The impact of the pulsed electrical field on the cyanide biodegradation process

was investigated in this work. In the experiment, $\textit{Pseudomonas fluorescens}$ bacteria was treated by the pulsed electrical field for 15 mins ($f = $~100~Hz, impulse duration is 1 ms) before adding to the solution with $\mathrm{Na[Ag(CN)_2]}$ complex, and the appropriate kinetics was described [1]. During the cyanide biodegradation process, cyanide blocks the respiratory centers (RCs) of bacteria, but simultaneously bacteria degrade cyanide using the respiratory mechanism [2]. Theoretical analysis of the cyanide biodegradation kinetics was carried out in [3].

The purpose of this work is to introduce a phenomenological model $(1-2)$ that explains the cyanide biodegradation process in [1], and to describe the impact of pulsed electrical field on respiratory parameters of bacteria.

$\begin{equation}
\frac{dn}{dt} = - \left(\gamma_0 + \gamma_1 C\right) n +
\left(g_0 + g_1 n\right) \left(1 - n\right) - a \left(1 - C\right)
\label{1}
\end{equation}$

$\begin{equation}
\frac{dC}{dt} = - \alpha n \frac{C}{C + C_m}
\label{2}
\end{equation}$

where $n$ is a relative number of active RCs that can degrade cyanide, $C$ is a cyanide concentration in the solution, $\gamma \left(C\right) = \gamma_0 + \gamma_1 C$ is the rate of RC deactivation for low cyanide concentrations, $\gamma_0$ and $\gamma_1$ are constants. $g \left(n\right) = g_0 + g_1 n$ is the rate of RC activation, $g_0$ and $g_1$ are constants. $\alpha$ is the maximum rate of the cyanide destruction, $C_m$ is the Michaelis constant, $a$ is the rate of RCs deactivation caused by-product generation in the solution. Note that the system (1-2) is already normalized.

During the analysis of the dependence of absorbed oxygen on cyanide concentration from [4], we identified the following relations: $\alpha / C_m = g_1 + g_0 / D^2 - \frac{\gamma_1}{AB}$ and $C_m = \frac{2}{B} \left(g_1 + g_0 / D^2 - \frac{\gamma_1}{AB}\right) / \left(2 \frac{\gamma_1}{AB} - 2\frac{g_0 A}{D^3} - g_1 - \frac{g_0}{D^2}\right)$, where $A$, $B$ and $D$ are constants. Thus parameters responsible for the rate of cyanide biodegradation are dependent on the parameters related to the respiratory activity of bacteria. In addition, we found that $\gamma_0 = g_1 - g_1 D - g_0 + g_0 / D$. For other parameters, we identified the dependencies on the voltage of the pulsed electrical field (Fig 1). $g_1$ and $\gamma_1$ have linear dependence on voltage. Parameter $a$ is not dependent on voltage. Also, we applied the aforementioned model and results to the cyanide biodegradation experiment in [4] after the re-normalization.

Figure 1. Dependencies of the system parameters on the voltage of pulsed electrical field.

[1] Podolska V.I, Yakubenko L.N., Ulberg. Z.R., ${\it et~al.}$ Effect of Weak Pulse Electric Fields on Surface Properties and Destructive Activity of Pseudomonas Bacteria.$\textit{Colloid Journal.}$ $\textbf{72}$, 830 (2010).

[2] Harris R.E., Bunch A.W., Knowles C.J. Microbial cyanide and nitrile metabolism.$\textit{Sci. Prog., Oxf.,}$ $\textbf{71}$: 293 (1987).

[3] Podolska V.I., Ermakov V.N., Yakubenko L.N., ${\it et~al.}$ Effect of low-intensity pulsed electric fields on the respiratory activity and electrosurface properties of bacteria. $\textit{Food Biophysics}$, $\textbf{4}$, 281 (2009).

[4] Yakubenko L.N., Podolska V.I., Vember V.E., Karamushka V.I. The influence of transition metal cyanide complexes on the electrosurface properties and energy parameters of bacterial cells, $\textit{Colloids and Surfaces A: Physicochemical and Engineering Aspects}$. $\textbf{104}$, 11 (1995)