Coupled Protein Diffusion and Folding in the Cell

When a protein unfolds in the cell, its diffusion coefficient is affected by its increased hydrodynamic radius and by interactions of exposed hydrophobic residues with the cytoplasmic matrix, including chaperones. We characterize protein diffusion by photobleaching whole cells at a single point, and imaging the concentration change of fluorescent-labeled protein throughout the cell as a function of time. As a folded reference protein we use green fluorescent protein. The resulting region-dependent anomalous diffusion is well characterized by 2-D or 3-D diffusion equations coupled to a clustering algorithm that accounts for position-dependent diffusion. Then we study diffusion of a destabilized mutant of the enzyme phosphoglycerate kinase (PGK) and of its stable control inside the cell. Unlike the green fluorescent protein control''s diffusion coefficient, PGK''s diffusion coefficient is a non-monotonic function of temperature, signaling ‘sticking’ of the protein in the cytosol as it begins to unfold. The temperature-dependent increase and subsequent decrease of the PGK diffusion coefficient in the cytosol is greater than a simple size-scaling model suggests. Chaperone binding of the unfolding protein inside the cell is one plausible candidate for even slower diffusion of PGK, and we test the plausibility of this hypothesis experimentally, although we do not rule out other candidates.     

Diffusion approximation of the stochastic process of microtubule assembly

Microtubules are protein polymers that guide intracellular motility. Stochastic switching of a microtubule between states of elongation, shortening, and pause is described in detail by the dynamic instability (DI) model. Recently we have described the dynamics of microtubules phenomenologically as generalized diffusion of their ends. Genesis of the diffusion dynamics and accuracy of diffusion model are studied in this work. It is shown that wandering of the end of a microtubule undergoing DI asymptotically approaches the Wiener diffusion process. Accuracy of the diffusion approximation is evaluated by comparing its predictions with results of simulation of DI. Stationary distributions of microtubule length and lifetime that are predicted by both models differ qualitatively between two cell types considered. However, predictions of the diffusion model are in each case practically identical to predictions of the DI model being also consistent with experimental data. The peculiar stochastic process of microtubule assembly thus converges at cell scale to a kind of widespread-in-nature diffusion process. This result is considered an example of qualitative change in dynamical properties in transition from the molecular to cellular level of biological organization. Additionally, it suggests employment of diffusion process theory in studying functions of microtubules in the cell.     

Molecular modeling and simulation of Mycobacterium tuberculosis cell wall permeability

The low permeability of the mycobacterial cell wall is thought to contribute to the intrinsic drug resistance of mycobacteria. In this study, the permeability of the Mycobacterium tuberculosis cell wall is studied by computer simulation. Thirteen known drugs with diverse chemical structures were modeled as solutes undergoing transport across a model for the M. tuberculosis cell wall. The properties of the solute-membrane complexes were investigated by means of molecular dynamics simulation, especially the diffusion coefficients of the solute molecules inside the cell wall. The molecular shape of the solute was found to be an important factor for permeation through the M. tuberculosis cell wall. Predominant lateral diffusion within, as opposed to transverse diffusion across, the membrane/cell wall system was observed for some solutes. The extent of lateral diffusion relative to transverse diffusion of a solute within a biological cell membrane may be an important finding with respect to absorption distribution, metabolism, elimination, and toxicity properties of drug candidates. Molecular similarity measures among the solutes were computed, and the results suggest that compounds having high molecular similarity will display similar transport behavior in a common membrane/cell wall environment. In addition, the diffusion coefficients of the solute molecules across the M. tuberculosis cell wall model were compared to those across the monolayers of dipalmitoylphosphatidylethanolamine and dimyristoylphosphatidylcholine, are two common phospholipids in bacterial and animal membranes. The differences among these three groups of diffusion coefficients were observed and analyzed.     

Phospholipids undergo hop diffusion in compartmentalized cell membrane

The diffusion rate of lipids in the cell membrane is reduced by a factor of 5-100 from that in artificial bilayers. This slowing mechanism has puzzled cell biologists for the last 25 yr. Here we address this issue by studying the movement of unsaturated phospholipids in rat kidney fibroblasts at the single molecule level at the temporal resolution of 25 micros. The cell membrane was found to be compartmentalized: phospholipids are confined within 230-nm-diameter (phi) compartments for 11 ms on average before hopping to adjacent compartments. These 230-nm compartments exist within greater 750-nm-phi compartments where these phospholipids are confined for 0.33 s on average. The diffusion rate within 230-nm compartments is 5.4 microm2/s, which is nearly as fast as that in large unilamellar vesicles, indicating that the diffusion in the cell membrane is reduced not because diffusion per se is slow, but because the cell membrane is compartmentalized with regard to lateral diffusion of phospholipids. Such compartmentalization depends on the actin-based membrane skeleton, but not on the extracellular matrix, extracellular domains of membrane proteins, or cholesterol-enriched rafts. We propose that various transmembrane proteins anchored to the actin-based membrane skeleton meshwork act as rows of pickets that temporarily confine phospholipids.     

Measurement of Biomolecular Diffusion in Extracellular Matrix Condensed by Fibroblasts Using Fluorescence Correlation Spectroscopy

The extracellular matrix (ECM) comprises the heterogeneous environment outside of cells in a biological system. The ECM is dynamically organized and regulated, and many biomolecules secreted from cells diffuse throughout the ECM, regulating a variety of cellular processes. Therefore, investigation of the diffusive behaviors of biomolecules in the extracellular environment is critical. In this study, we investigated the diffusion coefficients of biomolecules of various sizes, measuring from 1 to 10 nm in radius, by fluorescence correlation spectroscopy in contracted collagen gel caused by fibroblasts, a traditional culture model of dynamic rearrangement of collagen fibers. The diffusion coefficients of the biomolecules in control collagen gel without cells decreased slightly as compared to those in solution, while the diffusion coefficients of biomolecules in the contracted gel at the cell vicinity decreased dramatically. Additionally, the diffusion coefficients of biomolecules were inversely correlated with molecular radius. In collagen gels populated with fibroblasts, the diffusion coefficient at the cell vicinity clearly decreased in the first 24 h of culture. Furthermore, molecular diffusion was greatly restricted, with a central focus on the populated cells. By using the obtained diffusion coefficients of biomolecules, we calculated the collagen fiber condensation ratio by fibroblasts in the cell vicinity at 3 days of culture to represent a 52-fold concentration. Thus, biomolecular diffusion is restricted in the vicinity of the cells where collagen fibers are highly condensed.     

Measurement of local diffusion coefficients in biofilms by microinjection and confocal microscopy

A new technique for the determination of local diffusion coefficients in biofilms is described. It is based on the microinjection of fluorescent dyes and quantitative analysis of the subsequent plume formation using confocal laser microscopy. The diffusion coefficients of fluorescein (MW 332), TRITC-IgG (MW 150000) and phycoerythrin (MW 240000) were measured in the cell clusters and interstitial voids of a heterogeneous biofilm. The diffusivities measured in the voids were close to the theoretical values in water. Fluorescein had the same diffusivity in cell clusters, voids, and sterile medium. TRITC-IgG did not diffuse in cell clusters, presumably due to binding to the cell cluster matrix. After treatment of the biofilm with bovine serum albumin, binding capacity decreased and the diffusion coefficient could be measured. The diffusivity of phycoerythrin in cell clusters was impeded by 41%, compared to interstitial voids. From the diffusion data of phycoerythrin it was further calculated that the cell cluster matrix had the characteristics of a gel with 0.6 nm thick fibers and pore diameters of 80 nm. (c) 1997 John Wiley & Sons, Inc.     

A Highlights from MBoC Selection: Diffusion of GPI-anchored proteins is influenced by the activity of dynamic cortical actin

Molecular diffusion at the surface of living cells is believed to be predominantly driven by thermal kicks. However, there is growing evidence that certain cell surface molecules are driven by the fluctuating dynamics of cortical cytoskeleton. Using fluorescence correlation spectroscopy, we measure the diffusion coefficient of a variety of cell surface molecules over a temperature range of 24–37°C. Exogenously incorporated fluorescent lipids with short acyl chains exhibit the expected increase of diffusion coefficient over this temperature range. In contrast, we find that GPI-anchored proteins exhibit temperature-independent diffusion over this range and revert to temperature-dependent diffusion on cell membrane blebs, in cells depleted of cholesterol, and upon acute perturbation of actin dynamics and myosin activity. A model transmembrane protein with a cytosolic actin-binding domain also exhibits the temperature-independent behavior, directly implicating the role of cortical actin. We show that diffusion of GPI-anchored proteins also becomes temperature dependent when the filamentous dynamic actin nucleator formin is inhibited. However, changes in cortical actin mesh size or perturbation of branched actin nucleator Arp2/3 do not affect this behavior. Thus cell surface diffusion of GPI-anchored proteins and transmembrane proteins that associate with actin is driven by active fluctuations of dynamic cortical actin filaments in addition to thermal fluctuations, consistent with expectations from an “active actin-membrane composite” cell surface.     

Use of a membrane-bound fluorophore to characterize diffusion boundary layers around human erythrocytes.

A novel method is used to demonstrate the presence of diffusion boundary layers around erythrocytes following rapid mixing in a stopped-flow spectrophotometer and to estimate the apparent dimensions of the diffusion boundary layers. Pink erythrocyte ghosts labeled on their external surfaces with tetramethyl rhodamine isothiocyanate (TRITC) were mixed in a stopped-flow apparatus with 50 mM NaI in Ringer's solutions. I- is an effective collisional quencher of TRITC fluorescence. TRITC fluorescence after flow stopped decreased monoexponentially with time. The concentration of I- at the cell surface as a function of time was estimated from the dependence of TRITC fluorescence on I- concentration in steady-state experiments. The kinetics of the increase in I- concentration at the cell surface was fit to two diffusional models: a planar erythrocyte ghost bounded by planar diffusion boundary layer and a spherical erythrocyte surrounded by a spherical shell diffusion boundary layer. The planar model best fits the experimental data with a diffusion boundary layer 4.68 microns thick. Using the spherical model the experimental data is best fit by a 6.9 microns diffusion boundary layer.     

Modelling and Analysis of Planar Cell Polarity

Planar cell polarity (PCP) occurs in the epithelia of many animals and can lead to the alignment of hairs, bristles, and feathers. Here, we present two approaches to modelling this phenomenon. The aim is to discover the basic mechanisms that drive PCP, while keeping the models mathematically tractable. We present a feedback and diffusion model, in which adjacent cell sides of neighbouring cells are coupled by a negative feedback loop and diffusion acts within the cell. This approach can give rise to polarity, but also to period two patterns. Polarisation arises via an instability provided a sufficiently strong feedback and sufficiently weak diffusion. Moreover, we discuss a conservative model in which proteins within a cell are redistributed depending on the amount of proteins in the neighbouring cells, coupled with intracellular diffusion. In this case, polarity can arise from weakly polarised initial conditions or via a wave provided the diffusion is weak enough. Both models can overcome small anomalies in the initial conditions. Furthermore, the range of the effects of groups of cells with different properties than the surrounding cells depends on the strength of the initial global cue and the intracellular diffusion.     

Protein diffusion in mammalian cell cytoplasm

We introduce a new method for mesoscopic modeling of protein diffusion in an entire cell. This method is based on the construction of a three-dimensional digital model cell from confocal microscopy data. The model cell is segmented into the cytoplasm, nucleus, plasma membrane, and nuclear envelope, in which environment protein motion is modeled by fully numerical mesoscopic methods. Finer cellular structures that cannot be resolved with the imaging technique, which significantly affect protein motion, are accounted for in this method by assigning an effective, position-dependent porosity to the cell. This porosity can also be determined by confocal microscopy using the equilibrium distribution of a non-binding fluorescent protein. Distinction can now be made within this method between diffusion in the liquid phase of the cell (cytosol/nucleosol) and the cytoplasm/nucleoplasm. Here we applied the method to analyze fluorescence recovery after photobleach (FRAP) experiments in which the diffusion coefficient of a freely-diffusing model protein was determined for two different cell lines, and to explain the clear difference typically observed between conventional FRAP results and those of fluorescence correlation spectroscopy (FCS). A large difference was found in the FRAP experiments between diffusion in the cytoplasm/nucleoplasm and in the cytosol/nucleosol, for all of which the diffusion coefficients were determined. The cytosol results were found to be in very good agreement with those by FCS.     

Diffusion coefficients of glucose and ethanol in cell-free and cell-occupied calcium alginate membranes

The diffusivities of glucose and ethanol in cell-free and cell-occupied membranes of calcium alginate were measured in a diffusion cell. The lag time analysis was used. Diffusivities decreased with increasing alginate concentration and were comparable with those in water for a 2% alginate membrane. Glucose and ethanol concentrations had no effect on the respective diffusion coefficients. The ratio of ethanol diffusivity to glucose diffusivity in 2 and 4% alginate agreed closely with the inverse ratio of the hydrodynamic raii for the two molecules in water, indicating that the hydrodynamic theory of diffusion in liquids may be applicable to diffusion in dilute alginate gels. Also, the presence of 20% dead yeast cells had no effect on the diffusivities. The data reported can be used to study reaction and diffusion in immobilized cell reactors and cell physiology under immobilized conditions.     

A stirred bath technique for diffusivity measurements in cell matrices

A stirred bath technique was developed for determining effective diffusivities in cell matrices. The technique involves cell immobilization in a dilute gel which has negligible effect on solute diffusion. Agar and collagen were tested as immobilizing gels. Agar gel was shown to have minor interactions with the diffusion of various biological molecules, and was used for immobilization of Ehrlich Ascites Tumor (EAT) cells. Diffusivities of glucose and lactic acid were measured in EAT matrices for cell loadings between 20 and 45 vol %. Treatment with glutaraldehyde was effective in quenching the metabolic activity of the cells while preserving their physical properties and diffusive resistance. The measured data agree favorably with predictions based on Maxwell's equation for effective diffusion in a periodic composite material. The stirred bath technique is useful for diffusivity determinations in immobilized matrices or free slurries, and is applicable to both microbial and mammalian cell systems.     

A numerical study of oxygen diffusion in a spherical cell with the Michaelis-Menten oxygen uptake kinetics

A numerical method is presented for the solution of reaction diffusion systems in biology. The method is used to re-examine the oxygen diffusion in a spherical cell with the Michaelis-Menten oxygen uptake kinetics.     

Determination of cell membrane permeability in concentrated cell ensembles

The method of volume averaging is used to analyze the process of diffusion in concentrated cell ensembles in which significant resistance to mass transfer is caused by the cellular membrane. A general closure scheme is given that allows for direct theoretical prediction of effective diffusivities for any cellular geometry. Numerical results are presented for the classical parallelepiped arrangement used to model cellular systems, and these results are used in conjunction with experimental studies of concentrated cell ensembles to determine membrane permeabilities for solute diffusion in several cellular systems. Membrane permeabilities are compared with predictions from other models of diffusion in cellular systems.     

Random-walk models of cell dispersal included in mechanobiological simulations of tissue differentiation

Computational models have shown that biophysical stimuli can be correlated with observed patterns of tissue differentiation, and simulations have been performed that predict the time course of tissue differentiation in, for example, long bone fracture healing. Some simulations have used a diffusion model to simulate the migration and proliferation of cells with the differentiating tissue. However, despite the convenience of the diffusion model, diffusion is not the mechanism of cell dispersal: cells disperse by crawling or proliferation, or are transported in a moving fluid. In this paper, a random-walk model (i.e., a stochastic model), with and without a preferred direction, is studied as an approach to simulate cell proliferation/migration in differentiating tissues and it is compared with the diffusion model. A simulation of tissue differentiation of gap tissue in a two-dimensional model of a bone/implant interface was performed to demonstrate the differences between diffusion vs. random walk with a preferred direction. Results of diffusion and random-walk models are similar with respect to the change in the stiffness of the gap tissue but rather different results are obtained regarding tissue patterning in the differentiating tissues; the diffusion approach predicted continuous patterns of tissue differentiation whereas the random-walk model showed a more discontinuous pattern-histological results are not available that can unequivocally establish which is most similar to experimental observation. Comparing isotropic to anisotropic random walk (preferred direction of proliferation and cell migration), a more rapid reduction of the relative displacement between implant and bone is predicted. In conclusion, we have shown how random-walk models of cell dispersal and proliferation can be implemented, and shown where differences between them exist. Further study of the random-walk model is warranted, given the importance of cell seeding and cell dispersal/proliferation in many mechanobiological problems.     

Diffusion of low density lipoprotein-receptor complex on human fibroblasts

Diffusion of the complex consisting of low density lipoprotein (LDL) bound to its receptor on the surface of human fibroblasts has been measured with the help of an intensely fluorescent, biologically active LDL derivative, dioctadecylindocarbocyanine LDL (dil(3)-LDL). Fluorescence photobleaching recovering and direct video observations of the Brownian motion of individual LDL-receptor complexes yielded diffusion coefficients for the slow diffusion on cell surfaces and fast diffusion on membrane blebs, respectively. At 10 degrees C, less that 20 percent of the LDL-receptor complex was measurably diffusible either on normal human fibroblasts GM-3348 or on LDL-receptor- internalization-defective J.D. cells GM-2408A. At 21 degrees and 28 degrees C, the diffusion fractions of approximately 75 and 60 percent, respectively, on both cell lines. The lipid analog nitrobenzoxadiazolephosphatidylcholine (NBD-PC) diffused in the GM-2408A cell membrane at 1.5x10(-8) cm(2)/sec at 22 degrees C. On blebs induced in GM-2408A cell membranes, the dil(3)-LDL receptor complex diffusion coefficient increased to approximately 10(-9) cm(2)/s, thus approaching the maximum theoretical predictions for a large protein in the viscous lipid bilayer. Cytoskeletal staining of blebs with NBD- phallacidin, a fluorescent probe specific for F-actin, indicated that loss of the bulk of the F-actin cytoskeleton accompanied the release of the natural constraints on later diffusion observed on blebs. This work shows that the internalization defect of J.D. is not due to immobilization of the LDL-receptor complex since its diffusibility is sufficient to sustain even the internalization rates observed in the native fibroblasts. Nevertheless, as with many other cell membrane receptors, the diffusion coefficient of the LDL-receptor complex is at least two orders of magnitude slower on native membrane than the viscous limit approached on cell membrane blebs where it is released from lateral constraints. However, LDL-receptor diffusion may not limit LDL internalization in normal human fibroblasts.     

Solid state theory of competitive diffusion of associated Na+ and K+ in cells by free cation and vacancy (hole) mechanisms, with application to nerve

If, as recent evidence indicates, most cell potassium is associated with macromolecular fixed charge, then diffusion of potassium ions in cells might occur by (1) diffusion of the small fraction of free potassium in cell water (analogous to electrons in the conduction band of a semiconductor) or by (2) diffusion of vacancies on association sites (analogous to holes in a semiconductor). Derivations of the Fick first law of diffusion predict that partial substitution of sodium for potassium in the cell produces opposite effects on the effective diffusion constant of potassium for those mechanisms. Application of that substitution to nerve data suggests that rubidium ions diffuse by a free cation result when the nerve is clamped at its resting potential, but by a vacancy mechanism when the nerve is clamped at zero voltage.     

Relationships between branchial chloride cells and gas transfer in freshwater fish

The gill lamellar epithelium is composed of two predominant cell types, pavement cells and mitochondria-rich chloride cells. The chloride cells play a vital role in ionic regulation because they are the sites of Ca2+ and Cl- uptake from water. Consequently, lamellar chloride cell proliferation occurs in response to ionoregulatory challenges so as to increase the ion-transporting capacity of the gill. It has been argued that such chloride cell proliferation might increase the thickness of the blood-to-water diffusion barrier and thereby impede gas diffusion. This review focuses on the potential negative consequences of chloride cell proliferation on gas transfer and possible compensatory mechanisms that might minimise the extent of respiratory impairment. Two approaches were used to evoke chloride cell proliferation in rainbow trout, hormone treatment (growth hormone/cortisol) and exposure to soft water. In all cases, chloride cell proliferation was associated with a pronounced thickening of the lamellar diffusion barrier. The thickening of the diffusion barrier was associated with a significant impairment of gas transfer. Subsequent studies revealed that several compensatory physiological responses occurred concurrently with the chloride cell proliferation to alleviate or reduce the detrimental consequences of the thickened diffusion barrier. These included hyperventilation, an increased affinity of haemoglobin-oxygen binding and earlier onset of catecholamine release during acute hypoxia.     

Diffusion of methylene blue organic cation in the polymeric matrix of cell walls of the crustose lichen Cladonia rangiferina (L.) F. H. Wigg.

The diffusion within the polymeric matrix of the cell wall is a process that determines the possibility and the rate of ion penetration into cell. In this work, we quantitatively determined the diffusion of Methylene Blue cation within the cell walls isolated from the crustose lichen Cladonia rangiferina (L.) F. H. Wigg. and its possible contribution to the processes of absorption into the lichen thalli. The swelling coefficient of the cell wall matrix and the diffusion coefficient of the organic cation within the cell walls were determined. Our results show that lichen cell walls are characterized by a higher crosslinking degree and a smaller diffusion coefficient than plants.