx \big[Y(k_i+\delta)-Y(k_i)\big]/\delta $.

5. Gene-circuit-coupled degradation · petase_circuit.html

This is the only model where enzyme concentration is not a fixed input — it is itself the output of an upstream transcription/translation cascade, driven by promoter strength $p$, plasmid copy number $c$, and cell density $d$:

$$ \Delta\text{mRNA}_i = 0.002\,p\,c\,d \cdot w_i, \qquad w_1 = 1,\; w_2 = 0.8 $$ $$ [\text{PETase}] \mathrel{+}= 0.2\,\text{mRNA}_1, \qquad [\text{MHETase}] \mathrel{+}= 0.2\,\text{mRNA}_2, \qquad \text{mRNA}_i \mathrel{*}= 0.85 $$

PET breakdown itself is then zero-order in substrate and first-order only in enzyme concentration — there is no $K_m$ term at all, unlike every other model here:

$$ \frac{d[\text{PET}]}{dt} = -\,0.03\,[\text{PETase}], \qquad \frac{d[\text{MHET}]}{dt} = 0.03\,[\text{PETase}] - 0.04\,[\text{MHETase}] $$

6. Molar-mass stoichiometric pathway · intermediate.html (v7) & 2033_intermediate.html (v5)

The most detailed model in the set: it tracks an explicit intermediate (BHET) between PET and MHET, converts every flux through real molar masses, and feeds temperature and pH back into the reaction rates rather than treating them as fixed constants:

$$ f_1 = \frac{[\text{PET}]}{192.17}\cdot 0.16 \cdot \phi(\text{pH}) \cdot \theta(T), \qquad f_2, f_3 \;\text{analogous for BHET$\to$MHET, MHET$\to$TPA} $$ $$ \Delta[\text{PET}] = -f_1 M_{\text{PET}}, \quad \Delta[\text{BHET}] = (f_1-f_2)M_{\text{BHET}}, \quad \Delta[\text{MHET}] = (f_2-f_3)M_{\text{MHET}} $$ $$ \Delta[\text{TPA}] = f_3 M_{\text{TPA}}, \qquad \Delta[\text{EG}] = (f_2+f_3)M_{\text{EG}} $$

Molar masses (g/mol): PET 192.17, BHET 254.24, MHET 210.18, TPA 166.13, EG 62.07.

Two feedback loops make this model distinctive: reaction extent raises temperature ($\Delta T \mathrel{+}= 1.5f_1$, an exothermic-heat proxy), and acid byproduct lowers pH, which in turn slows $\phi(\text{pH})$ — a self-limiting reaction absent from every other model above. The v5 file (2033_intermediate.html) adds one further wrinkle: a crystallinity step-modifier, $ \text{crystMod} = 0.3 $ once $[\text{PET}] < 0.1\times\text{PET}_0$, representing a recalcitrant crystalline core that resists the final stage of digestion.

At a glance

Model	File	Time	Rate law	Mass-conserving?	Distinctive feature
X	`SimulationX_22May2026.html`	discrete	Michaelis–Menten	yes	baseline / reference case
Y	`SimulationY_22May2026.html`	discrete	linear ($S \ll K_m$ approx.)	no	MHET term ignores pool size; 1:1 duplication bug
Z	`SimulationZ_22May2026.html`	discrete	Hill, $n=1.8$	yes	cooperative binding + steep thermal cliff
ODE	`alternate_simulation.html`	continuous	saturable (RK45-integrated)	yes	built-in parameter sensitivity analysis
Circuit	`petase_circuit.html`	discrete	zero-order in substrate	yes	enzyme level is a dynamic output, not an input
Stoichiometric	`intermediate.html` (v7) `2033_intermediate.html` (v5)	discrete	molar-mass flux	yes	explicit BHET intermediate; pH/temperature feedback

In short: X–Z form a matched trio testing how one modeling choice (saturation law, thermal response, crystallinity penalty) changes outcomes on an otherwise identical scaffold. The ODE, circuit, and stoichiometric models each change the scaffold itself — continuous vs. discrete time, fixed vs. dynamically-produced enzyme, and lumped vs. explicit intermediates, respectively. Source simulations: SimulationX/Y/Z (24 May 2026), alternate_simulation.html (13 May 2026), petase_circuit.html & intermediate.html/2033_intermediate.html (12 Apr 2026).

Jett's Version: A model — built to be wrong, usefully.

The section below is a separate, independently-written draft, produced by a team member outside the main documentation process. Kept here for reference and comparison; not yet fact-checked by team leadership.

Every modelled number elsewhere on this wiki comes from one place: a small kinetic simulation of PET → MHET → TPA + EG. The model is intentionally simple, on the reasoning that every additional parameter is a degree of freedom that can't be constrained without more wet-lab data.

The equations

Two coupled Michaelis–Menten layers — PETase (surface) and MHETase (cytoplasmic) — with a substrate-saturation term accounting for the solid PET surface, treated as quasi-constant on the timescale of the experiment.

Parameters

Symbol	Value	Source
k_cat,P	0.04 s⁻¹	Tournier 2020 · WT PETase
K_M,P	132 µM	Austin 2018
k_cat,M	0.6 s⁻¹	Knott 2020 · MHETase
K_M,M	17 µM	Knott 2020 · MHETase
[E_P] surface	2 µM · effective	Estimated in-house

Sensitivity

The dominant parameter is k_cat,P: a 2× change moves the predicted 14-day conversion from 87% to somewhere between 56% and 99%. K_M is comparatively unimportant within an order of magnitude. The model would not survive k_cat,P being off by 10×.

Known wrongness

Three places this model is known to be wrong, left uncorrected because current bench data isn't precise enough to constrain the fix: PET surface area is treated as constant when it actually decreases as the polymer degrades; there's no mass-transfer term for the broth around the cell; and product inhibition by TPA on MHETase, which has been reported elsewhere, is ignored.

Continue to Jett's Version of Software → · Back to Jett's Version of Safety