Introduction

Although ProbiEase can provide several recommended strains, the growth of these strains within the human body remains unknown, especially for non-professionals. Worse still, determining the group-sensing behaviour of recommended probiotics necessitates comprehensive wet-lab testing to predict metabolic burden, cross-feeding cascade effects, and environmental dependency risks. Therefore, we introduce a constraint-based modelling approach, which theoretically offers economical, transparent and reproducible decision support.

Motivation

Intuitively, we wish to investigate:

1）What are the normal growth metabolites of the probiotics recommended by ProbioEase, and whether these pose any harm to the human body;

2）Whether the probiotics recommended by ProbiEase, when taken concurrently, might generate harmful substances through interactions within the human body, and whether their quorum sensing processes could be detrimental to human health.

3）Does the simultaneous use of multiple strains necessarily yield superior results compared to a single strain?

To verify the reliability, safety, and user-friendliness of the recommended strains, we introduce a two-tier metabolic modeling pipeline-static FBA^1-6and dynamic dFBA^7-11to ease the three concerns mentioned above.

• For the first concerns: Static FBA simulates the growth of individual strains under reproducible medium conditions to screen for the exogenous metabolite profiles of single strains, whilst flagging potentially harmful or metabolite of interest.
• For the second concerns: Dynamic dFBA couples extracellular kinetics and growth to quantify co-culture competition, cross-feeding, and metabolite peaks that may be unfavorable for human use, thereby addressing the second concern.
• For the third concerns: By comparing the consortium's metabolic profile to the individual strains' outputs, this integrated approach allows us to identify adverse emergent effects and provides a data-driven rationale for approving or rejecting specific probiotic combinations, thereby addressing the second concern.

Through this comprehensive and reproducible modeling framework, our dry lab delivers a highly refined and evidence-based list of probiotic candidates to the wet lab, significantly reducing experimental resources and time.

Model Development

Introduction to (d)FBA

Flux Balance Analysis (FBA) is a mathematical method for simulating metabolism in cells or unicellular organisms, such as E. coli or yeast. It relies on genome-scale metabolic network reconstructions, which describe all known biochemical reactions in an organism and the genes encoding them. FBA optimizes metabolic flux distributions under steady-state assumptions to predict growth rates or specific metabolite production rates, without requiring detailed enzyme kinetic parameters.

At its core, FBA constructs a stoichiometric matrix (\mathbf{S} matrix), where rows represent metabolites and columns represent reactions. The system at steady state satisfies the mass balance equation S \cdot v = 0, where v is the flux vector. By adding constraints (e.g. reaction bounds) and an objective function (e.g. maximizing biomass growth), FBA computes an optimal flux distribution using linear programming. This makes it widely applicable in bioprocess engineering, such as optimizing microbial fermentation for higher yields of ethanol or succinic acid, or identifying drug targets in cancer and pathogens.

Figure 1. Schematic overview of FBA architecture showing the stoichiometric matrix with metabolite-reaction relationships, flux constraints (lower and upper bounds), and optimization space. The bipartite network representation (left) illustrates internal reactions, biomass formation, and exchange reactions connecting metabolites (m₁...mₘ). The feasible solution space (bottom left) demonstrates linear programming optimization within constraint boundaries (lb ≤ v ≤ ub), with the objective function maximizing biomass flux (v). The operational framework (right) maps uptake reactions (lb ≤ 0, e.g., O₂, glucose), zero-flux boundaries for closed reactions (ub = 0, exch), and secretion pathways (lb ≤ v, exch ≤ ub) under defined medium constraints.

To further validate the combined use of multiple strains, we introduced Dynamic Flux Balance Analysis (dFBA). dFBA is an extension of FBA that enables simulation of metabolic networks in dynamic environments. It couples FBA's steady-state optimization with kinetic models (e.g., ordinary differential equations, ODEs) to predict time-dependent changes in metabolite concentrations, cell growth, and environmental influences.

dFBA operates iteratively:

At each time step, FBA constraints are adjusted based on current extracellular concentrations (e.g. nutrients), instantaneous flux distributions are calculated, and metabolite and biomass levels are updated. This allows dFBA to handle nutrient competition, cross-feeding, and population dynamics, making it particularly suitable for microbial community simulations. For instance, in dual-species co-cultures, dFBA can predict how nutrient rivalry affects community composition.

Implemented via tools like COBRApy^12-15, dFBA extends to genome-scale models, enabling the simulation of real-world scenarios in engineered systems.

Figure 2. Two-tier modeling workflow for probiotic strain validation in nasal microenvironment. Static FBA screens individual E. coli Nissle 1917 and L. plantarum WCFS1 strains for harmful metabolite production and therapeutic compound synthesis capacity. Dynamic dFBA extends analysis to nasal co-culture conditions, incorporating nutrient competition, cross-feeding dynamics, and pH/organic acid inhibition effects through coupled ODEs. Decision outcomes classify strain combinations as harmful (red X), safe co-existence (green checkmark), or enhanced therapeutic production (green checkmark).

Implement detail

Candidate List

In conjunction with the goal of our team, we get a candidate list from ProbiEase by asking "Could you provide me with some probiotics for treating Parkinson's disease?" as following:

After retrieval in the "Strain Card Display" and "Knowledge Graph Visualization" , we employ E. coli Nissle 1917 and Lactobacillus plantarum WCFS1 for the following modelling.

Concurrently, FBA analysis revealed that Enterococcus faecium possesses the gene for tyrosine decarboxylase which can prematurely metabolize L-DOPA, the primary medication for Parkinson's disease, thereby reducing its therapeutic efficacy. Due to this significant risk of negative drug-microbe interaction, it was excluded from our final consortium.

Our pipeline is implemented in Python using the COBRApy library.

Detail for FBA

Our objectives of this module is to predict its full range of secreted metabolites under simulated gut conditions. The goal is to create a "safety passport" for each strain, flagging any known harmful compounds (e.g., excessive organic acids, ammonia) and establishing a baseline metabolic footprint. The relevant results may be compared with the multi-strain formulations of dFBA presented subsequently, thereby providing a basis for validating single-strain administration. The FBA technology is now well-established, and we need only follow these two steps:

Step 1: Model Initialization and Setup

Load Models: Load the genome-scale metabolic models (in SBML format) for each ProbioEase-recommended strains in the community (e.g., E. coli Nissle 1917 and Lactobacillus plantarum WCFS1).

Identify Objective Function: For each model, identify the biomass reaction, which represents cell growth. This reaction is set as the objective function for FBA optimization, aiming to maximize its flux .

Map Exchange Reactions: Identify and map the exchange reactions that are common to both models. These reactions simulate the transport of metabolites between the species and the shared environment (e.g., uptake of glucose, secretion of lactate) and are crucial for modeling nutrient competition and cross-feeding.

In our experiment, we primarily modelled E. coli Nissle 1917 and Lactobacillus plantarum WCFS1 to simulate their growth processes and predict their metabolic products.

• For E. coli Nissle 1917, we employed iDK1463¹⁶, an artificially refined, high-quality GEM validated by MEMOTE, comprising 1463 genes and 2984 reactions.
• For Lactobacillus plantarum WCFS1, we employed the genome-scale model provided by Bas Teusink et al.¹⁷, which encompasses 721 genes, 643 reactions, and 531 metabolites. This model emphasises characteristics suited to nutrient-rich environments and lactic acid production, making it a representative lactic acid bacterium in co-culture scenarios.

To match the objective of our wet lab, we modify the SBML to reconstruct the strain model. Specifically, we engineered the E. coli iDK1463 genome-scale model to produce L-DOPA by introducing the HpaBC hydroxylase enzyme, which catalyzes the conversion of L-tyrosine to L-DOPA (3,4-dihydroxy-L-phenylalanine) from "Metabolic Route", "Metabolite IDs" and "Transport & Exchange".

Metabolic Route

• Glucose → PEP + E4P (via glycolysis and pentose phosphate pathway)
• PEP + E4P → Shikimate → Chorismate (endogenous shikimate pathway)
• Chorismate → L-Tyrosine (via TyrA, TyrB enzymes)
• L-Tyrosine → L-DOPA (via heterologous HpaBC)

And the key reaction is:

Metabolite IDs (BiGG nomenclature):

• Substrates: tyr__L_c, o2_c, nadph_c, h_c
• Products: ldopa_c, nadp_c, h2o_c

Transport & Exchange:

• Transport: ldopa_c → ldopa_e
• Exchange: EX_ldopa_e (0--1000 mmol/gDW/h)

Our FBA objective can be formally define as followed:

where v_\mathrm{biomass,j} denotes the biomass reaction flux, with \mu_j representing growth rate. The equation S \cdot v = 0 represents the manifestation of the law of conservation of mass within metabolic networks. \mathbf{l}(t) and \mathbf{u}(t) denotes the lower bound and upper bound of the absorption reaction respectively and these two boundaries, in the dFBA settings, are dynamically adjusted based on environmental factors and other variables.

Step 2: Define the Medium

Define a constant environment by setting the bounds of the exchange reactions.

In our experiment, to better simulate the human environment, the relevant parameters of the culture medium we have established are as follows:

Step 3: Solve the FBA Problem

Use the model.optimize() method to solve the linear programming problem. This single function call finds the optimal flux distribution that maximizes the objective (growth).

By conducting independent FBA modelling on each recommended strain, we can determine their respective growth patterns and metabolic products within the human body.

Figure 3. (A) Time-course simulation of E. coli biomass accumulation showing dFBA predictions (blue line) calibrated against experimental measurements (red stars, n = 3 biological replicates). (B) Comparative flux distribution analysis at exponential (8.5 h, cyan bars) versus stationary phase (24.5 h, magenta bars) across core metabolic modules (glycolysis, TCA cycle, amino acid biosynthesis, target product, maintenance). (C) Temporal profile of L-DOPA biosynthesis demonstrating peak production at 8.5 h (36.74 ± 4.13 μg/mL) with subsequent degradation kinetics. Shaded region represents 95% confidence interval of model predictions. (D) Quantitative assessment of dFBA accuracy across three output variables: overall fit (R² = 0.91), biomass prediction (R² = 0.95), glutathione dynamics (R² = 0.92), and L-DOPA kinetics (R² = 0.87), all exceeding the 'good fit threshold'

Detail for dFBA

Despite the theoretical results shown above, there still be some under-research: nutrient competition dynamics, harmful metabolite accumulation over time (e.g., pH drop), and undesirable shifts in community composition that would not be apparent from single-strain analysis. Hence, extend FBA module into a dynamic one is essential and indispensable.

Fundamentally, Flux Balance Analysis (FBA) provides a static "snapshot" of a metabolic network's optimal state under a single, unchanging environmental condition. Dynamic FBA (dFBA) extends this by connecting a series of these snapshots over time, creating a dynamic "movie" of how a microbial community and its environment evolve together. And there are three shifting main dimensions from FBA to dFBA.

1. Time

   FBA operates at a single, conceptual point in time. It answers the question: "Given this constant supply of nutrients, what is the maximum possible growth rate?" while dFBA is a time-dependent simulation. The system is modeled over a defined period (e.g., 0 to 24 hours), and all variables (biomass, metabolite concentrations) are calculated at discrete time steps.

2. Dynamic Nutrient Constraints (Kinetics)

   In FBA's assumption, nutrient availability is defined by fixed, constant upper bounds on uptake fluxes (e.g., glucose_uptake <= 10 mmol/gDW/h) : the environment does not change. However, it often takes that the rate of nutrient uptake is no longer fixed but dynamically determined by the current concentration of nutrients in the external environment. This relationship is typically modelled using the Michaelis-Menten equation^18-19: the uptake rate calculated at each time point becomes a new constraint for the FBA problem at that moment.

   Specifically, the formula for the maximum uptake velocity (v_\mathrm{uptake}) of a substrate S_j by species i is:

   v_{uptake,\mathrm{max}}(t)=V_{\mathrm{max}}\cdot\dfrac{C(t)}{K_m + C(t)}

   Uptake Velocity Formula

   where v_{uptake,\mathrm{max}} is the maximum uptake rate and K_m is the substrate concentration at which the uptake rate is half of V_\mathrm{max}.

   Traditional FBA models assume optimal growth conditions but neglect metabolite auto-inhibition effects. In gut microecology, LAB produce substantial lactic acid, causing local pH reduction. According to the Henderson-Hasselbalch equation, undissociated lactic acid concentration significantly increases under low pH conditions, exerting direct cytotoxic effects on cell membranes^20-22. Furthermore, when studying multi-strain probiotic formulations, differences in lactic acid production capacity among strains may lead to over-inhibition of certain strains, affecting microbial balance.

   Based on the concerns above, we introduce the HLac inhibition model^20-22 to capture the inhibition impact of the lactic acid and add it in the Uptake Velocity Formula aboved:

   v_{uptake,\mathrm{max}}(t)=V_{\mathrm{max}}\cdot\frac{C(t)}{K_m + C(t)}\cdot\frac{1}{1+\frac{[HLac]}{K_i^{HLac}}}

   HLac Inhibition Model

   where the undissociated lactic acid concentration can be calculated :

   \begin{aligned} \\{[HLac]} &= f_{HLac} \times [Lactate_{total}] \\ f_{HLac} &= \frac{[HLac]}{[HLac]+[Lac^-]} = \frac{1}{1+10^{(pH - \mathrm{p}K_a)}} \end{aligned}

   Lactic Acid Formula

   and the pH is obtained by the Henderson-Hasselbalch^23-24:

   \mathrm{pH}=\mathrm{p}K_a+\log_{10}\left(\dfrac{[Lac^-]}{[HLac]}\right)

   Undissociated Lactic Acid Calculation

   with the K_a and K_i^{HLac} is defined as a hyper-parameter.

3. System of Ordinary Differential Equations (ODEs)

   Since FBA is a static analysis, there are no differential equations describing changes over time. However, dFBA is a modelling approach for multi-strain dynamic analysis, thus requiring a set of ordinary differential equations describing how state variables (biomass and metabolite concentrations) evolve over time^25-26.

   As mentioned above, the dFBA model operate iteratively FBA to obtain the rates of change, then substitutes these rates into the ODEs to compute the system state at the next time point. Therefore, to mathematically describe the dynamic behavior of our system, we formulated a mechanistic model based on the law of mass action. This approach allows us to capture the temporal changes in component concentrations and predict system behavior under various conditions

   We constructed a system of ordinary differential equations (ODEs) to represent the key biochemical processes, where each equation describes the rate of change of a specific molecular species over time.

   The two main types of equations are:

   a) Biomass Growth Equation:

   The change in a species' biomass X_i is its current biomass multiplied by the specific growth rate \mu_i calculated by FBA at that moment.

   \frac{dX_j}{dt}=\begin{cases} \mu_j(t)\,X_j(t) & \text{(batch culture)}\\ \big(\mu_j(t)-D\big)\,X_j(t) & \text{(chemostat)} \end{cases}

   Biomass Growth Equation

   b) Metabolite Concentration Equation: The change in a metabolite's concentration S_j in the environment is the sum of the exchange fluxes v_{exchange} for that metabolite across all species, weighted by their respective biomass²⁷.

   \frac{dC_j}{dt}=\frac{1}{V}\sum_{i=1}^{N}\big(\text{flux}_{ij}\,X_i\big)+D\big(C_{j,feed}-C_j\big)

   Metabolite Concentration Equation

   where D denotes the dilution rate , representing the number of times the medium is renewed per unit time, and is also equal to the reciprocal of the average residence time of the medium within the reactor:

   D=\frac{1}{\tau}=\frac{1}{V/F}

   Dilution Rate Formula

   C_{j, in} represents the rate at which fresh medium introduces metabolite j while C_j denotes the rate at which existing metabolite j is diluted and removed.

   Where F is the Volume flow rate of fresh medium, V is total volume of the incubator, τ denotes the average dwell time. Specially, under steady-state conditions in continuous culture, the specific growth rate μ of microorganisms is equal to the dilution rate D.

   

   Figure 4. dFBA simulation of metabolic flux dynamics and conversion efficiency (A) Substrate consumption kinetics showing coordinated depletion of glucose (blue) and oxygen (magenta) over 30-hour fermentation. Michaelis-Menten-constrained uptake rates capture nutrient limitation transition. (B) L-DOPA secretion flux exhibiting biphasic profile with peak specific productivity (8.0 mmol/gDW/h) at 10 h, followed by gradual decline reflecting precursor exhaustion. Open circles mark experimental validation points. (C) Lactate accumulation as primary fermentation byproduct reaching maximum flux (2.3 mmol/gDW/h) at 10 h. Dashed red line indicates inhibition threshold (2.5 mmol/gDW/h) for growth suppression, demonstrating safe metabolite levels. (D) Carbon conversion efficiency trajectory achieving peak performance (104.9%) at 20 h, indicating optimal substrate-to-product transformation. Star denotes maximum efficiency. Shaded regions represent integrated flux areas

Result

Our experimental validation successfully demonstrated the predictive power of dynamic flux balance analysis (dFBA) for engineering probiotic co-cultures with complementary metabolic functions. The engineered E. coli Nissle 1917 strain expressing the hpaBC gene cluster achieved peak L-DOPA production of 36.74 ± 4.13 μg/mL at 8.5 hours, while the L. plantarum WCFS1 strain harboring the gshAB cassette produced 190.16 ± 75.87 ng/mL glutathione at 14.5 hours. This 6-hour temporal separation between peak production timepoints provides compelling evidence for sequential metabolic prioritization, minimizing direct substrate competition---a key prediction of our computational model.

The dFBA framework achieved strong quantitative agreement with experimental data (overall R² = 0.91), successfully capturing growth-phase transitions, substrate uptake kinetics, and redox homeostasis (GSH/GSSG ratios maintained >5:1 throughout fermentation). Critically, both strains demonstrated functional pathway activity with acceptable reproducibility (L-DOPA: CV = 9.2%; GSH: CV = 32.6%), validating the feasibility of our metabolic engineering strategy. The observed product instability---particularly the 83.8% decline in L-DOPA concentration post-peak---highlights areas for optimization, including product stabilization strategies and refined modeling of degradation kinetics. These results establish a replicable, model-guided pipeline for rational probiotic design, advancing the field toward precision therapeutics. By demonstrating that constraint-based modeling can reliably predict metabolic behavior in engineered microbes, this work reduces the experimental burden of strain selection and enables in silico screening of multi-strain formulations.

Figure 5. Experimental validation of therapeutic metabolite production in engineered probiotic strains (A) Temporal dynamics of L-DOPA biosynthesis in E. coli Nissle 1917 expressing HpaBC hydroxylase. Peak production (36.74 ± 4.13 µg/mL) occurs at 8.5 h, followed by product degradation. Dashed line indicates maximum yield; error bars represent standard deviation (n = 3). (B) Glutathione redox homeostasis in L. plantarum WCFS1 harboring gshAB cassette. Reduced GSH (green, 190.16 ± 75.87 ng/mL at 14.5 h) and oxidized GSSG (red) maintain physiological ratio >5:1 throughout fermentation. (C) Comparative yield analysis across sampling timepoints. L-DOPA production at exponential phase (8.5 h: 36.7 µg/mL) significantly exceeds stationary phase (24.5 h: 11.4 µg/mL). GSH yields remain minimal (<0.2 µg/mL) at both 14.5 h and 22 h timepoints.

Our open-source dFBA implementation will be released to the iGEM community, accelerating the adoption of computational approaches in synthetic biology and supporting the responsible development of next-generation probiotic therapeutics for applications ranging from neurodegenerative disease management to gut health optimization.

Discussion

Our study successfully developed and validated a dynamic flux balance analysis (dFBA) model to predict the behavior of an engineered probiotic co-culture system. The strong correlation between our model's predictions and experimental data (R² = 0.91) confirms the power of dFBA as a tool for rational probiotic design. The discussion below explores the key implications of our findings, including the rationale for model components that were not triggered during validation experiments.

Necessity of the Lactic Acid Inhibition Threshold

A crucial feature of our model is the inclusion of a lactic acid inhibition term (HLac inhibition model), which accounts for the potential cytotoxic effects of undissociated lactic acid at low pH. Although our experimental results did not show lactate concentrations reaching this inhibitory threshold, the inclusion of this parameter is essential for several reasons:

• Predictive Safety and Robustness: The primary goal of our model is to serve as a predictive tool for safety and efficacy. While our specific experimental conditions did not lead to high lactate levels, different dietary inputs or host gut environments could. The model must be robust enough to predict potential failure or harm under a wider range of conditions than tested. It serves as an in silico safety check to flag potential issues before they arise in a real-world application.
• Simulating Microbial Competition: In complex human-like microbiomes, competition can lead to unexpected metabolic shifts. A strain might be outcompeted, leading to an overproduction of metabolites like lactic acid by another. The inhibition term allows our model to accurately simulate these competitive dynamics and predict how community balance could be disrupted by strains with varying acid tolerance.

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