Influence of reaction and diffusion on spatial organization of mitochondria and effectiveness factors in skeletal muscle cell design

A mathematical model is developed to analyze the influence of chemical reaction and diffusion processes on the intracellular organization of mitochondria in skeletal muscle cells. The mathematical modeling approach uses a reaction-diffusion analysis of oxygen, ATP, and ADP involved in energy metabolism and mitochondrial function as governed by oxygen supply, volume fraction of mitochondria, and rates of reaction. Superimposed upon and coupled to the continuum species material balances is a cellular automata (CA) approach governing mitochondrial life cycles in response to the metabolic state of the cell. The effectiveness factor (η), defined as the ratio of reaction rate in the system with finite rates of diffusion to those in the absence of any diffusion limitation is used to assess diffusional constraints in muscle cells. The model shows the dramatic effects that the governing parameters have on the mitochondrial cycle of life and death and how these effects lead to changes in the distribution patterns of mitochondria observed experimentally. The model results showed good agreement with experimental results on mitochondrial distributions in mammalian muscle fibers. The η increases as the mitochondrial population is redistributed toward the fiber periphery in response to a decreased availability of oxygen. Modification of the CA parameters so that the mitochondrial lifecycle is more sensitive to the oxygen concentration caused larger mitochondrial shifts to the edge of the cell with smaller changes in oxygen concentration, and thus also lead to increased values of η. The present study shows that variation in oxygen supply, muscle activity and mitochondrial ATP supply influence the η and are the important parameters that can cause diffusion limitations. In order to prevent diffusion constraints, the cell resorts to shifts in their mitochondrial population towards the cell periphery, thus increasing η.     

Analyzing the functional properties of the creatine kinase system with multiscale 'sloppy' modeling

In this study the function of the two isoforms of creatine kinase (CK; EC 2.7.3.2) in myocardium is investigated. The 'phosphocreatine shuttle' hypothesis states that mitochondrial and cytosolic CK plays a pivotal role in the transport of high-energy phosphate (HEP) groups from mitochondria to myofibrils in contracting muscle. Temporal buffering of changes in ATP and ADP is another potential role of CK. With a mathematical model, we analyzed energy transport and damping of high peaks of ATP hydrolysis during the cardiac cycle. The analysis was based on multiscale data measured at the level of isolated enzymes, isolated mitochondria and on dynamic response times of oxidative phosphorylation measured at the whole heart level. Using 'sloppy modeling' ensemble simulations, we derived confidence intervals for predictions of the contributions by phosphocreatine (PCr) and ATP to the transfer of HEP from mitochondria to sites of ATP hydrolysis. Our calculations indicate that only 15±8% (mean±SD) of transcytosolic energy transport is carried by PCr, contradicting the PCr shuttle hypothesis. We also predicted temporal buffering capabilities of the CK isoforms protecting against high peaks of ATP hydrolysis (3750 μM*s(-1)) in myofibrils. CK inhibition by 98% in silico leads to an increase in amplitude of mitochondrial ATP synthesis pulsation from 215±23 to 566±31 μM*s(-1), while amplitudes of oscillations in cytosolic ADP concentration double from 77±11 to 146±1 μM. Our findings indicate that CK acts as a large bandwidth high-capacity temporal energy buffer maintaining cellular ATP homeostasis and reducing oscillations in mitochondrial metabolism. However, the contribution of CK to the transport of high-energy phosphate groups appears limited. Mitochondrial CK activity lowers cytosolic inorganic phosphate levels while cytosolic CK has the opposite effect.     

Diffusional constraints on energy metabolism in skeletal muscle

Aerobic metabolic flux depends on the diffusion of high-energy phosphate molecules (e.g., ATP and phosphocreatine) from the mitochondria to cellular ATPases, as well as the diffusion of other molecules (e.g., ADP, Pi) back to the mitochondria. Here, we develop an approach for evaluating the influence of intracellular metabolite diffusion on skeletal muscle aerobic metabolism through the application of the effectiveness factor (η). This parameter provides an intuitive and informative means of quantifying the extent to which diffusion limits metabolic flux. We start with the classical approach assuming an infinite supply of substrate at the fiber boundary, and we expand this model to ultimately include nonlinear boundary and homogeneous reactions. Comparison of the model with experimental data from a wide range of skeletal muscle types reveals that most muscle fibers are not substantially limited by diffusion (η close to unity), but many are on the brink of rather substantial diffusion limitation. This implies that intracellular metabolite diffusion does not dramatically limit aerobic metabolic flux in most fibers, but it likely plays a role in limiting the evolution of muscle fiber design and function.     

The rate of the deoxygenation reaction limits myoglobin- and hemoglobin-facilitated O₂ diffusion in cells

A mathematical model describing facilitation of O(2) diffusion by the diffusion of myoglobin and hemoglobin is presented. The equations are solved numerically by a finite-difference method for the conditions as they prevail in cardiac and skeletal muscle and in red cells without major simplifications. It is demonstrated that, in the range of intracellular diffusion distances, the degree of facilitation is limited by the rate of the chemical reaction between myglobin or hemoglobin and O(2). The results are presented in the form of relationships between the degree of facilitation and the length of the diffusion path on the basis of the known kinetics of the oxygenation-deoxygenation reactions. It is concluded that the limitation by reaction kinetics reduces the maximally possible facilitated oxygen diffusion in cardiomyoctes by ～50% and in skeletal muscle fibers by ～ 20%. For human red blood cells, a reduction of facilitated O(2) diffusion by 36% is obtained in agreement with previous reports. This indicates that, especially in cardiomyocytes and red cells, chemical equilibrium between myoglobin or hemoglobin and O(2) is far from being established, an assumption that previously has often been made. Although the "O(2) transport function" of myoglobin in cardiac muscle cells thus is severely limited by the chemical reaction kinetics, and to a lesser extent also in skeletal muscle, it is noteworthy that the speed of release of O(2) from MbO(2), the "storage function," is not limited by the reaction kinetics under physiological conditions.     

Sensitivity analysis of reaction-diffusion constraints in muscle energetics

Theoretical and experimental studies of aerobic metabolism on a wide range of skeletal muscle fibers have shown that while all fibers normally function within the reaction control regime, some fibers operate near the transition region where reaction control switches to diffusion control. Thus, the transition region between reaction and diffusion control may define the limits of muscle function, and analysis of factors that affect this transition is therefore needed. In order to assess the role of all important model parameters, a sensitivity analysis (SA) was performed to define the parameter space where muscle fibers transition from reaction to diffusion control. SA, performed on a previously developed reaction–diffusion model, shows that the maximum rate for the ATPase reaction (V_max,ATPase), boundary oxygen concentration in the capillary supply (O), the mitochondrial volume fraction (ε_mito), and the diffusion coefficient of oxygen ( ) are the most sensitive parameters affecting this transition to diffusion control. It is demonstrated that fibers are not limited by diffusion for slow reactions (V_max,ATPase < 25 mM/min), high oxygen supply for the capillaries (O ≥ 35 µM), and large amounts of mitochondria (ε_mito ≥ 0.1). These conditions are applicable to muscle cells spanning a very broad range of animals. Within the diffusion‐controlled region, the overall metabolic rate and ATP concentrations have much higher sensitivity to the diffusion coefficient of oxygen than to the diffusion coefficients of the other metabolites (ATP, ADP, P_i). Biotechnol. Bioeng. 2012; 109:559–571. © 2011 Wiley Periodicals, Inc.     

Reaction–diffusion constraints in living tissue: Effectiveness factors in skeletal muscle design

A mathematical model was developed to analyze the effects of intracellular diffusion of O₂ and high‐energy phosphate metabolites on aerobic energy metabolism in skeletal muscle. We tested the hypotheses that in a range of muscle fibers from different species (1) aerobic metabolism was not diffusion limited and (2) that fibers had a combination of rate and fiber size that placed them at the brink of substantial diffusion limitation. A simplified chemical reaction rate law for mitochondrial oxidative phosphorylation was developed utilizing a published detailed model of isolated mitochondrial function. This rate law was then used as a boundary condition in a reaction–diffusion model that was further simplified using the volume averaging method and solved to determine the rates of oxidative phosphorylation as functions of the volume fraction of mitochondria, the size of the muscle cell, and the amount of oxygen delivered by the capillaries. The effectiveness factor, which is the ratio of reaction rate in the system with finite rates of diffusion to those in the absence of any diffusion limitations, defined the regions where intracellular diffusion of metabolites and O₂ may limit aerobic metabolism in both very small, highly oxidative fibers as well as in larger fibers with lower aerobic capacity. Comparison of model analysis with experimental data revealed that none of the fibers was strongly limited by diffusion, as expected. However, while some fibers were near substantial diffusion limitation, most were well within the domain of reaction control of aerobic metabolic rate. This may constitute a safety factor in muscle that provides a level of protection from diffusion constraints under conditions such as hypoxia. Biotechnol. Bioeng. 2011; 108:104–115. © 2010 Wiley Periodicals, Inc.     

High-energy phosphate transfer in human muscle: diffusion of phosphocreatine

The creatine kinase (CK) reaction is central to muscle energetics, buffering ATP levels during periods of intense activity via consumption of phosphocreatine (PCr). PCr is believed to serve as a spatial shuttle of high-energy phosphate between sites of energy production in the mitochondria and sites of energy utilization in the myofibrils via diffusion. Knowledge of the diffusion coefficient of PCr (D(PCr)) is thus critical for modeling and understanding energy transport in the myocyte, but D(PCr) has not been measured in humans. Using localized phosphorus magnetic resonance spectroscopy, we measured D(PCr) in the calf muscle of 11 adults as a function of direction and diffusion time. The results show that the diffusion of PCr is anisotropic, with significantly higher diffusion along the muscle fibers, and that the diffusion of PCr is restricted to a ～28-μm pathlength assuming a cylindrical model, with an unbounded diffusion coefficient of ～0.69 × 10(-3) mm(2)/s. This distance is comparable in size to the myofiber radius. On the basis of prior measures of CK reaction kinetics in human muscle, the expected diffusion distance of PCr during its half-life in the CK reaction is ～66 μm. This distance is much greater than the average distances between mitochondria and myofibrils. Thus these first measurements of PCr diffusion in human muscle in vivo support the view that PCr diffusion is not a factor limiting high-energy phosphate transport between the mitochondria and the myofibrils in healthy resting myocytes.     

Gizzard myoglobin contents and feeding habits in avian species

In an attempt to consider physiological function of myoglobin (Mb), we determined Mb contents of gizzard smooth muscles with special reference to feeding habits in 85 avian species of 19 orders. The Mb content in 44 species of herbivorous birds was 7.52+/-3.81 mg/g wet muscle, which was significantly higher than the value of 2.34+/-1.74 mg/g in 41 species of carnivorous ones (P<0.001). Buffering capacity, as determined by in vitro titration method, was 37.3+/-5.5 slykes/g in gizzard smooth muscles of 75 species and 60.7+/-10.5 slykes in breast skeletal muscles of 77 species (P<0.001), which suggests a significantly higher dependence, almost comparable to cardiac muscles, of the gizzard muscular function on aerobic metabolism. Together with the fact that blood circulation in the gizzard is very low at resting, and might be further limited during activity, we conclude that the higher Mb content in gizzards of herbivorous birds is an adaptation, to allow storage and/or facilitated diffusion of oxygen, during process of high mechanical work required to grind down hard and fibrous vegetable food under the conditions of limited circulatory supply.     

Fatigue resistance of rat extraocular muscles does not depend on creatine kinase activity

Background  

Creatine kinase (CK) links phosphocreatine, an energy storage system, to cellular ATPases. CK activity serves as a temporal and spatial buffer for ATP content, particularly in fast-twitch skeletal muscles. The extraocular muscles are notoriously fast and active, suggesting the need for efficient ATP buffering. This study tested the hypotheses that (1) CK isoform expression and activity in rat extraocular muscles would be higher, and (2) the resistance of these muscles to fatigue would depend on CK activity.     

The unique mitochondrial form and function of Antarctic channichthyid icefishes

Antarctic icefishes of the family Channichthyidae are the only vertebrate animals that as adults do not express the circulating oxygen-binding protein hemoglobin (Hb). Six of the 16 family members also lack the intracellular oxygen-binding protein myoglobin (Mb) in the ventricle of their hearts and all lack Mb in oxidative skeletal muscle. The loss of Hb has led to substantial remodeling in the cardiovascular system of icefishes to facilitate adequate oxygenation of tissues. One of the more curious adaptations to the loss of Hb and Mb is an increase in mitochondrial density in cardiac myocytes and oxidative skeletal muscle fibers. The proliferation of mitochondria in the aerobic musculature of icefishes does not arise through a canonical pathway of mitochondrial biogenesis. Rather, the biosynthesis of mitochondrial phospholipids is up-regulated independently of the synthesis of proteins and mitochondrial DNA, and newly-synthesized phospholipids are targeted primarily to the outer-mitochondrial membrane. Consequently, icefish mitochondria have a higher lipid-to-protein ratio compared to those from red-blooded species. Elevated levels of nitric oxide in the blood plasma of icefishes, compared to red-blooded notothenioids, may mediate alterations in mitochondrial density and architecture. Modifications in mitochondrial structure minimally impact state III respiration rates but may significantly enhance intracellular diffusion of oxygen. The rate of oxygen diffusion is greater within the hydrocarbon core of membrane lipids compared to the aqueous cytosol and impeded only by proteins within the lipid bilayer. Thus, the proliferation of icefish's mitochondrial membranes provides an optimal conduit for the intracellular diffusion of oxygen and compensates for the loss of Hb and Mb. Currently little is known about how mitochondrial phospholipid synthesis is regulated and integrated into mitochondrial biogenesis. The unique architecture of the oxidative muscle cells of icefishes highlights the need for further studies in this area.     

Similar mitochondrial activation kinetics in wild-type and creatine kinase-deficient fast-twitch muscle indicate significant Pi control of respiration

Past simulations of oxidative ATP metabolism in skeletal muscle have predicted that elimination of the creatine kinase (CK) reaction should result in dramatically faster oxygen consumption dynamics during transitions in ATP turnover rate. This hypothesis was investigated. Oxygen consumption of fast-twitch (FT) muscle isolated from wild-type (WT) and transgenic mice deficient in the myoplasmic (M) and mitochondrial (Mi) CK isoforms (MiM CK(-/-)) were measured at 20°C at rest and during electrical stimulation. MiM CK(-/-) muscle oxygen consumption activation kinetics during a step change in contraction rate were 30% faster than WT (time constant 53 ± 3 vs. 69 ± 4 s, respectively; mean ± SE, n = 8 and 6, respectively). MiM CK(-/-) muscle oxygen consumption deactivation kinetics were 380% faster than WT (time constant 74 ± 4 s vs. 264 ± 4 s, respectively). Next, the experiments were simulated using a computational model of the oxidative ATP metabolic network in FT muscle featuring ADP and Pi feedback control of mitochondrial respiration (J. A. L. Jeneson, J. P. Schmitz, N. A. van den Broek, N. A. van Riel, P. A. Hilbers, K. Nicolay, J. J. Prompers. Am J Physiol Endocrinol Metab 297: E774-E784, 2009) that was reparameterized for 20°C. Elimination of Pi control via clamping of the mitochondrial Pi concentration at 10 mM reproduced past simulation results of dramatically faster kinetics in CK(-/-) muscle, while inclusion of Pi control qualitatively explained the experimental observations. On this basis, it was concluded that previous studies of the CK-deficient FT muscle phenotype underestimated the contribution of Pi to mitochondrial respiratory control.     

In vivo (31)P-NMR diffusion spectroscopy of ATP and phosphocreatine in rat skeletal muscle

The aim of this study was to measure the diffusion of ATP and phosphocreatine (PCr) in intact rat skeletal muscle, using (31)P-NMR. The acquisition of the diffusion-sensitized spectra was optimized in terms of the signal-to-noise ratio for ATP by using a frequency-selective stimulated echo sequence in combination with adiabatic radio-frequency pulses and surface coil signal excitation and reception. Diffusion restriction was studied by measuring the apparent diffusion coefficients of ATP and PCr as a function of the diffusion time. Orientation effects were eliminated by determining the trace of the diffusion tensor. The data were fitted to a cylindrical restriction model to estimate the unbounded diffusion coefficient and the radial dimensions of the restricting compartment. The unbounded diffusion coefficients of ATP and PCr were approximately 90% of their in vitro values at 37 degrees C. The diameters of the cylindrical restriction compartment were approximately 16 and approximately 22 microm for ATP and PCr, respectively. The diameters of rat skeletal muscle fibers are known to range from 60 to 80 microm. The modelling therefore suggests that the in vivo restriction of ATP and PCr diffusion is not imposed by the sarcolemma but by other, intracellular structures with an overall cylindrical orientation.     

Oxygen delivery by blood determines the maximal VO2 and work rate during whole body exercise in humans: in silico studies

It has been proposed by Saltin (J Exp Biol 115: 345-354, 1985) that oxygen delivery by blood is limiting for maximal work and oxygen consumption in humans during whole body exercise but not during single-muscle exercise. To test this prediction quantitatively, we developed a static (steady-state) computer model of oxygen transport to and within human skeletal muscle during single-muscle (quadriceps) exercise and whole body (cycling) exercise. The main system fluxes, namely cardiac output and oxygen consumption by muscle, are described as a function of the "primary" parameter: work rate. The model is broadly validated by comparison of computer simulations with various experimental data. In silico studies show that, when all other parameters and system properties are kept constant, an increase in the working muscle mass from 2.5 kg (single quadriceps) to 15 kg (two legs) causes, at some critical work intensity, a drop in oxygen concentration in muscle cells to (very near) zero, and therefore oxygen supply by blood limits maximal oxygen consumption and oxidative ATP production. Therefore, the maximal oxygen consumption per muscle mass is significantly higher during single-muscle exercise than during whole body exercise. The effect is brought about by a distribution of a limited amount of oxygen transported by blood in a greater working muscle mass during whole body exercise.     

Is creatine kinase responsible for fatigue? Studies of isolated skeletal muscle deficient in creatine kinase.

Creatine kinase (CK) is a key enzyme for maintaining a constant ATP/ADP ratio during rapid energy turnover. To investigate the role of CK in skeletal muscle fatigue, we used isolated whole muscles and intact single fibers from CK-deficient mice (CK(-/-)). With high-intensity electrical stimulation, single fibers from CK(-/-) mice displayed a transient decrease in both tetanic free myoplasmic [Ca(2+)] ([Ca(2+)](i), measured with the fluorescent dye indo-1) and force that was not observed in wild-type fibers. With less intense, repeated tetanic stimulation single fibers and EDL muscles, both of which are fast-twitch, fatigued more slowly in CK(-/-) than in wild-type mice; on the other hand, the slow-twitch soleus muscle fatigued more rapidly in CK(-/-) mice. In single wild-type fibers, tetanic force decreased and [Ca(2+)](i) increased during the first 10 fatiguing tetani, but this was not observed in CK(-/-) fibers. Fatigue was not accompanied by phosphocreatine breakdown and accumulation of inorganic phosphate in CK(-/-) muscles. In conclusion, CK is important for avoiding fatigue at the onset of high-intensity stimulation. However, during more prolonged stimulation, CK may contribute to the fatigue process by increasing the myoplasmic concentration of inorganic phosphate.     

Mitochondrial coupling in vivo in mouse skeletal muscle

The coupling of mitochondrial ATP synthesis and oxygen consumption (ratio of ATP and oxygen fluxes, P/O) plays a central role in cellular bioenergetics. Reduced P/O values are associated with mitochondrial pathologies that can lead to reduced capacity for ATP synthesis and tissue degeneration. Previous work found a wide range of values for P/O in normal mitochondria. To measure mitochondrial coupling under physiological conditions, we have developed a procedure for determining the P/O of skeletal muscle in vivo. This technique measures ATPase and oxygen consumption rates during ischemia with ³¹P magnetic resonance and optical spectroscopy, respectively. This novel approach allows the independent quantitative measurement of ATPase and oxygen flux rates in intact tissue. The quantitative measurement of oxygen consumption is made possible by our ability to independently measure the saturations of hemoglobin (Hb) and myoglobin (Mb) from optical spectra. Our results indicate that the P/O in skeletal muscle of the mouse hindlimb measured in vivo is 2.16 ± 0.24. The theoretical P/O for resting muscle is 2.33. Systemic treatment with 2,4-dinitrophenol to partially uncouple mitochondria does not affect the ATPase rate in the mouse hindlimb but nearly doubles the rate of oxygen consumption, reducing in vivo P/O to 1.37 ± 0.22. These results indicate that only a small fraction of the oxygen consumption in resting mouse skeletal muscle is nonphosphorylating under physiological conditions, suggesting that mitochondria are more tightly coupled than previously thought. P/O; oxidative phosphorylation; proton leak; optical spectroscopy     

Anisotropy and temperature dependence of myoglobin translational diffusion in myocardium: implication for oxygen transport and cellular architecture

Pulsed field gradient NMR methods have determined the temperature-dependent diffusion of myoglobin (Mb) in perfused rat myocardium. Mb diffuses with an averaged translational diffusion coefficient (DMb) of 4.24-8.37x10(-7)cm2/s from 22 degrees C to 40 degrees C and shows no orientation preference over a root mean-square displacement of 2.5-3.5 microm. The DMb agrees with the value predicted by rotational diffusion measurements. Based on the DMb, the equipoise diffusion PO2, the PO2 in which Mb-facilitated and free O2 diffusion contribute equally to the O2 flux, varies from 2.72 to 0.15 in myocardium and from 7.27 to 4.24 mmHg in skeletal muscle. Given the basal PO2 of approximately 10 mmHg, the Mb contribution to O2 transport appears insignificant in myocardium. In skeletal muscle, Mb-facilitated diffusion begins to contribute significantly only when the PO2 approaches the P50. In marine mammals, the high Mb concentration confers a predominant role for Mb in intracellular O2 transport under all physiological conditions. The Q10 of the DMb ranges from 1.3 to 1.6. The Mb diffusion data indicate that the postulated gel network in the cell must have a minimum percolation cutoff size exceeding 17.5 A and does not impose tortuosity within the diffusion root mean-square displacement. Moreover, the similar Q10 for the DMb of solution versus cell Mb suggests that any temperature-dependent alteration of the postulated cell matrix does not significantly affect protein mobility.     

The creatine kinase reaction: a simple reaction with functional complexity

The classical role of PCr is seen as a reservoir of high-energy phosphates defending cellular ATP levels under anaerobic conditions, high rates of energy transfer or rapid fluctuations in energy requirement. Although the high concentration of PCr in glycolytic fast-twitch fibers supports the role of PCr as a buffer of ATP, the primary importance of the creatine kinase (CK) reaction may in fact be to counteract large increases in ADP, which could otherwise inhibit cellular ATPase-mediated systems. A primary role for CK in the maintenance of ADP homeostasis may explain why, in many conditions, there is an inverse relationship between PCr and muscle contractility but not between ATP and muscle contractility. The high rate of ATP hydrolysis during muscle contraction combined with restricted diffusion of ADP suggests that ADP concentration increases transiently during the contraction phase (ADP spikes) and that these are synchronized with the contraction. The presence of CK, structurally bound in close vicinity to the sites of ATP utilization, will reduce the amplitude and duration of the ADP spikes through PCr-mediated phosphotransfer. When PCr is reduced, the efficiency of CK as an ATP buffer will be reduced and the changes in ADP will become more prominent. The presence of ADP spikes is supported by the finding that other processes known to be activated by ADP (i.e. AMP deamination and glycolysis) are stimulated during exercise but not during anoxia, despite the same low global energy state. Breakdown of PCr is driven by increases in ADP above that depicted by the CK equilibrium and the current method to calculate ADPfree from the CK reaction in a contracting muscle is therefore questionable.     

Intracellular diffusion of adenosine phosphates is locally restricted in cardiac muscle

Recent studies have revealed the structural and functional interactions between mitochondria, myofibrils and sarcoplasmic reticulum in cardiac cells. Direct channeling of adenosine phosphates between organelles identified in the experiments indicates that diffusion of adenosine phosphates is limited in cardiac cells due to very specific intracellular structural organization. However, the mode of diffusion restrictions and nature of the intracellular structures in creating the diffusion barriers is still unclear, and, therefore, a subject of active research. The aim of this work is to analyze the possible role of two principally different modes of restriction distribution for adenosine phosphates (a) the uniform diffusion restriction and (b) the localized diffusion limitation in the vicinity of mitochondria, by fitting the experimental data with the mathematical model. The reaction-diffusion model of compartmentalized energy transfer was used to analyze the data obtained from the experiments with the skinned muscle fibers, which described the following processes: mitochondrial respiration rate dependency on exogenous ADP and ATP concentrations; inhibition of endogenous ADP-stimulated respiration by pyruvate kinase (PK) and phosphoenolpyruvate (PEP) system; kinetics of oxygen consumption stabilization after addition of 2 mM MgATP or MgADP; ATPase activity with inhibited mitochondrial respiration; and buildup of MgADP concentration in the medium after addition of MgATP. The analysis revealed that only the second mechanism considered--localization of diffusion restrictions--is able to account for the experimental data. In the case of uniform diffusion restrictions, the model solution was in agreement only with two measurements: the respiration rate as a function of ADP or ATP concentrations and inhibition of respiration by PK + PEP. It was concluded that intracellular diffusion restrictions for adenosine phosphates are not distributed uniformly, but rather are localized in certain compartments of the cardiac cells.     

Experimental and theoretical considerations on oxygen supply for animal cell growth in fixed-bed reactors.

The supply of oxygen is a crucial parameter when cultivating animal cells in fixed-bed reactors because of the reaction-diffusion limitation within the porous carriers. To reduce limitation and increase productivity, the dissolved oxygen concentration was raised to above air saturation (hyperoxia) in long-term experiments using hybridoma cultures. This resulted in a threefold increase of the steady-state antibody production at high dilution rates compared to air saturated medium. A reaction-diffusion model was developed as a tool to describe the oxygen distribution in fixed-bed systems. The model corresponded well to the experimental data. It was also used to study the influence of several parameters on the performance of the fixed-bed system, such as the carrier size, the dissolved oxygen concentration, or the superficial flow velocity. By adapting the model it was shown that reaction-diffusion limitation is generally not a problem for other substrates such as glucose or glutamine.     

Enzymatic activities and ATP-induced fluorescence enhancement of myosin from fast and slow skeletal and cardiac muscles.

The maximal ATP-induced enhancement of fluorescence and the dependence of this enhancement on ATP concentration were determined for myosins from fast and slow skeletal and cardiac muscle of the rabbit. With myosins from slow and cardiac muscle modifications in the preparative procedure and chromatography on DEAE-Sephadex were required to obtain preprations which were free of actin, which exhibited the maximal fluorescence enhancement and which bound two moles of ATP per mole of myosin. Since the fluorescence enhancement of cardiac and slow muscle myosins is labile at slightly alkaline pH, it was also necessary to minimize incubation at pH greater than 7 in order to attain the maximal enhancement. With fast muscle myosin the changes in preparative procedure, together with chromatography, led to a 50 to 100% increase in the steady-state rate of ATP hydrolysis and fluorescence enhancement, without changing the maximal binding of ATP. From a comparison of the rate of steady-state hydrolysis of ATP with the rate of decay of the enhanced fluorescence, it appears that for all three myosins, both ATP binding sites have the same enzymatic activity, the steady-state rate per site being slower for cardiac and slow muscle myosins than for fast muscle myosin.