Diffusion coefficients of endogenous cytosolic proteins from rabbit skinned muscle fibers

Abstract

Efflux time courses of endogenous cytosolic proteins were obtained from rabbit psoas muscle fibers skinned in oil and transferred to physiological salt solution. Proteins were separated by gel electrophoresis and compared to load-matched standards for quantitative analysis. A radial diffusion model incorporating the dissociation and dissipation of supramolecular complexes accounts for an initial lag and subsequent efflux of glycolytic and glycogenolytic enzymes. The model includes terms representing protein crowding, myofilament lattice hindrance, and binding to the cytomatrix. Optimization algorithms returned estimates of the apparent diffusion coefficients, D(r,t), that were very low at the onset of diffusion (∼10(-10) cm(2) s(-1)) but increased with time as cytosolic protein density, which was initially high, decreased. D(r,t) at later times ranged from 2.11 × 10(-7) cm(2) s(-1) (parvalbumin) to 0.20 × 10(-7) cm(2) s(-1) (phosphofructose kinase), values that are 3.6- to 12.3-fold lower than those predicted in bulk water. The low initial values are consistent with the presence of complexes in situ; the higher later values are consistent with molecular sieving and transient binding of dissociated proteins. Channeling of metabolic intermediates via enzyme complexes may enhance production of adenosine triphosphate at rates beyond that possible with randomly and/or sparsely distributed enzymes, thereby matching supply with demand.

Figure 1

Experimental setup and radial diffusion of endogenous cytosolic proteins into relaxing solution from skinned fiber segments of rabbit psoas muscle. (A) The experimental protocol, where each fiber is placed sequentially in either two or three drops of relaxing solution (∼10 μL each) for a specified period of time ranging from 2 s to 20 min (see text). (B) Proteins separated by SDS polyacrylamide gel electrophoresis with silver-stained gel. Proteins are identified as in Maughan et al. (3). Lanes 2–4, cytosolic protein fractions obtained by sequentially incubating the skinned fiber for 35 s (lane 2, load 5.4 μL = 51% of total volume), 80 s (lane 3, load 7.2 μL = 68% of total), and 1440 s (lane 4, load 10 μL = 90% of total) in 10 μL relaxing solution drops. Lane 1, cytomatrix fraction (residual fiber, load 5 μL = 14% of total). Fiber radius, 29.5 μm; fiber length, 6.56 mm.

Figure 2

(A–G) Radial diffusion time courses for seven glycolytic enzymes. Ordinate, amount of protein, M(t/a²), relative to the total, M_∞, that diffuses from a segment of a skinned psoas fiber; abscissa, elapsed time fiber remains in each drop divided by the square of the fiber radius. Experiments were performed according to the following protocol. Skinned fibers were transferred sequentially from oil to drop 1, where they remained for variable periods of time, then through oil (<1 s) to drop 2, where they remained for 600 s. Average length of fiber segments, ∼6 mm; average radius, 20.6 ± 4.3 μm (mean ± SD) In a subset of fibers (the three-drop experiment), fibers remained for variable periods in drops 1 and 2 before being transferred to drop 3 (600 s). Curves are generated from numerical solutions of the Constant D model (hatched lines) and Variable D model (solid lines). (H) Duplicate of F (pyruvate kinase) at expanded timescale. The equilibration time for endogenous pyruvate kinase is comparable to that reported for exogenous Rh-pyruvate kinase (55). See text for details.

Figure 3

(A–D) Radial diffusion time courses for four cytosolic proteins. Ordinate, abscissa, and procedures are as in Fig. 2. Curves are generated from numerical solutions of the Constant D model (hatched lines) and Variable D model (solid lines). Note that the initial diffusional lag is evident in C and D. Fiber dimensions are as in Fig. 2. See text for details.

Figure 4

(A) D (Constant D model) and D(r,t) (Variable D model) evaluated at later times versus protein molecular weight contrasted against predicted Stokes-Einstein relationships, with and without steric hindrance. Open and solid circles represent diffusion coefficients determined with the Constant D model, and those determined with the Variable D model (D(r,t) evaluated at t/a² = 0.35 where r = a, i.e., the fiber radius), respectively. The dotted and dashed lines give the Stokes-Einstein relations using diffusion coefficients determined experimentally by Young et al. (35), without and with, respectively, the lattice hindrance term. The slopes of the double log plots are about −1, consistent with an inverse relationship between diffusion coefficient and hydrodynamic radius. (B) D/D_w (Constant D model) and D(r,t)/D_w (Variable D model) at t/a² = 0.35 and r ∼ a as functions of the hydrodynamic radius. The Variable D curve is plotted according to Eq. 9, where values of D(r,t), D_w, and R_h are from Table 2. Straight dashed lines are linear regression fits, and curved dotted lines are 95% confidence limits. Although the general form of Eq. 9 is nonlinear, the resulting plot (solid circles) is, to the naked eye, essentially linear for the parameter values used (R_o = 5.25 nm, L = 12.85 nm, and R_h = 1.83–5.69 nm), yielding an x axis intercept (i.e., the sieving radius) of 7.6 nm, i.e., a value close to that obtained by the linear fit.