Electrical Impedance Spectroscopy with Bacterial Biofilms: Neuronal-like Behavior

Abstract

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.

Keywords: bacteria; biofilm; electrical impedance spectroscopy; negative capacitance; neuron; voltage-gated ion channel.

Figure 1

(a) Growth curve for DH5α and DH5α Δkch over 24 h from a plate reader. OD is the optical density. (b) Representative impedance spectrum for DH5α showing the imaginary impedance (−Z_im) plotted as a function of the real impedance (Z_Re). Inset: Equivalent circuit model was used to fit the data. The solid line represents the model fit using the equivalent electric circuit (EC) shown in the inset, and the dots represent the experimental data. (c) Representative impedance spectrum for DH5α Δkch. Inset: Equivalent circuit model used to fit the data. The solid line represents the model fit using the EC shown in the inset, and the dots represent the experimental data. (d) Comparison between EIS spectra of both strains obtained after the 24 h biofilm culture. All data were obtained from at least three experimental replicates. Red arrows show the direction of an increasing frequency. CPE is the constant phase element. R_sol and R_ct are the solution resistance and contact resistance of DH5α Δkch, respectively. R_ct1 and R_ct2 are the contact resistances of wild-type DH5α biofilms.

Figure 2

(a) Variation of EIS spectra of DH5α biofilm as a function of growth time. Solid lines represent the model fits using the EC shown in the inset of Figure 1b and dots represent the experimental data. (b) Variation of EIS spectra of DH5α Δkch biofilm as a function of growth time. Solid lines represent the model fits using the EC shown in the inset of Figure 1c, and the dots represent the experimental data. (c) Time-dependent evolution of the charge transfer resistance in DH5α and DH5α Δkch biofilm. For DH5α, the R_ct2 from a low-impedance arc was used. (d) Antibiotic-dependent changes in the EIS spectra obtained from DH5α biofilm. Red arrows show the direction of increasing frequency.

Figure 3

(a) Electrical impedance spectra of DH5α biofilms at voltages 0.1–0.8 V. (b) Electrical impedance spectra of DH5α at DC bias voltages 0.4–0.8 V, highlighting the negative capacitance. (c) Electrical impedance spectra of DH5α Δkch at DC bias voltages 0.1–0.8 V. (d) Electrical impedance spectra of DH5α Δkch at DC bias voltages 0.4–0.8 V, highlighting the negative capacitance. Red arrows show the direction of increasing frequency.

Figure 4

(a) Partial equivalent circuit (EC) for the frequency domain Hodgkin–Huxley model for a single variety of voltage-gated ion channel, based on information given in ref (5). (b) EC used to fit the EIS data for the Q channel in DH5α Δkch, Figure 3d (0.4–0.6 V). (c) EC used to fit the EIS data for the Kch channel in the wild-type DH5α, Figure 3b (0.4–0.7 V). (d) Values of the resistance for the range of applied voltages for the Q ion channel. Data were obtained from Figure 3d using the EC fit of Figure 4b. R_Q and R_n are the resistances across the Q ion channel and its gating variable n, respectively. (e) Values of time constant for the R_nL_n branch of the Q channel (Figure 4b) for the range of applied voltages. L_n is the inductance across the gating variable n. (f) Values of the resistance for the range of applied voltages for the Kch ion channel of DH5α. Data obtained from Figure 3b using the EC fit of Figure 4c. R_Kch and R_m are the resistances across the Kch ion channel and its gating variable m, respectively. (g) Values of the time constant for the R_mL_m branch of the Kch channel (Figure 4c, Figure 3b) for the range of applied voltages. L_m is the inductance across the gating variable m. (h) Representative Bode plot (the change in the impedance modulus |Z| as a function of frequency) for both strains of E. coli at an applied DC bias of 0.4 V. Solid lines represent model fits using the EC (Figure 4c, DH5α; Figure 4b, DH5α Δkch), and the dots represent the experimental data. (i) Representative Bode plot (the change in the phase as a function of frequency) for both strains at an applied DC bias of 0.4 V. Solid lines represent the model fits using the EC (Figure 4c, DH5α; Figure 4b, DH5α Δkch), and the dots represent the experimental data. CPE is the constant phase element. R_sol and R_ct are the solution resistance and contact resistance, respectively.