Modeling of Photosynthesis Process and Assessing Of Phytoplankton Dynamics Based On Droop Model

The work focuses on the modeling the light-dependent growth of Arthrospira platensis. During the experimental study, we obtained a batch curve, which characterizes the presence of a long linear phase. We showed that the constant culture productivity is determined by the light conditions in which cells are located. The simplest model of the light-dependent growth of a batch culture is proposed. The model is based on the assumption that the specific growth rate is determined by the surface irradiation, the light absorption coefficient, and the concentration of chlorophyll a. Verification of the obtained equations indicates that the constant productivity is observed only in the case of a hyperbolic decrease chlorophyll a content and other structural compounds of microalgal biomass. A method for rapid assessment of the concentration of photosynthetic pigments in the A. platensis culture by its absorption spectrum using the sum of Gaussian curves is proposed. Mathematical decomposition of the absorption spectrum of A. platensis was carried out, all Gaussian parameters were calculated. For the red part of the spectrum, a simple expression is presented that allows one to estimate the concentration of chlorophyll a and phycobiliproteins. The native extinction coefficient of chlorophyll a at 678 nm was calculated to be 65 l·g-1·cm-1. We proposed an algorithm for determining the concentration of photosynthetic pigments directly from the true absorption spectrum of the A. platensis culture without interfering with its growth processes.

Quantitative Regularities of Growth of Arthrospira platensis Batch Culture

Lelekov¹,

Chernyshev²,

Klochkova³

2022

Two Approaches to Modeling Phytoplankton Biomass Dynamics Based on the Droop Model

Abakumov¹,

Pak²

2022

This work continues the study of the Droop model based on the concept of cell quota. Description of the photosynthetic processes in phytoplankton includes in the model structure. The concept of chlorophyll quota is used. It is the proportion of photosynthetic substances in plant cells. In addition to the chlorophyll quota, the photosynthetic activity of phytoplankton is determined by external conditions, primarily by the level of photosynthetically active radiation (PAR). The model is based on separating the dependence of phytoplankton reproduction on external conditions according to the stages of photosynthesis. The light stage is largely determined by the PAR, and the dark stage is limited by the nutrient resource under the controlling influence of the temperature of the aquatic environment. In order to develop the model, the storage of energy in the light stage of photosynthesis is described in detail. Energy is stored in the form of energy-intensive substances in macroergic molecules (macroergs). The most common cell macroerg is adenosine triphosphate (ATP). The proportion of ATP in phytoplankton varies depending on the light regime and on the energy amount stored in the dark stage. The model includes the Droop kinetics and equations for the dynamics of the chlorophyll quota and the ATP pool. The conditions for the existence and stability of equilibrium solutions are compared for the same values of parameters common to both models. The greatest influence on the dynamic modes of the minimum value of the cell quota has been established. The proportion of biomass associated with the light period of photosynthesis is also significant. For the first model that is the biomass produced during daylight hours. And in terms of the second model, it is the biomass formed due to the energy of ATP stored in the light phase. The influence of the structure of dynamic models on the daily and annual dynamics of phytoplankton was revealed. Scenarios of behavior of models under various lighting conditions, including constant and periodically changing lighting, have been studied.

Mathematical Model of Phytoplankton Interspecific Competition for Food Resource

Abakumov,

Kozitskaya

2023

The phytoplankton in an aquatic ecosystem is the basis of its life activity and the main producing link. The functioning of phytoplankton in same time depends on environmental factors: mineral nutrition, photosynthetically active solar radiation, water temperature and other less significant ones. Sunlight is a stable factor, varying predictably over time and space. The water temperature is the small regulatory factor. Concentrations of mineral substances can change quite quickly and significantly, this much influences on plant organisms. Thus, mineral nutrition is a basic environmental factor of influence to phytoplankton. On the other hand, in large aquatic basin such as seas and oceanic areas the distribution of living organisms is very heterogeneous in space. These two aspects – nutrient and spatial heterogeneity – are the focus of this article. A model of competitive interaction is considered using the example of two species of phytoplankton. The phytoplankton move passively in water what is simulated by the diffusion process. The model contains one non-trivial stationary and spatially homogeneous equilibrium and two trivial ones, i.e. degenerate in at least one species of phytoplankton. Trivial equilibria are stable only in some “degenerate” situations. The non-trivial equilibrium in “normal” conditions is stable to temporal and spatial disturbances. The behavior of solutions near a nontrivial equilibrium for a stationary living environment and in cases of its nonstationary is studied. Perturbation of a nontrivial equilibrium in a stationary environment leads to relatively long-term deviations from equilibrium and a slow return to it. The instability of trivial equilibria increases the spatial heterogeneity of solutions. At the same time, the nontrivial equilibrium computationally demonstrates weak properties of global stability in time. The unsteadiness of the environment is simulated by the unsteadiness of the influx of nutrients. It has been shown that the distribution of nutrients can lead to significant heterogeneity in the distribution of individuals across the spatial habitat.