Obstructed metabolite diffusion within skeletal muscle cells in silico.

Using a Monte Carlo simulation technique, we have modeled 3D diffusion of low molecular weight metabolites inside a skeletal muscle cell. The following structural elements are considered: (i) a regular lattice of actin and myosin filaments inside a myofibril, (ii) the membranes of sarcoplasmic reticulum and mitochondria surrounding the myofibrils, (iii) a set of myofibrils inside a skeletal muscle cell encircled by the outer cell membrane, and (iv) an additional set of regular intracellular structures ("macrocompartments") embedded into the cell interior. The macrocompartments are considered to simulate diffusion restrictions because of hypothetical cylindrical structures (16-22 µm in diameter) suggested earlier (de Graaf et al. Biophys J 78: 1657-1664, 2000). This model allowed us to calculate the apparent coefficients of particle diffusion in the radial and axial directions, D(app)(⊥) and D(app)(II), respectively. Particle movements in the axial direction are considered, at first approximation, as unrestricted diffusion (D(app)(II) = const). The apparent coefficient of radial diffusion, D(app)(⊥), decreases with time because of particle collisions with myofilaments and other rigid obstacles. Results of our random walk simulations are in fairly good agreement with experimental data on NMR measurements of restricted radial diffusion of phosphocreatine in white and red skeletal muscles of goldfish (Kinsey et al. NMR Biomed 12:1-7, 1999). Particle reflections from the low-permeable borders of macrocompartments (efficient diameter, D(eff)(MC) ≈ 9.2-10.4 µm) are the prerequisite for agreeing theoretical and experimental data. The low-permeable coverage of hypothetical macrocompartments (99.8% of coverage) provides the main contribution to time-dependent decrease in D(app)(⊥).

Molecular system bioenergics of the heart: experimental studies of metabolic compartmentation and energy fluxes versus computer modeling.

In this review we analyze the recent important and remarkable advancements in studies of compartmentation of adenine nucleotides in muscle cells due to their binding to macromolecular complexes and cellular structures, which results in non-equilibrium steady state of the creatine kinase reaction. We discuss the problems of measuring the energy fluxes between different cellular compartments and their simulation by using different computer models. Energy flux determinations by (18)O transfer method have shown that in heart about 80% of energy is carried out of mitochondrial intermembrane space into cytoplasm by phosphocreatine fluxes generated by mitochondrial creatine kinase from adenosine triphosphate (ATP), produced by ATP Synthasome. We have applied the mathematical model of compartmentalized energy transfer for analysis of experimental data on the dependence of oxygen consumption rate on heart workload in isolated working heart reported by Williamson et al. The analysis of these data show that even at the maximal workloads and respiration rates, equal to 174 µmol O(2) per min per g dry weight, phosphocreatine flux, and not ATP, carries about 80-85% percent of energy needed out of mitochondria into the cytosol. We analyze also the reasons of failures of several computer models published in the literature to correctly describe the experimental data.

The creatine kinase phosphotransfer network: thermodynamic and kinetic considerations, the impact of the mitochondrial outer membrane and modelling approaches.

In this review, we summarize the main structural and functional data on the role of the phosphocreatine (PCr)--creatine kinase (CK) pathway for compartmentalized energy transfer in cardiac cells. Mitochondrial creatine kinase, MtCK, fixed by cardiolipin molecules in the vicinity of the adenine nucleotide translocator, is a key enzyme in this pathway. Direct transfer of ATP and ADP between these proteins has been revealed both in experimental studies on the kinetics of the regulation of mitochondrial respiration and by mathematical modelling as a main mechanism of functional coupling of PCr production to oxidative phosphorylation. In cells in vivo or in permeabilized cells in situ, this coupling is reinforced by limited permeability of the outer membrane of the mitochondria for adenine nucleotides due to the contacts with cytoskeletal proteins. Due to these mechanisms, at least 80% of total energy is exported from mitochondria by PCr molecules. Mathematical modelling of intracellular diffusion and energy transfer shows that the main function of the PCr-CK pathway is to connect different pools (compartments) of ATP and, by this way, to overcome the local restrictions and diffusion limitation of adenine nucleotides due to the high degree of structural organization of cardiac cells.

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

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.

Random walk analysis of restricted metabolite diffusion in skeletal myofibril systems.

The purpose of this work was the development of a basal mathematical model for the diffusion of low-molecular metabolites in a skeletal muscle cell. A three-dimension diffusion of low-molecular particles was simulated by a Monte-Carlo method (random walks of diffusing molecules). The model takes into account the following structural elements: (i) a regular lattice of actin and myosin filaments inside a myofibril; (ii) the membranes of sarcoplasmic reticulum and mitochondria surrounding the myofibrils; (iii) a set of myofibrils inside a skeletal muscle cell. We simulated diffusion of particles in the bulk of intracellular water phase and their reflections from the rigid surfaces of intracellular structures. The model allowed to calculate the apparent coefficients of particle diffusion in the axial and radial directions, Dparallel(app) and Dperpendicular(app), respectively. In accordance with experimental data from literature, the coefficient Dparallel(app) was independent of time. The coefficient of radial diffusion Dperpendicular(app) decreased with time to steady state values similar to that determined by the NMR diffusion spectroscopy methods. The interactions of diffusing particles with thin and thick filaments of myofibrils could explain the decrease in the Dperpendicular(app) value by a factor of 20%. The collisions of particles with myofilaments began to reveal themselves as a gradual decrease in the Dperpendicular(app) value at early stages of diffusion (t1/2 approximately equal to 0.05 microsec). The contribution of particle reflections from the membranes of sarcoplasmic reticulum and mitochondria to the retardation of the radial diffusion was about of 20-30%, depending on porosity of a membranous shield around the myofibril. For conventional sizes of a membranous shield (diameter 2 microm), the interactions of particles with the shield caused a decrease in the Dperpendicular(app) value with a half-time t1/2 approximately equal to 0.5 msec. This time is essentially lower by a factor about of 100 than that found in published NMR measurements. When we considered diffusion of particles inside a cell compartment confined to impermeable membranous shield, the reflection of particles from this shield led the drastic decrease in the radial diffusion coefficient (Dperpendicular(app) --> porportional to when t --> porportional to). This pattern of the Dperpendicular(app)(t) time-course might be expected in the NMR measurements on skeletal muscle tissue where a sarcolemma represents an impermeable shield for ATP and PCr molecules.