Mathematical Modeling of the Amensal Relation Between Pseudomonas Aeruginosa and Micrococcus Luteus – Experimental and Simulation Studies

Large numbers of microbial operations in industries employ mixed populations and in natural systems mixed culture of microorganisms are the rule rather than the exception. The mixed species interact in complex ways. Amensalism is a negative kind of interaction in which the growth of one species is inhibited by the presence of another, whose growth is unaltered due to interaction. The experimental studies (batch conditions) on the pure and mixed culture operations of the bacterial system Pseudomonas aeruginosa and Micrococcus luteus proved the existence of amensal interaction against luteus species. The experiments were carried out with various initial substrate concentrations (0, 100, 200, 300 and 400 mg/ml) to study its influence on the pure and mixed culture growth. Suitable models were developed to predict the pure and associated growth rates based on logistic equations. The k values in the logistic equation remained constant with respect to the initial substrate dosage for both the species (pseudomonas species: 0.2417 h^-1; micrococcus species: 0.2066 h^-1). However the other constant β showed decreasing trend (cubic polynomial) with increasing glucose concentrations for both the species. The interaction effect of species 2 on 1 is negligible whereas the interaction function f₂₁(x₁, x₂) for the second by the first species is found to be second order. The interaction parameter a₂₁ varies as a cubic polynomial with respect to the initial substrate concentration. Extension of the batch case equations to continuous operation was carried out using Chemostat model. The simulation studies yielded the range of dilution rates to be maintained for coexistence of both the species for the various initial concentrations and the respective steady state microbial concentrations.