Electrical Impedance Spectroscopy with Bacterial Biofilms: Neuronal-like Behavior

Negative capacitance at low frequencies for spiking neurons was first demonstrated in 1941 (K. S. Cole) by using extracellular electrodes. The phenomenon subsequently was explained by using the Hodgkin–Huxley model and is due to the activity of voltage-gated potassium ion channels. We show that Escherichia coli (E. coli) biofilms exhibit significant stable negative capacitances at low frequencies when they experience a small DC bias voltage in electrical impedance spectroscopy experiments. Using a frequency domain Hodgkin–Huxley model, we characterize the conditions for the emergence of this feature and demonstrate that the negative capacitance exists only in biofilms containing living cells. Furthermore, we establish the importance of the voltage-gated potassium ion channel, Kch, using knock-down mutants. The experiments provide further evidence for voltage-gated ion channels in E. coli and a new, low-cost method to probe biofilm electrophysiology, e.g., to understand the efficacy of antibiotics. We expect that the majority of bacterial biofilms will demonstrate negative capacitances.


Bacterial biofilm culture
E. coli biofilm was used as the functional layer material.A day preceding the EIS experiment, the E. coli strains, DH5α and a DH5α ∆kch mutant were collected from a -80 o C glycerol stock and streaked on an agar plate.On the day of the experiment, a single colony of the cell was transferred into 10 ml of Luria Broth (LB) media (Table S4).The glass universal containing the bacterial suspension was incubated overnight at 200 rpm at 37 o C. The next day, 100 µl of the inoculum was pipetted into a fresh 10 ml LB and incubated in a shaking incubator at 200 rpm and at 37 o C for 4.5 hours or  600 .Cells were subsequently adjusted to a starting concentration of 2 x 10 6 CFU/ml for all the ≈ 0.8 strains to ensure the same number of cells in all experiments.CFU/ml was calculated using the plate counting technique.Thereafter, 3 ml of the cell suspension was transferred onto an ITO electrode in the electrochemical cell.Cells were allowed 2 h to enhance cell attachment on the electrode surface at 37 o C. Subsequently, 35 ml of fresh sterile LB was added to the cell suspension in the electrochemical cell to ensure proper electrical contact with the reference and counter electrodes.Cells were left to grow statically for 24 hrs at 37 o C incubator.The optical density of the cells was measured using a spectrophotometer (JENWAY, Cole-Parmer UK).Each experiment was conducted in fresh electrolyte to eliminate the effect of culture media on the results.

Working electrode cleaning, treatment, and functionalization
The transparent indium tin oxide (ITO) electrode (Sigma Aldrich) was employed as the conducting electrode.The ITO electrode integrates well with bacterial substrates 1,2 .Prior to inoculation of the cell suspension on the ITO electrodes (2 x 2 cm 2 ), surface pretreatment was carried out to improve bacterial cell adhesion and biofilm cultivation 3,4 .The ITO surface was cleaned by sequentially sonicating for 10 min each in deionized water, acetone, and ethanol.The electrode was dried under nitrogen blow and subsequently treated with UV-ozone for 5 min.Following bacterial cell growth as described above, the biofilm cultivated for 24 hrs on the ITO serves as the electroactive layer material.The ITO electrode was not reused after each experiment.

Device setup and electrochemical impedance spectroscopy
EIS experiments were conducted on a GAMRY potentiostat Reference 600 Plus (GAMRY INSTRUMENTS, UK) using an electrochemical cell with a platinum counter electrode (CH Instruments Inc, US), an ITO working electrode and an Ag/AgCl reference electrode (CH Instruments Inc, US).A schematic diagram of the apparatus is shown in Fig. S1.After the biofilm was grown for 24 h, EIS was performed at a small AC amplitude of 10 mV, a potential of 0 V and a frequency range from 0.2-10 5 Hz.Under the same conditions, EIS analysis was conducted at set times of 16, 18, 20, 22 and 24 h to monitor the spectral evolution during growth.The same procedure was employed for both E. coli DH5α and DH5α ∆kch mutant strains.To monitor the EIS of dead cells, the disinfectant Virkon (at a concentration of 1% (1:100)) was added after 24 hrs of cell cultivation.The EIS data was collected 2 to 3 hrs after the addition of the disinfectant.This ensures no viable cells were left in the biofilm.For the antibiotics experiments, we employed rifampicin at 50 µg/ml and streptomycin at 5 µg/ml.Data was collected 3 hrs after the addition of the antibiotics.
To study the effect of varying applied voltages, EIS experiments were performed at a constant small AC amplitude of 10 mV at different DC bias voltages ranging from 0.1 V to 0.8 V.The frequency sweep was maintained from 0.2 to 10 5 Hz.For all experiments, data acquisition, analysis and modeling were done with the GAMRY software (See Table 2).
Subsequently, P1 lysate of the donor strain (E. coli K-12 BW25113 ∆kch-mutant) was prepared and transduced into the recipient (E. coli DH5α).Once more, the same primers were used to establish the absence of the Kch gene in our new strain, the E. coli DH5α ∆kch mutant.

Mathematical model of the frequency domain impedance response of E. coli biofilms
A single channel time-dependent Hodgkin-Huxley model 6 was developed to explain the stressdependent electrical signalling in B. subtilis biofilms 7 .We extended this model to understand the twochannel mediated membrane potential dynamics in E. coli biofilms in response to blue light stress 8 .In the current work, we used the same two-channel Hodgkin-Huxley model as our previous study in E.
coli 8   Each circuit element which depends on the voltage can then be deduced as stated below: Other considerations for the development of the equivalent circuit model: a) The Gamry software provides similar fits to those using analytic expressions explicitly implemented in Python i.e. using the Hodgkin-Huxley model described above.
b) The negative capacitances have values that are a robust feature of all reasonable models used to describe the data (the key experimental finding) and correspond to a clear feature in the data (an arc the 4 th quadrant of the impedance data).A promising method would be to adapt the agent based model presented in our previous eLife article 8 to predict impedance spectra.To our knowledge this has not previously been achieved in the literature on electrical impedance spectroscopy from any cells or colloids, although there has been some success using finite element models on tissue.
f) The contact resistance R ct describes the transfer of charge from the electrodes to the film.In the specific case of biofilms, it is expected to be due to a complex range of effects including adsorption to the electrodes by extracellular polymeric substance, adhesion complexes on the membranes of the bacteria (e.g.pili) and electrophysiological effects of the bacteria membrane potential (e.g.voltagegated ion channels).
g) All the bacteria biofilms studied have a very similar number of bacterial cells.It is expected that the DC bias voltage required to observe negative capacitance will scale with the number and type of bacterial cells.Furthermore, the DC bias voltage is expected to scale with the logarithm of the potassium concentration within the growth media (it is a Nernstian membrane potential).
h) The constant phase element (CPE) is commonly invoked in electrical impedance spectroscopy experiments to account for a power law background.Its origins are still debated for inorganic materials, although the non-integer power-law scaling indicates it could be a fractal effect e.g. with biofilms it could be due to the fractal structure of the extracellular polymeric substance or the fractal (anomalous) dynamics of the ions in the biofilm.

Comparison with previous impedance spectroscopy measurements from bacteria bacterial biofilms
Why have negative capacitances not been previously observed from bacteria or bacterial biofilms?
We believe a principal issue is the small value of the impedance for single bacteria.Much higher signal to noise can be achieved using large numbers of bacteria in bacterial biofilms.Thus biofilms provide higher resolution electrical impedance spectra.
Furthermore, the culture of biofilms is a specialist area and they were only first recognized as separate well defined states of bacterial physiology in the late 1970s (Costerton coined the word in 1978).This will have obstructed older studies.
A critical requirement to observe the negative capacitance is the application of a DC bias voltage.Many of the previous studies have neglected to explore the phenomenon (we were motivated by the recent article of Bou et al 11 in 2021) and it could require bespoke instrumentation to be developed in some cases (we were fortunate that is was a standard feature on the commercial Gamry apparatus).
Below we consider some key previous articles in the EIS literature: Analysis: the authors develop a bespoke microfluidic EIS device with a lock-in amplifier.They assume a simple equivalent circuit to describe single bacteria and do not measure the phase information directly to produce the true EIS measurements required to observe negative capacitances.

Fig S1 .
Fig S1.Schematic diagram showing the arrangement of the sample cell for electrical impedance spectroscopy experiments with bacterial biofilms.The biofilm is grown on the ITO working electrode.The reference electrode is Ag/AgCl and the counter electrode is platinum.A Gamry Reference 600 Plus potentiostat is used to meaure the biofilm impedances.

Fig S2 :
Fig S2: (a) The real impedance plotted as a function of frequency from experiments with the (  ) wildtype DH5α biofilms (Fig 1b) (mean ± SD for three repeats).b) Imaginary impedance as a ( -  ) function of frequency from the wildtype DH5α biofilms (Fig 1b).c) Representative data showing that our proposed minimal equivalent circuit provides a good fit to experimental data with the imaginary plotted as a function of the real impedance .The equivalent circuits of Figures 4b and ( -  ) (  ) 4c were used for the mutant and wildtype respectively.The solid lines are model fits and the dots are the experimental data at the applied DC bias voltage of 0.5 V.The plot also compares differences in the impedance arcs at similar DC bias voltages for both strains.Each point shows a separate frequency.d) EIS data for DH5α biofilm with no viable cells (subjected to Virkon for 2 hours) for different DC bias voltages showing the complex impedance as a function of the real impedance .Each ( -  ) (  ) point shows a separate frequency.Red arrows show the direction of increasing frequency.
Eqn 17 allows the frequency domain response of the electrical equivalent circuit Fig 4c of the E. coli biofilm to be calculated.
c) Simultaneous use of wild type and Kch knock down mutants allows the ambiguity in the modelling to be reduced.Availability of more ion channel mutants would provide additional sensitivity in determining the origins of the currents.d) Two of the resistor values in the parallel branch are coupled in the model (R Q and R l ).They could be lumped together, but they are considered separately so that an identical equivalent circuit is used in both the current manuscript and our previous eLife article8 .The other branches of the model are decoupled in the model due to their different frequency dependencies.e) Our equivalent circuit model is for the entire biofilm (in general it is common in electrical impedance spectroscopy to create such equivalent circuits for entire films).It would be interesting to explicitly incorporate the activity of ion channels for the response of each individual cell and then combine them with coupling effects to describe the entire biofilm.This has not yet been done for bacterial cells in the literature.

Table S1 :
The parameters extracted from model fits to the EIS spectra of E. coli DH5α ∆kch (its gating variable n respectively.wasused to represent all the voltage-gated ion  channels present in the DH5α ∆kch.is the inductance across the gating variable n. is the time     constant across the branch of the circuit, Fig 4b.

Table S2 :
Parameters extracted from the fits to the EIS spectra of E. coli DH5α (Fig 3b) using the model in Fig 4c.is the applied DC bias voltage.

Table S3 :
The impedance modulus at low frequency for both strains of E. coli biofilm for the range of applied DC bias voltages.Data was obtained at 0.25 Hz across the range of applied voltages with Bode plots similar to Fig 4h.The frequency of 0.25 Hz is equivalent to a log Frequency value of -0.6.||represents the modulus of the impedance at a specific frequency.isthe applied DC bias voltage.

Table S4 :Table S3 :
Media recipe, bacterial strains, software and EIS components used in experiments on E. coli biofilms.
to understand electrical impedance spectroscopy measurements with E. coli biofilms.ionchannels because negative capacitances are observed, but no negative resistances (no sodium-type ion channels are observed).To model AC perturbations of the HH model, a Laplace transform of eqns 1, 5, 6 and 7 yields   =     , 10   + 1 Fig S4: A Hodgkin-Huxley equivalent circuit model for the time-dependent conductance of E. coli  (  ) represents the capacitive current across the membrane.Fig S4 shows the equivalent circuit used in the HH model of E. coli biofilms in which the bacteria are modelled with two ion channels Kch and Q.The currents through the ionic channels (the equivalent resistors) and the cell membrane (the equivalent capacitor) in Fig S4 are ℎ =  ℎ (  - ℎ ), 3 and   =   (  -  ).we therefore extended this version of the HH model to develop a minimal model for the frequency domain impedance response of E. coli biofilms under small AC perturbations i.e. we include two potassium-type  +   +  ℎ +   .16 Substituting the eqns 10-15 into 16, we obtain  = [ They stress the importance of electroactive metabolites and the adhesion to the electrodes, but miss the effect of bacterial spiking potentials and voltage-gated ion channels.Kim, T., Kang, J., Lee, J. H. & Yoon, J. Influence of attached bacteria and biofilm on double-layer capacitance during biofilm monitoring by electrochemical impedance spectroscopy.Water Res 45, 4615-4622 (2011).Analysis: a commercial CH instrument instrument was used for EIS.A constant phase element (CPE) was needed to describe the data, similar to the current study.The authors do not apply a DC bias voltage.The effect of bacterial spiking potentials and voltage-gated ion channels is neglected.Barreiros dos Santos, M. et al.Highly sensitive detection of pathogen Escherichia coli O157:H7 by electrochemical impedance spectroscopy.Biosens Bioelectron 45, 174-180 (2013).Analysis: a Princeton Applied Research VMP2 multipotentiostat was used for EIS.The device was optimised for low concentrations of pathogenic E. coli.A constant phase element was used to analyse the data.The authors do not apply a DC bias voltage.The effect of bacterial spiking potentials and voltage-gated ion channelsis is neglected.Yang, Y. et al Measurement of the low-frequency charge noise of bacteria.Physical Review E 105, 064413 Analysis: bespoke apparatus is used to consider P. aeruginosa biofilms EIS.The authors do not apply a DC bias voltage.