Modern Physics Letters B Vol. 26, No. 5 (2012) 1150031 (9 pages) c  World Scientiﬁc Publishing Company DOI: 10.1142/S021798491150031X SYNCHRONIZATION IN BIOCHEMICAL SUBSTANCE EXCHANGE BETWEEN TWO CELLS DRAGUTIN T. MIHAILOVI ´ C Division of Biophysics, Department of Field and Vegetable Crop, Faculty of Agriculture, University of Novi Sad, Dositej Obradovic Sq. 8, Novi Sad, Serbia guto@polj.uns.ac.rs IGOR BALA ˇ Z Department of Physics, Faculty of Sciences, University of Novi Sad, Dositej Obradovic Sq. 5, Novi Sad, Serbia ibalaz@polj.uns.ac.rs Received 26 September 2011 Revised 18 October 2011 In this paper, Mihailovi´ c et al.[Mod. Phys. Lett. B 25 (2011) 2407–2417] introduce a simpliﬁed model of cell communication in a form of coupled diﬀerence logistic equa- tions. Then we investigated stability of exchange of signaling molecules under variability of internal and external parameters. However, we have not touched questions about syn- chronization and eﬀect of noise on biochemical substance exchange between cells. In this paper, we consider synchronization in intercellular exchange in dependence of environ- mental and cell intrinsic parameters by analyzing the largest Lyapunov exponent, cross sample entropy and bifurcation maps. Keywords : Intercellular communication; substances exchange; stability; coupled lo- gistic maps; synchronization; bifurcation maps; biophysical modeling; protein self- organization. 1. Introduction The eﬀort towards formalizing a model of process of material exchange between cells is still in its infancy and much remains to be completed to build a mature theory. For a model to be useful, it must be able to predict characteristics and behaviors of the biophysical system. This means that the model has to be framed to explicitly describe constraints that bind the system. That eﬀort is still going up over stairways that have not a complete structure. One of the hard tasks in build- ing those stairways are issues related to stability, 2 robustness, 3 synchronization 4,5 and noise 6,7 of the system. In essence, the usual biophysical model consists of an ensemble of interacting grid-cells, evolving according to the chosen model, with the interaction provided by the prescribed physical model. Such a system becomes the 1150031-1