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Cardiovascular Research 2002 53(1):48-58; doi:10.1016/S0008-6363(01)00474-6
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Copyright © 2001, European Society of Cardiology

Water content and its intracellular distribution in intact and saline perfused rat hearts revisited

Mayis K Alieva,*, Pierre Dos Santosb, Jacqueline A Hoerterc, Sybille Sobolld, Alexander N Tikhonove and Valdur A Saksf

aInstitute of Experimental Cardiology, Cardiology Research Center, 3rd Cherepkovskaya Street 15A, 121552 Moscow, Russia
bINSERM U-441, Pessac, France
cINSERM U-446, Chatenay-Malabry, France
dInstitut fur Physiologische Chemie I, Duesseldorf, Germany
eFaculty of Physics, M.V. Lomonosov Moscow State University, Moscow, Russia
fUniversity of Joseph Fourier, Grenoble, France and National Institute of Chemical Physics and Biophysics, Tallinn, Estonia

* Corresponding author. Tel.: +7-095-414-67-55; fax: +7-095-414-66-99 aliev_m_k{at}mtu-net.ru

Received 4 May 2001; accepted 3 August 2001


   Abstract
Top
 Abstract
1. Introduction
 2. Water in intact...
 3. Water in saline...
 4. Concentrations of...
 References
 
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 H2O/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.

KEYWORDS wm, wet mass; dm, dry mass; SPH, standardized perfused heart; swm, wet mass of SPH; sdm, dry mass of SPH


   1. Introduction
Top
 Abstract
 1. Introduction
2. Water in intact...
 3. Water in saline...
 4. Concentrations of...
 References
 
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 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 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].


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  		Table 1 Main published data on the water and dry mass contents in saline perfused and in vivo hearts

 
There is also wide range of estimations of water content in mitochondria: from 1.0 µl/mg protein according to [27] to 1.8 µl/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+ channel [33] or by ischemic preconditioning of the organ [34] protects the 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
Top
 Abstract
 1. Introduction
 2. Water in intact...
3. Water in saline...
 4. Concentrations of...
 References
 
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, 14C-inulin or 14C-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 14C-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 14C-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].


Figure 1
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  		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 (IS+PB) 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 (106±11 g/kg wm, n=10) and interstitial space (153±11 g/kg wm, n=5) 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/kg–80 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/kg–116 g/kg) may be due to some artifacts. For example, extracellular plasma space for inulin determined by Dobson and Cieslar, 212±10 g/kg wm, is identical to that determined by Polimeni et al. [25], 209±7 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 175±5 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 (153–34), respectively. The artifacts in tracer methods will be considered below (Section 3.3).


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  		Table 2 General parameters of main tissue compartments of in vivo blood-perfused rat heart related to 1 kg of tissue wet mass

 
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 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 wmx0.16) and 9 g/kg wm (116 g/kg wmx0.08), 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 790±10 ml/kg wm. With minor correction for the water content in the assumed blood remnants in heart chambers (26 g/kg wmx0.84=21.8 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)=211.3 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 H2O/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.


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  		Table 3 Most probable intracellular water and dry mass distribution in intact rat heart related to 1 kg of tissue wet mass

 
The dry mass contents in these compartments (third column in Table 3) were obtained by multiplying {rho}D,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 {rho}D,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 ({rho}D,X/{rho}D,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]

Formula (1)
In this equation, {rho}D,cell is the cellular dry mass related to kg wm (189.2 g in Table 3). Finally, we obtain

Formula (1a)

The water contents in cellular compartments (MH2O, 4th column in Table 3) were calculated according to modified Eq. (2) from [43]

Formula (2)
where VV,X is the volume (2nd column in Table 3), MD is a dry mass content (3rd column in Table 3), {rho}D,X is a density of the dry mass in the compartment X determined according to Eq. (1a), and {rho}S is the density of solid cellular dry mass ({rho}S=1.3166 g/cm3). The value of {rho}S was estimated by dividing the cellular dry mass (189.2 g/kg wm, Table 3) by its volume (758.5 ml of cell volume–614.8 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 [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 µl/mg dm (180.2/89.4, Table 3), practically coincides with value of 1.93 µl/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 µl/mg protein are obtained. These values are considerably higher than data reported for isolated rat liver mitochondria (1.96±22 µl/mg protein (n=9), measured with 14C-polyethylene glycol) [48], and for isolated rat heart mitochondria (1.80±0.27 µl/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 (MH2O) 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.

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 H2O/g dm [52,53]. To function, globular proteins require a threshold level of hydration, about 0.4 g H2O 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 –8 to 20°C 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 µl of H2O/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 H2O/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 (189.2x0.3, Table 3) or 9% of total cellular water (56.8/614.8x100%, 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 H2O/g dm, is not sufficient to form complete monomolecular water layer around each macromolecule [63]. 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 H2O/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.


   3. Water in saline perfused hearts
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 Abstract
 1. Introduction
 2. Water in intact...
 3. Water in saline...
4. Concentrations of...
 References
 
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=189.2 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=0.00134 g/ml) and volumes of vascular and interstitium spaces (Table 2), is low, 0.25 g (Dperfx(75.5+109.4) 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 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: 226±14 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 dmx(226/211.3)+0.25 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.

3.2 First exploration of standardized perfused heart model
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, 468±34 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 59Co (cobaltcyanide as extracellular marker) and 1H (H2O 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 3H 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 (468±34 ml/kg wm). These authors used 31P 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 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 31P 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 (468±34 ml/kg swm, n=4) 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 23.8±5.6% (n=4), 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)/615x100=20.9%.

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-molecular-weight markers (LMM: 35SO4 or 14C-sucrose) or 3H-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 (23.8±5.6% (n=4), 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 (468±34 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/kgx0.92). The 34 ml of plasma water, when actually distributed in cellular water, will give 5.5% tracer penetration into cells (34/615x100%). In the same way, based on the 14C-mannitol-determined value of 173±8 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/kgx0.92), the possible in vivo percentage of 14C-mannitol penetration into cardiomyocytes would equal 8.5% (52.4/615x100). 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 H2O/kg wm of intact heart or 615 ml/189.4 g sdm=3.25 ml cellular H2O/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 sdm=3.03 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].

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 (2.50x(211/189.4)/(1–0.085)). Thus, the cell hydration for data of Polimeni and Buraczewski [69] can be estimated as 9.9% (3.34/3.04x100). 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 100±1% 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.


   4. Concentrations of intracellular metabolites in intact and ‘standardized’ perfused hearts
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 Abstract
 1. Introduction
 2. Water in intact...
 3. Water in saline...
 4. Concentrations of...
References
 
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 23.8±2.6 µmol 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 µmol ATP/kg swm (23.8x202.6). 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 (321+55+153, 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 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 swmx0.7). 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.

Time for primary review 27 days.


   Acknowledgements
 
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.


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 2. Water in intact...
 3. Water in saline...
 4. Concentrations of...
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