Mathematical Models of Electrical Activity in Plants

Abstract

Electrical activity plays an important role in plant life; in particular, electrical responses can participate in the reception of the action of stressors (local electrical responses and oscillations) and signal transduction into unstimulated parts of the plant (action potential, variation potential and system potential). Understanding the mechanisms of electrical responses and subsequent changes in physiological processes and the prediction of plant responses to stressors requires the elaboration of mathematical models of electrical activity in plant organisms. Our review describes approaches to the simulation of plant electrogenesis and summarizes current models of electrical activity in these organisms. It is shown that there are numerous models of the generation of electrical responses, which are based on various descriptions (from modifications of the classical Hodgkin-Huxley model to detailed models, which consider ion transporters, regulatory processes, buffers, etc.). A moderate number of works simulate the propagation of electrical signals using equivalent electrical circuits, systems of excitable elements with local electrical coupling and descriptions of chemical signal propagation. The transmission of signals from a plasma membrane to intracellular compartments (endoplasmic reticulum, vacuole) during the generation of electrical responses is much less modelled. Finally, only a few works simulate plant physiological changes that are connected with electrical responses or investigate the inverse problem: reconstruction of the type and parameters of stimuli through the analysis of electrical responses. In the conclusion of the review, we discuss future perspectives on the simulation of electrical activity in plants.

Connection of the Photochemical Reflectance Index (PRI) with the Photosystem II Quantum Yield and Nonphotochemical Quenching Can Be Dependent on Variations of Photosynthetic Parameters among Investigated Plants: A Meta-Analysis

“…can reveal a new field for use of the photochemical reflectance index. In particular, PRI can potentially be used for fast and remote investigations of systemic photosynthetic responses induced by long-distance stress signals, including electrical [140][141][142][143][144][145][146][147], hydraulic [148], and Reactive Oxygen Species (ROS) [149] signals which strongly influence photosynthetic processes (e.g., the nonphotochemical quenching).…”

Communication in Plants: Comparison of Multiple Action Potential and Mechanosensitive Signals With Experiments

“…Note that the channel k 1 (opening) and k 2 (closing) reaction rate constants depend on the membrane potential crossing a specific threshold value, resulting in the generation of an AP signal. We also note that these rate constants are exponentially dependent on the membrane potential as discussed in [11]. The AP signal propagates from one cell to another, resulting in multiple APs impacting a single cell.…”

Communication and Information Theory of Single Action Potential Signals in Plants

“…Some other work presents a model with an electrical processes developing on plasma-lemma of cell without stimulation [42]. There are some models which aim to present a theoretical and mathematical model of AP generation and propagation for plants [6], [21].…”

“…Note that the channel k 1 (opening) and k 2 (closing) reaction rate constants depend the on membrane potential crossing a specific threshold value, resulting in AP signal generation. We also note that these rate constants are exponentially dependent on the membrane potential similar to [21]. For simplicity we can replace differential Equation (1) for the membrane potential by following stationary equation as per the models given in [3], [23]:…”