Three-state mathematical model for the assessment of DCMU-treated photosystem II heterogeneity.

Photosystem II (PSII) is one of the main pigment-protein complexes of photosynthesis which is highly sensitive to unfavorable environmental factors. The heterogeneity of PSII properties is essential for the resistance of autotrophic organisms to stress factors. Assessment of the PSII heterogeneity may be used in environmental monitoring for on-line detection of contamination of the environment. We propose an approach to assess PSII oxygen-evolving complex and light-harvesting antenna heterogeneity that is based on mathematical modeling of the shape of chlorophyll a fluorescence rise of 3-(3,4-dichlorophenyl)-1,1-dimethylurea-treated samples. The hierarchy of characteristic times of the processes considered in the model makes it possible to reduce the model to a system of three ordinary differential equations. The analytic solution of the reduced three-state model is expressed as a sum of two exponential functions, and it exactly reproduces the solution of the complete system within the time range from microseconds to hundreds of milliseconds. The combination of several such models for reaction centers with different properties made it possible to use it as an instrument to study PSII heterogeneity. PSII heterogeneity was studied for Chlamydomonas at different intensities of actinic light, for Scenedesmus under short-term heating, and for Chlorella grown in nitrate-enriched and nitrate-depleted media.

Mathematical Simulation of Electron Transport in the Primary Photosynthetic Processes.

Summarized results of investigation of regulation of electron transport and associated processes in the photosynthetic membrane using methods of mathematical and computer modeling carried out at the Department of Biophysics, Faculty of Biology, Lomonosov Moscow State University, are presented in this review. Detailed kinetic models of processes in the thylakoid membrane were developed using the apparatus of differential equations. Fitting of the model curves to the data of spectral measurements allowed us to estimate the values of parameters that were not determined directly in experiments. The probabilistic method of agent-based Monte Carlo modeling provides ample opportunities for studying dynamics of heterogeneous systems based on the rules for the behavior of individual elements of the system. Algorithms for simplified representation of Big Data make it possible to monitor changes in the photosynthetic apparatus in the course of culture growth in a photobioreactor and for the purpose of environmental monitoring. Brownian and molecular models describe movement and interaction of individual electron carrier proteins and make it possible to study electrostatic, hydrophobic, and other interactions leading to regulation of conformational changes in the reaction complexes. Direct multiparticle models explicitly simulate Brownian diffusion of the mobile protein carriers and their electrostatic interactions with multienzyme complexes both in solution and in heterogeneous interior of a biomembrane. The combined use of methods of kinetic and Brownian multiparticle and molecular modeling makes it possible to study the mechanisms of regulation of an integral system of electron transport processes in plants and algae at molecular and subcellular levels.

Simulating the Interplay between the Uptake of Inorganic Phosphate and the Cell Phosphate Metabolism under Phosphorus Feast and Famine Conditions in Chlorella vulgaris.

Using a mathematical simulation approach, we studied the dynamics of the green microalga Chlorella vulgaris phosphate metabolism response to shortage and subsequent replenishing of inorganic phosphate in the medium. A three-pool interaction model was used to describe the phosphate uptake from the medium, its incorporation into the cell organic compounds, its storage in the form of polyphosphates, and culture growth. The model comprises a system of ordinary differential equations. The distribution of phosphorous between cell pools was examined for three different stages of the experiment: growth in phosphate-rich medium, incubation in phosphate-free medium, and phosphate addition to the phosphorus-starving culture. Mathematical modeling offers two possible scenarios for the appearance of the peak of polyphosphates (PolyP). The first scenario explains the accumulation of PolyP by activation of the processes of its synthesis, and the decline in PolyP is due to its redistribution between dividing cells during growth. The second scenario includes a hysteretic mechanism for the regulation of PolyP hydrolysis, depending on the intracellular content of inorganic phosphate. The new model of the dynamics of P pools in the cell allows one to better understand the phenomena taking place during P starvation and re-feeding of the P-starved microalgal cultures with inorganic phosphate such as transient PolyP accumulation. Biotechnological implications of the observed dynamics of the polyphosphate pool of the microalgal cell are considered. An approach enhancing the microalgae-based wastewater treatment method based on these scenarios is proposed.