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Cardiovascular Research 53 (2002) 48–58 www.elsevier.com / locate / cardiores Review Water content and its intracellular distribution in intact and saline perfused rat hearts revisited Mayis K. Aliev a , *, Pierre Dos Santos b , Jacqueline A. Hoerter c , Sybille Soboll d , Alexander N. Tikhonov e , Valdur A. Saks f a Institute of Experimental Cardiology, Cardiology Research Center, 3 rd Cherepkovskaya Street 15 A, 121552 Moscow, Russia b INSERM U-441, Pessac, France c INSERM U-446, Chatenay-Malabry, France d Institut fur Physiologische Chemie I, Duesseldorf, Germany e Faculty of Physics, M.V. Lomonosov Moscow State University, Moscow, Russia f University of Joseph Fourier, Grenoble, France and National Institute of Chemical Physics and Biophysics, Tallinn, Estonia Received 4 May 2001; accepted 3 August 2001 Abstract Precise estimation of cellular water content is a necessary basis for quantitative studies of metabolic control in the heart; however, marked discrepancies in water spaces of heart tissue are found in the literature. Reasons for this wide diversity are analyzed, and the conclusion is that the most probable value of total intracellular water content is 615 ml H 2 O / kg of wet mass (wm) and intracellular content of dry substance is 189 g / kg wm in intact in vivo rat heart. An extracellular water of 174 ml per kg wm and 22 g of dry mass per kg wm in vascular and interstitium spaces account for the rest of the tissue mass. These values can be directly related to normoosmotic saline perfused hydrated hearts, characterized by water accumulation in the extracellular spaces. Due to essentially intact heart cells, the experimentally determined dry mass, water and metabolite contents of these hydrated hearts can be extrapolated to the original morphological configuration of an intact heart muscle before the onset of edema. Such an ‘extrapolated’ heart is defined as a standardized perfused heart (SPH). SPH is the heart in its original morphological configuration, characterized by cell density and cellular water contents of the intact heart, but with perfusate in the extracellular spaces. The total cellular water is distributed in the cell compartments of SPH and intact hearts according to volumes of particular compartments and density of their dry mass. The volumes of bulk water phases in different organelles, accessible to diffusion of low molecular metabolites, were obtained after corrections for the fraction of ‘bound’ water of 0.3 g per g of compartmental dry mass content. The diffusible water spaces are proposed to be 321, 55, 153, 21 and 8 ml / kg wm for myofibrils, sarcoplasm, mitochondria, sarcoplasmic reticulum and nuclei, respectively. The SPH model allows direct comparison of metabolic data for intact and perfused hearts. We used this model to analyze the penetration of extracellular marker into cells of intact and hydrated perfused rat hearts. 2002 Elsevier Science B.V. All rights reserved. Keywords: Interstitial space; Intra / extracellular ions; Mitochondria; Myocytes; NMR 1. Introduction A precise estimation of water content in tissue and in different subcellular compartments is the basis of in vivo calculations of the rates of biochemical reactions [1], the Abbreviations: wm, wet mass; dm, dry mass; SPH, standardized perfused heart; swm, wet mass of SPH; sdm, dry mass of SPH *Corresponding author. Tel.: 17-095-414-67-55; fax: 17-095-414-6699. E-mail address: aliev m [email protected] (M.K. Aliev). ] ] energy fluxes between cellular compartments [2], the concentration gradients of ions [3], the membrane potential of mitochondria in situ [4], as well as of quantitative studies of metabolic control in different organs, including hearts. In pathological situations, such as early stages of cardiac hypertrophy [5] and cardiac ischemia [6–10], cardiomyocytes undergo significant cellular edema due to increase in cellular osmolarity. Cell swelling causes stretch Time for primary review 27 days. 0008-6363 / 02 / $ – see front matter 2002 Elsevier Science B.V. All rights reserved. PII: S0008-6363( 01 )00474-6 M.K. Aliev et al. / Cardiovascular Research 53 (2002) 48 – 58 and / or deformation of cell membranes and of the underlying cytoskeletal network [11]. These events lead to essential changes in the activities of cellular transporters and ion channels, cell membrane potential, protein and carbohydrate metabolism, lipogenesis and gene expression. As a consequence, these alterations of cellular hydration have been suggested in hepatic cells to be a new important mechanism for metabolic control, linking cell function to hormonal and environmental alterations (for reviews see [12,13]). The relevance of this mechanism for the metabolic control in cardiac cells is currently under consideration (for reviews see [11,14]). However, exploration of this topic requires an accurate estimation of the cardiac cell water contents. Osmotic effects, underlying the metabolic control by cell volume regulation, were first studied by Overton [15]. According to his works, 65% of total cellular water is osmotically active in cell volume regulation, while the remaining 35% of water molecules are bound to biopolymers and cellular membranes. Functional significance of bound water in cellular metabolism was clearly demonstrated in resting cysts of Artemia salina [16]. When the humidity level drops below 30% (30 g of water per 100 g of their dry mass), the cyst metabolism completely stops. At a humidity level of 35%, metabolic pathways of carbohydrates, amino acids and Krebs cycle are activated, while further increase in humidity, up to 63%, activates the pathways of protein and nucleic acid synthesis, and cells can perform all the essential metabolic reactions necessary for their development. Despite the great number of publications, the Overton’s concept of cellular bound and osmotically inactive water is still a matter of discussions (for references see reviews [1,17–21]). The detailed analysis of conflicting results should be based on reliable data on water contents in muscle cells and its intracellular distribution. However, until now, there is no final agreement even on the total water contents in normal cardiac cells. Table 1 lists the main published data on the water and dry mass contents in saline perfused and intact hearts. This table demonstrates (column 4) a wide variability of water estimates, from 1.81 [24] up to 3.15 ml / g dm [23]. There is also wide range of estimations of water content in mitochondria: from 1.0 ml / mg protein according to [27] to 1.8 ml / mg protein [28], corresponding to 9.2 or 16.5% of total cellular water, respectively [29]. The total volume occupied by mitochondria in the normal cardiac cell equals to 33–35% [30,31]. A correct estimation of mitochondrial water is fundamental for our understanding of the role of mitochondria in pathological situation. For example, ischemia, besides increasing the total cell hydration, causes pathological dehydration of mitochondrial matrix and reciprocal swelling of mitochondrial intermembrane space [32]. Preventing these mitochondrial alterations by opening the mitochondrial ATP-sensitive K 1 channel [33] or by ischemic preconditioning of the organ [34] protects the 49 heart against ischemia–reperfusion damage. Besides, ischemic preconditioning also prevents the cell hydration [7] or may even lead to cardiomyocyte dehydration [35]. In this communication, we analyze the results of different published studies on total intracellular water contents in saline perfused hearts and in normal hearts in vivo, and evaluate possible artifacts leading to current underestimation of cardiac cellular water contents and discrepancies in the data. Based on these results, we suggest that the most probable value of total cellular water content is 3.25 ml / kg dm, and propose its intracellular distribution, corrected for a fraction of bound water of 0.3 g per 1 g of the compartmental dry mass. 2. Water in intact hearts 2.1. Total cellular water Recently Dobson and Cieslar [26] and Cieslar et al. [36] performed tracer estimation of intracellular, interstitial and blood spaces in the intact rat myocardium in vivo. Extracellular tracers, 14 C-inulin or 14 C-mannitol, were injected intravenously 30 min before taking samples of heart tissue and blood [26]. Various parameters were measured: (i) tracer contents in hearts, blood and blood plasma; (ii) total water contents in tissue determined by gravimetric heart drying procedure; (iii) perfusion bed volumes (vascular plus capillary volumes) obtained by enzymatic determination of 2,3-diphosphoglycerate (specific marker of red blood cells) contents in blood and tissue. Their estimation of cellular water contents in intact rat hearts, 2.75 and 2.64 ml / g dm (Table 1, column 4), appears very high when compared with recent direct estimation of Clarke et al. [24], 1.81 ml / g dm, or Dobson [3], 2.4 ml / g dm (Table 1). Because of the importance of this topic, let us consider in more detail the experimental results of Dobson and Cieslar [26]. Two misuses of their data should be noted. First, with 14 C-mannitol, which completely distributes in erythrocytes [26], the plasma space (total tissue counts divided by specific activity of tracer in blood plasma) corresponds to the relative mass of extracellular space but not to its water content (Table 1, column 2). This is because the mass of plasma is a sum of water and dry matter masses of plasma. Second, with 14 C-inulin which is completely excluded from erythrocytes [26], the plasma space outlines the volume of extracellular space without erythrocytes (Fig. 1A). Therefore, we reevaluated these data and compared them with the results of morphometry measurements performed under the same conditions [30,37]. Morphometry estimates are most reliable due to the advantage of direct measurements and corrections for compression factors [30,37]. We considered only the measurements with inulin because they are commonly considered as more reliable [38–40]. 50 Table 1 Main published data on the water and dry mass contents in saline perfused and in vivo hearts Reference Protocol Experimental data Dry mass (g / kg wm) Perfused hearts, working model of Neely (WH) or Langendorff perfusion (LP) Morgan et al. [22] Rat, WH 18965 (20 min perfusion, n56) a Guinea-pig, WH (15 min perfusion, n59) 13963 Cell. H 2 O in SPH model (ml / kg swm) 513 Extracellular H 2 O (ml / kg wm) Cellular H 2 O, (ml / kg wm) 1000 g – (112) 33167 by 3 H-sorbitol 480612 2.5460.13 259617 by 3 H-inulin 602620 4.3260.24 439648 by 14 C-urea 3.1560.23 a,b Masuda et al. [3] Rat, WH (50 min perfusion, n59) 14763 508615 by 14 C-mannitol 34868 2.3760.10 486 Clarke et al. [24] Rat, LP (30 min perfusion, n56) 11364 682655 by 31 P-PPA (NMR) 205659 by 31 P-DMMP (NMR) 1.8160.59 367 Askenazy and Navon [10] Rat, LP (20 min perfusion, n536) by 1 H-H 2 O (NMR) 2.5060.06 507 by 59 Co-cobaltcyanide (NMR) In vivo hearts Clarke et al. [24] Rat (tracer equilibration 0.5–3 h, n56) 22364 15666 by 3 H-sucrose in blood 621610 2.7860.09 Polimeni et al. [25] Rat (tracer equilibration 10–160 min, n58) 21467 20967 by 3 H-inulin in plasma 57767 2.7660.12 Dobson and Cieslar [26] Rat (tracer equilibration 30 min, n55) 210610 212610 by 14 C-inulin in plasma 236612 by 14 C-mannitol in plasma 578610 2.7560.18 615 554612 2.6460.18 615 c 210610 Dry mass contents were estimated by gravimetry of dried tissue sample; extracellular water contents were estimated from the radioactivity of indicated tracer in the tissue sample or by NMR spectroscopy (NMR) of indicated compound in the tissue. PPA and DMMP are phenylphosphonate and dimethyl methylphosphonate, respectively. Cellular water contents were estimated as total tissue water minus its extracellular content, 10002(columns 112). For perfused hearts, the total cellular water content by the SPH model was obtained by multiplying the data of column 4 by the dry mass content in SPH, 202.6 g / kg swm (see 2.1). Throughout this paper we assume that the mass of 1 ml of water equals 1 g. a Exposure time to 3 H-inulin, 5–8 min, was too short in this protocol to attain complete equilibration; this leads to underestimation of extracellular space size and respective overestimation of cellular water content per dry mass unit. b 14 C-urea at the given time exposure, 13–15 min, labels only part of total tissue water [23]. c For total cellular water content by SPH model see Section 2.1. M.K. Aliev et al. / Cardiovascular Research 53 (2002) 48 – 58 Bunger [23] Cell. H 2 O ml per g dry mass, 3/1 M.K. Aliev et al. / Cardiovascular Research 53 (2002) 48 – 58 51 Fig. 1. Schematic presentation of the main tissue compartments: cellular (Cell), interstitial (IS) and vascular perfusion bed (PB) in blood perfused intact hearts (A), saline perfused hydrated hearts (B) and assumed standardized perfused hearts (C). In intact hearts (A) extracellular spaces (IS1PB) are filled with plasma and blood cells in PB. In saline perfused hearts (B) the washout of plasma proteins leads to saline accumulation in the extracellular spaces due to more filtration at a given hydrostatic pressure. Cellular water contents in these hearts could be the same as in the intact ones because the saline is isoosmotic to cardiomyocytes. The SPH model (C) defines the heart in the original morphological configuration of the intact heart in which saline replaces plasma and blood cells in the extracellular space. We found that the values obtained by Dobson and Cieslar [26] for blood (106611 g / kg wm, n510) and interstitial space (153611 g / kg wm, n55) sizes were calculated correctly. These data were evaluated by comparison with the direct morphometry estimates of Anversa et al. [30] for intact rat hearts in comparable units (g / kg wm), presented in Table 2. It is evident that the estimates of Dobson and Cieslar are certainly higher than corresponding values obtained from morphometry measurements: 80 g / kg wm for capillary bed size and 116 g / kg wm for interstitium plus T-system sizes (Table 2). The weight difference of 26 g (106 g / kg280 g / kg) for perfusion bed size can be accounted for by the persistence of blood remnants in heart chambers after the freeze clamping procedure [26]. For this reason, we chose to use the morphometry value (75.5 ml / kg wm, Table 2) as a reliable measure of heart perfusion bed volume. The difference of 37 g for interstitium sizes (153 g / kg2116 g / kg) may be due to some artifacts. For example, extracellular plasma space for inulin determined by Dobson and Cieslar, 212610 g / kg wm, is identical to that determined by Polimeni et al. [25], 20967 g / kg wm, under similar conditions (Table 1). However, Polimeni et al. [25] found the extrapolated time-zero inulin plasma space, obtained from a series of eight measurements performed every 30 min after tracer bolus injection, to be lower by 34 g / kg wm, leading to an actual value of 17565 g / kg wm. Taking this correction into account, the interstitial space determined by morphometry methods and tracer methods can be considered to be similar, 116 ml / kg wm and 119 ml / kg wm (153234), respectively. The artifacts in tracer methods will be considered below (Section 3.3). This analysis gives an important conclusion: with appropriate corrections for artifacts the data from tracer measurements in the intact hearts are similar to morphometry estimations, substantiating each other. As a consequence, it Table 2 General parameters of main tissue compartments of in vivo blood-perfused rat heart related to 1 kg of tissue wet mass Extracellular space a Volume (ml) Weight (g)b Dry mass (g)c Water content (ml)c Vascular bed Interstitium 75.562.8 8063 1360.6 6764 109.466.3 11666 960.6 10767 Cell Total (tissue) 758.5612.8 80469 189611 615621 943.465.3 1000 211610 789610 a The original morphometry data of Anversa et al. [30], 8063 ml / l for capillary bed volume and 11666 ml / l for interstitium plus T-system volumes, were converted into ml / kg wm units using the value of 1.0660.006 g / ml wm [41] for heart tissue density. b The compartmental weights were obtained by back multiplying the volumes by the mean density of tissue, 1.06 g / ml. c See Section 2.1 for explanation. M.K. Aliev et al. / Cardiovascular Research 53 (2002) 48 – 58 52 seems reasonable to use the morphometry estimates of extracellular space sizes of Table 2 as a reliable basis for considering water contents in the in vivo rat heart. Taking into account the dry mass contents measured in the blood (16%) [26] and blood plasma (8%) [26], the dry mass contents in vascular bed and interstitium compartments of intact rat heart can be estimated as 13 g / kg wm (80 g / kg wm30.16) and 9 g / kg wm (116 g / kg wm3 0.08), respectively (Table 2). The water contents in vascular bed and interstitium, 67 ml / kg wm and 107 ml / kg wm, respectively (Table 2), are calculated as the difference between weights and dry mass contents. Total tissue water content measured by Dobson and Cieslar [26] is 790610 ml / kg wm. With minor correction for the water content in the assumed blood remnants in heart chambers (26 g / kg wm30.84521.8 ml / kg wm) we obtain a value of 768.2 ml of tissue water (790 ml–21.8 ml) in 974 g (1000–26 g) of heart tissue, that is 788.7 ml of tissue water per kg wm (Table 2). The corrected total dry mass content in heart tissue is (1000–788.7)5211.3 g / kg wm (Table 2). Thus, the total cellular water space of intact heart can be calculated as the difference between tissue and extracellular water contents that is 614.8 ml / kg wm [(788.7– 67.2– 106.7) ml / kg wm] (Table 2). In the same way the intracellular dry mass content was calculated as 189.2 g / kg wm (Table 2). These final values of 615 ml H 2 O / kg wm and 189 g dm / kg wm, obtained from a revaluation of data from the literature, can be treated as the most probable estimates of total cellular water and dry mass contents in intact rat hearts. Based on these estimates, we may consider the distribution of water and dry mass in main cellular compartments of intact rat heart. 2.2. Intracellular water distribution Table 3 presents the water contents in different cellular compartments calculated on the basis of the morphometry determination of Anversa et al. [31] for rat left ventricular myocardium, and the measured densities of dry masses in cellular organelles [43]. In our calculations we assumed that the total cellular space of 758.5 ml / kg wm (Table 2) is distributed among cellular compartments according to their contribution to total cellular volume and density of dry mass in particular compartments. The dry mass contents in these compartments (third column in Table 3) were obtained by multiplying rD,X (the density of the dry mass in the compartment X in g / ml) by VV,X (the volume of this compartment, related to kg wm, ml / kg wm, column 2 of Table 3). The values of rD,0 (the density of dry mass in the reference compartment (myofibrils) in g / ml) were obtained by solving Eq. (1) in [43] under the assumption that the relative densities of dry masses ( rD,X / rD,0 ) are equal to 0.76 in the sarcoplasm and nuclei, 1.0 in the myofibrils, 1.04 in the sarcoplasmic reticulum, and 1.78 in mitochondria [43] O( r rD,cell 5 rD,0 3 x D,X / rD,0 ) 3VV,X (1) In this equation, rD,cell is the cellular dry mass related to kg wm (189.2 g in Table 3). Finally, we obtain rD,X 5 rD,0 3 ( rD,X / rD,0 ) (1a) The water contents in cellular compartments (MH 2 O , 4th column in Table 3) were calculated according to modified Eq. (2) from [43] MH 2 O 5VV,X 3 (1 1 (1 2 1 /rS ) 3 rD,X ) 2 MD (2) where VV,X is the volume (2nd column in Table 3), MD is a dry mass content (3rd column in Table 3), rD,X is a density of the dry mass in the compartment X determined according to Eq. (1a), and rS is the density of solid cellular dry mass ( rS 51.3166 g / cm 3 ). The value of rS was estimated by dividing the cellular dry mass (189.2 g / kg wm, Table 3) by its volume (758.5 ml of cell volume2614.8 ml of cellular water, Table 3). The data for mitochondria presented in Table 3 need special consideration. First, the in vivo mitochondria are characterized by a high relative density of dry mass (up to 47.2% of cellular dry mass) and a high relative amount of protein. For comparison, the protein content in the matrix of perfused rat hearts was determined by non-polar fractionation technique as 40.5% of total cellular protein [37]. Taking into account that the protein content in mitochondrial matrix is about 88% of mitochondrial protein Table 3 Most probable intracellular water and dry mass distribution in intact rat heart related to 1 kg of tissue wet mass Cellular compartment Myofibrils Sarcoplasm Mitochondria Sarcoplasmic reticulum Nucleus Total % of cell volume [31] 53.9 8.7 32.7 3.5 [42] 1.2 100.0 Volume of compartment (ml) Dry mass in compartment (g) Total water in compartment (ml) Water space for diffusion (ml) 408.8 66.0 248.0 26.6 9.1 82.7 10.1 89.4 5.6 1.4 346.0 58.3 180.2 22.3 8.0 321 55 153 20 8 758.5 189.2 614.8 558 M.K. Aliev et al. / Cardiovascular Research 53 (2002) 48 – 58 [44], the protein content in intact mitochondria should be 46% (40.5% / 0.88). This value is comparable with the dry mass content of in vivo mitochondria. Second, the predicted water content of in vivo mitochondria, 2.02 ml / mg dm (180.2 / 89.4, Table 3), practically coincides with value of 1.93 ml / mg dm, determined for in situ rat heart mitochondria by X-ray microanalysis [43]. Taking into consideration the mitochondrial protein content, which comprises in rat heart mitochondria about 75% of their dry mass [45–47], the values of 2.69 and 2.58 ml / mg protein are obtained. These values are considerably higher than data reported for isolated rat liver mitochondria (1.96622 ml / mg protein (n59), measured with 14 C-polyethylene glycol) [48], and for isolated rat heart mitochondria (1.8060.27 ml / mg protein, measured with inulin) [28]. To explain these discrepancies, it should be noted that isolated and native mitochondria are characterized by different architecture. The architecture of in vivo mitochondria is stabilized by cytoskeleton [17]. This may preclude the shrinkage of mitochondrial matrix detected in isolated mitochondria [49]. The shrinkage of mitochondrial matrix in isolated mitochondria depends on the composition of the isolation media [50], of the ionic composition and pH of incubation media and of the metabolic state of mitochondria [48]. This means that the isolated mitochondria cannot be used as a decisive reference for the estimation of in vivo mitochondrial water volumes. Underestimation of water contents in isolated mitochondria may arise also from partial permeability of their outer membranes to inulin [50]. Thus, it seems reasonable to consider the data of Table 3 as the most probable ones for distribution of water and dry mass in the cellular compartments of intact rat heart. These values, mainly based on the analysis of data for rat hearts, can be directly applied to hearts of other species characterized by the same density of cellular dry mass in vivo. Cellular water distribution in this case can be predicted (as in Table 3) from morphometry data on cellular compartments in the hearts of ten different animal species, including humans [51]. 2.3. Volume of intracellular aqueous domains accessible for low molecular metabolites Table 3 shows in column 4 the contents of total water (MH 2 O ) in heart cell and its compartments. However, to calculate the real concentrations of low molecular metabolites (ATP, PCr, Cr, Pi, glucose, etc.) in cell compartments, we need to know the volumes of bulk aqueous domains accessible to these metabolites (Wa ). Thus, we have to correct the content of total water inside the cell for the fraction of water molecules that drop out of the aqueous bulk phase. These are the ‘immobilized’ osmotically inactive water molecules bound to biopolymers and cellular membranes. 53 The concept of cellular bound and osmotically inactive water, first proposed by Overton [15] in 1902, is still a matter of controversy (for references see reviews [1,17– 21]). An average amount of water bound to proteins was evaluated as 0.3 g H 2 O / g dm [52,53]. To function, globular proteins require a threshold level of hydration, about 0.4 g H 2 O per g dry protein [54]. In lipid membranes, about 14–18 water molecules are bound to one lipid molecule [55]. Nucleic acids contain 10–11 molecules of water per pair of bases (for references see review [56]). The fraction of bound water was evaluated by different methods. As early as in 1930, Hill [57] measured the water vapor tensions for frog’s blood and skeletal muscles by the thermoelectric method. He concluded that the dominant portion of cell water (94%) behaves as a usual solvent, while the osmotically ‘inert’ fraction of water was about 6%. Similar results were obtained later by other methods. Belton et al., studying the proton relaxation in frog skeletal muscles by the NMR method, concluded that at a temperature ranging from 28 to 208C approximately 94% of total water in the tissues corresponded to bulk water while the remaining fraction (6%) was strongly immobilized [58]. Outhred and George [59] confirmed the limited mobility of several percent of cellular water. To discriminate between bulk and immobilized water, other workers used osmotic effects. For instance, Garlid [60] squeezed the water out of the matrix of rat liver mitochondria by a progressive increase in osmolality by non-permeant sucrose in the incubation media. Extrapolating the matrix water contents to the limit of infinite concentration of sucrose, he obtained a fraction of osmotically inactive water of 0.28 ml of H 2 O / mg dm. Unlike water, the content of DMSO (dimethylsulphoxide) in the matrix was extrapolated to zero, indicating the complete removal of bulk water from the matrix [60]. Thus, DMSO molecules do not penetrate into the osmotically inactive cell water domains [61]. Based on these data, we could accept 0.3 g H 2 O / g dm as the most probable content of bound water in the cell. This value corresponds to 56.8 g of cellular water / kg wm in intact hearts (189.230.3, Table 3) or 9% of total cellular water (56.8 / 614.83100%, Table 3). This is osmotically inert fraction of cell water [57] characterized by strongly immobilized water protons [58]. The main portion of cell water (about 91%) belongs to osmotically active water from the bulk phase aqueous domains where the low molecular metabolites and water molecules can freely diffuse. Garlid [60,62] considered the fraction of osmotically inactive water as an aqueous phase with abnormal solvent properties for low molecular permeant nonelectrolytes, such as glycerol, ethanol, urea and antipyrin. It is important to note that the amount of bound water, 0.3 g H 2 O / g dm, is not sufficient to form complete monomolecular water layer around each macromolecule [63]. 54 M.K. Aliev et al. / Cardiovascular Research 53 (2002) 48 – 58 Therefore, in such abnormal solvent phase, the ‘solution’ of nonelectrolytes might be considered as the replacement of bound water molecules by nonelectrolyte ones or as the inclusion of nonelectrolyte molecules between the immobilized water ones. In both cases, the nonelectrolytes are expected to be immobilized and osmotically inactive. The real interaction of low molecular nonelectrolytes with macromolecules is a rather complex event [64–67]. Based on accepted value of bound water space, 0.3 g H 2 O / g dm, we have calculated the probable sizes of compartmental water spaces, accessible for the diffusion of low molecular metabolites (Table 3, last column). The data were calculated as the difference between total water content in the given compartment and 0.3 g of bound water per gram of the compartmental dry mass. The relevance of the data presented in Table 3 to saline perfused hydrated hearts is considered below. most precise because these authors dried the finely powdered frozen tissue instead of using the conventional procedure using the whole heart. The dry mass of intact hearts obtained by conventional procedures is higher: 226614 g / kg wm (data from 33 references with n $ 8, reviewed by Polimeni [68]). Standardized dry mass for such hearts, dried by conventional procedures, can be estimated as 202.6 g sdm / kg wm (189.2 g dm3(226 / 211.3)10.25 g dm). The concept of SPH gives the opportunity for a direct comparison of metabolic control data in the intact and hydrated perfused hearts, as the cellular water contents and its intracellular distribution are assumed similar in both cases. Using this model, the measured water or metabolite contents must be expressed per assumed 189.4 or 202.6 g sdm of SPH (see above) and then distributed in the water of cellular compartments. An example of using this model of SPH is given below. 3. Water in saline perfused hearts 3.2. First exploration of standardized perfused heart model 3.1. Standardization problem In normoosmotic saline perfused hearts, cardiomyocytes essentially preserve their functional capabilities, dry mass and metabolite contents. Assuming that due to isoosmolarity of perfusing solution the water content per cell volume remains the same as in intact heart, we can evaluate the changes in the morphological configuration (defined as the respective contribution of perfusion bed, interstitium and cellular space to total tissue volume) occurring upon saline perfusion. These changes are mainly characterized by a decreased cardiomyocyte density due to water accumulation in the extracellular spaces (Fig. 1B, columns 1 and 2 of Table 1), caused by the replacement of blood and plasma by saline perfusate in the vascular space and interstitium, respectively. Because cells are assumed to be essentially intact, the measured dry mass, water and metabolite contents of hydrated hearts can be extrapolated to the original morphological configuration of heart muscle before the onset of edema. We suggest defining such an extrapolated heart as a standardized perfused heart (SPH). SPH is the heart in its original morphological configuration but with perfusate in the extracellular spaces (Fig. 1C). The dry mass of such a standardized heart (standard dry mass (sdm)) is the sum of cellular dry mass (DM,cell 5189.2 g, Table 3) and the dry mass of perfusate in the vascular and interstitium spaces. The dry mass of perfusate, calculated as product of dry mass density of perfusate (Dperf 5 0.00134 g / ml) and volumes of vascular and interstitium spaces (Table 2), is low, 0.25 g (Dperf 3(75.51109.4) ml). So, the dry mass of standardized heart is 189.4 g sdm / kg wm. The dry mass value of standardized heart is based on the corrected dry mass estimate of Dobson and Cieslar [26] (211 g / kg wm, Table 2). This value can be taken as the Assuming that standardized dry mass of conventionally dried heart is equal to 202.6 g sdm / kg wm, we can estimate the maximal amount of cellular water in saline perfused hearts from the reported data on their cellular water and dry mass contents. These values, obtained by simple multiplication of column 4 data in Table 1 by the dry mass contents in SPHs, 202.6 g sdm / kg wm, are listed in column 5 of Table 1. The mean value of four estimations of the literature data, 468634 ml / kg wm of standardized heart, is lower than the predicted maximal water content of 615 ml / kg wm. Considering these data, we can point out two important topics. First, the value of total water content for SPH obtained from data of Askenazy and Navon [10] (507 ml / kg swm) is the same as that obtained from data of Morgan et al. [22] (513 ml / kg swm). This confirms that the new multinuclear NMR method for continuous monitoring of 59 Co (cobaltcyanide as extracellular marker) and 1 H (H 2 O as total water marker) signal intensities [10] is as reliable as the classic method based on the measurements of total water contents by gravimetry of dried tissue using radioactivity of 3 H sorbitol as extracellular tracer [22]. Because of non-invasiveness and possibility of continuous monitoring of cellular water contents, the NMR method of Askenazy and Navon [10]can be considered as more advantageous. Second, the value for standardized water spaces obtained from data of Clarke et al. [24] (367 ml / kg swm) is lower than the averaged value (468634 ml / kg wm). These authors used 31 P NMR spectroscopy to monitor dimethyl methylphosphonate (DMPP) and phenylphosphonate (PPA) contents in perfused hearts. DMPP was used as a marker of total water spaces, and PPA as a pH-sensitive marker of extracellular spaces. Careful examination of M.K. Aliev et al. / Cardiovascular Research 53 (2002) 48 – 58 NMR spectrum in Fig. 1 of this paper reveals asymmetry of the PPA resonance with some shoulder-like left-side directed enlargement. Taking into account the usual pH difference about 0.4 unit between intra- and extracellular spaces in myocardium and pH-sensitivity of PPA, this shoulder-like enlargement may be caused by penetration of PPA into more acidic environment of heart cells. Indeed, this shoulder appears quite clearly in the 31 P NMR spectra after 28 min of heart ischemia, when intracellular pH decreases to 6.1 (Fig. 2 in Ref. [24]). These data can be considered as a first direct manifestation of intracellular penetration of extracellular markers, suggested previously by Polimeni [68] and Polimeni and Buraczewski [69] for all low-molecular ‘extracellular’ markers. The penetration of PPA into cardiomyocytes may be the reason for low standardized cellular water contents obtained by Clarke et al. [24] as compared with other estimations (Table 1). Taken together, the data of Clarke et al. [24] and Polimeni [25,68,69] suggest that the origin of differences between calculated (468634 ml / kg swm, n54) and predicted (615 ml / kg wm) standardized cellular water contents could be the penetration of the ‘extracellular markers’ into cardiomyocytes. The maximum percentage of penetration can be evaluated as 23.865.6% (n54), that is the average of four normalized differences between predicted standardized (column 5 in Table 1) and calculated (column 3 in Table 1) water spaces. For example, for data of Masuda et al. [3], this normalized difference is (615–486) / 6153100520.9%. This example clearly shows how, using the SPH model, we can compare the absolute estimates of water contents obtained by different methods and authors. 3.3. Extracellular marker penetration into heart cells Recently we attempted to quantify the penetration of extracellular markers into cells of saline perfused isolated guinea pig hearts [38]. Kinetic curves for low-molecularweight markers (LMM: 35 SO 4 or 14 C-sucrose) or 3 H-inulin washout from the perfused hearts were analyzed by mathematical model of tracer exchange in the extracellular spaces of perfused myocardium [70]. This kinetic model permits the estimation of the volumes of vascular perfusion bed and interstitium and the extent of penetration of extracellular tracer into heart cells. Extracellular marker penetration into cells was evaluated as 28.1% for LMM and 18.2% for inulin. LMM penetration into cardiomyocytes was 1.54-fold higher than inulin. The percentage of low-molecular tracer leakage into cells, 28.1%, is comparable with presumed percentage of tracer penetration for chosen published data (23.865.6% (n54), see Section 3.2). These data indicate that the actual in vitro tracer penetration into cellular space may be high enough to account for aforesaid difference between calculated 55 (468634 ml / kg wm) and predicted (615 ml / kg wm, Table 2) standardized cellular water contents. Possible leakage of ‘extracellular tracer’ into cardiomyocytes in vivo can be estimated from the data of Dobson and Cieslar [26]. With inulin, the plasma excess in tracer-determined compared to morphometry-determined interstitium spaces, is 37 g (see Section 2.1). This aliquot will contain 34 ml of water per kg wm of tissue (37 g / kg30.92). The 34 ml of plasma water, when actually distributed in cellular water, will give 5.5% tracer penetration into cells (34 / 6153100%). In the same way, based on the 14 C-mannitol-determined value of 17368 g / kg wm for interstitium space [26], we obtain a 57 g / kg wm overestimation of the real interstitium space (173–116). With water contents of 52.4 ml in these aliquots (57 g / kg3 0.92), the possible in vivo percentage of 14 C-mannitol penetration into cardiomyocytes would equal 8.5% (52.4 / 6153100). Again, as in vitro, penetration of low-molecular tracers into cardiomyocytes is increased by a factor of 1.54 (8.5% / 5.5%) when compared to inulin. Lower percentages of tracer penetrations in vivo may indicate the better conservation of cardiomyocytes under blood perfusion conditions. From these calculations and the basic assumption that under normoosmotic saline perfusion the heart cells essentially retain their original water contents, we conclude that the value of 615 ml cellular H 2 O / kg wm of intact heart or 615 ml / 189.4 g sdm53.25 ml cellular H 2 O / g sdm (see Section 3.1) will represent an actual measure of total cellular water contents in standardized normoosmotic perfused hydrated rat hearts. To use this value, the dry mass of perfused hearts should be determined very carefully, as in paper of Dobson and Cieslar [26] (see Section 3.1). For the conventionally dried hearts the proposed cellular water contents will be 615 ml / 202.6 g sdm53.03 ml / g sdm. 3.4. Content of intracellular water in the hearts with cellular edema Standardized heart model implies that normal cardiomyocytes preserve their in vivo water content per cell volume unit. However, it has been reported that, compared to intact hearts, cardiomyocytes of saline perfused hearts accumulate 33.5% additional amount of water, even in normoosmotic perfusion medium [69]. This high value is likely overestimated. Indeed, the basic isoosmotic perfusion formula theoretically supposes complete preservation of initial (in vivo) water contents in the well-oxygenated cardiomyocytes of saline perfused hearts. This consideration is reinforced by recent direct demonstration that in saline perfused hearts the cardiomyocytes quickly (in a few minutes) respond to any changes in osmolarity of perfusate by accumulation or loss of total cellular water [10]. 56 M.K. Aliev et al. / Cardiovascular Research 53 (2002) 48 – 58 Therefore, we reanalyzed the data of Polimeni and Buraczewski [69]. They compared the morphometrically measured in vitro cardiomyocyte water content of 3.34 ml / g dm with in vivo cellular water contents of 2.50 ml / g dm previously measured by Polimeni [25] (see Fig. 2 in Ref. [69]). Polimeni used low-molecular extracellular tracers to determine the contents of cellular water in intact hearts [37]. Taking into account the ratio of dry mass contents in standardized (189.4 g / kg swm, see Section 2.2) and intact (211 g / kg wm, Table 2) hearts, as well as possible 8.5% penetration of low-molecular tracer into intact cardiomyocytes (see Section 3.3), the actual content of cellular water in vivo in the experiments of Polimeni [37] can be calculated as 3.04 ml / g sdm (2.503(211 / 189.4) /(120.085)). Thus, the cell hydration for data of Polimeni and Buraczewski [69] can be estimated as 9.9% (3.34 / 3.043100). This value, lower than the 33.5% reported by Polimeni and Buraczewski [69], appears more acceptable. A predicted slight cell hydration in saline perfused hearts suggests an experimental re-evaluation of osmolarity values in all used ‘normoosmotic’ crystalloid perfusion media. The actually isoosmotic well oxygenated perfusion solution should guarantee 10061% conservation of initial (in vivo) water contents in cardiomyocytes of otherwise hydrated hearts. Only with actually isoosmotic (normoosmotic) perfusion media the model of standardized saline perfused heart can be successively used for metabolic analysis. This example also shows the usefulness of the SPH model for the analysis of data in hydrated hearts. explained by the underestimation of the volume of total cellular water (see details in Section 3.3). The cellular contents of charged ATP and PCr molecules, determined by chemical and NMR techniques, are similar in the majority of experiments (see review of Saks [1]). This means that the vast majority of these molecules belong to free (unbound) molecules. When we cannot neglect the bound metabolites, special corrections should be taken into account to determine the concentrations of free metabolites. Our analysis based on the SPH model demonstrates that this approach can be used to evaluate the most probable values of cellular water contents and metabolite concentrations in intact and hydrated hearts. The SPH model supposes normalization of values per dry mass of tissue, since the determination of tissue dry mass is rather simple and essentially free from severe artifacts. Such a normalization has an advantage over the conventional practice of normalizing the measured values to wet mass or protein mass of hydrated hearts, since the determination of actual tissue wet mass of hydrated heart can be severely affected by postperfusional manipulations [38,40]. The measured protein contents in hydrated hearts are sometimes very high, up to 155 mg / g wm [71], while even in the SPH hearts the protein content, taken as 70% of dry mass content [29,44], must be lower, about 133 mg / g wm (189.4 g dm / kg swm30.7). Potentially, the SPH model may be the basis for unified treatment of data in heart bioenergetics, allowing the direct comparison of metabolic data from different works. 4. Concentrations of intracellular metabolites in intact and ‘standardized’ perfused hearts Acknowledgements Having evaluated volumes of the bulk water domains where metabolites can diffuse, one can calculate the concentration, Ci , of a certain metabolite i as the ratio of the total amount of this metabolite, Mi , to the diffusion accessible water space of the compartment, Vi , (Table 3, last column). For example, for a chemically measured ATP content of 23.862.6 mmol per g dm of perfused rat heart [24], the calculations of ATP concentration will be performed in two steps. First, the ATP content will be expressed per 202.6 g dm of standardized heart, yielding 4822 mmol ATP/ kg swm (23.83202.6). Second, assuming for simplicity (for details see Ref. [2]) a uniform distribution of ATP in the diffusion accessible water domains of myofibril, sarcoplasm and mitochondria with a pooled volume of 529 ml / kg swm (3211551153, Table 3), we obtain an ATP concentration in all these compartments of about 9.12 mM. The original estimate by Clarke et al. [24] of the cellular ATP, 10.1 mM, is higher, despite the fact that they normalized the ATP content per whole fraction of estimated total cellular water. This discrepancy could be The authors wish to thank Professors V.I. Lobyshev, Moscow State University, Russia, and V.I. Kapelko, Cardiology Research Center, Moscow, Russia, for valuable discussions; Dr. K.D. Garlid, Oregon Graduate Institute of Science and Technology, USA, for constructive advice and critical analysis of the text and an anonymous reviewer for valuable comments. Part of this work was supported by grant 00-04-48330 from the Russian Foundation for Basic Researches (MKA and ANT) and INTAS grant 99-1086 (ANT). MKA thanks INSERM for a 3-month support in France. References [1] Saks VA, Khuchua ZA, Vasilyeva EV, Belikova YuO, Kuznetsov AV. Metabolic compartmentation and substrate channeling in muscle cells. Role of coupled creatine kinases in in vivo regulation of cellular respiration – a synthesis. Mol Cell Biochem 1994;133– 134:155–192. [2] Aliev MK, Saks VA. Compartmentalized energy transfer in cardiomyocytes: use of mathematical modeling for analysis of in vivo regulation of respiration. Biophys J 1997;73:428–445. M.K. Aliev et al. / Cardiovascular Research 53 (2002) 48 – 58 [3] Masuda T, Dobson GP, Veech RL. The Gibbs–Donnan near-equilibrium system of heart. J Biol Chem 1990;265:20321–20334. [4] Wan B, Doumen C, Duszynski J, Salama G, LaNoue KF. A method of determining electrical potential gradient across mitochondrial membrane in perfused rat heart. Am J Physiol 1993;265:H445– H452. [5] Meerson FZ. The myocardium in hyperfunction, hypertrophy and heart failure. Circ Res 1969;25(Suppl II):88. [6] Amano J, Sunamori M, Kameda T, Okamura T, Suzuki A. Correlation among water content, left ventricular function, coronary blood flow, and myocardial metabolism after hypothermic ischemic cardiac arrest. Adv Myocardiol 1983;4:465–471. [7] Murry CE, Richard VJ, Reimer KA, Jennings RB. Ischemic preconditioning slows energy metabolism and delays ultrastructural damage during a sustained ischemic episode. Circ Res 1990;66:913– 931. [8] Qui Y, Hearse DJ. Comparison of ischemic vulnerability and responsiveness to cardioplegic protection in crystalloid-perfused versus blood-perfused hearts. J Thoracic Cardiovasc Surg 1992;103:960–968. [9] Garcia-Dorado D, Oliveras J, Gili G et al. Analysis of myocardial oedema by magnetic resonance imaging early after coronary artery occlusion with or without reperfusion. Cardiovasc Res 1993;27:1462–1469. [10] Askenazy A, Navon G. Continuous monitoring of intracellular volumes in isolated rat hearts during normothermic perfusion and ischemia. J Mag Res 1997;124:42–50. [11] Vandenberg JI, Rees SA, Wright AR, Powell T. Cell swelling and ion transport pathways in cardiac myocytes. Cardiovasc Res 1996;32:85–97. [12] Haussinger D, Lang F, Gerok W. Regulation of cell function by the cellular hydration state. Am J Physiol 1994;267:E343–E355. [13] Weiergraber O, Haussinger D. Hepatocellular hydration: signal transduction and functional implications. Cell Physiol Biochem 2000;10:409–416. [14] Deaton LE. Comparative aspects of cellular-volume regulation in cardiomyocytes. Physiol Zool 1997;70:379–390. [15] Overton E. Beitrage zur allgemeinen Muskel-und Nervenphisiologie II. Pflugers Arch 1902;92:346–386. [16] Clegg JS. Interrelationships between water and cellular matabolism in Artemia cysta. VI. RNA and protein synthesis. J Cell Physiol 1977;91:143–154. [17] Saks VA, Dos Santos P, Gellerich FN, Diolez P. Quantitative studies on enzyme–substrate compartmentation, functional coupling and metabolic channeling in muscle cells. Mol Cell Biochem 1998;184:291–307. [18] Ling GN. The polarized multilayer theory of cell water. In: Keith AD, editor, The aqueous cytoplasm, New York: Marcel Dekker, 1979, pp. 23–60. [19] Ling GN. In search of the physical basis of life, New York: Plenum Press, 1985. [20] Belton PS, Ratcliffe RG. NMR and compartmentation in biological tissues. Progr NMR Spectrosc 1985;17:241–279. [21] Garlid KD. The state of water in biological systems. Int Rev Cytol 2000;192:281–302. [22] Morgan HE, Regen DM, Park CR. Identification of a mobile carrier-mediated sugar transport system in muscle. J Biol Chem 1964;239:369–374. [23] Bunger R. Compartmented pyruvate in perfused working heart. Am J Physiol 1985;249:H439–H449. [24] Clarke K, Anderson R, Nedelec JF, Foster D, Ally A. Intracellular and extracellular spaces and the direct quantification of molar intracellular concentrations of phosphorus metabolites in the isolated rat heart using 31 P NMR spectroscopy and phosphonate markers. Mag Res Med 1994;32:181–188. [25] Polimeni PP, Cutilletta AF, Otten MD. Cation distributions in the hypertrophic myocardium (aortic construction) of the rat. Cardiovasc Res 1983;17:170–176. 57 [26] Dobson PF, Cieslar JH. Intracellular, interstitial and plasma spaces in the rat myocardium in vivo. J Mol Cell Cardiol 1997;29:3357– 3363. [27] LaNoue KF, Walajtys EJ, Williamson JR. Regulation of glutamate metabolism and interactions with the citric acid cycle in rat heart mitochondria. J Biol Chem 1973;248:7171–7183. [28] Kauppinen RA, Hiltunen JK, Hassinen I. Subcellular distribution of phosphagens in isolated perfused rat heart. FEBS Lett 1980;112:273–276. [29] Bunger R, Soboll S. Cytosolic adenylates and adenosine release in perfused working rat heart. Comparison of whole tissue with cytosolic non-aqueous fractionation analysis. Eur J Biochem 1986;159:203–212. [30] Anversa P, Olivetti G, Melissari M, Loud AV. Morphometric study of myocardial hypertrophy induced by abdominal aortic stenosis. Lab Invest 1979;40:341–349. [31] Anversa P, Levicky V, Beghi C, McDonald SL, Kikkawa Y. Morphometry of exercise-induced right ventricular hypertrophy in the rat. Circ Res 1983;52:57–64. [32] Kowaltowski AJ, Seetharaman S, Paucek P, Garlid KD. Bioenergetic consequences of opening the mitochondrial ATP-sensitive K 1 channel of heart mitochondria. Am J Physiol 2001;280:H649–H657. [33] Garlid KD, Paucek P, Yarov-Yarovoj V et al. Cardioprotective effect of diazoxide and its interaction with mitochondrial ATP-sensitive K 1 channels: possible mechanism of cardioprotection. Circ Res 1997;81:1072–1082. [34] Laclau MN, Boudina S, Thambo JB et al. Cardioprotection by ischemic preconditioning preserves mitochondrial function and functional coupling between adenine nucleotide translocase and creatine kinase. J Mol Cell Cardiol 2001;33:947–956. [35] Askenazy N, Navon G. Intermittent ischemia: energy metabolism, cellular volume regulation, adenosine and insights into preconditioning. J Mol Cell Cardiol 1997;29:1715–1730. [36] Cieslar J, Huang MT, Dobson GP. Tissue spaces in rat heart, liver and skeletal muscle in vivo. Am J Physiol 1998;275:R1530–R1536. [37] Polimeni PI. Extracellular space and ionic distribution in rat ventricle. Am J Physiol 1974;227:676–683. [38] Aliev MK, Khatkevich AN, Tsyplenkova VG, Meertsuk FE, Kapelko VI. Tracer kinetics analysis of the extracellular spaces in saline perfused hearts. Exp Clin Cardiol 2001, in press. [39] Fisher RB, Lindsay DB. The action of insulin on the penetration of sugars into the perfused rat heart. J Physiol 1956;131:526–541. [40] Taylor IM, Huffines WD, Young DT. Tissue water and electrolytes in an isolated perfused rat’s heart preparation. J Appl Physiol 1961;16:95–102. [41] Cellarius YuG, Eriskovskaya NK. Stereological study of absolute total volumes of structural components of the myocardium in hypertrophy. Bull Exper Biol Med 1979;87:627–630, [Russian]. [42] Page E, McCallister LP. Quantitative electron microscopic description of heart muscle cells. Application to normal, hypertrophied and thyroxin-stimulated hearts. Am J Cardiol 1973;31:172–181. [43] von Zgliniski T, Bimmer M. The intracellular distribution of ions and water in rat liver and heart cells. J Microsc 1987;146:77–85. [44] Albers B, Bray D, Lewis J et al. In: Molecular biology of the cell, New York, London: Garland, 1983, p. 487. [45] Clejan S, Jonas E, Collipp PJ, Fugler L, Maddaiah VT. Influence of growth hormone and thyroxine on thermotropic effects of respiration and 1-anilino-8-naphthalene sulphonate fluorescence and on lipid composition of cardiac membranes. Biochim Biophys Acta 1981;678:250–256. [46] Daum G. Lipids of mitochondria. Biochim Biophys Acta 1985;822:1–42. [47] Horikawa Y, Goel A, Somlyo AP, Somlyo AV. Mitochondrial calcium in relaxed and tetanized myocardium. Biophys J 1998;74:1579–1590. [48] Holian A, Wilson DF. Relationship of transmembrane pH and electrical gradients with respiration and adenosine 59-triphosphate synthesis in mitochondria. Biochemistry 1980;19:4213–4221. 58 M.K. Aliev et al. / Cardiovascular Research 53 (2002) 48 – 58 [49] Beavis AD, Brannan RD, Garlid KD. Swelling and contraction of the mitochondrial matrix. J Biol Chem 1985;260:13424–13433. [50] Werkheiser WC, Bartley W. The study of steady-state concentrations of internal solutes of mitochondria by rapid centrifugal transfer to a fixation medium. Biochem J 1957;66:79–91. [51] Barth E, Stammler G, Speiser B, Schaper J. Ultrastructural quantitation of mitochondria and myofibrils in cardiac muscle from 10 different animal species including man. J Mol Cell Cardiol 1992;24:669–681. [52] Bull H, Breese K. Protein hydration. I. Binding sites. Arch Biochem Biophys 1968;128:488–496. [53] Kuntz JD. Hydration of macromolecules. III. Hydration of polypeptides. J Am Chem Soc 1971;93:514–516. [54] Rupley JA, Careri G. Protein hydration and function. Adv Protein Chem 1991;41:37–172. [55] Luzardo MC, Amalfa F, Nunez AM et al. Effect of trehalose and sucrose on the hydration and dipole potential of lipid bilayers. Biophys J 2000;78:2452–2458. [56] Yevdokimov YM, Golo VL, Salyanov VI, Lortkipanidze GB, Kats EI. The ‘phantom’ structure of solvent and the packing of doublestranded molecules of nucleic acids in particles of mesomorphic dispersions. Biofizika (Biophys Russia) 2000;45:1029–1038. [57] Hill AV. The state of water in muscle and blood and the osmotic behavior of muscle. Proc Roy Soc 1930;B106:477–505. [58] Belton PS, Jackson RR, Packer KJ. Pulsed NMR studies of water in striated muscle. I. Transverse nuclear spin relaxation times and freezing effects. Biochim Biophys Acta 1972;286:16–25. [59] Outhred RK, George EP. Water and ions in muscle and model systems. Biophys J 1973;13:97–103. [60] Garlid KD. Overview of our understanding of intracellular water in hydrated cells. In: Crowe JH, Clegg JS, editors, Dry biological systems, New York: Academic, 1978, pp. 3–19. [61] Elford BC. Non-solvent water in muscle. Nature 1970;227:282–283. [62] Garlid KD. Aqueous phase structure in cells and organelles. In: Drost-Hansen W, Clegg JS, editors, Cell-associated water, New York: Academic, 1979, pp. 293–361. [63] Khurgin YI, Sherman FB, Tusupkaliev U. Izotermy gidratatsii globulyarnyh belkov v dinamicheskom rezhime (The hydration isotherms of globular proteins in the dynamic mode). Biokhimia (Biochemistry USSR) 1977;42:490–497. [64] Kuntz JD. Hydration of macromolecules. II. Effects of urea on protein hydration. J Am Chem Soc 1971;93:514–516. [65] Priev A, Almagor A, Yedgar S, Gavish B. Glycerol decreases the volume and compressibility of protein interior. Biochemistry 1996;35:2061–2066. [66] Avdulov NA, Chochina SV, Daragan VA et al. Direct binding of ethanol to bovine serum albumin: a fluorescent and 13 C NMR multiplet relaxation study. Biochemistry 1996;35:340–347. [67] Tsai AM, Neumann DA, Bell LN. Molecular dynamics of solid-state lysozyme as affected by glycerol and water: a neutron scattering study. Biophys J 2000;79:2728–2732. [68] Polimeni PI, Measurement of myocardial electrolyte distributions. In: Linden RJ (ed). Techniques in the Life Sciences, P3 / II. Cardiovascular Physiology. Elsevier, Shannon, 1984;P317:1–34. [69] Polimeni PI, Buraczewski SI. Expansion of extracellular tracer space in the isolated heart perfused with crystalloid solutions: extracellular space, trans-sarcolemmal leakage, or both? J Mol Cell Cardiol 1988;20:15–22. [70] Aliev MK. The analysis of extracellular calcium exchange in perfused myocardium using mathematical modeling. J Mol Cell Cardiol 1989;21:849–863. [71] Dos Santos P, Aliev MK, Diolez P et al. Metabolic control of contractile performance in isolated perfused rat heart. Analysis of experimental data by reaction: diffusion mathematical model. J Mol Cell Cardiol 2000;32:1703–1734.