ISSN 1990-7478, Biochemistry (Moscow) Supplement Series A: Membrane and Cell Biology, 2009, Vol. 3, No. 2, pp. 101–115. © Pleiades Publishing, Ltd., 2009. Original Russian Text © F.I. Ataullakhanov, N.O. Korunova, I.S. Spiridonov, I.O. Pivovarov, N.V. Kalyagina, M.V. Martinov, 2009, published in Biologicheskie Membrany, 2009, Vol. 26, No. 3, pp. 163–179. 101 1 The ionic asymmetry of cells, i.e., the fact that the concentrations of Na + , K + , Ca 2+ ions inside the cells are strongly different from their concentrations in extracel- lular liquids, is known for a long time [1]. This phe- nomenon has been and is explained in different ways [2]. It seems quite natural to assume that such asymme- try provides the sensitivity of cells to damage [3–5]. Another supposition, indisputable with respect to excit- able cells, is the statement that the ionic asymmetry is needed for electric potential generation and for ensur- ing the electric activity of cells [6–9]. One more version is that the presence of ion gradient permits active trans- port of various useful substances into a cell [10–12]. Each of these assumptions is reasonable in relation to the same types of cells and may be disputed in relation to other types. However, ionic asymmetry exists in all cells without exception. Moreover, the concentrations of univalent cations are practically the same in the cells of all types [1]. Such surprising uniformity compels us to think that the ionic asymmetry is an element of one of the most basic cell systems. In recent years is has become clear that it is really so, because any cell consists of a great number of molecules, which are absent in the environ- ment, and these molecules generate an excess osmotic pressure in a cell, so that cells must resist osmosis and control their volume. This is the same basic problem for 1 The article is translated by the authors. any cell as, for example, energy supply. For the first time, the idea of association of ionic asymmetry with osmoregulation was apparently suggested in the work of Tosteson published in 1959 [13]; it was described in more details by Tosteson and Hoffman in 1960 [14]. Nearly half a century has passed since that time, and we finally begin to understand that the necessity of main- taining constant cell volume appears simultaneously with the very first cells in the course of evolution. For this purpose, nature has invented ion pumps, special channels, and a number of other notable systems, which provide the cell with fantastic stability and autonomy. We are still far from complete understanding of the whole picture; however, what we know anyway opens up a harmonious and beautiful multilevel system of cell volume control. This regulation has been studied best in the red blood cells (RBCs) of mammals; hence, volume control in a human RBC will be in the focus of attention in this paper. Mathematical models played a key role in the study of cell volume control [15–21]. The models provided answer to quite a number of questions, which were either very difficult or impossible to answer experimen- tally, predicted a series of unexpected connections in cell metabolism, and helped us to understand why a cell needs some senseless (on the face of it) biochemical reactions. In recent years, mathematical modeling has become popular. At the same time, the overwhelming majority How Erythrocyte Volume Is Regulated, or What Mathematical Models Can and Cannot Do for Biology 1 F. I. Ataullakhanov a–c , N. O. Korunova b , I. S. Spiridonov b , I. O. Pivovarov c , N. V. Kalyagina d , and M. V. Martinov b a Center for Theoretical Problems of Physicochemical Pharmacology, Russian Academy of Sciences, Moscow, 119991 Russia; e-mail: fazly@hc.comcor.ru b National Research Center for Hematology, Russian Academy of Medical Sciences, Moscow, 125167 Russia c Physics Department, Moscow Lomonosov State University, Moscow, 119991 Russia d Bauman State Technical University, Moscow, 105005 Russia; Received January 31, 2009 Abstract—Modern concepts of the red blood cell (RBC) volume regulation are considered. It is shown that the system of ion pumps and channels in the cell membrane ensures the physiological value of volume with a pre- cision of about 10% even at 5- to 7-fold variations of passive membrane permeability for ions. Particular atten- tion is paid to mathematical models for evaluation of the role of different molecular mechanisms in the RBC volume control. It is shown that many questions, for example, ‘why the Na + ,K + -ATPase pumps the ions in oppo- site directions’ or ‘what is the physiological role of Ca 2+ -activated K + -channels’, cannot be answered without adequate mathematical models of such complex control systems as cell volume control. Key words: red blood cell, Na + ,K + -pump, Ca 2+ -activated K + -channels, cell volume, mathematical models. DOI: 10.1134/S1990747809020019