Bolus contaminant dispersion in oscillating flow in curved tubes.

The investigation of longitudinal dispersion of tracer substances in unsteady flows has biomechanical application in the study of heat and mass transport within the bronchial airways during normal, abnormal, and artificial pulmonary ventilation. To model the effects of airway curvature on intrapulmonary gas transport, we have measured local gas dispersion in axially uniform helical tubes of slight pitch during volume-cycled oscillatory flow. Following a small argon bolus injection into the flow field, the time-averaged effective diffusion coefficient (Deff/Dmol) for axial transport of the contaminant was evaluated from the time-dependent local argon concentration measured with a mass spectrometer. The value of (Deff/Dmol) is extracted from the curve of concentration versus time by two techniques yielding identical results. Experiments were conducted in two helical coiled tubes (delta = 0.031, lambda = 0.022 or delta = 0.085, lambda = 0.060) over a range of 2 < alpha < 15, 3 < A < 15, where delta is the ratio of tube radius to radius of curvature, lambda is the ratio of pitch height to radius of curvature, alpha is the Womersley parameter or dimensionless frequency, and A is the stroke amplitude or dimensionless tidal volume. Experimental results show that, when compared to transport in straight tubes, the effective diffusivity markedly increases in the presence of axial curvature. Results also compare favorably to mathematical predictions of bolus dispersion in a curved tube over the ranges of frequency and tidal volume studied.     

Gas dispersion in volume-cycled tube flow. I. Theory.

A mathematical theory is derived for the dispersion of a contaminant bolus introduced into a fully developed volume-cycled oscillatory pipe flow. The convection-diffusion equation is solved for a tracer gas bolus by expressing the local concentration field as a series expansion of derivatives of the area-averaged concentration. The local, as well as the area-averaged, concentration is determined for a uniform initial slug or Gaussian bolus. The effect of various flow parameters such as Womersley parameter, Schmidt number, and tidal volume is investigated. The overall dispersion is characterized by a time-averaged effective diffusion coefficient, which for long duration coincides with previous dispersion theories based on a constant linear axial concentration profile. The effective diffusion coefficient can be determined from the local time history of concentration, independent of the spatial location or the initial tracer bolus. Furthermore the local peaks of the concentration-time curve follow a decaying curve dictated by the time-averaged effective diffusion coefficient. Thus the theory is directly applicable for dispersion measurements in oscillatory tube flows, a basis for the pulmonary airways application, as shown by Gaver et al. (J. Appl. Physiol. 72: 321-331, 1992).     

Tracer diffusion in F-actin and Ficoll mixtures. Toward a model for cytoplasm.

We have previously reported that self-diffusion of inert tracer particles in the cytoplasm of living Swiss 3T3 cells is hindered in a size-dependent manner (Luby-Phelps, K., D.L. Taylor, and F. Lanni. 1986. J. Cell Biol. 102:2015-2022; Luby-Phelps, K., P.E. Castle, D.L. Taylor, and F. Lanni. 1987. Proc Natl. Acad. Sci. USA. 84:4910-4913). Lacking a theory that completely explains our data, we are attempting to understand the molecular architecture responsible for this phenomenon by studying tracer diffusion in simple, reconstituted model systems. This report contains our findings on tracer diffusion in concentrated solutions of Ficoll 70 or Ficoll 400, in solutions of entangled F-actin filaments, and in solutions of entangled F-actin containing a background of concentrated Ficoll particles or concentrated bovine serum albumin (BSA). A series of size-fractionated fluorescein-Ficolls were used as tracer particles. By fluorescence recovery after photobleaching (FRAP), we obtained the mean diffusion coefficients in a dilute, aqueous reference phase (Do), the mean diffusion coefficients in the model matrices (D), and the mean hydrodynamic radii (RH) for selected tracer fractions. For each model matrix, the results were compared with similar data obtained from living cells. As in concentrated solutions of globular proteins (Luby-Phelps et al., 1987), D/Do was not significantly size-dependent in concentrated solutions of Ficoll 400 or Ficoll 70. In contrast, D/Do decreased monotonically with increasing RH in solutions of F-actin ranging in concentration from 1 to 12 mg/ml. This size dependence was most pronounced at higher F-actin concentrations. However, the shape of the curve and the extrapolated value of D/Do in the limit, RH----O did not closely resemble the cellular data for tracers in the same size range (3 less than RH less than 30 nm). In mixtures of F-actin and Ficoll or F-actin and BSA, D/Do was well approximated by D/Do for the same concentration of F-actin alone multiplied by D/Do for the same concentrations of Ficoll or BSA alone. Based on these results, it is possible to model the submicroscopic architecture of cytoplasm in living cells as a densely entangled filament network (perhaps made up of F-actin and other filamentous structures) interpenetrated by a fluid phase crowded with globular macromolecules, which in cytoplasm would be primarily proteins.     

MR diffusion tensor spectroscopy and imaging.

This paper describes a new NMR imaging modality--MR diffusion tensor imaging. It consists of estimating an effective diffusion tensor, Deff, within a voxel, and then displaying useful quantities derived from it. We show how the phenomenon of anisotropic diffusion of water (or metabolites) in anisotropic tissues, measured noninvasively by these NMR methods, is exploited to determine fiber tract orientation and mean particle displacements. Once Deff is estimated from a series of NMR pulsed-gradient, spin-echo experiments, a tissue's three orthotropic axes can be determined. They coincide with the eigenvectors of Deff, while the effective diffusivities along these orthotropic directions are the eigenvalues of Deff. Diffusion ellipsoids, constructed in each voxel from Deff, depict both these orthotropic axes and the mean diffusion distances in these directions. Moreover, the three scalar invariants of Deff, which are independent of the tissue's orientation in the laboratory frame of reference, reveal useful information about molecular mobility reflective of local microstructure and anatomy. Inherently tensors (like Deff) describing transport processes in anisotropic media contain new information within a macroscopic voxel that scalars (such as the apparent diffusivity, proton density, T1, and T2) do not.     

Effect of cell arrangement and interstitial volume fraction on the diffusivity of monoclonal antibodies in tissue.

We present theoretical calculations relating the effective diffusivity of monoclonal antibodies in tissue (Deff) to the actual diffusivity in the interstitium (Dint) and the interstitial volume fraction phi. Measured diffusivity values are effective values, deduced from concentration profiles with the tissue treated as a continuum. By using homogenization theory, the ratio Deff/Dint is calculated for a range of interstitial volume fractions from 10 to 65%. It is assumed that only diffusion in the interstitial spaces between cells contributes to the effective diffusivity. The geometries considered have cuboidal cells arranged periodically, with uniform gaps between cells. Deff/Dint is found to generally be between (2/3) phi and phi for these geometries. In general, the pathways for diffusion between cells are not straight. The effect of winding pathways on Deff/Dint is examined by varying the arrangement of the cells, and found to be slight. Also, the estimates of Deff/Dint are shown to be insensitive to typical nonuniformities in the widths of gaps between cells. From our calculations and from published experimental measurements of the effective diffusivity of an IgG polyclonal antibody both in water and in tumor tissue, we deduce that the diffusivity of this molecule in the interstitium is one-tenth to one-twentieth its diffusivity in water. We also conclude that exclusion of molecules from cells (an effect independent of molecular weight) contributes as much as interstitial hindrance to the reduction of effective diffusivity, for small interstitial volume fractions (around 20%). This suggests that the increase in the rate of delivery to tissues resulting from the use of smaller molecular-weight molecules (such as antibody fragments or bifunctional antibodies) may be less than expected.     

Characterization of a pilot plant airlift tower loop bioreactor. I: evaluation of the phase properties with model media

Investigations were carried out in a 9 m high, 4 m(3) volume, pilot plant airlift tower loop bioreactor with a draft tube. The reactor was characterized by measuring residence time distributions of the gas phase using pseudostochastic tracer signals and a mass spectrometer and by evaluating the mixing in the liquid phase with single-pulse tracer inputs. The local gas holdup and the bubble size (piercing length) were measured with two-channel electrical conductivity probes. The mean residence times and the intensities of the axial mixing in the riser and downcomer and the circulation times of the phases as well as the fraction of the recirculated gas phase were evaluated. The gas holdup in the riser is nearly uniform along the reactor. In the downcomer, it diminishes from top to bottom. The liquid phase dispersion coefficients, D(L), are smaller than those measured in the corresponding bubble columns. In the pilot plant with tap water the following relationship was found: D(Lr) = cw(SG) (n); with c = 203.4; n = 0.5;D(Lr)(cm(2) s(-1);) and W(SG)(cm s(-1)) where D(Lr) is the longitudinal dispersion coefficient in the riser and W(SG) is the superficial gas velocity. The gas phase dispersion coefficients in the riser of the pilot plant, D(Gr), are also enlarged with increasing superficial gas velocity, W(SG), however, no simple relationship exists. Parameter D(Gr) is the highest in the presence of antifoam agents, intermediate in tap water, and the smallest in ethanol solution.     

Measurement of axial diffusivities in a model of the bronchial airways.

Values for the effective axial diffusivity D for laminar flow of a gas species in the bronchial airways have been obtained as a function of the mean axial gas velocity u by experiment measurements of benzene vapor dispersion in a five generation glass tube model of the bronchial tree. For both inspiration and expiration D is seen to be approximately a linear function of u over the range of Reynolds' numbers 30-2,000 corresponding to peak flows in bronchial generations 0-13 under resting breathing conditions. The diffusivity for expiration is seen to be approximately one-third that for inspiration due presumably to increased radial mixing at bifurcations during expiration. The effective diffusivities relative to the molecular diffusivity can be expressed by the formulas D/Dmol = 1 + 1.08 NPe for inspiration and D/Dmol = 1 + .37 N-Pe for expiration. These velocity dependent diffusivities help to explain the short transit times of gas boluses from mouth to alveoli and will aid in the analysis of airway gas mixing by mathematical transport equations.     

The role of fixed and mobile buffers in the kinetics of proton movement

We derive a simple expression for the effective diffusion coefficient of protons in Fick's second law, Deff, when both spatially fixed, HF, and mobile, HM, buffers are present. These buffers are present at moderately high concentrations ([Ftot], [Mtot] greater than 1 mM) in most biological systems. We consider only the case where the protonation reactions remain at equilibrium during the diffusion process. When the pH is to the alkaline side of the pK values of the fixed and mobile buffers ([H+] less than KF, KM), the effective diffusion coefficient of protons in Ficks second law is: (Formula: see text) where DH is the diffusion coefficient of the protons free in the aqueous phase and DHM is the diffusion coefficient of the mobile buffer. The equation illustrates three features of diffusion in a buffered system. Firstly, the effective diffusion coefficient of protons is always lower than the diffusion coefficient of free protons. Secondly, increasing the concentration of fixed buffers always decreases Deff. Thirdly, increasing the concentration of mobile buffer can increase Deff when fixed buffers are present.     

High-frequency ventilation of ducks and geese

We studied gas exchange in anesthetized ducks and geese artificially ventilated at normal tidal volumes (VT) and respiratory frequencies (fR) with a Harvard respirator (control ventilation, CV) or at low VT-high fR using an oscillating pump across a bias flow with mean airway opening pressure regulated at 0 cmH2O (high-frequency ventilation, HFV). VT was normalized to anatomic plus instrument dead space (VT/VD) for analysis. Arterial PCO2 was maintained at or below CV levels by HFV with VT/VD less than 0.5 and fR = 9 and 12 s-1 but not at fR = 6 s-1. For 0.4 less than or equal to VT/VD less than or equal to 0.85 and 3 s-1. less than or equal to fR less than or equal to 12 s-1, increased VT/VD was twice as effective as increased fR at decreasing arterial PCO2, consistent with oscillatory dispersion in a branching network being an important gas transport mechanism in birds on HFV. Ventilation of proximal exchange units with fresh gas due to laminar flow is not the necessary mechanism supporting gas exchange in HFV, since exchange could be maintained with VT/VD less than 0.5. Interclavicular and posterior thoracic air sac ventilation measured by helium washout did not change as much as expired minute ventilation during HFV. PCO2 was equal in both air sacs during HFV. These results could be explained by alterations in aerodynamic valving and flow patterns with HFV. Ventilation-perfusion distributions measured by the multiple inert gas elimination technique show increased inhomogeneity with HFV. Elimination of soluble gases was also enhanced in HFV as reported for mammals.(ABSTRACT TRUNCATED AT 250 WORDS)     

Axial dispersion in respiratory bronchioles and alveolar ducts

The mixing of gases in the pulmonary acinus was characterized by analyzing axial gas dispersion during steady flow in models of respiratory bronchioles and alveolar ducts. An analysis (method of moments) developed for addressing dispersion in porous media was used to derive an integral expression for the axial dispersion coefficient (D*). Evaluation of D* required solving the Navier-Stokes equations for the flow field and a convection-diffusion type equation arising from the analysis. D* was strongly dependent on alveolar volume per central duct volume, the aperture size through which the alveoli communicate with the central duct, and the Péclet number (Pe). At smaller Pe (flow rate) D* was substantially smaller than the molecular diffusion coefficient, whereas at larger Pe (flow rate) D* was much greater than the Taylor-Aris result for flow-enhanced dispersion in straight tubes. Also, flow-enhanced dispersion became appreciable at smaller Pe than indicated by the Taylor-Aris result. These behaviors transcend both the lower and upper limits established previously for gas mixing in the pulmonary acinus.     

Quantitative evaluation of cell orientation in culture.

A quantitative method to assess mutual orientation of cells in cultures on a substrate includes the following operations: (1) the cellular groups to be evaluated are chosen; (2) position of the long axis for each nucleus of the group is determined; (3) the axis OX is arbitrary chosen for every group and the angles alphai between the long axis of every nucleus i and the axis OX are measured. Every nucleus i corresponds to a vector of unit length ei with the angles 2alpha. D, the mean of the vectors ei for every cell group is calculated. This value of D is compared with a set of values of D computed according to a model of mutual orientation studies in a simulation experiment. In this model the group of n vectors consists of a fraction of Kn parallel vectors (o less than or equal to K less than or equal to I) and of (I minus K)n randomly oriented vectors. K corresponding to the computed D which is equal to the experimental value of D is considered as an index of orientation for the group. Contact orientation with respect to the relief of the substrate may be evaluated as a root mean square deviation sigma0 to the angles between the long axes of cell nuclei and the direction of relief. Examples of the measurements of K and sigma0 in cell cultures are given.     

Residence time distributions of gas flowing through rotating drum bioreactors

Residence time distribution studies of gas through a rotating drum bioreactor for solid-state fermentation were performed using carbon monoxide as a tracer gas. The exit concentration as a function of time differed considerably from profiles expected for plug flow, plug flow with axial dispersion, and continuous stirred tank reactor (CSTR) models. The data were then fitted by least-squares analysis to mathematical models describing a central plug flow region surrounded by either one dead region (a three-parameter model) or two dead regions (a five-parameter model). Model parameters were the dispersion coefficient in the central plug flow region, the volumes of the dead regions, and the exchange rates between the different regions. The superficial velocity of the gas through the reactor has a large effect on parameter values. Increased superficial velocity tends to decrease dead region volumes, interregion transfer rates, and axial dispersion. The significant deviation from CSTR, plug flow, and plug flow with axial dispersion of the residence time distribution of gas within small-scale reactors can lead to underestimation of the calculation of mass and heat transfer coefficients and hence has implications for reactor design and scale-up.     

Pendelluft and mixing in a single bifurcation lung model during high-frequency oscillation

A single bifurcation with an adjustable daughter branch compliance ratio (VR) was used to simultaneously study pendelluft and longitudinal mixing during flow oscillations at frequencies (f) of 1-15 Hz and amplitudes (VOp) of 25-150 ml/s. Mixing coefficients (Deff) were determined from the dispersion of a CO2 bolus centered at the bifurcation point, and pendelluft volume was computed as a fraction of mother branch tidal volume (PVF) using measurements of airflow in the daughter branches. Plotted against frequency, PVF was a bell-shaped curve insensitive to the value of VOp. When VR = 2, a PVF peak of 0.25 appeared at f = 3 Hz, and when VR = 5, a PVF peak of 0.75 appeared at f = 4 Hz. After normalization by control values at VR = 1, Deff curves were also bell shaped, insensitive to the value of VOp and with peaks appearing at the same frequencies as the PVF peaks. The normalized Deff peak values were 1.7 when VR = 2 and 4.0 when VR = 5. The similarities in the PVF and Deff curves imply a direct relationship between pendelluft and enhanced mixing.     

Lateral diffusion of lipids and glycophorin in solid phosphatidylcholine bilayers. The role of structural defects

The lateral mobility of the lipid analog N-4-nitrobenzo-2-oxa-1,3 diazole phosphatidylethanolamine and of the integral protein glycophorin in giant dimyristoylphosphatidylcholine vesicles was studied by the photobleaching technique. Above the temperature of the chain-melting transition (Tm = 23 degrees C), the diffusion coefficient, Dp, of the protein [Dp = (4 +/- 2) X 10(-8) cm2/s at 30 degrees C] was within the experimental errors equal to the corresponding values DL of the lipid analog. In the P beta 1 phase the diffusion of lipid and glycophorin was studied as a function of the probe and the protein concentration. (a) At low lipid-probe content (cL less than 5 mmol/mol of total lipid), approximately 20% of the probe diffuses fast (D approximately equal to 10(-8) - 10(-9) cm2/s), while the mobility of the rest is strongly reduced (D less than 10(-10) cm2/s). At a higher concentration (cp approximately 20 mmol), all probe is immobilized (D less than 10(-10) cm2/s). (b) Incorporation of glycophorin up to cp = 0.4 mmol/mol of total lipid leads to a gradual increase of the fraction of mobile lipid probe due to the lateral-phase separation into a pure P beta 1 phase and a fraction of lipid that is fluidized by strong hydrophilic lipid-protein interaction. (c) The diffusion of the glycophorin molecules is characterized by a slow and a fast fraction. The latter increases with increasing protein content, which is again due to the lateral-phase separation caused by the hydrophilic lipid-protein interaction. The results are interpreted in terms of a fast transport along linear defects in the P beta 1 phase, which form quasi-fluid paths for a nearly one dimensional and thus very effective transport. Evidence for this interpretation of the diffusion measurements is provided by freeze-fracture electron microscopy.     

Hindered diffusion of high molecular weight compounds in brain extracellular microenvironment measured with integrative optical imaging.

This paper describes the theory of an integrative optical imaging system and its application to the analysis of the diffusion of 3-, 10-, 40-, and 70-kDa fluorescent dextran molecules in agarose gel and brain extracellular microenvironment. The method uses a precisely defined source of fluorescent molecules pressure ejected from a micropipette, and a detailed theory of the intensity contributions from out-of-focus molecules in a three-dimensional medium to a two-dimensional image. Dextrans tagged with either tetramethylrhodamine or Texas Red were ejected into 0.3% agarose gel or rat cortical slices maintained in a perfused chamber at 34 degrees C and imaged using a compound epifluorescent microscope with a 10 x water-immersion objective. About 20 images were taken at 2-10-s intervals, recorded with a cooled CCD camera, then transferred to a 486 PC for quantitative analysis. The diffusion coefficient in agarose gel, D, and the apparent diffusion coefficient, D*, in brain tissue were determined by fitting an integral expression relating the measured two-dimensional image intensity to the theoretical three-dimensional dextran concentration. The measurements in dilute agarose gel provided a reference value of D and validated the method. Values of the tortuosity, lambda = (D/D*)1/2, for the 3- and 10-kDa dextrans were 1.70 and 1.63, respectively, which were consistent with previous values derived from tetramethylammonium measurements in cortex. Tortuosities for the 40- and 70-kDa dextrans had significantly larger values of 2.16 and 2.25, respectively. This suggests that the extracellular space may have local constrictions that hinder the diffusion of molecules above a critical size that lies in the range of many neurotrophic compounds.     

Diffusion-limited forward rate constants in two dimensions. Application to the trapping of cell surface receptors by coated pits.

A variety of receptors are known to aggregate in specialized cell surface structures called coated pits, prior to being internalized when the coated pits close off. At 37 degrees C on human fibroblasts, as well as on other cell types, a recycling process maintains a constant number of coated pits on the cell surface. In this paper, we explore implications for receptor aggregation and internalization of the two types of recycling models that have been proposed for the maintenance of the coated pit concentration. In one model, coated pits alternate between accessible and inaccessible states at fixed locations on the cell surface, while in the other model, coated pits recycle to random locations on the cell surface. We consider receptors that are randomly inserted in the membrane, move by pure diffusion with diffusion coefficient D, and are instantly and irreversibly trapped when they reach a coated pit boundary (the diffusion limit). For such receptors, we calculate for each of the two models: the mean time tau to reach a coated pit, the forward rate constant k+ for the interaction of a receptor with a coated pit, and the fraction phi of receptors aggregated in coated pits. We show that for the parameters that characterize coated pits on human fibroblasts, the way in which coated pits return to the surface has a negligible effect on the values of tau, k+, and phi for mobile receptors, D greater than or equal to 1.0 X 10(-11) cm2/s, but has a substantial effect for "immobile" receptors, D much less than 1 X 10(-11) cm2/s. We present numerical examples to show that it may be possible to distinguish between these models if one can monitor slowly diffusing receptors (D less than 1 X 10(-11) cm2/s) on cells whose coated pits have relatively short lifetimes (less than or equal to 1 min). Finally, we show that for the low-density lipoprotein (LDL) receptor on human fibroblasts (D = 4.5 X 10(-11) cm2/s), the predicted and observed values of K+ and phi are in close agreement. Therefore, even for slowly diffusing LDL receptor, unaided diffusion as the transport mechanism of receptors to coated pits is consistent with measured rates of LDL internalization.     

Fast diffusion along defects and corrugations in phospholipid P beta, liquid crystals.

The diffusion of a fluorescent lipid analogue in liquid crystals of the anisotropic P beta, phase of dimyristoylphosphatidylcholine (DMPC) had been found to be highly variable, suggesting structural defect pathways. Fluorescence photobleaching recovery (FPR) experiments imply two effective diffusion pathways with coefficients differing by at least 100. This is consistent with fast diffusion along submicroscopic bands of disordered material ("defects") in the bilayer corrugations characteristic of this phase. Due to strains during transformation from the L alpha phase, the axis of the corrugations is ordinarily disrupted by mosaic patches rotationally disoriented within the mean plane of the molecular bilayers, although larger oriented domains are sometimes adventitiously aligned into microscopically visible striped textures. The corrugations are also systematically aligned along positive disclinations pairs or "oily streaks." Thus, fast diffusion occurs parallel to the disclination lines and along the textured stripes. FPR results yield an upper limit on the effective diffusion in the ordered material of D less than or equal to 2 X 10(-16) cm2/s at 22 degrees C, D less than or equal to 3 X 10(-17) cm2/s at 13 degrees C. In contrast the diffusion coefficient along defect pathways where disordered ribbons are aligned is D approximately 4 X 10(-11) cm2/s at 16 degrees C.     

Generalized dispersion in a synovial fluid of human joints

An unsteady convective diffusion in a synovial fluid of human joints modeled as a power-law fluid is studied using the generalized dispersion model of Gill and Sankara-subramanian [12]. The contributions of convection and diffusion, and pure convection on the dispersion of nutrient are investigated in detail. It is shown that the effect of decrease in non-Newtonian parameter is to decrease the dispersion coefficient. The mean concentration distribution appears to increase as the non-Newtonian parameter decreases upto a certain value of the axial distance. Beyond this point, however, the reverse pattern is observed.     

Anomalous diffusion of proteins due to molecular crowding

We have studied the diffusion of tracer proteins in highly concentrated random-coil polymer and globular protein solutions imitating the crowded conditions encountered in cellular environments. Using fluorescence correlation spectroscopy, we measured the anomalous diffusion exponent alpha characterizing the dependence of the mean-square displacement of the tracer proteins on time, r(2)(t) approximately t(alpha). We observed that the diffusion of proteins in dextran solutions with concentrations up to 400 g/l is subdiffusive (alpha < 1) even at low obstacle concentration. The anomalous diffusion exponent alpha decreases continuously with increasing obstacle concentration and molecular weight, but does not depend on buffer ionic strength, and neither does it depend strongly on solution temperature. At very high random-coil polymer concentrations, alpha reaches a limit value of alpha(l) approximately 3/4, which we take to be the signature of a coupling between the motions of the tracer proteins and the segments of the dextran chains. A similar, although less pronounced, subdiffusive behavior is observed for the diffusion of streptavidin in concentrated globular protein solutions. These observations indicate that protein diffusion in the cell cytoplasm and nucleus should be anomalous as well, with consequences for measurements of solute diffusion coefficients in cells and for the modeling of cellular processes relying on diffusion.     

Crowding and confinement effects on protein diffusion in vivo

The first in vivo measurements of a protein diffusion coefficient versus cytoplasmic biopolymer volume fraction are presented. Fluorescence recovery after photobleaching yields the effective diffusion coefficient on a 1-mum-length scale of green fluorescent protein within the cytoplasm of Escherichia coli grown in rich medium. Resuspension into hyperosmotic buffer lacking K+ and nutrients extracts cytoplasmic water, systematically increasing mean biopolymer volume fraction, , and thus the severity of possible crowding, binding, and confinement effects. For resuspension in isosmotic buffer (osmotic upshift, or Delta, of 0), the mean diffusion coefficient, , in cytoplasm (6.1 +/- 2.4 microm2 s(-1)) is only 0.07 of the in vitro value (87 microm2 s(-1)); the relative dispersion among cells, sigmaD/ (standard deviation, sigma(D), relative to the mean), is 0.39. Both and sigmaD/ remain remarkably constant over the range of Delta values of 0 to 0.28 osmolal. For a Delta value of > or =0.28 osmolal, formation of visible plasmolysis spaces (VPSs) coincides with the onset of a rapid decrease in by a factor of 380 over the range of Delta values of 0.28 to 0.70 osmolal and a substantial increase in sigmaD/. Individual values of D vary by a factor of 9 x 10(4) but correlate well with f(VPS), the fractional change in cytoplasmic volume on VPS formation. The analysis reveals two levels of dispersion in D among cells: moderate dispersion at low Delta values for cells lacking a VPS, perhaps related to variation in phi or biopolymer organization during the cell cycle, and stronger dispersion at high Delta values related to variation in f(VPS). Crowding effects alone cannot explain the data, nor do these data alone distinguish crowding from possible binding or confinement effects within a cytoplasmic meshwork.