Linking diôusion to cyanide biodegradation kinetics

Abstract

We present a comprehensive theoretical framework linking cyanide diffusion through bacterial outer membranes to biodegradation kinetics in gram-negative bacteria. Our analysis focuses on the transport of various cyanide compounds (free cyanide CN^-, thiocyanate SCN^-, and metal-cyanide complexes like [Ag(CN)2]^-, [Fe(CN)6]^3-/4-, etc.) through general porins OmpF, OmpC, OmpA, and OprF, and establishes quantitative criteria for determining when biodegradation becomes diffusion-limited [1]. The diffusion process is significantly influenced by electrostatic effects, particularly the Donnan potential across the outer membrane which creates strong selectivity against negatively charged cyanides. For instance, based on our calculations, [Ag(CN)2]^- exhibits substantially higher permeability than [Fe(CN)6]^4-, correlating with experimental observations of their relative impact on bacterial respiratory activity [1]. We introduce a novel procedure based on the Goldman-Hodgkin-Katz flux equation to quantify when cyanide biodegradation transitions from a kinetically-controlled to a diffusion-limited process [1]. The key parameter is the ratio ΔC_in / C_in^eq, where ΔC_in represents the concentration difference between equilibrium C_in^eq and steady-state concentrations in the periplasmic space. When this ratio is negligible (< 0.05), diffusion is significantly faster than biodegradation, enabling model simplification. This approach allows transition from complex multi-compartment models considering both extracellular and periplasmic cyanide concentrations to simplified kinetic models based solely on measurable extracellular concentration. Applied to experimental studies with P. fluorescens and P. pseudoalcaligenes, we demonstrate that diffusion remains significantly faster than biodegradation across typical concentration ranges, validating the use of simplified Michaelis–Menten kinetics in terms of extracellular cyanide concentrations [1]. These findings provide theoretical foundations for optimizing biological cyanide treatment processes.