doi: 10.15389/agrobiology.2015.3.298eng

UDC 635.65:573.22

Supported by Russian Science Foundation (project № 14-26-00094).


N.I. Vorobyov, N.A. Provorov

All-Russian Research Institute for Agricultural Microbiology, Federal Agency of Scientific Organizations, 3, sh. Podbel’skogo, St. Petersburg, 196608 Russia,

Received March 24, 2015


A basic property of Rhizobia is the ability to compete for nodule formation under a multi strain inoculation. Its regulation remains poorly understood, thus limiting advances in biotechnological studies to improve the effectiveness of Rhizobia microbial preparations. The mathematical model of Rhizobia Nodulation Competitiveness (RNC) for describing a multi strains inoculation of leguminous plants is created (RNC-model). In the RNC-model we took into account that under Quorum Sensing regulation (QS-regulation) in soil niches not only the bacteria number in the niche, but a cell’s migration into adjacent niches is limited. The RNC-model represents a power-law nonlinear dependence of cell’s migration from a niche from the cell’s spatial density in the niche (the power value is less than 1). According to the formula of the RNC-model, the relative proportion of migratory cells from niche habitat decreases under increasing cell’s density. We suggest that after a multi strains inoculation in the rhizosphere of plants the bacterial strains with a large cells migration flow from the niche habitat (with big RNC) will be presented in large amounts. The verification and parametric identification (migration activity of strains, the index of frequency-dependent selection) of the RNC-model were carried out with using the previously published experimental data. The analysis of RNC-model’s parameters, calculated with using these data, showed that rizobia strains with a large migratory activity and a small index of frequency-dependent selection form a large migratory flow of cells from the niche habitat and demonstrate large RNC. The genetic modification of rhizobia with the aim of improving the RNC may cause the intensification of migration flows of strain cells from the niche habitat and the accelerated spending of niche resources. The intensive migration of cells from soil niche may lead to premature consumption of niche’s resource and cause a cell death of rhizobia before they form symbiosis with legume plants. The considered features of survival and migration of rhizobia in natural soil conditions must be considered, especially, in the development of microbial preparations with prolonged action.

Keywords: mathematical models, Rhizobia, nodulation competitiveness, Quorum Sensing regulation, migration, frequency-dependent selection.


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