Kinetic Monte Carlo simulation of the initial phases of chlorophyll fluorescence from photosystem II

Abstract

Kinetic Monte Carlo (KMC) simulation is employed to represent the photochemical reactions involved in the initial phases of chlorophyll fluorescence (ChlF) emission from photosystem II (PSII). Comparison with a differential equation representation reveals similarities and differences. Both KMC and differential equation models can describe the kinetic variations and show the main characteristics of ChlF emission. Differential equation models are simpler to implement but have limitations that warrant future improvements.

Introduction

In the plant photosynthetic process, absorbed light energy by chlorophyll molecules may be transferred forward and used for photochemical reactions, or dissipated as heat or fluorescence (Butler, 1978, Goltsev et al., 2003, Krause and Weis, 1991, Lavergene and Trissl, 1995, Stirbet et al., 1998, Vredenberg, 2004, Taiz and Zeiger, 2006). Because chlorophyll fluorescence (ChlF) competes for energy with photochemical reactions (Lubitz et al., 2008), the dynamics of ChlF is affected by photosynthetic activities (Kautsky and Hirsch, 1931, Stribet and Strasser, 1996, Rohacek and Bartak, 1999, Rohacek, 2002). This makes ChlF a useful indicator of plant physiology and environmental changes (DeEll and Toivonen, 2003, Guo and Tan, 2010, Rodriguez and Greenbaum, 2009, Zivcak et al., 2008).

Kinetic models are used to describe ChlF dynamics and to extract quantitative information from measured ChlF (Lazár, 2009, Lazár and Jablonský, 2009, Vredenberg, 2000, Vredenberg, 2008, Vredenberg, 2011, Vredenberg and Prasil, 2009). Differential equations have been commonly employed to represent the reaction kinetics (Chernev et al., 2006, Baake and Schloder, 1992, Goltsev and Yordanov, 1997, Guo and Tan, 2009, Guo and Tan, 2011, Lazár and Schansker, 2009, Zhu et al., 2005). While differential equations are compact and convenient to use, they have limitations in representing certain aspects of the process. These limitations may or may not be significant for a given application but need to be analyzed and understood.

Each reaction center (RC) functions as an individual unit and each has one plastoquinone A (Q_A) site and one plastoquinone B (Q_B) site (Guo and Tan, 2009, Guo et al., 2010). An electron entering an RC is carried first by Q_A, then Q_B and later steps (Goltsev and Yordanov, 1997, Blankenship, 2002). The individuality of the RCs and the order of events within an RC can be represented by first-order differential equations with possible combinations of Q_A and Q_B states as state variables as was done in Guo et al. (2010). ChlF emission, however, involves numerous antennas and a pool of plastoquinones corresponding to each RC. There are then thousands of combinations of redox or excitation states, which makes it practically impossible to use first-order kinetics to represent the reactions. Tokarčík (2012) attempted to model ChlF from PSII by using pi-calculus though potential limitations of differential equations were not specifically discussed. Using concentrations of individual chemical species as state variables result in a compact set of second-order differential equations as done in Guo and Tan (2011). The second-order differential equations, however, implicitly assume a well-mixed system. The effects of this assumption have not been demonstrated. Xin et al. (2013) simulated PSII ChlF by the Monte Carlo method with explicit description of PSII activities; however, a comparison of the results from Monte Carlo simulation and differential equations was not provided.

In this work, kinetic Monte Carlo (KMC) simulation (Gillespie, 1976, Gillespie, 1977) is used to represent the discrete events involved in the initial phases of PSII ChlF emission. Since KMC simulation can represent a large number of individual RCs and other members of the electron transport chain without resorting to assumptions, this gives an opportunity to compare KMC and differential equation models.