The sensitivity of fast muscle contractile function to the major components of the sarcomere Ca(2+)-cycling system.

A reaction-diffusion model of a muscle sarcomere was developed to evaluate the sensitivity of force characteristics to diffusion and Ca(2+)-cycling components. The model compared well to experimental force measurements. Diffusion led to Ca(2+) gradients that enhanced maximal force and accelerated relaxation compared to when diffusion was infinitely fast. However, a modest increase in sarcomere length or radius led to a decrease in maximal force. Lowering the Ca(2+) release rate caused a lower maximal force, but increasing the rate led to only modest gains in maximal force while incurring much greater ATP costs associated with reuptake. Greater parvalbumin binding rates decreased maximal force but enhanced relaxation, and this effect was magnified when Ca(2+) uptake rates were lowered as may occur during fatigue. These results show a physiological set of parameters that lead to a functional sarcomere of known dimensions and contractile function, and the effects of parameter variation on muscle function.

Oxygen control of intracellular distribution of mitochondria in muscle fibers.

Mitochondrial density in skeletal muscle fibers is governed by the demand for aerobic ATP production, but the heterogeneous distribution of these mitochondria appears to be governed by constraints associated with oxygen diffusion. We propose that each muscle fiber has an optimal mitochondrial distribution at which it attains a near maximal rate of ATP consumption (RATPase ) while mitochondria are exposed to a minimal oxygen concentration, thus minimizing reactive oxygen species (ROS) production. We developed a coupled reaction-diffusion/cellular automata (CA) mathematical model of mitochondrial function and considered four fiber types in mouse extensor digitorum longus (EDL) and soleus (SOL) muscle. The developed mathematical model uses a reaction-diffusion analysis of metabolites including oxygen, ATP, ADP, phosphate, and phosphocreatine (PCr) involved in energy metabolism and mitochondrial function. A CA approach governing mitochondrial life cycles in response to the metabolic state of the fiber was superimposed and coupled to the reaction-diffusion approach. The model results show the sensitivity of important model outputs such as the RATPase , effectiveness factor (η) and average oxygen concentration available at each mitochondrion to local oxygen concentration in the fibers through variation in the CA model parameter θdet , which defines the sensitivity of mitochondrial death to the oxygen concentration. The predicted optimal mitochondrial distributions matched previous experimental findings. Deviations from this optimal distribution corresponding to higher CA model parameter values (a more uniform mitochondrial distribution) lead to lower aerobic rates. In contrast, distributions corresponding to lower CA model parameter values (a more asymmetric distribution) lead to an increased exposure of mitochondria to oxygen, usually without substantial increases in aerobic rates, which would presumably result in increased ROS production and thus increased risks of cytotoxicity.

The formation and functional consequences of heterogeneous mitochondrial distributions in skeletal muscle.

Diffusion plays a prominent role in governing both rates of aerobic metabolic fluxes and mitochondrial organization in muscle fibers. However, there is no mechanism to explain how the non-homogeneous mitochondrial distributions that are prevalent in skeletal muscle arise. We propose that spatially variable degradation with dependence on O(2) concentration, and spatially uniform signals for biogenesis, can account for observed distributions of mitochondria in a diversity of skeletal muscle. We used light and transmission electron microscopy and stereology to examine fiber size, capillarity and mitochondrial distribution in fish red and white muscle, fish white muscle that undergoes extreme hypertrophic growth, and four fiber types in mouse muscle. The observed distributions were compared with those generated using a coupled reaction-diffusion/cellular automata (CA) mathematical model of mitochondrial function. Reaction-diffusion analysis of metabolites such as oxygen, ATP, ADP and PCr involved in energy metabolism and mitochondrial function were considered. Coupled to the reaction-diffusion approach was a CA approach governing mitochondrial life cycles in response to the metabolic state of the fiber. The model results were consistent with the experimental observations and showed higher mitochondrial densities near the capillaries because of the sometimes steep gradients in oxygen. The present study found that selective removal of mitochondria in the presence of low prevailing local oxygen concentrations is likely the primary factor dictating the spatial heterogeneity of mitochondria in a diversity of fibers. The model results also suggest decreased diffusional constraints corresponding to the heterogeneous mitochondrial distribution assessed using the effectiveness factor, defined as the ratio of the reaction rate in the system with finite rates of diffusion to that in the absence of any diffusion limitation. Thus, the non-uniform distribution benefits the muscle fiber by increasing the energy status and increasing sustainable metabolic rates.

Facilitated diffusion of myoglobin and creatine kinase and reaction-diffusion constraints of aerobic metabolism under steady-state conditions in skeletal muscle.

The roles of creatine kinase (CK) and myoglobin (Mb) on steady-state facilitated diffusion and temporal buffering of ATP and oxygen, respectively, are assessed within the context of a reaction-diffusion model of muscle energetics. Comparison of the reaction-diffusion model with experimental data from a wide range of muscle fibers shows that the experimentally observed skeletal muscle fibers are generally not limited by diffusion, and the model further indicates that while some muscle fibers operate near the edge of diffusion limitation, no detectable effects of Mb and CK on the effectiveness factor, a measure of diffusion constraints, are observed under steady-state conditions. However, CK had a significant effect on average ATP concentration over a wide range of rates and length scales within the reaction limited regime. The facilitated diffusion functions of Mb and CK become observable in the model for larger size cells with low mitochondrial volume fraction and for low boundary O(2) concentration and high ATP demand, where the fibers may be limited by diffusion. From the transient analysis it may be concluded that CK primarily functions to temporally buffer ATP as opposed to facilitating diffusion while Mb has a small temporal buffering effect on oxygen but does not play any significant role in steady-state facilitated diffusion in skeletal muscle fibers under most physiologically relevant regions.

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 2°), the mitochondrial volume fraction (ε(mito)), and the diffusion coefficient of oxygen (DO 2) 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 2° ≥ 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)).

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.

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 O(2) 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 O(2) 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.

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 (eta). 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 (eta 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 roles of ozone and zeolite on reactive dye degradation in electrical discharge reactors.

In this study high voltage pulsed corona electrical discharge advanced oxidation processes (AOPs) were applied to bleach and degrade C.I. Reactive Green 8 and C.I. Reactive Red 45 organic dyes in water solutions. Two types of hybrid gas/liquid high voltage electrical discharge (corona) reactors, known as hybrid series and hybrid parallel were studied. The difference between these reactors relates to electrode configuration, which affects the amounts of ozone, hydrogen peroxide and hydroxyl radicals produced. Experiments were conducted using dye concentrations of 20 mgl(-1) and 75 mgl(-1), with and without NH4ZSM5 zeolite addition in order to determine possible effects of added solid particles to total process efficiency. The role of ozone in combination with zeolites was assessed through comparative direct ozonation experiments with ozone supplied by an ozone generator. UV/VIS spectrophotometric measurements and measurements of total organic carbon (TOC) were used for the determination of decolorization and mineralization rates.

The removal of Direct Orange 39 by pulsed corona discharge from model wastewater.

Untreated wastewater from the dye industry and dyehouses cannot be directly discharged into the environment due to the high content of organic matter and intensive colouration, even with low concentrations of dye. In this paper, the application of a high voltage pulsed electrical discharge in the aqueous phase has been assessed for the dye degradation. Experiments were conducted in a batch reactor using model wastewater of the commercial water-soluble monoazo dye C.I. Direct Orange 39 (DO39). The effects of zeolite and ferrous sulphate in combination with the corona discharge were examined. Experiments were conducted for a range of process parameters including pH, conductivity, type and amount of zeolite, and ferrous sulphate concentration. A mathematical model to describe the kinetics of DO39 degradation in the corona reactor was developed. Aqueous phase pulsed streamer corona discharge as a method for coloured wastewater treatment showed very high effectiveness in the case of iron salt addition (Fenton's reaction). Low pH enhanced dye removal by corona in the absence of zeolite, thus implying that the acid properties of zeolites are important in dye degradation. Ecological parameters such as COD, TC, IC, TOC and IC50 measured before and after corona treatment showed that the treated wastewater can be discharged into the environment or reused as process water.

When can the Ogston-Morris-Rodbard-Chrambach model be applied to gel electrophoresis?

The Ogston-Morris-Rodbard-Chrambach theory of gel electrophoresis is consistent with predictions from the volume averaging method with respect to the equivalence of the accessible volume fraction to the ratios of gel mobility to free solution mobility and the gel diffusion coefficient to free solution diffusion coefficient for the limiting case of small molecule electrophoresis with low electrical fields, low gel concentrations, and nonconductive gel fibers. When these conditions are not valid, more extensive calculations are required to determine the mobility and diffusion coefficient ratios as functions of the geometry and electrical field within the gel. The volume averaging theory shows that it is important to account for the electrical conductivity properties of the fibers that make up a gel electrophoresis medium, and this aspect is consistent with early theories of transport phenomena in gel electrophoresis.

Transdermal water mobility in the presence of electrical fields using MR microscopy.

Magnetic resonance microscopy of skin from hairless rats under the influence of electrical fields was conducted for two cases: 1) low voltage constant electrical fields and 2) high-voltage short pulse, electrical fields. Under conditions of the low voltage and low current iontophoresis, i.e., 0 to 20 V, and 0 to 0.5 mA/cm2, it was found that the skin structure, as observed by magnetic resonance microscopy, did not significantly change until 20 Volts were applied across the 0.1 cm thick skin. Under these conditions, the viable epidermis appeared to swell, and this result corresponded to observations from scanning electron microscopy and other research from the literature. High voltage electrical fields, i.e., 220 V 1 ms pulses repeated once per second, appeared to hydrate the stratum corneum as is consistent with published literature on electroporation. In the case of iontophoresis, water self-diffusion coefficients in the epidermis and hair follicle regions at all voltages were affected by the electrical field. Statistical analysis at the 95% confidence level for the comparison of the average differences between diffusion coefficients with the electrical field on and with the electrical field off for pair matched pixels for the viable epidermis show that for 5 V (p = 0.00377), 10 V (p = 0.0108), 20 V (p = 0.0219) regimes there are statistically significant (p < or = 0.05) changes due to the applied electric field. The same analysis for the hair follicle region at 5 V (p = 6.89 x 10(-7)), 10 V (p = 1.42 x 10(-5)), 20 V (p = 3.23 x 10(-3)) also show statistically significant changes (p < or = 0.05). When the electroporation pulse was applied, the water diffusion coefficients increased by about 30% to 6.6 x 10(-6) cm2/s +/- 2.4 x 10(-7) cm2/s and 8.3 x 10(-6) cm2/s +/- 3.7 x 10(-7) cm2/s, for the epidermis and hair follicle regions, respectively. Significant differences were noted between diffusion coefficients in the viable epidermis and the hair follicles for all cases.

Analysis of cell growth kinetics and substrate diffusion in a polymer scaffold.

The cultivation of cartilage cells (chondrocytes) in polymer scaffolds leads to implants that may potentially be used to repair damaged joint cartilage or for reconstructive surgery. For this technique to be medically applicable, the physical parameters that govern cell growth in a polymer scaffold must be understood. This understanding of cell behavior under in vitro conditions, where diffusion is the primary mode of transport of nutrients, may aid in the scale-up of the cartilage generation process. A mathematical model of chondrocyte generation and nutrient consumption is developed here to analyze the behavior of cell growth in a biodegradable polymer matrix for a series of different thickness polymers. Recent literature has implied that the diffusion of nutrients is a major factor that limits cell growth (Freed et al., 1994). In the present paper, a mathematical model is developed to directly relate the effects of increasing cell mass in the polymer matrix on the transport of nutrients. Reaction and diffusion of nutrients in the cell-polymer system are described using the fundamental species continuity equations and the volume averaging method. The volume averaging method is utilized to derive a single averaged nutrient continuity equation that includes the effective transport properties. This approach allows for the derivation of effective diffusion and rate coefficients as functions of the cell volume fraction. The cell volume fraction as a function of time is determined by solution of a material balance on cell mass. Growth functions including the Moser, a modified Contois, and an nth-order heterogeneous growth kinetic model are evaluated through a parameter analysis, and the results are compared to experimental data found in the literature. The results indicate that cellular functions in conjunction with mass transfer processes can account partially for the general trends in the cell growth behavior for various thickness polymers. The Contois growth function appeared to describe the data more accurately in terms of the lag period at early times and the long time limits. However, all kinetic growth functions required variations in the kinetic parameters to fully describe the effects of polymer thickness. This result implies that restricted diffusion of nutrients is not the sole factor limiting cell growth when the thickness of the polymer is changed. Therefore, further experimental data and model improvements are needed to accurately describe the cell growth process.

Effects of spatial variation of cells and nutrient and product concentrations coupled with product inhibition on cell growth in a polymer scaffold.

The effects of spatial variation of cells and nutrient and product concentration, in combination with product inhibition in cell growth kinetics on chondrocyte generation in a polymer scaffold, are analyzed. Experimental studies reported previously have demonstrated spatial dependence in the cultivation of chondrocytes. In the present study, the cell-polymer system is assumed to consist of two distinct phases. The cells, fluid, polymer matrix, and extracellular matrix comprise one phase, and the other phase consists of a fluid and polymer matrix. The only two species in the fluid considered to affect cell growth are the nutrient and product. The multiphase transport process of these two species in the cell-polymer system is described by the species continuity equations and corresponding boundary conditions for each individual phase. A volume-averaging approach is utilized for this system to derive averaged species continuity equations for the nutrient and product concentrations. The volume-averaging approach allows for a single species in a two-phase system to be represented by a single averaged continuity equation. Competitive product inhibition, saturation kinetics of substrate, and cell population control are assumed to affect the cell growth kinetics. A modified Contois growth kinetic model is used to represent the three factors that affect cell growth. A parameter analysis is performed and the results are compared qualitatively with experimental data found in the literature.

Diffusional anisotropy is induced by subcellular barriers in skeletal muscle.

The time- and orientational-dependence of phosphocreatine (PCr) diffusion was measured using pulsed-field gradient nuclear magnetic resonance (PFG-NMR) as a means of non-invasively probing the intracellular diffusive barriers of skeletal muscle. Red and white skeletal muscle from fish was used because fish muscle cells are very large, which facilitates the examination of diffusional barriers in the intracellular environment, and because they have regions of very homogeneous fiber type. Fish were cold-acclimated (5 degrees C) to amplify the contrast between red and white fibers. Apparent diffusion coefficients, D, were measured axially, D(axially) and radially, D(radially), in small muscle strips over a time course ranging from 12 to 700 ms. Radial diffusion was strongly time dependent in both fiber types, and D decreased with time until a steady-state value was reached at a diffusion time approximately 100 ms. Diffusion was also highly anisotropic, with D(axially) being higher than D(radially) for all time points. The time scale over which changes in D(radially) occurred indicated that the observed anisotropy was not a result of interactions with the thick and thin filament lattice of actin and myosin or restriction within the cylindrical sarcolemma, as has been previously suggested. Rather, the sarcoplasmic reticulum (SR) and mitochondria appear to be the principal intracellular structures that inhibit mobility in an orientation-dependent manner. This work is the first example of diffusional anisotropy induced by readily identifiable intracellular structures.

Pluronic copolymer liquid crystals: unique, replaceable media for capillary gel electrophoresis.

Liquid crystalline solutions of Pluronic copolymers are versatile alternatives to solutions of entangled, random coil polymers as replaceable media for capillary gel electrophoresis (CGE). Pluronic copolymers are tri-block polymers of poly(ethylene oxide) [(EO)x] and poly(propylene oxide) [(PO)y] with the general formula (EO)x(PO)y(EO)x. Large micelles form in aqueous solutions in which central, hydrophobic cores of (PO)y segments are surrounded by "brushes" of hydrated (EO)x tails. Solutions of Pluronic F127 (BASF Performance Chemicals) in a concentration range of about 18-30% are liquids at refrigerator temperatures (< or = 5 degrees C) and are easily introduced into capillaries. A self-supporting, gel-like liquid crystalline phase is formed as the temperature is raised to > or = 20 degrees C. This liquid crystalline phase consists of spherical micelles with diameters of 17-18 nm which pack with local cubic symmetry. CGE in Pluronic F127 liquid crystals separates species within several chemical classes as varied as nucleoside monophosphates and organic dyes, oligonucleotides of 4-60 nucleotides, DNA fragments of 50-3000 base pairs (bp), and supercoiled plasmid DNAs of 2000-10,000 bp. Mechanisms of molecular sieving in polymer liquid crystals must differ in fundamental ways from separations in random polymer gels because molecules move around uncrosslinked obstacles that are larger than the smallest dimensions of typical analytes. Molecular sieving in Pluronic liquid crystals is envisioned to occur as molecules squeeze between hydrated (EO)x strands of micelle brushes, or through brushtips and interstitial spaces between micelles. Small molecules such as nucleotides appear to separate by a different mechanism involving partitioning between hydrophilic and hydrophobic environments. This process is termed "hydrophobic interaction electrophoresis". The unique structures of Pluronic copolymers and their liquid crystalline phases provide new challenges and opportunities in separations science.

Electrophoresis in lyotropic polymer liquid crystals.

Excellent electrophoretic separations of a variety of biological molecules can be accomplished by using uncharged, triblock copolymers as the "gel" media. These copolymers form uncrosslinked, lyotropic liquid crystalline phases of large micelles between which molecules must travel. Unlike crosslinked hydrogels in common use, these alternative media have highly ordered internal structures. Pluronic F127, representative of the copolymer class, contains poly(ethylene oxide) (EO) and poly(propylene oxide) (PO) units with an approximate molecular formula (EO)106(PO)70(EO)106. Concentrated (18-30%) solutions of Pluronic F127 are freely flowing liquids at low temperature (0-5 degrees C) but form gel-like, cubic liquid crystals of large, spherical micelles when warmed. The utility of these media is illustrated by separations of linear, double-stranded DNA up to 3,000 bp long by conventional electrophoresis, and of single-stranded DNAs from 4 to 60 nt long by capillary electrophoresis. Extraordinary separations of supercoiled DNAs were also obtained by capillary electrophoresis. The versatility, availability, and ease of use of Pluronic polymers offer major advantages over conventional media for preparative and high performance analytical separations of nucleic acids and other biomolecules. Mechanisms of molecular transport and separation operating in polymer liquid crystals must differ in fundamental ways from those in crosslinked gels. Lyotropic polymer liquid crystals are unique systems for elucidating mechanisms of macromolecule migration in ordered, dense media, and provide opportunities in separations science.

Templated pores in hydrogels for improved size selectivity in gel permeation chromatography.

The pore structures of cross-linked polyacrylamide gels can be altered by polymerizing in the presence of high concentrations of unreactive, micellar surfactant cosolutes which act as "templates". Removal of surfactant after polymerization is expected to leave pores with the approximate shape and dimensions of the surfactant micelles. A simple model was developed to simulate gel permeation chromatography (GPC) separations of globular proteins on templated gels. The model assumes that the partition coefficient for sieving of a protein is equal to the fraction of gel volume accessible to a sphere with a radius equal to the protein Stokes radius. The total gel volume is considered to include a fraction that is a conventional, random gel matrix and a remaining fraction contributed by templated pores. The pore size distribution of the conventional gel was estimated using the Ogston equation, which approximates the matrix as a random collection of long, thin, rigid fibers. Templated pores were assumed to have a Gaussian distribution of radii centered about some mean determined by the micelle radius. In comparison to conventional media, gels with templated pores are predicted to exhibit more sharply defined exclusion limits and improved resolution over a narrow size range centered on the mean templated pore size. Selectivity and resolution are expected to increase as the volume fraction of templated pores is increased and as the dispersion of templated pore radius is decreased. Small changes in template radius lead to large changes in the molecular weight range of optimal separation of globular proteins. It should be possible to create a series of GPC media that collectively offer high resolution over the molecular weight range of most globular proteins of interest.

Reaction-diffusion analysis of the effects of temperature on high-energy phosphate dynamics in goldfish skeletal muscle.

Thermal acclimation results in dramatic changes in the fractional volume of mitochondria within skeletal muscle of teleost fish. We investigated the hypothesis that changes in mitochondrial volume represent a compensatory response to temperature-induced changes in intracellular diffusion coefficients (D) of the high-energy phosphate compounds ATP and creatine phosphate (PCr). Using 31P nuclear magnetic resonance spectroscopy, we determined DPCr and DATP in goldfish (Carassius auratus) skeletal muscle at 25 degrees C and 5 degrees C: DPCr was 3.28 +/- 0.18 x 10(-6) cm2s-1 at 25 degrees C and 2.00 +/- 0.90 x 10(-6) cm2s-1 at 5 degrees C: DATP was 2.13 +/- 0.16 x 10(-6) cm2s-1 at 25 degrees C and was estimated to be 1.30 x 10(-6) cm2s-1 at 5 degrees C. There was no evidence for an effect of acclimation temperature or fiber type on DATP or DPCr. A mathematical reaction-diffusion model was used to calculate profiles of [ATP], [PCr] and the free energy of ATP hydrolysis (delta GATP) in activated goldfish muscle fibers at 5 degrees C and 25 degrees C. The results showed spatial and temporal constancy of [ATP], [PCr] and delta GATP in red fibers at both temperatures, regardless of changes in acclimation temperature or mitochondrial density. The model also showed spatial and temporal constancy of [ATP] in white fibers at 5 degrees C and 25 degrees C, but gradients in [PCr] and delta GATP developed in white fibers under all conditions of temperature and acclimation temperature. These gradients were attenuated in cold-acclimated animals by cold-induced increases in mitochondrial density. However, the model shows that the proximal stimulus for temperature-induced changes in mitochondrial volume density in muscle is not a disruption in intracellular diffusion of high-energy phosphates.