USING A NONANALYTICAL APPROACH TO MODEL NONLINEAR DYNAMICS IN PHOTOSYNTHESIS AT THE PHOTOSYSTEM LEVEL¹

Abstract

Nonlinear dynamics in photon capture and uptake at the photosystem level may have a strong effect on photosynthetic yield. However, the magnitude of such effects is difficult to estimate theoretically because nonlinear systems often cannot be represented accurately using equations. A nonanalytical simulation was developed that used a simple decision tree and Monte Carlo methods, instead of equations, to model how a population of photosystems absorbs and utilizes photons from an ambient light field. This simulation replicated realistic kinetics in the closure and variable fluorescence yield of PSII on the single-turnover timescale, as well as the saturating behavior in light-driven electron flow that is observed in nature with increasing irradiance. This simulation indicated that the transfer of absorbed photon energy among PSII units can introduce strong nonlinear enhancement in light-driven electron flow. However, this effect was seen only in populations with particular photosynthetic states as determined by physiological properties of PSII. Other populations with the same degree of energy transfer but with different photosynthetic states exhibited little enhancement in electron flow and, in some cases, a reduction. This nonanalytical approach provides a simple means to quantify theoretically how nonlinear dynamics in photosynthesis arise at the photosystem level and how these dynamics may act to enhance or constrain photosynthetic rates and yields. Such simulations can provide quantitative insight into different physiological bases of nonlinear light-harvesting dynamics and identify those that would have the strongest theoretical influence and thus warrant closer experimental examination.Key index words: model; Monte Carlo; nonanalytical; nonlinear; photosynthesis; photosystem; phytoplankton; PSII; simulation Abbreviations: FRR (FRRF), fast repetition rate (fluorometer); RCII, reaction center II Several analytical equations have been used to parameterize the photosynthesis-irradiance (P-E) relationship of plants and algae. These include rectangular hyperbolae (Maskell 1928, Baly 1935, Thornley 1998, hyperbolic tangents (Jassby and Platt 1976), quadratics (Smith 1936), exponentials (Webb et al. 1974), and other more complex forms (Bannister 1979, Thornley 1998). These equations all express the saturation of P with increasing E that is observed in nature and are useful in ecological models for characterizing the approximate photosynthetic state of plants and algae. Yet these equations do not provide a mechanistic description of the specific physiological factors that control the P-E relationship. The parameters in these equations are purely empirical and lack concise physiological definitions (Abbott 1993).A mechanistic model for the saturating P-E relationship can also be derived from physiological first principles by using target theory, which describes photon capture and uptake at the photosystem level in terms of two physiological properties of photosystems: their mean functional cross-section (r) to absorb ...