Model representation

We first represented the different microorganisms and molecular species of interest and the associated processes using the Systems Biology Graphical Notation (SBGN) standard (Figure 1) (Le Novère et al., 2009). For more details on the meaning of these symbols, see this link.

This representation provided a clear overview of the envisioned process, making it easier to identify which components needed to be modeled. In this framework, PFOS is degraded by an uncharacterized pathway in Labrys portucalensis, generating inhibitory by-products (short-chain PFAS, SC-PFAS) and supporting growth (Wijayahena et al., 2025). SC-PFAS are then degraded by our optimized dehalogenase in Pseudomonas putida, which also produces inhibitory by-products and substrates for growth (Farajollahi et al., 2024). Having established what to model, the next step was to choose how to model it.

A system of ordinary differential equations (ODEs)

To describe the dynamics of the system, we implemented a system of ordinary differential equations (ODEs) to represent the concentrations of substrates, products, and microorganisms over time. ODE-based modeling allows us to simulate time-course dynamics, track the evolution of each species, and uncover non-intuitive behaviors of the system. This model forms an efficient basis to drive laboratory experiments and optimize rationally the entire process.

We implemented the ODEs system in Copasi (version 4.45 build 298), an open access modeling software. Its user-friendly interface allowed rapid implementation and testing of the model. By entering parameters and reaction equations, and selecting appropriate rate laws, Copasi automatically generated the system of ODEs.

Choosing rate laws

The first version of our model (PFAway-model_V1) was based directly on our representation (Figure 1). It included 23 parameters and 6 reactions. Units were standardized as hours (h) for time, liters (L) for volumes, and grams (g) and milimoles (mmol) for amounts of cells and molecules. For each reaction, we identified the most appropriate rate laws, from which we established the system of ODEs.

Modeling species dynamics:

Figure 2: Global reactions occurring during the PFAway process.

In our system, L. portucalensis degrades PFOS into shorter chain PFAS (primarily trifluoroacetate, TFA, and perfluoropropionic acid, PFPrA) through unknown metabolic pathways. These Short Chain (SC) PFAS are subsequently degraded by the optimized dehalogenase in P. putida, generating fluoride ions, sulfonic acid, and organic acids in defined stoichiometric ratios (Figure 1 & 2) (Wijayahena et al., 2025). Because the exact nature of these organic acids remains unclear (see Design page), we assumed trifluoroacetate (TFA) defluorination results in acetate production. These transformations were modeled using the Michaelis-Menten equation, where degradation of substrates and apparition of products depend on the maximum enzymatic rate (V_max) and substrate affinity (K_m):

- For PFOS degradation, the concentration of L. portucalensis is considered since more bacteria will accelerate degradation:

Here and later, [Lp] represents L. portucalensis concentration, V_maxLp designates the maximal specific degradation rate of PFOS by L. portucalensis and K_m the affinity of the bacteria for PFOS.

- SC PFAS degradation by the dehalogenase in P. putida was modeled following the same reasoning:

Here and later, [Pp] denotes P. putida concentration, V_maxDeHa symbolizes the maximal specific degradation rate of SC PFAS by the dehalogenase and K_m the affinity of the enzyme for SC PFAS.

- Sulfonic acid is produced during the degradation of PFOS with a one to one ratio (Figure 2):

- Similarly, for fluoride ions:

- Organic acids are produced alongside fluoride ions in two conversion processes by the two bacteria (Figure 2). They are also consumed by each bacteria to support growth, resulting in the following ODE:

Here, qOA L.p and qOA P.p represent the specific uptake rate of organic acids by L. portucalensis and P. putida, respectively. These terms were calculated using the following formula, where µ represents the specific growth rate and Y the growth yield:

Modeling growth and inhibition:

Organic acids produced during the degradation of PFOS serve as growth substrates for both microorganisms. We modeled growth using the Monod equation (Monod, 1949) which allows the calculation of the specific growth rate of an organism depending on its maximum specific growth rate (µ_max), its substrate affinity (K_S) and the substrate concentration ([S]):

However, PFOS, SC PFAS, and fluoride ions also inhibit growth at high concentration. We modeled these inhibitions using a hyperbolic inhibition equation where I is the inhibitor and K_i the corresponding inhibition constant:

Combining substrate dependency with inhibition yields for all species to calculate the specific growth rate (µ):

Finally, microbial biomass growth was modeled as:

PFAway-model_V1 contains a total of 7 species (two microorganisms and 5 metabolites) and 6 reactions, with a total of 23 parameters.

Testing model behavior

With our ODEs system constructed, we next evaluated whether it behaved as expected. For this initial test, we assigned arbitrary values to each parameter and ran the first simulation. The simulated dynamics is shown in Figure 3.

A first simulation was done with 10 mM of PFOS (Figure 3A). As expected for our system, the model predicted a steep decrease in PFOS concentration, accompanied by increases in fluoride ions, organic acids, and sulfonic acids. SC PFAS concentrations rose initially but then decreased due to degradation by the dehalogenase. These results confirmed that PFAS degradation may function as intended.

However, the microorganisms did not seem to grow (their concentrations were stable), and organic acids were not consumed. To understand these predictions, we performed a second simulation with 100 mM organic acid (to promote strong growth) and no PFOS (to avoid inhibition) (Figure 3B). In this case, changes in both microbial and organic acid concentrations were much clearer: with abundant substrate and no inhibition, bacteria consumed the organic acids to fuel their growth. This demonstrated that microbial growth and organic acid consumption may also be observed.

Estimating K_i

From our experiments, we obtained µ_max values for both bacteria under different inhibitor concentrations (Figure 3A and B)(see Results page). We focused particularly on fluoride ions (abundantly produced during our process), PFPrA, and TFA (both possible products of PFOS degradation (Wijayahena et al., 2025)). Our goal was to estimate the K_i values characterizing the inhibitory effects of these compounds on microbial growth.

We used the parameter estimation task of Copasi to estimate µ_max and K_i of the hyperbolic inhibition equation from our experimental data, using the Levenberg - Marquardt optimization method.

The hyperbolic inhibition equation provided a good fit for NaF inhibition (Figure 4A), with K_i estimates of 29.9 ± 6.8 mM for P. putida WT and 68.1 ± 19.8 mM for L. portucalensis. However, the fit was poor for PFPrA and TFA (Figure 4B). We therefore needed to change our way of modeling SC PFAS inhibition.

We tested the Hill equation, commonly used for modeling inhibition and toxicity at the population level (Bounias, 1989). For NaF, both equations fit comparably (Figure 4A), but comparison of residuals (which represent the difference between simulated and experimental data) revealed lower residuals for the hyperbolic model (Figure 4C), so we retained it for NaF inhibition. For PFPrA and TFA, however, the Hill equation fits much better, reducing residuals tenfold compared with the hyperbolic model (Figure 4D).

Using the Hill equation, we estimated K_i values for P. putida WT as 36.1 ± 2.2 mM (PFPrA) and 35.8 ± 2.3 mM (TFA). For L. portucalensis, the Hill equation slightly improved SDs, giving K_i values of 30.5 ± 6.2 mM (PFPrA) and 39.6 ± 10.5 mM (TFA).

Thus, the close proximity between the two values and their overlapping SD encouraged us to make no difference in the model between these two molecules and simply refer to them as SC PFAS.

This estimation process also enabled comparison of the engineered P. putida pSEVA428-fluC strain with the WT strain (Figure 5). Using NaF inhibition data, COPASI estimated a K_i of 57.4 ± 10.3 mM for fluC, nearly double that of WT (29.9 ± 6.8 mM), and the difference was statistically significant (p = 0.018, two-tailed unpaired t-test).

These findings highlighted that the hyperbolic inhibition equation was insufficient for modeling SC PFAS inhibition, necessitating modifications to use the Hill equation in the model.

Modifying the model

As described earlier, bacterial growth and inhibition were initially modeled using the Monod equation combined with the hyperbolic inhibition equation. While this adequately described NaF inhibition, SC PFAS inhibition was better captured with the Hill equation:

We therefore modified inhibition modeling for SC PFAS and PFOS:

This modification produced the second version of our model, PFAway-model_V2, which included 27 parameters and more accurately accounted for PFAS inhibition. For PFOS, we lacked sufficient data to estimate K_i values and therefore assumed similar behavior to SC PFAS due to structural similarities.

After implementing such crucial modifications, we verified that the model still behaved as expected.

Testing the updated model

We repeated our first simulations (Figure 3), this time using experimental values rather than guesses (Figure 6). For P. putida WT (Figure 6A), PFOS disappeared from the medium while fluoride ions and sulfonic acids accumulated. SC PFAS was generated and degraded. Organic acids appeared only briefly before being rapidly consumed, while microbial populations grew at different rates, dissociating their growth curves (unlike in Figure 3A).

However, these simulations relied on arbitrary kinetic parameters for the PFOS degradation rate for PFOS degradation. To demonstrate the feasibility of our process, more realistic values were required.

Demonstrating feasibility

Using literature-based kinetic parameters (Farajollahi et al., 2024; Wijayahena et al., 2025), we simulated PFAS degradation under more realistic conditions (Figure 7). At real environmental concentrations (see Human Practices page) (Figure 7A), degradation of 90% of total PFAS took over 3500 h. At 1000× concentrated conditions (Figure 7B), degradation was similar, suggesting the fact that initial PFOS concentration had limited impact on degradation time, underscoring the robustness of the process.

These results demonstrate feasibility under both environmentally-observed and concentrated PFOS concentrations, but they also highlight the need for further optimization since a degradation time of 3500 h (equivalent to 146 days) is impractically long.

Optimizing initial microorganisms concentration

L. portucalensis and P. putida are both involved in PFAS degradation. A higher bacterial load increases the overall degradation potential. Therefore, increasing the inoculum size could accelerate the process. We first scanned for the optimal concentration range of L. portucalensis, as it is the first organism to interact with PFAS (between 1 g/L and 10 g/L Figure 8A).

The scan revealed that PFAS degradation time decreases according to an inverse exponential relationship with bacterial concentration. Increasing the L. portucalensis concentration from 1 g/L to 3.7 g/L reduced the degradation time by 93 hours, from 6469 h to 6376 h. Beyond this point, further increases in concentration resulted in only marginal improvements, indicating limited benefit above 3.7 g/L.

We then performed a similar scan for P. putida (Figure 8B). Here, the effect was more pronounced. Increasing the concentration from 1 g/L to 4.6 g/L reduced the predicted degradation time from 6376 h to 1413 h, a reduction of 4963 h. Beyond 4.6 g/L, the gains became negligible, following the same inverse exponential trend.

These investigations showed that optimizing microorganism concentrations can drastically reduce degradation time. We determined that the minimum effective concentrations are 3.7 g/L for L. portucalensis and 4.6 g/L for P. putida. Using the OD-to-dry weight correlation factor for P. putida (Vogeleer et al., 2024), we converted these values into optical density units: OD₆₀₀ = 6.49 for P. putida and OD₆₀₀ = 8.07 for L. portucalensis. These OD values can be used in entrepreneurship applications to estimate the required quantity of immobilized cells (see Entrepreneurship page).

Reducing degradation time to 1413 h represents a major improvement compared to the initial 6469 h required. However, further optimization remains possible.

Optimizing dehalogenase

One of the team’s main goals is to improve the activity of a dehalogenase so that it can more efficiently degrade poly-fluorinated substrates such as TFA when expressed in P. putida. To achieve this, we planned to use orthogonal replication (see Design page). However, before initiating experiments, it was essential to clearly define the kinetic parameter targets. To guide this objective, we performed model-based evaluation of the effects of independently improving the enzyme’s K_m and V_max using the parameter scan task of Copasi (with K_m ranged between 1 and 30 mM, and V_max between 0.01 and 30 mmol/h).

The K_m scan revealed a proportional decrease in degradation time as K_m decreased (Figure 9A). For every 1 mM reduction in K_m, the degradation time decreased by approximately 48 h (± 1.85). Assuming that the K_m for difluoroacetate (DFA) is similar to that for TFA, reducing the enzyme’s K_m from 27.6 mM (Farajollahi et al., 2024) to 13.775 mM would halve the degradation time from 1413 h to 725 h.

Turning to V_max, the scan showed an inverse exponential relationship (Figure 9B). Literature indicates that the dehalogenase has a very low V_max on TFA (Farajollahi et al., 2024), which we estimated at 0.01 mmol/h. Doubling this value would also reduce the degradation time by half, consistent with the K_m results.

Simultaneously doubling both parameters would allow PFAS degradation in under 382 h. This need for significant improvement strongly justifies the use of orthogonal replication. Indeed, this technique has previously been reported to enhance GFP fluorescence by up to 1000-fold (Tian et al., 2024). Although the initial values considered here may not fully capture the enzyme’s true interaction with TFA, it is likely that a greater-than-twofold increase in both affinity and activity will be required. Employing such a powerful engineering method is therefore well justified.

Based on these analyses, a K_m of 13.8 mM and a V_max of 0.02 mmol/h represent the minimum performance goals our team should aim for in order to obtain a potent dehalogenase capable of degrading SC PFAS. Importantly, higher V_max values could compensate for higher K_m values, and vice versa. Achieving these improved parameters would enable faster degradation; however, one additional optimization step remained for our process.

Optimizing initial PFOS concentration

To optimize an enzymatic process, one can either modulate the enzyme itself or adjust the substrate concentration. With this in mind, we investigated the optimal PFOS concentration to use in our system. Previous simulations showed that increasing the initial PFOS concentration did not significantly affect degradation time (Figure 7A and B). However, as we had only tested two concentrations, we lacked information about the maximum concentration that could be used without slowing the process. To address this, we performed a final parameter scan in Copasi (with PFOS concentration between 1.04 × 10^-6 and 100 mM) (Figure 10).

The scan revealed that increasing PFOS from 1.04 × 10^-6 mM to 1.23 × 10^-2 mM resulted in only a 20 h increase in degradation time (from 380 h to 400 h). This small delay would be acceptable if it allowed us to decontaminate a larger quantity of PFAS in a single run. Beyond this concentration, however, degradation time increased sharply, reaching 800 h at 0.1 mM PFOS.

These findings suggest that concentrating samples up to 10 000-fold near the laboratory could still be feasible without substantially increasing degradation time (see Figure 7A). This also opens the possibility of targeting highly contaminated areas, such as specific sites identified on European contamination maps (see Human Practices page).

Taken together, these three optimization strategies allowed us to identify the most effective parameter ranges for our process. Compared to the five and a half months initially required, our optimized system is now predicted to degrade 90% of total PFAS in just 16 days. We selected these three optimization axes because each intuitively influences degradation time, though we recognize that this choice remains somewhat biased. Therefore, having optimized these intuitively key parameters, we performed a global sensitivity analysis to identify the next optimization steps.

Sensitivity analysis

To complement targeted scans and provide a global and quantitative view on the control exerted by each parameter, we conducted a sensitivity analysis on all 27 parameters, quantifying their effect on time to degrade 90% of total PFAS. For this purpose, we used the Sensitivity analysis task of Copasi. Copasi returns the control coefficient (C) exerted by each parameter (p) on a metric of interest, which is calculated as follow:

In our case, the metric of interest is the time required to degrade 90% of the total PFAS in the medium (t).

Each coefficient quantifies the relative change in the degradation time t in response to a relative change δ of the parameter p. If the degradation time is not impacted by the parameter p, the corresponding coefficient will be zero. A positive (negative) value indicates that an increase in p increases (reduces) the degradation time. A coefficient of 1 indicates that a change in x % of the parameter results in a change of x % of the degradation time.

This analysis therefore provides a more global and quantitative understanding to further optimize the process.

Table 1: Results of the sensibility analysis. Ratio values < 0.01 are represented in the drop down below.

Parameter	Ki SC_PFAS	Ki PFOS	[Lp]	Vmax PFOS	[Pp]	Vmax SC_PFAS
Control coefficient	0.89	0.1	-0.11	-0.11	-0.89	-0.89

In our context, the key metric used was the time required to degrade 90% of the total PFAS in the medium. Ideally, this metric should decrease. The positive control observed for the SC PFAS K_m (Table 1) corroborates our earlier conclusion that lowering this value is essential. Similarly, microorganism concentrations and the SC PFAS V_max were confirmed to have a significant impact on the process, with higher values leading to shorter degradation times (Table 1).

The only two parameters with a notable impact that we did not explore in detail were the PFOS K_m and V_max. However, optimizing these remains a dead end for now, as the PFAS degradation pathway in L. portucalensis has not yet been characterized.

Overall, this sensitivity analysis confirmed that we have identified and optimized all currently alterable parameters of our system, enabling us to address some of the team’s most important questions regarding the efficiency of our process.