The diffusive mobility of solutes chemically connected by reversible reactions in cells is analyzed as a problem of facilitated diffusion. By this term we mean that the diffusive flux of any substance, X, which is in one metabolic pathway, is effectively increased when it participates in a second and equilibrium reaction with another substance Y because the total flux of X in the pathway is the sum of the fluxes of X and Y. This notion is generalized and is seen to include the familiar enhanced intracellular diffusion of oxygen by oxymyoglobin. In this framework the function of creatine kinase (CK) is seen to have two aspects: 1) phosphocreatine (PCr) via the CK reaction buffers the cellular ATP and ADP concentrations and 2) transport of high-energy phosphates is predominantly in the chemical form of PCr. This predominance of PCr is a consequence of the maintained ATP, ADP, and total creatine levels and of the apparent equilibrium constant of the reaction. Thus experimental results demonstrating the transport aspects of the CK reaction emphasize only one feature of a more general notion of facilitated diffusion by near-equilibrium metabolic reactions and do not per se establish the existence of any physical or functional compartmentation of ATP, ADP, PCr, or creatine. PCr can be a large source for increasing inorganic phosphate levels during contractile activity, possibly as a metabolic regulator. Neither the transport nor buffer aspects can be quantitatively important in cells with small distances between ATP-utilizing and ATP-generating sites, such as is the case with cardiac myofibrils and mitochondria.

A simple analysis of the "phosphocreatine shuttle"

Phosphagens are phosphorylated guanidino compounds that are linked to energy state and ATP hydrolysis by corresponding phosphagen kinase reactions: phosphagen + MgADP + H(+) guanidine acceptor + MgATP. Eight different phosphagens (and corresponding phosphagen kinases) are found in the animal kingdom distributed along distinct phylogenetic lines. By far, the creatine phosphate/creatine kinase (CP/CK) system, which is found in the vertebrates and is widely distributed throughout the lower chordates and invertebrates, is the most extensively studied phosphagen system. Phosphagen kinase reactions function in temporal ATP buffering, in regulating inorganic phosphate (Pi) levels, which impacts glycogenolysis and proton buffering, and in intracellular energy transport. Phosphagen kinase reactions show differences in thermodynamic poise, and the phosphagens themselves differ in terms of certain physical properties including intrinsic diffusivity. This review evaluates the distribution of phosphagen systems and tissue-specific expression of certain phosphagens in an evolutionary and functional context. The role of phosphagens in regulation of intracellular Pi levels likely evolved early. Thermodynamic poise of the phosphagen kinase reaction profoundly impacts this capacity. Furthermore, it is hypothesized that the capacity for intracellular targeting of CK evolved early as a means of facilitating energy transport in highly polarized cells and was subsequently exploited for temporal ATP buffering and dynamic roles in metabolic regulation in cells displaying high and variable rates of aerobic energy production.

Evolution and physiological roles of phosphagen systems

This review focuses on the theory of oxygen transport to tissue and presents the state of the art in mathematical modeling of transport phenomena. Results obtained with the classic Krogh tissue-cylinder model and recent advances in mathematical modeling of hemoglobin-oxygen kinetics, the role of hemoglobin and myoglobin in facilitating oxygen diffusion, and the role of morphologic and hemodynamic heterogeneities in oxygen transport in the microcirculation are critically discussed. Mathematical models simulate different parts of the pathway of oxygen molecules from the red blood cell, through the plasma, the endothelial cell, other elements of the vascular wall, and the extra- and intracellular space. Special attention in the review is devoted to intracapillary transport, which has been the subject of intensive theoretical research in the last decade. Models of pre- and postcapillary oxygen transport are also discussed. Applications to specific organs and tissues are reviewed, including skeletal muscle, myocardium, brain, lungs, arterial wall, and skin. Unresolved problems and major gaps in our knowledge of the mechanisms of oxygen transport are identified.

Theory of oxygen transport to tissue.

Skeletal muscles of mice deficient in muscle creatine kinase lack burst activity.

Resting and maximal mass-specific metabolic rates scale inversely with body mass. Small hummingbirds achieve the highest known mass-specific metabolic rates among vertebrate homeotherms. Maximal capacities for O2 and substrate delivery to muscle mitochondria, as well as mitochondrial oxidative capacities in these animals may be at the upper limits of what are structurally and functionally possible given the constraints inherent in vertebrate design. Such constraints on the evolutionary design of functional capacities may play an important role in determining the lower limits to vertebrate homeotherm size and the upper limits to mass-specific metabolic rate.

Hummingbird flight: sustaining the highest mass-specific metabolic rates among vertebrates.

A model for oxygen transfer to cells from capillaries is considered in which mitochondria are either clustered at the cell periphery around capillaries or homogeneously distributed through the cytosol. The capillary required to supply cells utilizing oxygen at the same rate is much less when mitochondria cluster around capillaries. Two alternative mechanisms are considered for distributing energy from peripheral mitochondria to the rest of the cell; i.e., diffusion of ATP or creatine phosphate with enough creatine kinase to ensure equilibrium between the ~P carriers. The latter has clear advantages and would appear to be adequate to supply a fairly large mitochondria-free cell core (e.g., 24-μm diameter) with very little change in ADP levels or in the free energy of ATP hydrolysis at maximum work rates. Thus, a viable alternative to the traditional Krogh model is presented which takes into account the inhomogeneity of the diffusion pathway as a result of mitochondrial clustering.

K. Rakusan

Papers

A model for intracellular energy transport.