Hydrodynamic chronoamperometry for probing kinetics of anaerobic microbial metabolism – case study of Faecalibacterium prausnitzii

Monitoring in vitro the metabolic activity of microorganisms aids bioprocesses and enables better understanding of microbial metabolism. Redox mediators can be used for this purpose via different electrochemical techniques that are either complex or only provide non-continuous data. Hydrodynamic chronoamperometry using a rotating disc electrode (RDE) can alleviate these issues but was seldom used and is poorly characterized. The kinetics of Faecalibacterium prausnitzii A2-165, a beneficial gut microbe, were determined using a RDE with riboflavin as redox probe. This butyrate producer anaerobically ferments glucose and reduces riboflavin whose continuous monitoring on a RDE provided highly accurate kinetic measurements of its metabolism, even at low cell densities. The metabolic reaction rate increased linearly over a broad range of cell concentrations (9 × 104 to 5 × 107 cells.mL−1). Apparent Michaelis-Menten kinetics was observed with respect to riboflavin (KM = 6 μM; kcat = 5.3×105 s−1, at 37 °C) and glucose (KM = 6 μM; kcat = 2.4 × 105 s−1). The short temporal resolution allows continuous monitoring of fast cellular events such as kinetics inhibition with butyrate. Furthermore, we detected for the first time riboflavin reduction by another potential probiotic, Butyricicoccus pullicaecorum. The ability of the RDE for fast, accurate, simple and continuous measurements makes it an ad hoc tool for assessing bioprocesses at high resolution.

The cyclic voltammograms (CV) recorded on a GC RDE at 5 mV.s -1 in anaerobic salt solution with 140 μM RF showed 2 well-defined peaks centered around ⎼ 396 ± 4 mV vs. Ag/AgCl (n = 3), with a peak to peak separation ΔEp of 41 ± 2 mV ( Fig. S1(A), thin line). These features are in good agreement with a reversible two-electron step electrochemical process with an apparent formal potential E 0' RF/RFH2 of ⎼ 400 ± 2 mV vs. Ag/AgCl (recalculated from 1 and 2 for pH 6.5 and 37 °C) and a theoretical ΔEp of 31 mV 3 . where n = 2 is the number of electrons exchanged, F the Faraday constant, DRF the diffusion coefficient of RF, ν the kinematic viscosity of water (6.92 × 10 -3 cm 2 .s -1 at 37 °C), ω the rotation speed (rad s -1 ) and [RF] the dissolved RF concentration (M). From the Levich slopes of 3 independent measurements, the diffusion coefficient DRF at 37 °C was determined at (6.32 ± 0.22) × 10 -6 cm 2 .s -1 . This value is in good agreement with a literature value of 6.13 × 10 -6 cm 2 .s -1 obtained for a fully reduced RFH2 solution (Fig. S2) and provided a very similar diffusion coefficient (6.46 × 10 -6 cm 2 .s -1 ) as expected for only 2 hydrogen atoms addition without conformation change for this large molecule (MRF = 376 g.mol -1 ). The more accurate mean value of DRF (for the oxidized state RF) will be kept for calculating either [RF] or [RFH2] as RF solutions were made from analytical-grade powder without further treatment. The Levich model for RDE formally allows the monitoring of the concentration of an electroactive specie when the latter is not consumed/produced in the diffusion layer of the RDE ( Fig. S5, top). In our case, the monitored RFH2 is also continuously produced in the diffusion layer by F. prausnitzii metabolism, which could modify the current recorded on the RDE for a specific RFH2 concentration in the bulk (Fig. S5, bottom). The aim of the following model is to assess this putative impact to formally prove the relevance of using the Levich equation to accurately monitor [RFH2] and its production rate. For that, we shall solve the diffusion equation in the case of an homogeneous production of RFH2, which allows to obtain the evolution of the current density over time.  The model is developed assuming these hypothesizes:

Supplementary
1) t = 0 is defined as the starting point of the reaction and so the initial concentration of product is nil: C(x, t=0) = 0 ; 2) the RDE potential is sufficiently high to record the anodic mass transfer limiting current density jla, i.e. the maximal consumption of RFH2 on the electrode surface: 3) the homogeneous metabolic reaction rate r is assumed to be maximal and time

a) Evolution of RFH2 concentration profile in the diffusion layer
The evolution of RFH2 concentration C(x,t) in the diffusion layer over time is therefore described by the following differential equation with these boundary conditions (diffusion equation with constant production): This equation is homologous to an inhomogeneous heat equation with a time dependent boundary condition. The solution ( , ) C x t of (S1) is obtained by posing ) , . By replacing into (S1), we find that the unknown function ( , ) u x t is solution of the following inhomogeneous heat equation: where the the series is convergent.

b) Validation of the Levich approximation for calculating the reaction rate
The current density jla(t) is proportional to the RFH2 flux J(0,t) at the electrode surface (Faraday law): The factor 2 being the number of electrons exchanged per RFH2 molecules oxidized.
And the RFH2 diffusive flux follows Fick's first law at x = 0: And the derivative of C(x,t) with respect to x: Finally, at x = 0 (electrode surface), the complete solution for the current density is: ) in (S9) is already more than 5 orders of magnitude smaller than the sum of the two following terms (equal at  3 4 ).
Consequently, for t   a good approximation consists in neglecting the series with respect to the two other terms, and (S9) becomes: The value of τ depends on δ which is well defined for a RDE 3 : The evolution of the current density with time for t ≥ τ is the derivative of (S10) with respect to t: And by replacing δ (from (S11)): Finally, the relation between the metabolic reaction rate r and the slope of the chronoamperogram ( t j la   ) is rigorously: Which are indeed the equation (7) and (6) stated in the main text of the study, respectively, and used to determine r.
The insignificant impact of the metabolic reaction in the diffusion layer was also confirmed experimentally (Fig. S6). There, the slope of the chronoamperogram monitoring a constant reaction rate increased proportionally with ω 1/2 , as predicted by (S14). Since the diffusion layer thickness (and therefore the amount of RFH2 produced per second in the layer) decreases linearly with ω 1/2 , a significant impact of the local homogeneous reaction would have broken the proportional relationship observed in Fig. S6.

c) Validation of the Levich approximation for monitoring [RFH2]
In this study we assumed that [RFH2] could be continuously recorded by monitoring the current density according to the Levich model.
We proved that very quickly after the reaction started, the current density follows: Where the constant term 3  reflect the impact of the homogeneous reaction in the diffusion layer and the second term increasing linearly with t is the Levich current only due to the specie coming from the bulk. It is clear that the relative impact of the reaction in the diffusion layer decreases over time. This impact becomes less than 1 % of the Levich current for:

b) anaerobic 96-well plate incubations for RF reduction in non-growing conditions
F. prausnitzii cell suspensions were prepared in the range of 5.2 × 10 6 -1.7 × 10 10 cells.mL -1 in the non-growing solution (see Method section) with and without 170 µM RF to achieve the highest RF concentration in the wells. These suspensions were diluted 1:1 in the non-growing solution with 170 µM RF to achieve a RF concentration range from 5.3 -170 µM. In this way the optimal bacteria-RF combination for monitoring RF reduction kinetics spectrophotometrically can be found in one experimental run. The 96-well plate was incubated in the anaerobic workstation and read-outs were made were made every 30s for the first ~ 2 h and every 60 s for the next ~ 6 h to be able to capture enough data points to determine the fastest kinetics at the highest bacterial concentrations using Xfluor™ software. The bacterial concentration was stable over the time of incubation as determined by incidental measurement at OD620nm ( Figure S18).
Ag/AgCl, 2000 rpm, 150 µM RF, 11 mM glucose, 3.5 × 10 6 cells.mL -1 F. prausnitzii. Arrows represent increasing additions from a 1 M sodium lactate stock solution leading to lactate concentrations presented in Fig. 6. Grey dotted lines stress the stability of initial and final slopes, which is a necessary condition for measurement validation. Punctual decreases in current for the last, largest additions reflect the corresponding small dilution of RFH2 (the final increase in volume with respect to the initial volume is 4.7%). This limited dilution of bacteria is taken into account for the calculation of the normalized rate presented in Fig. 6. No significant impact is expected nor taken into account from the small dilution of glucose and RF since both are still at saturation for F. prausnitzii (see Fig. 3). Inset: zoom on the 3 first additions. Figure S13. Polarization curves recorded before (thick red line) and after (thin black line) 50mM sodium butyrate addition, 160 µM RF, 10 mV.s -1 , 2000 rpm. The quasiinvariance of the curves shows the very little impact of butyrate on the solution viscosity up to 50 mM. Figure S14. Evolution of RF reduction rate with sodium sulphate concentration (n = 2). Results from CAs recorded at -0.25 V vs. Ag/AgCl, 2000 rpm, 150 µM RF, 11 mM glucose, 3.7 × 10 7 cell.mL -1 F. prausnitzii. Normalization is done with respect to the initial, stable rate before Na2SO4 addition. The non-significant impact of the salt concentration shows that neither the increase in ionic strength nor osmolarity were influencing the sodium carboxylates impacts presented in Fig. 6.