Multicomponent diffusion in polymeric liquids.

It is shown how the phase-space kinetic theory of polymeric liquid mixtures leads to a set of extended Maxwell-Stefan equations describing multicomponent diffusion. This expression reduces to standard results for dilute solutions and for undiluted polymers. The polymer molecules are modeled as flexible bead-spring structures. To obtain the Maxwell-Stefan equations, the usual expression for the hydrodynamic drag force on a bead, used in previous kinetic theories, must be replaced by a new expression that accounts explicitly for bead-bead interactions between different molecules.

Role of tumor–host interactions in interstitial diffusion of macromolecules: Cranial vs. subcutaneous tumors

The large size of many novel therapeutics impairs their transport through the tumor extracellular matrix and thus limits their therapeutic effectiveness. We propose that extracellular matrix composition, structure, and distribution determine the transport properties in tumors. Furthermore, because the characteristics of the extracellular matrix largely depend on the tumor–host interactions, we postulate that diffusion of macromolecules will vary with tumor type as well as anatomical location. Diffusion coefficients of macromolecules and liposomes in tumors growing in cranial windows (CWs) and dorsal chambers (DCs) were measured by fluorescence recovery after photobleaching. For the same tumor types, diffusion of large molecules was significantly faster in CW than in DC tumors. The greater diffusional hindrance in DC tumors was correlated with higher levels of collagen type I and its organization into fibrils. For molecules with diameters comparable to the interfibrillar space the diffusion was 5- to 10-fold slower in DC than in CW tumors. The slower diffusion in DC tumors was associated with a higher density of host stromal cells that synthesize and organize collagen type I. Our results point to the necessity of developing site-specific drug carriers to improve the delivery of molecular medicine to solid tumors.

Proton transfer from the bulk to the bound ubiquinone QB of the reaction center in chromatophores of Rhodobacter sphaeroides: Retarded conveyance by neutral water

The mechanism of proton transfer from the bulk into the membrane protein interior was studied. The light-induced reduction of a bound ubiquinone molecule QB by the photosynthetic reaction center is accompanied by proton trapping. We used kinetic spectroscopy to measure (i) the electron transfer to QB (at 450 nm), (ii) the electrogenic proton delivery from the surface to the QB site (by electrochromic carotenoid response at 524 nm), and (iii) the disappearance of protons from the bulk solution (by pH indicators). The electron transfer to QB− and the proton-related electrogenesis proceeded with the same time constant of ≈100 μs (at pH 6.2), whereas the alkalinization in the bulk was distinctly delayed (τ ≈ 400 μs). We investigated the latter reaction as a function of the pH indicator concentration, the added pH buffers, and the temperature. The results led us to the following conclusions: (i) proton transfer from the surface-located acidic groups into the QB site followed the reduction of QB without measurable delay; (ii) the reprotonation of these surface groups by pH indicators and hydronium ions was impeded, supposedly, because of their slow diffusion in the surface water layer; and (iii) as a result, the protons were slowly donated by neutral water to refill the proton vacancies at the surface. It is conceivable that the same mechanism accounts for the delayed relaxation of the surface pH changes into the bulk observed previously with bacteriorhodopsin membranes and thylakoids. Concerning the coupling between proton pumps in bioenergetic membranes, our results imply a tendency for the transient confinement of protons at the membrane surface.

Spectral diffusion and the energy landscape of a protein

We present a novel type of spectral diffusion experiment in the millikelvin range to characterize the energy landscape of a protein as compared with that of a glass. We measure the time evolution of spectral holes for more than 300 hr after well-defined initial nonequilibrium conditions. We show that the model of noninteracting two-level systems can describe spectral diffusion in the glass, but fails for the protein. Our results further demonstrate that randomness in the energy landscape of a protein shows features of organization. There are “deep minimum” states separated by barriers, the heights of which we are able to estimate. The energy landscape of a glass is featureless by comparison.

cAMP compartmentation is responsible for a local activation of cardiac Ca2+ channels by beta-adrenergic agonists.

The role of cAMP subcellular compartmentation in the progress of beta-adrenergic stimulation of cardiac L-type calcium current (ICa) was investigated by using a method based on the use of whole-cell patch-clamp recording and a double capillary for extracellular microperfusion. Frog ventricular cells were sealed at both ends to two patch-clamp pipettes and positioned approximately halfway between the mouths of two capillaries that were separated by a 5-micron thin wall. ICa could be inhibited in one half or the other by omitting Ca2+ from one solution or the other. Exposing half of the cell to a saturating concentration of isoprenaline (ISO, 1 microM) produced a nonmaximal increase in ICa (347 +/- 70%; n = 4) since a subsequent application of ISO to the other part induced an additional effect of nearly similar amplitude to reach a 673 +/- 130% increase. However, half-cell exposure to forskolin (FSK, 30 microM) induced a maximal stimulation of ICa (561 +/- 55%; n = 4). This effect was not the result of adenylyl cyclase activation due to FSK diffusion in the nonexposed part of the cell. To determine the distant effects of ISO and FSK on ICa, the drugs were applied in a zero-Ca solution. Adding Ca2+ to the drug-containing solutions allowed us to record the local effect of the drugs. Dose-response curves for the local and distant effects of ISO and FSK on ICa were used as an index of cAMP concentration changes near the sarcolemma. We found that ISO induced a 40-fold, but FSK induced only a 4-fold, higher cAMP concentration close to the Ca2+ channels, in the part of the cell exposed to the drugs, than it did in the rest of the cell. cAMP compartmentation was greatly reduced after inhibition of phosphodiesterase activity with 3-isobutyl-methylxanthine, suggesting the colocalization of enzymes involved in the cAMP cascade. We conclude that beta-adrenergic receptors are functionally coupled to nearby Ca2+ channels via local elevations of cAMP.

Intranuclear diffusion and hybridization state of oligonucleotides measured by fluorescence correlation spectroscopy in living cells

Fluorescein-labeled oligodeoxynucleotides (oligos) were introduced into cultured rat myoblasts, and their molecular movements inside the nucleus were studied by fluorescence correlation spectroscopy (FCS) and fluorescence recovery after photobleaching (FRAP). FCS revealed that a large fraction of both intranuclear oligo(dT) (43%) and oligo(dA) (77%) moves rapidly with a diffusion coefficient of 4 × 10−7 cm2/s. Interestingly, this rate of intranuclear oligo movement is similar to their diffusion rates measured in aqueous solution. In addition, we detected a large fraction (45%) of the intranuclear oligo(dT), but not oligo(dA), diffusing at slower rates (≤1 × 10−7 cm2/s). The amount of this slower-moving oligo(dT) was greatly reduced if the oligo(dT) was prehybridized in solution with (unlabeled) oligo(dA) prior to introduction to cells, presumably because the oligo(dT) was then unavailable for subsequent hybridization to endogenous poly(A) RNA. The FCS-measured diffusion rate for much of the slower oligo(dT) population approximated the diffusion rate in aqueous solution of oligo(dT) hybridized to a large polyadenylated RNA (1.0 × 10−7 cm2/s). Moreover, this intranuclear movement rate falls within the range of calculated diffusion rates for an average-sized heterogeneous nuclear ribonucleoprotein particle in aqueous solution. A subfraction of oligo(dT) (15%) moved over 10-fold more slowly, suggesting it was bound to very large macromolecular complexes. Average diffusion coefficients obtained from FRAP experiments were in agreement with the FCS data. These results demonstrate that oligos can move about within the nucleus at rates comparable to those in aqueous solution and further suggest that this is true for large ribonucleoprotein complexes as well.

Radial and longitudinal diffusion of myoglobin in single living heart and skeletal muscle cells

We have used a fluorescence recovery after photobleaching (FRAP) technique to measure radial diffusion of myoglobin and other proteins in single skeletal and cardiac muscle cells. We compare the radial diffusivities, Dr (i.e., diffusion perpendicular to the long fiber axis), with longitudinal ones, Dl (i.e., parallel to the long fiber axis), both measured by the same technique, for myoglobin (17 kDa), lactalbumin (14 kDa), and ovalbumin (45 kDa). At 22°C, Dl for myoglobin is 1.2 × 10−7 cm2/s in soleus fibers and 1.1 × 10−7 cm2/s in cardiomyocytes. Dl for lactalbumin is similar in both cell types. Dr for myoglobin is 1.2 × 10−7 cm2/s in soleus fibers and 1.1 × 10−7 cm2/s in cardiomyocytes and, again, similar for lactalbumin. Dl and Dr for ovalbumin are 0.5 × 10−7 cm2/s. In the case of myoglobin, both Dl and Dr at 37°C are about 80% higher than at 22°C. We conclude that intracellular diffusivity of myoglobin and other proteins (i) is very low in striated muscle cells, ≈1/10 of the value in dilute protein solution, (ii) is not markedly different in longitudinal and radial direction, and (iii) is identical in heart and skeletal muscle. A Krogh cylinder model calculation holding for steady-state tissue oxygenation predicts that, based on these myoglobin diffusivities, myoglobin-facilitated oxygen diffusion contributes 4% to the overall intracellular oxygen transport of maximally exercising skeletal muscle and less than 2% to that of heart under conditions of high work load.

Diffusion-limited contact formation in unfolded cytochrome c: estimating the maximum rate of protein folding.

How fast can a protein fold? The rate of polypeptide collapse to a compact state sets an upper limit to the rate of folding. Collapse may in turn be limited by the rate of intrachain diffusion. To address this question, we have determined the rate at which two regions of an unfolded protein are brought into contact by diffusion. Our nanosecond-resolved spectroscopy shows that under strongly denaturing conditions, regions of unfolded cytochrome separated by approximately 50 residues diffuse together in 35-40 microseconds. This result leads to an estimate of approximately (1 microsecond)-1 as the upper limit for the rate of protein folding.

Intracellular pH in adipocytes: effects of free fatty acid diffusion across the plasma membrane, lipolytic agonists, and insulin.

The main function of white adipose tissue is to store nutrient energy in the form of triglycerides. The mechanism by which free fatty acids (FFA) move into and out of the adipocyte has not been resolved. We show here that changes in intracellular pH (pH1) in adipocytes correlate with the movement of FFA across cellular membranes as predicted by the Kamp and Hamilton model of passive diffusion of FFA. Exposure of fat cells to lipolytic agents or external FFA results is a rapid intracellular acidification that is reversed by metabolism of the FFA or its removal by albumin. In contrast, insulin causes an alkalinization of the cell, consistent with its main function to promote esterification. Inhibition of Na+/H+ exchange in adipocytes does not prevent the changes in pHi caused by FFA, lipolytic agents, or insulin. A fatty acid dimer, which diffuses into the cell but is not metabolized, causes an irreversible acidification. Taken together, the data suggest that changes in pHi occur in adipocytes in response to the passive diffusion of un-ionized FFA (flip-flop) into and out of the cell and in response to their metabolism and production within the cell. These changes in pHi may, in turn, modulate hormonal signaling and metabolism with significant impact on cell function.