https://orcid.org/0009-0006-4643-3663
Figures
Abstract
Bioelectrochemical systems that combine living microbes with electrochemical devices are emerging as platforms for sustainable energy and chemical production. Phenazine-based organic redox flow batteries (RFBs) already achieve high-capacity, long-lived negolytes, but their performance is limited by electrolyte degradation. Recent work has demonstrated that genetically engineered, phenazine-producing Escherichia coli can regenerate degraded anolyte species in an operating RFB, suggesting a new class of “bio-batteries.” However, there is little quantitative understanding of how microbial physiology, phenazine toxicity, and electrochemical operating conditions jointly constrain performance. Here we develop a zero-dimensional mechanistic model that couples an engineered E. coli chassis to a phenazine-based flow battery half-cell. The microbial module includes Monod-type substrate uptake, growth-associated phenazine biosynthesis, first-order phenazine degradation, and a Hill-type toxicity term informed by pyocyanin’s micromolar-scale inhibitory effects. The electrochemical module computes Nernstian anode potentials from reduced/oxidized phenazine, adds a lumped area-specific resistance, and explicitly simulates charge discharge cycles with voltage cut-off criteria. We then sweep phenazine production strength, initial biomass loading, toxicity, and mediator stability to map the design space. The model predicts a strong trade-off between instantaneous current density and long-term capacity: high phenazine production and biomass can briefly reach 1.5 × 10−3 mA·cm ⁻ ² current densities but rapidly trigger toxicity-driven collapse, whereas more conservative designs deliver low current over an extended time period. When embedded in a simple RFB cycling protocol, moderate-production designs converge to a quasi-steady discharge capacity that is far below that of state-of-the-art phenazine RFBs, but exhibit partial self-regeneration of mediator capacity across cycles. Our results quantify the fundamental constraints of phenazine-based microbial anolytes and highlight engineering priorities, such as enhanced host tolerance and low-toxicity mediators, required for bio-batteries to become competitive or to occupy niche low-power, self-regenerating roles.
Citation: King SM, King MR (2026) Systems modeling of a phenazine-producing Escherichia coli bio-battery anolyte. PLoS One 21(4): e0347163. https://doi.org/10.1371/journal.pone.0347163
Editor: Xiaoliang Wei, Indiana University Purdue University Indianapolis (IUPUI), UNITED STATES OF AMERICA
Received: January 15, 2026; Accepted: March 26, 2026; Published: April 27, 2026
Copyright: © 2026 King, King. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Data Availability: Data Availability Statement: All model equations, parameter sets, and analysis scripts used in this study were implemented in Python (version 3.12) and the model is available as a public GitHub repository, including (i) The python code of the model (ii) The SBML representation of the microbial-phenazine subsystem (iii) sample data set: https://github.com/kingsim276/-Systems-modeling-of-a-phenazine-producing-Escherichia-coli-bio-battery-anolyte.
Funding: The author(s) received no specific funding for this work.
Competing interests: The authors have declared that no competing interests exist.
1. Introduction
Bioelectrochemical systems (BES) and microbial electrochemical technologies (MET) combine living cells with electrodes to convert chemical energy into electrical energy, drive reduction reactions, or synthesize value-added products [1–4]. Classical examples include microbial fuel cells and microbial electrolysis cells, in which electroactive biofilms catalyze anodic oxidation or cathodic reduction using organic substrates or waste streams [1,3]. Over the past decade, BES research has expanded from power generation towards microbial electrosynthesis, wastewater treatment, and integrated bioreactors, but scaling these systems to practically relevant power densities and long lifetimes remains a central challenge [2,5].
In parallel, redox flow batteries (RFBs) have emerged as promising technologies for grid-scale energy storage, offering decoupled power and energy, long cycle life, and flexible sizing [6–8]. Concerns over the sustainability, end-of-life management, costly recycling processes, and material intensity of conventional battery technologies have reinforced interest in alternative electrochemical platforms for niche applications, including bioelectrochemical systems and biobatteries [9–11]. Aqueous organic RFBs (AORFBs) are particularly attractive because organic redox-active molecules can be synthetically tuned for potential, solubility, and stability [6,12,13]. Phenazine derivatives have gained attention as highly soluble, reversible negolytes capable of high capacities at moderate concentrations [6,8,14]. Many phenazine-based electrolytes suffer from degradation pathways such as tautomerization and side-chain cleavage, especially at low redox potential, which limit lifetime and increase maintenance costs [7,8,15].
A recently proposed strategy to mitigate electrolyte degradation is to place living, genetically engineered microbes directly in the anolyte so that they can “repair” or regenerate degraded redox-active species during operation. Simoska and co-workers reported an RFB in which a phenazine-producing Escherichia coli strain regenerates degraded phenazine anolyte, markedly improving cycling stability [16]. Their work established a proof of concept for biological anolyte regeneration and motivated the broader idea of bio-batteries in which microbial metabolism maintains or adjusts electrolyte composition in situ. This approach complements earlier BES concepts where electroactive biofilms produce current directly and points to a hybrid device class blending flow-battery architectures with living catalysts [3,5].
Microbial electrochemistry has shown that microbial physiology and metabolite toxicity strongly limit current production and stability in BES [1–3]. Phenazines exemplify this dual role. In Pseudomonas aeruginosa, the phenazine pyocyanin functions as a redox-active virulence factor that generates reactive oxygen species and damages both microbes and host tissues [17–19]. In planktonic and biofilm cultures, pyocyanin exhibits micromolar minimum inhibitory concentrations against E. coli and other Gram-negative bacteria, with reported Minimum Inhibitory Concentration (MIC) values in the tens of µg·mL ⁻ ¹ (tens of µM) range [20,21]. Thus, a microbial chassis that produces phenazines to sustain an RFB also faces a risk of self-poisoning, implying an intrinsic trade-off between mediator production and cell viability.
Systems biology and genome-scale modeling offer natural tools to analyze such trade-offs. The E. coli genome-scale metabolic model iML1515 and its successors encode thousands of reactions and metabolites and can quantitatively predict growth and flux distributions under diverse genetic and environmental conditions [22–24]. Recent work has started to integrate thermodynamic and kinetic constraints, as well as machine learning, to capture enzyme and pathway limitations more accurately [23,25]. However, these models rarely include explicit electrochemical boundary conditions or mediator speciation, and they are not typically linked to stack-level RFB operation. Conversely, many RFB modeling studies treat electrolyte composition and degradation phenomenologically, without resolving underlying microbial processes that could regenerate or reshape the anolyte [6,7].
There is therefore a conceptual gap: we lack mechanistic yet tractable models that jointly describe (i) microbial growth and mediator production, (ii) mediator toxicity and stability, and (iii) electrochemical response and cycling in a flow-battery-like configuration. Such a model would enable systematic evaluation of design variables, including mediator production rate, biomass loading, toxicity threshold, degradation kinetics, electrode area, and ohmic resistance, and provide quantitative guidance on whether bio-batteries can approach the power and energy density of conventional AORFBs or instead occupy lower-power, self-regenerating niches. A structural comparison of representative BES, systems-biology, and RFB modeling frameworks is provided in Table 1 to clarify the niche addressed by the present formulation.
We address this gap by developing a zero-dimensional mechanistic model of a phenazine-producing E. coli anolyte coupled to a simplified phenazine-based RFB half-cell. The microbial module consists of Monod-type substrate uptake and biomass growth, growth-associated phenazine biosynthesis with an optional non-growth term, first-order phenazine degradation, and a Hill-type toxicity function parameterized to reflect micromolar-scale inhibition by pyocyanin and related phenazines in non-native hosts [17,18,20]. The electrochemical module uses a Nernst equation to relate reduced and oxidized phenazine concentrations to anode potential, includes a lumped area-specific resistance, and computes current density from phenazine oxidation at the electrode [6,7]. We then embed this module in a simple charge-discharge protocol with a voltage cut-off, allowing direct simulation of capacity vs. cycle number for different microbial designs.
Using this framework, we systematically explored how phenazine production strength, initial biomass, toxicity threshold, and mediator stability affect: (i) instantaneous current density, (ii) cumulative charge passed before toxicity or depletion, and (iii) long-term cycling performance. We compare the resulting current densities and capacities to reported values for phenazine-based AORFBs and discuss the extent to which engineered bio-batteries can realistically compete with or complement purely synthetic systems [6,8,15,28]. Finally, we use the model to identify specific biological and electrochemical targets such as increased phenazine tolerance, lower-toxicity mediators, and optimized electrode areas, which would be needed to close the performance gap. The accompanying SBML representation of the microbial phenazine subsystem is intended as a reusable component for future multiscale models integrating genome-scale metabolism, mediator chemistry, and device-level operation.
2. Materials and methods
2.1. Model overview
We developed a zero-dimensional, mechanistic model of an engineered Escherichia coli strain producing a soluble phenazine redox mediator that serves as the negolyte in a redox-flow-type bio-battery. The model couples microbial growth, substrate uptake, phenazine biosynthesis and toxicity, and first-order phenazine degradation to a simple electrochemical description of the anolyte, including Nernstian potential, ohmic losses, and explicit charge-discharge cycling.
The microbial module is intentionally coarse-grained from genome-scale reconstructions of E. coli metabolism such as iML1515 by aggregating central carbon metabolism into effective kinetic rates. Phenazine speciation and anode behavior are informed by recent phenazine-based negolytes and anolytes designed for aqueous and non-aqueous redox flow batteries. The overall bioelectrochemical configuration is consistent with the broader literature on bioelectrochemical reactors and zero-dimensional RFB cells and stack models.
All state variables are defined per unit anolyte volume: biomass concentration [gDW·L ⁻ ¹], extracellular substrate
[mmol·L ⁻ ¹], reduced phenazine
[mmol·L ⁻ ¹], oxidized phenazine
[mmol·L ⁻ ¹], and total phenazine
. Time is measured in hours.
2.2. Microbial growth and substrate uptake
Substrate uptake is modeled with a Monod-type expression for the specific uptake rate [mmol·gDW ⁻ ¹·h ⁻ ¹]:
where is the maximum specific uptake rate and
is the half-saturation constant. Reported aerobic glucose uptake rates and yields for E. coli were used to select
= 10 mmol gDW ⁻ ¹ h ⁻ ¹ and a biomass yield
= 0.09 gDW mmol ⁻ ¹, corresponding to ~0.5 gDW per g glucose under aerobic conditions [29].
The base specific growth rate [h ⁻ ¹] is given by:
Biomass and substrate balances are:
where is an effective growth rate that includes phenazine toxicity (Section 2.3).
2.3. Phenazine production, degradation, and toxicity
Phenazine production is described by a Luedeking-Piret-type rate that is primarily growth-associated:
where [mmol·gDW ⁻ ¹] is the growth-associated coefficient and
[mmol·gDW ⁻ ¹·h ⁻ ¹] is a non-growth-associated term. This reflects that phenazine biosynthesis in native producers is tightly coupled to central metabolism and growth, while allowing for constitutive production if desired [29,30].
Reduced and oxidized phenazine dynamics are:
where [h ⁻ ¹] is a first-order degradation rate capturing spontaneous phenazine degradation, side reactions, or irreversible adsorption, and
[mmol·L ⁻ ¹·h ⁻ ¹] is the electrode-mediated oxidation/reduction flux defined in Section 2.4.
Phenazines such as pyocyanin are known to be redox-active toxins that inhibit both producer and non-producer strains in the low-to-mid micromolar range [28,31,32]. To capture this, we scale the base growth rate by a Hill-type toxicity function of total phenazine:
With = 0.01 mmol L ⁻ ¹ (10 µM) and Hill coefficient
= 2. These values were selected to produce growth inhibition of the same order of magnitude as reported pyocyanin sensitivity in non-native hosts, while allowing exploration of more tolerant designs by varying
. Essentially,
is interpreted as an effective inhibition scale in the phenomenological toxicity term rather than as a direct one-to-one representation of a single experimentally measured MIC. Reported toxicity values for pyocyanin and related phenazines span a relatively broad range depending on the specific phenazine derivative, organism, and assay conditions. As a result, the choice of
was intended as a conservative order-of-magnitude parameter representing the onset of growth suppression in a simplified model of a non-native phenazine-producing E. coli host, rather than as a strain-specific fitted threshold. More detailed calibration would require direct toxicity measurements for the relevant engineered strain and phenazine mixture under the intended operating conditions.
2.4. Electrochemical half-cell, Nernst potential and ohmic loss
We treat the anolyte as a well-mixed compartment in which the reduced phenazine is oxidized at the anode with a first-order rate constant:
Where the lumped parameter summarizes mass-transfer and heterogeneous electron-transfer limitations at the electrode. The resulting current density j [A·m ⁻ ²] is:
where is the number of electrons per phenazine redox event,
is Faraday’s constant (96485 C·mol ⁻ ¹), and
[m²·L ⁻ ¹] is electrode area per unit anolyte volume. The anode potential
[V vs SHE] is given by the Nernst equation for a simple one-step redox couple:
with standard potential chosen to lie within the range of reported aqueous phenazine negolytes. The cathode is represented as an ideal counter-electrode at fixed potential
The open-circuit cell voltage is:
To account for ohmic losses, we introduce a single area-specific resistance [Ω·m²], representing ionic resistance in the membrane and electrolytes. The terminal cell voltage is then:
This lumped description is consistent with widely used zero-dimensional RFB models and stack-level frameworks that combine Nernstian potentials with ohmic and kinetic losses. All electrochemical and cycling parameters used in the half-cell and redox-flow-battery modules are summarized in Table 2.
2.5. Charge-discharge protocol and cycle definition
To study long-term performance, we implemented an explicit charge/discharge protocol. During discharge, the current density is determined by electrochemical oxidation of the reduced mediator pool via , and the coupled ODE system is integrated until either a fixed maximum discharge time
is reached or the cell voltage drops below a prescribed cut-off
(typically 0.6 V), analogous to cut-off criteria in redox-flow battery cycling tests. The discharge capacity per cycle
[A·h·m ⁻ ²] is computed as:
During recharge, we impose a constant charging current density (A·m ⁻ ²) in the opposite direction, while biomass and substrate are held fixed over the short recharge interval. The imposed current is converted to an effective phenazine flux:
with the negative sign indicating reduction of to
. Phenazine balances during recharge become:
and the Nernst and ohmic relations are evaluated at each time point to obtain . Repeated application of discharge and recharge phases from the final state of the previous cycle yields capacity vs. cycle-number profiles for each microbial design.
2.6. Parameterization and numerical implementation
Baseline parameters were chosen from the literature where available and otherwise selected to be physiologically and electrochemically plausible for an exploratory design study. Aerobic uptake and yield parameters for E. coli were guided by chemostat and constraint-based modeling studies (Table 3) [33]. Phenazine redox properties (standard potential, solubility, and stability) were guided by recent high capacity phenazine anolyte and negolyte reports. Zero-dimensional RFB modeling literature provided typical ranges for area-specific resistance and current densities in aqueous cells. Unless otherwise noted, simulations were performed with = 10 mmol gDW ⁻ ¹ h ⁻ ¹,
= 0.09 gDW mmol ⁻ ¹,
,
,
, electrode area density
, and ohmic resistance
Phenazine production strength
and initial biomass
were treated as design variables and systematically varied as described below.
All ODE systems were implemented in Python (version 3.12) and integrated using an explicit Euler scheme with time step Δt = 0.01–0.05 h. For parameter sweeps, we simulated up to 200 h of operation or until phenazine concentrations exceeded a specified toxicity threshold. The microbial phenazine subsystem, including a cumulative capacity variable, was also encoded in SBML Level 2 Version 4 to enable independent reuse and extension in standard systems biology software, and is provided as a supplemental file along with the Python implementation [34–37].
2.7. Use of generative AI
During the preparation of this work, the authors used ChatGPT (OpenAI, model GPT-5.1 Thinking) to assist with drafting and editing sections of the manuscript, improving code structure and documentation, and supporting implementation of the computational model. ChatGPT was also used as an interactive aid during equation development and model prototyping; however, all equations, assumptions, parameter choices, code, simulations, and scientific interpretations were reviewed, validated, and finalized by the authors. After using this tool, the authors independently checked and edited all content as needed and take full responsibility for the content of this article.
3. Results
3.1. Baseline dynamics of a phenazine-producing bio-anolyte
We first simulated batch operation of a phenazine-producing E. coli anolyte to establish baseline system behavior (Fig 1). Biomass (E. coli) increased monotonically during the initial growth phase, accompanied by rapid substrate consumption. Phenazine is produced in the reduced form but is rapidly oxidized at the anode under baseline extraction rates, resulting in an oxidized-dominant mediator pool with only a transient reduced fraction. This regime reflects a kinetically-limited extraction process rather than accumulation of reduced mediator. As phenazine concentration increased, current density decreased to the 0.25 x 10−3 milliamp-per-square-centimeter range before approaching zero as substrate depletion, mediator degradation, and toxicity effects became significant. The coupled electrochemical model predicts a decline in cell voltage as ohmic losses increase with current density and the anode potential shifts positive with increasing oxidized mediator fraction.
Time evolution of (A) biomass concentration , (B) substrate concentration
, (C) total phenazine concentration
, and (D) current density and cell voltage for a batch culture of a phenazine-producing E. coli anolyte. Phenazine production is growth-associated and coupled to electrochemical oxidation at the anode. Current density increases with phenazine accumulation before plateauing as substrate depletion, mediator degradation, and toxicity effects become significant. Cell voltage decreases with increasing current due to ohmic losses and shifts in anode potential. Simulation parameters correspond to the baseline design described in the Methods.
These results establish a physically consistent baseline in which microbial growth, mediator production, and electrochemical extraction are tightly coupled, and motivate exploration of design trade-offs governing power output and operational stability.
3.2. Design-space exploration of phenazine production and biomass loading
To identify design regimes capable of maximizing electrical output, we performed a parameter sweep over the phenazine production coefficient (αₚ) and initial biomass concentration (X₀), computing the time-averaged current density prior to toxicity-induced shutdown (Fig 2). Increasing either αₚ or X₀ initially enhances current density by accelerating phenazine accumulation and electrode turnover. However, beyond a moderate regime, further increases in either parameter produce diminishing returns due to rapid accumulation of toxic phenazine concentrations.
Heat map of time-averaged current density as a function of the phenazine production coefficient and initial biomass concentration
. Each point represents a batch simulation terminated upon reaching a phenazine toxicity threshold or the maximum simulation time. Moderate values of
and
maximize average current density, whereas more aggressive designs rapidly accumulate toxic phenazine concentrations and exhibit reduced effective performance. This design space highlights a fundamental trade-off between instantaneous power output and operational stability.
The resulting design space reveals a ridge of optimal performance at intermediate αₚ and X₀ values, highlighting a fundamental trade-off between aggressive mediator production and long-term viability. Designs optimized solely for instantaneous power density are predicted to fail rapidly, whereas more conservative designs operate for extended periods but at substantially lower current densities. In the following sections, we refer to designs with αₚ values near the center of this viable ridge as moderate-production regimes, and to designs near the upper bound of αₚ that maximize instantaneous current density as high-production regimes.
The current densities predicted here are lower than those reported for experimental E. coli bioelectrochemical systems. The peak modeled value in the present study is approximately 1.5 × 10 ⁻ ³ mA cm ⁻ ², whereas reported phenazine flow cells commonly operate at 20–100 mA cm ⁻ ² depending on molecular design and cycling conditions [38]. This implies that achieving comparable performance would require roughly a 4–5 order of magnitude increase in effective current-generating capacity. Within the present framework, that improvement would need to arise from combined increases in the accessible reduced phenazine inventory, the microbial rate of mediator regeneration, and the electrode-area-normalized extraction rate, together with reduced transport and ohmic limitations. The present model describes a plausible low-power microbial operating regime rather than an immediately competitive redox-flow-battery architecture. The design objective for such a system may be better understood as achieving sustained, self-regenerating electrochemical output within biologically accessible constraints, while future improvements in mediator production, microbial tolerance, and electrochemical utilization could increase performance further.
3.3. Coupling microbial dynamics to redox-flow battery cycling
We next embedded the microbial anolyte model within a simplified redox flow battery framework incorporating Nernstian electrode potentials, ohmic losses, and voltage cut-offs during discharge and recharge. The purpose of this analysis is to evaluate the internal consistency of the coupled biological and electrochemical dynamics under cycling, rather than to predict long-term durability. Following an initial transient in which mediator inventory and redox state adjust, the system converges to a steady cycling regime in which successive discharges reach the voltage cut-off at similar redox states. As a result, discharge capacity increases during early cycles and subsequently plateaus, remaining approximately constant even over extended cycling within the present model (Figs 3,4).
Discharge capacity as a function of cycle number for a moderate-production design and a high-production design. Each cycle consists of a discharge step governed by Nernstian electrode potentials, ohmic losses, and a voltage cut-off, followed by a recharge step that regenerates reduced phenazine. The moderate-production design exhibits relatively stable capacity over multiple cycles, whereas the high-production design shows higher initial capacity but more pronounced capacity fade due to mediator degradation and toxicity-induced suppression of microbial activity.
Time evolution of (A) current density and (B) cell voltage during a single discharge cycle for the moderate-production design. Current density decreases continuously as reduced phenazine is oxidized and the anode potential shifts positive. Discharge terminates when the cell voltage reaches the prescribed cut-off, illustrating the direct coupling between microbial mediator availability and battery-level performance metrics.
Fig 3 compares cycling behavior under moderate and high mediator production rates. While higher production alters the initial transient behavior by accelerating mediator accumulation during early cycles, both designs converge to the same steady-state discharge capacity once a repeatable cycling regime is established. In both cases, capacity is not prescribed or conserved but instead emerges dynamically from the interaction between microbial mediator production, electrochemical extraction, and the imposed voltage cut-off. The convergence of capacity across cycles therefore reflects the establishment of a repeatable cycling trajectory rather than an assumption of intrinsic stability.
This steady behavior arises because the net mediator inventory per cycle stabilizes once mediator production during growth phases and electrochemical reduction during recharge collectively balance degradation losses. Capacity stability is thus an emergent outcome of the modeled dynamics and is not enforced by conservation constraints or fixed capacity assumptions. Within this mathematical framework, extending the number of simulated cycles does not induce additional capacity fade in the absence of additional time-dependent degradation mechanisms.
While first-order mediator degradation is included explicitly, the model does not capture additional time-dependent degradation mechanisms such as progressive loss of microbial activity, spatial concentration gradients, biofilm formation, or mass-transfer limitations near the electrode surface. These effects could reduce effective mediator transport, alter local toxicity exposure, and further limit electron-transfer rates, thereby changing both current output and apparent operating stability. The trends reported here should therefore be interpreted as idealized system-level behavior under well-mixed conditions, while future models should incorporate spatial transport and surface-associated microbial growth to better represent practical bioelectrochemical devices.
Single-cycle discharge profiles (Fig 4) demonstrate that current density decays continuously within each discharge as the reduced phenazine fraction is oxidized and cell voltage approaches the cut-off threshold. These results illustrate how microbial physiology and redox kinetics jointly determine battery-level metrics such as discharge capacity and voltage efficiency.
3.4. Sensitivity to phenazine toxicity and degradation
To assess the relative influence of host tolerance and mediator stability on electrochemical performance, we performed a sensitivity analysis on the phenazine inhibitory concentration () and the mediator degradation rate constant (
) for a moderate-production design (Fig 5). Two parameters in the model capture the main biological and chemical limits of the system.
represents how tolerant the bacteria are to phenazine toxicity: when phenazine concentrations approach or exceed this level, cell growth slows down and phenazine production is suppressed. In contrast,
represents how quickly phenazine is irreversibly lost from the system through chemical degradation or other non-recoverable pathways, regardless of microbial activity. These parameters distinguish between limits set by microbial viability and limits set by mediator stability, allowing the model to separately assess how host tolerance and phenazine lifetime constrain bio-battery performance. Furthermore,
represents the phenazine concentration at which microbial metabolism becomes significantly inhibited, and
quantifies first-order loss of phenazine from both redox states.
Dependence of time-averaged current density on (A) the phenazine inhibitory concentration () and (B) the first-order phenazine degradation rate constant (
) for a moderate production design. Increasing Kinh enhances current density by reducing toxicity-induced suppression of microbial growth and mediator production. Increasing kdeg produces a modest increase in average current density by limiting phenazine accumulation and delaying toxicity, despite faster irreversible mediator loss. These trends reflect coupled biological-chemical effects under a toxicity-limited operating protocol rather than intrinsic improvements in electrochemical efficiency.
Increasing from 5 to 20 µM leads to a clear increase in average current density, reflecting reduced toxicity-induced suppression of microbial metabolism and more efficient electron delivery during discharge. This trend indicates that host tolerance primarily controls the achievable power output rather than the duration of operation under fixed discharge windows.
The dependence of average current density on mediator degradation rate reflects the coupled nature of mediator stability and microbial toxicity in the model. Increasing the degradation rate reduces the accumulation of total phenazine, which in turn delays toxicity-induced suppression of microbial growth and phenazine production. Microbial activity and mediator regeneration are sustained for a larger fraction of the operating window, leading to a modest increase in the time-averaged current density despite faster irreversible mediator loss. This trend arises from the interaction between degradation and toxicity rather than from improved electrochemical efficiency and should not be interpreted as an inherent benefit of mediator instability. Metrics that directly quantify stored charge or discharge capacity continue to decrease with increasing degradation, consistent with physical expectations. Because simulations are terminated when total phenazine exceeds a toxicity threshold (or when the maximum simulation time is reached), changes in and
can affect both the time horizon over which current is produced and the resulting time-averaged current. Fig 5 should be interpreted as a rate/viability sensitivity under a toxicity-limited operating protocol, rather than as a fixed-window comparison of power at identical discharge durations.
3.5. Phenazine redox speciation dynamics
We examined the temporal evolution of reduced and oxidized phenazine pools for the moderate-production design (Fig 6). Following an initial transient in which reduced phenazine briefly accumulates, the mediator pool rapidly shifts toward the oxidized form: decreases to near zero while
rises quickly to a maximum and remains the dominant species for the remainder of the operating window. Consequently, the reduced fraction
drops sharply within the first hours and stays close to zero thereafter, indicating that mediator oxidation at the anode outpaces net replenishment of the reduced pool under these operating conditions.
Time courses of (A) reduced phenazine concentration , (B) oxidized phenazine concentration
, and (C) reduced fraction
for the moderate-production design under batch operation. Phenazine accumulates predominantly in the reduced form during early growth, with the reduced fraction remaining near unity until electrochemical oxidation and degradation become comparable to production. The evolving redox speciation directly influences anode potential, voltage utilization, and susceptibility to toxicity.
At later times, gradually declines even though it is not converted back to
in the model. This behavior reflects irreversible mediator loss processes represented by the degradation term (e.g., chemical decay, adsorption, or effective washout of electrochemically active phenazine), which dominate once
is depleted and the oxidation flux becomes negligible. These dynamics indicate an oxidized-skewed mediator regime that limits the availability of reduced mediator for sustained discharge and constrains voltage utilization. Shifting toward a more balanced redox state would require increasing the effective reduction flux relative to oxidation (e.g., lowering current demand or current density via larger electrode area, and/or enhancing microbial electron delivery capacity), thereby maintaining a larger accessible reduced mediator fraction during operation.
4. Conclusions
In this study, we developed a mechanistic systems-level model that couples microbial growth and phenazine biosynthesis to electrochemical energy extraction and redox flow battery cycling. By integrating Monod-type growth kinetics, growth-associated mediator production, toxicity and degradation effects, and explicit Nernstian electrochemistry, the model provides a unified framework for evaluating the feasibility of phenazine-based bio-batteries.
Our results reveal a fundamental trade-off between power density and operational stability: aggressive phenazine production and high biomass loading can transiently achieve 1.5 x 10−3 milliamp-per-square-centimeter current densities but rapidly drive the system into toxicity-induced collapse, whereas more conservative designs operate for extended periods at much lower power. Sensitivity analysis identifies mediator stability and host tolerance as primary bottlenecks, with improvements in chemical robustness yielding gains in both current density and lifetime. When embedded within a simplified redox flow battery architecture, the microbial anolyte exhibits partial self-regeneration of capacity across cycles, albeit at energy and power densities below those of state-of-the-art abiotic systems.
The model is most immediately useful as a design-screening framework for identifying favorable operating regimes and prioritizing which biological and electrochemical constraints should be targeted experimentally. Future studies may validate these predictions using bench-scale bioelectrochemical systems. A phenazine-producing E. coli strain grown in an H-cell or flow-through reactor with a defined mediator concentration could be used to track current output, biomass growth, substrate consumption, and mediator stability over time under varying production strengths and substrate conditions. Such measurements would allow direct comparison with the model trajectories and help identify which parameter assumptions require refinement.
Future work with this modeling approach could include complete genome-scale metabolism managed by coupling the dynamic framework to constraint-based models like dFBA. Through this or other forms of large-scale flux analysis, this highly scalable strategy allows for the representation of intracellular metabolism using stoichiometric flux balances, bypassing the need for explicit kinetic equations for all molecular species.
The modeled bio-battery does not compete directly with conventional batteries for high-power applications, it highlights potential niches for living electrochemical systems in low-power, self-maintaining, or resource-constrained environments. The framework presented here provides quantitative guidance for engineering microbial electrochemical systems and establishes a foundation for future studies that integrate more detailed metabolic networks, spatial transport, and experimental validation.
References
- 1. Wang H, Ren ZJ. A comprehensive review of microbial electrochemical systems as a platform technology. Biotechnol Adv. 2013;31(8):1796–807. pmid:24113213
- 2. Zheng T, Li J, Ji Y, Zhang W, Fang Y, Xin F, et al. Progress and prospects of bioelectrochemical systems: electron transfer and its applications in the microbial metabolism. Front Bioeng Biotechnol. 2020;8:10. pmid:32083069
- 3. Corona-Martínez DA, Martínez-Amador SY, Rodríguez-De la Garza JA, Laredo-Alcalá EI, Pérez-Rodríguez P. Recent advances in scaling up bioelectrochemical systems: a review. BioTech (Basel). 2025;14(1):8. pmid:39982275
- 4. Choudhary M, Verma P, Ray S. A comprehensive review on bio-electrochemical systems for wastewater treatment: process, electricity generation and future aspect. Environ Dev Sustain. 2024.
- 5. Horváth-Gönczi NN, Bagi Z, Szuhaj M, Rákhely G, Kovács KL. Bioelectrochemical Systems (BES) for Biomethane Production—Review. Fermentation. 2023;9(7):610.
- 6. Hollas A, Wei X, Murugesan V, Nie Z, Li B, Reed D, et al. A biomimetic high-capacity phenazine-based anolyte for aqueous organic redox flow batteries. Nat Energy. 2018;3(6):508–14.
- 7. Chen Y, Zeng C, Fu Y, Bao J, Gao P, Chen JQ, et al. Evaluating large scale aqueous organic redox flow battery performance with a hybrid numerical and machine learning framework. Pacific Northwest National Laboratory (PNNL). Richland, WA (United States); 2024.
- 8. Xu J, Pang S, Wang X, Wang P, Ji Y. Ultrastable aqueous phenazine flow batteries with high capacity operated at elevated temperatures. Joule. 2021;5(9):2437–49.
- 9. Choi S. Biofuel cells and biobatteries: misconceptions, opportunities, and challenges. Batteries. 2023;9:119.
- 10. Rezaie M, Mohammadifar M, Choi S. Dissolvable Probiotic-Powered Biobatteries: A Safe and Biocompatible Energy Solution for Transient Applications. Small. 2025;21:2502633.
- 11. Chandrasekhar G, Bhattacharyya S, Zhang X, Pramanik A, Amiri M, Terlier T, et al. Plasma-Assisted Sustainable Recovery of Critical Minerals from Li-Ion Battery Waste. Adv Mater. 2026;38(8):e15201. pmid:41347812
- 12. de la Cruz C, Molina A, Patil N, Ventosa E, Marcilla R, Mavrandonakis A. New insights into phenazine-based organic redox flow batteries by using high-throughput DFT modelling. Sustainable Energy Fuels. 2020;4(11):5513–21.
- 13. Romadina EI, Akkuratov AV, Simoska O, Stevenson KJ. Phenazine-based compound as a universal water-soluble anolyte material for the redox flow batteries. Batteries. 2022;8(12):288.
- 14. Xie X, Kong T, Gao J, Li R, Wang Y. A low-redox-potential phenazine-based negolyte with high stability for aqueous organic flow batteries. Chem Sci. 2025;16(47):22368–75. pmid:41164296
- 15. Simoska O, Rhodes Z, Carroll E, Petrosky KN, Minteer SD. Biological anolyte regeneration system for redox flow batteries. Chem Commun (Camb). 2023;59(15):2142–5. pmid:36727430
- 16. Noto MJ, Burns WJ, Beavers WN, Skaar EP. Mechanisms of pyocyanin toxicity and genetic determinants of resistance in staphylococcus aureus. J Bacteriol. 2017;199(17):e00221-17. pmid:28607159
- 17. Gonçalves T, Vasconcelos U. Colour me blue: the history and the biotechnological potential of pyocyanin. Molecules. 2021;26(4):927. pmid:33578646
- 18. Mudaliar SB, Bharath Prasad AS. A biomedical perspective of pyocyanin from Pseudomonas aeruginosa: its applications and challenges. World J Microbiol Biotechnol. 2024;40(3):90. pmid:38341389
- 19. Shouman H, Said HS, Kenawy HI, Hassan R. Molecular and biological characterization of pyocyanin from clinical and environmental Pseudomonas aeruginosa. Microb Cell Fact. 2023;22(1):166. pmid:37644606
- 20. DeBritto S, Gajbar TD, Satapute P, Sundaram L, Lakshmikantha RY, Jogaiah S, et al. Isolation and characterization of nutrient dependent pyocyanin from Pseudomonas aeruginosa and its dye and agrochemical properties. Sci Rep. 2020;10(1):1542. pmid:32005900
- 21. Monk JM, Lloyd CJ, Brunk E, Mih N, Sastry A, King Z, et al. iML1515, a knowledgebase that computes Escherichia coli traits. Nat Biotechnol. 2017;35(10):904–8. pmid:29020004
- 22. Bernstein DB, Akkas B, Price MN, Arkin AP. Evaluating E. coli genome-scale metabolic model accuracy with high-throughput mutant fitness data. Mol Syst Biol. 2023;19(12):e11566. pmid:37888487
- 23. van ’t Hof M, Mohite OS, Monk JM, Weber T, Palsson BO, Sommer MOA. High-quality genome-scale metabolic network reconstruction of probiotic bacterium Escherichia coli Nissle 1917. BMC Bioinformatics. 2022;23(1):566. pmid:36585633
- 24. Yang X, Mao Z, Zhao X, Wang R, Zhang P, Cai J, et al. Integrating thermodynamic and enzymatic constraints into genome-scale metabolic models. Metab Eng. 2021;67:133–44. pmid:34174426
- 25. Liu Q, Li Y, Qiu Y, Zhang J, Cheng H, Song Z, et al. Deep eutectic solvents for high-efficiency recovery of valuable metals from spent lithium-ion batteries: rational design and mechanistic insights. Green Chem. 2025;27(35):10735–54.
- 26.
A genome-scale metabolic flux model of Escherichia coli K–12 derived from the EcoCyc database. https://pmc.ncbi.nlm.nih.gov/articles/PMC4086706/?utm_source=chatgpt.com. Accessed 2026 March 22.
- 27. Mourouga G, Schaerer RP, Yang X, Janoschka T, Schmidt TJ, Schumacher JO. Physics-based 0D-U-I-SoC cell performance model for aqueous organic redox flow batteries. Electrochimica Acta. 2022;415:140185.
- 28. Zeng H, Yang A. Bridging substrate intake kinetics and bacterial growth phenotypes with flux balance analysis incorporating proteome allocation. Sci Rep. 2020;10(1):4283. pmid:32152336
- 29. Rhodes Z, Simoska O, Dantanarayana A, Stevenson KJ, Minteer SD. Using structure-function relationships to understand the mechanism of phenazine-mediated extracellular electron transfer in Escherichia coli. iScience. 2021;24(9):103033. pmid:34522869
- 30. Huang W, Wan Y, Su H, Zhang Z, Liu Y, Sadeeq M, et al. Recent Advances in Phenazine Natural Products: Biosynthesis and Metabolic Engineering. J Agric Food Chem. 2024;72: 21364–79.
- 31. Castañeda-Tamez P, Ramírez-Peris J, Pérez-Velázquez J, Kuttler C, Jalalimanesh A, Saucedo-Mora MÁ, et al. Pyocyanin Restricts Social Cheating in Pseudomonas aeruginosa. Front Microbiol. 2018;9:1348. pmid:29997585
- 32. Meirelles LA, Newman DK. Both toxic and beneficial effects of pyocyanin contribute to the lifecycle of Pseudomonas aeruginosa. Mol Microbiol. 2018;110(6):995–1010. pmid:30230061
- 33. Yang X, Mao Z, Zhao X, Wang R, Zhang P, Cai J, et al. Integrating thermodynamic and enzymatic constraints into genome-scale metabolic models. Metab Eng. 2021;67:133–44. pmid:34174426
- 34. Moutinho TJ Jr, Neubert BC, Jenior ML, Papin JA. Quantifying cumulative phenotypic and genomic evidence for procedural generation of metabolic network reconstructions. PLoS Comput Biol. 2022;18(2):e1009341. pmid:35130271
- 35. Pearcy N, Hu Y, Baker M, Maciel-Guerra A, Xue N, Wang W, et al. Genome-Scale Metabolic Models and Machine Learning Reveal Genetic Determinants of Antibiotic Resistance in Escherichia coli and Unravel the Underlying Metabolic Adaptation Mechanisms. mSystems. 2021;6(4):e0091320. pmid:34342537
- 36.
Wei X, Wang W, HOLLAS AM, Sprenkle VL, Nie Z, Li B. Highly stable phenazine derivatives for aqueous redox flow batteries. 2018. https://patents.google.com/patent/WO2018231926A1/en
- 37. Picioreanu C, Head IM, Katuri KP, van Loosdrecht MCM, Scott K. A computational model for biofilm-based microbial fuel cells. Water Research. 2007;41: 2921–2940. https://doi.org/10.1016/j.watres.2007.04.009
- 38. Ortiz-Martínez VM, Salar-García MJ, de los Ríos AP, Hernández-Fernández FJ, Egea JA, Lozano LJ. Developments in microbial fuel cell modeling. Chemical Engineering J. 2015;271:50–60.