Title: Stability of synchronization in the process of biochemical substance exchange in a diffusively coupled ring-like arrangement of cells in plants

Dragutin T. Mihailovic

University of Novi Sad, Serbia


Dragutin T. Mihailovic is Professor in Meteorology, Biophysics and Environmental Fluid Mechanics at the University of Novi Sad (Serbia). He was the Visiting Professor at University at Albany, The State University of New York at Albany, Visiting Scientist at the University of Agriculture, Wageningen and Norwegian Meteorological Institute. He has more than 100 peer-reviewed scientific papers in SCI(E) journals. He edited and wrote seven books and one monograph. He was the member of the Editorial Board of Environmental Modeling and Software (1992-2010) and reviewer in 15 scientific journals. He was the principal investigator in many international projects with U.S.A  and several European countries


Understanding how local intra-cellular biochemical exchange processes and global features, like environment and system size, influence the robustness, adaptability and evolution of the collective behavior of multi-cell systems is one of the most challenging topics in the biology of complex systems today. Information coupling and the exchange of biophysical substances among the components of multi-cell systems are both driven by a range of intrinsic and extrinsic factors. Many authors have invested significant contributions to the understanding of multi-cell system dynamics through studies of the stability of the synchronized state, which is required for robust functioning of the multi-cell system in the face of noise and perturbation. However, they considered cells as completely uniform particles, without internal structure and without the ability to change their behavior. In actuality, it is well known that in natural conditions, cells spend most of the time in the stationary phase which is characterized by a decrease in growth rate, slowdown of all metabolic processes and increase in resistance to several stress conditions. Since these and many other processes in a cell are defined as diffusion-like, it is important to see: (i) how these processes can be better represented in models, by introducing affinity in the diffusive coupling associated with biochemical substance exchange; and (ii) how intra-cellular dynamics are affected by the perturbation of parameters that represent the influence of the environment, cell coupling and cell affinity. In this study we numerically investigate a model of a diffusively coupled ring-like arrangement of cells in plants (specifically in roots). To model the dynamics of individual cells we propose a map with cell affinity, which is a generalization of the logistic map. First, the basic features of a one-cell system are studied in terms of the Lyapunov exponent, Kolmogorov complexity and Sample Entropy. Second, the notion of observational heterarchy, which is a perpetual negotiation process between different levels of the description of a phenomenon, is reviewed. After these preliminaries, we study how the active coupling induced by the consideration of the observational heterarchy modifies the synchronization property of the model with N=100 cells. It is shown numerically that the active coupling enhances synchronization of biochemical substance exchange in several different conditions of cell affinity.