Translational Diffusion in Lipid Membranes beyond the Saffman-Delbrück Approximation

The Saffman-Delbrück approximation is commonly used in biophysics to relate the membrane inclusion size to its translational diffusion coefficient and membrane viscosity. However, this approximation has a restricted validity range, and its application to determination of inclusion sizes from diffusion data may in certain cases lead to unreliable results. At the same time, the model by Hughes et al. (Hughes, B. D., B. A. Pailthorpe, and C. R. White. 1981. J. Fluid Mech. 110:349-372.), providing diffusion coefficients of membrane inclusions for arbitrary inclusion sizes and viscosities of the membrane and surrounding fluids, involves substantial computational efforts, which prevents its use in practical data analysis. We develop a simple and accurate analytical approximation to the Hughes et al. model and demonstrate its performance and utility by applying it to the recently published experimental data on translational diffusion of micrometer-sized membrane domains.     

Computational studies of ligand diffusion in globins: I. Leghemoglobin

The thermally assisted diffusion of a small ligand (carbon monoxide) through a protein matrix (lupine leghemoglobin) is investigated computationally. The diffusion paths are calculated by a variant of the time-dependent Hartree approximation which we call LES (locally enhanced sampling). The variant which was recently introduced by Elber and Karplus is based on the classical TDSCF approximation of Gerber et al. The simulation enables more significant search for diffusion pathways than was possible before. This is done by increasing the number of ligand trajectories using a single trajectory for the protein. We compare qualitatively diffusion rates in leghemoglobin and in myoglobin. The calculation shows that the diffusion in leghemoglobin is much faster than the diffusion in myoglobin, in agreement with experiment. The gate in leghemoglobin is opened by fluctuations at a close contact between the B/C and the G helices. The most relevant fluctuation is the rigid shift of the C helix with respect to the G helix. This path is not observed in a comparable calculation for myoglobin. This finding is rationalized by the lack of the D helix in leghemoglobin and a significantly more flexible CE loop. Supporting experimental evidence for the importance of the CE loop in leghemoglobin can be found in the kinetics studies of Gibson et al.     

Diffusional dynamics of an active rhodamine-labeled 1,4-dihydropyridine in sarcolemmal lipid multibilayers.

A "membrane bilayer pathway" model, involving ligand partition into the bilayer, lateral diffusion, and receptor binding has been invoked to describe the 1,4-dihydropyridine (DHP) calcium channel antagonist receptor binding mechanism. In an earlier study (Chester et al. 1987. Biophys. J. 52:1021-1030), the diffusional component of this model was examined using an active fluorescence labeled DHP calcium channel antagonist, nisoldipine-lissamine rhodamine B (Ns-R), in purified cardiac sarcolemmal (CSL) lipid multibilayers. Diffusion coefficient measurements on membrane-bound drug and phospholipid at maximum bilayer hydration yielded similar values (3.8 x 10(-8) cm2/s). However, decreases in bilayer hydration resulted in dramatically reduced diffusion coefficient values for both probes with substantially greater impact on Ns-R diffusion. These data suggested that hydration dependent diffusional differences could be a function of relative probe location along the bilayer normal. In this communication, we have addressed the relative effect of the rhodamine substituent on Ns-R diffusion complex by examining the diffusional dynamics of free rhodamine B under the same conditions used to evaluate Ns-R complex and phospholipid diffusion. X-ray diffraction studies were performed to determine the Ns-R location in the membrane and model the CSL lipid bilayer profile structure to give a rationale for the differences in probe diffusional dynamics as a function of interbilayer water space.     

Obstructed metabolite diffusion within skeletal muscle cells in silico

Using a Monte Carlo simulation technique, we have modeled 3D diffusion of low molecular weight metabolites inside a skeletal muscle cell. The following structural elements are considered: (i) a regular lattice of actin and myosin filaments inside a myofibril, (ii) the membranes of sarcoplasmic reticulum and mitochondria surrounding the myofibrils, (iii) a set of myofibrils inside a skeletal muscle cell encircled by the outer cell membrane, and (iv) an additional set of regular intracellular structures ("macrocompartments") embedded into the cell interior. The macrocompartments are considered to simulate diffusion restrictions because of hypothetical cylindrical structures (16-22 μm in diameter) suggested earlier (de Graaf et al. Biophys J 78: 1657-1664, 2000). This model allowed us to calculate the apparent coefficients of particle diffusion in the radial and axial directions, D(app)(⊥) and D(app)(II), respectively. Particle movements in the axial direction are considered, at first approximation, as unrestricted diffusion (D(app)(II) = const). The apparent coefficient of radial diffusion, D(app)(⊥), decreases with time because of particle collisions with myofilaments and other rigid obstacles. Results of our random walk simulations are in fairly good agreement with experimental data on NMR measurements of restricted radial diffusion of phosphocreatine in white and red skeletal muscles of goldfish (Kinsey et al. NMR Biomed 12:1-7, 1999). Particle reflections from the low-permeable borders of macrocompartments (efficient diameter, D(eff)(MC) ≈ 9.2-10.4 μm) are the prerequisite for agreeing theoretical and experimental data. The low-permeable coverage of hypothetical macrocompartments (99.8% of coverage) provides the main contribution to time-dependent decrease in D(app)(⊥).     

Free volume model for lipid lateral diffusion coefficients. Assessment of the temperature dependence in phosphatidylcholine and phosphatidylethanolamine bilayers

The lipid lateral diffusion coefficients, DT, in fluid-phase phosphatidylcholine and phosphatidylethanolamine bilayers have been analysed in terms of the free-volume diffusion model by fitting the expression: DT = AT exp[- B/(T - T0)] to the observed temperature dependence, where A, B and T0 are the parameters to be optimized. Application of an unconstrained optimization procedure to data obtained from excimer formation (Galla et al. (1979) J. Membrane Biol. 48, 215-236) and from fluorescence photobleaching (Vaz et al. (1985) Biochemistry 24, 781-786) provides statistical evidence for a free-volume model as opposed to a simple Stokes-Einstein model (T0 = 0), only in certain cases. In the instances for which the parameter T0 can be determined with a reasonable degree of accuracy, it is found that this characteristic temperature at which the free volume extrapolates to zero lies below the bilayer gel-to-fluid phase transition temperature and does not coincide with the pre-transition temperature for phosphatidylcholines.     

Effect of aminoacylation on tRNA conformation

Translational diffusion coefficients have been simulated for various conformations of tRNA^Phe (yeast) by bead models, in order to analyze data obtained by dynamic light scattering on the free and the aminoacylated form. The 18% increase of the translational diffusion coefficient upon deacylation, reported by Potts et al. (1981), could not be represented by any change of the L-hinge angle, but could only be simulated by a conformation change to an extended form with extensive dissociation of base pairs. Since extensive unpairing is not consistent with evidence accumulated in the literature, the change of the diffusion coefficient must be mainly due to processes other than intramolecular conformational changes.     

Avoiding the SCAMs

Dendrites from the same neuron usually avoid contact with one another, a behavior known as self-avoidance. In this issue of Neuron and in the upcoming May 4, 2007 issue of Cell, a pair of studies by Soba et al. and Hughes et al. and a study by Matthews et al., respectively, identify products from the highly alternatively spliced Dscam gene as central to this behavior in Drosophila. Signaling induced by adhesion between identical isoforms triggers repulsion between sister dendrites.     

Generalized Stein's model for anatomically complex neurons

A neuron with a large dendritic structure is considered. The number of synapses located on the dendrites is substantially higher than on the soma. The synaptic input effect on the neuronal excitability decreases with distance between a synapse ending and the trigger zone. Two areas are distinguished in accordance with the effect of synaptic input--dendritic and somatic. The dendritic area, when compared to the soma, is characterized by much higher intensity of its activation but the amplitudes of synaptically evoked changes of the membrane potential at the trigger zone are in general small. This situation is suitable for a diffusion approximation. However, on the soma, especially in the proximity of the trigger zone, the membrane potential changes are a large fraction of the threshold depolarization. The membrane potential at the trigger zone is modelled by a one-dimensional stochastic process. The diffusion Ornstein-Uhlenbeck process serves as a basis of the model; however, at the moments of somatic synapses activation its voltage changes in jumps. Their sizes represent the amplitudes of the evoked postsynaptic potentials. The unimodal histograms of interspike intervals can be explained by the model. The values of the coefficient of variation greater than one are connected with substantial inhibition.     

Motility analysis of circularly swimming bull spermatozoa by quasi-elastic light scattering and cinematography.

The Rayleigh-Gans-Debye approximation is used to predict the electric field autocorrelation functions of light scattered from circularly swimming bull spermatozoa. Using parameters determined from cinematography and modeling the cells as coated ellipsoids of semiaxes a = 0.5 micrometers, b = 2.3 micrometers, and c = 9.0 micrometers, we were able to obtain model spectra that mimic the data exactly. A coat is found to be a necessary attribute of the particle. It is also clear that these model functions at 15 degrees may be represented by the relatively simple function used before by Hallett et al. (1978) to fit data from circularly swimming cells, thus giving some physical meaning to these functional shapes. Because of this agreement the half-widths of experimental functions can now be interpreted in terms of an oscillatory frequency for the movement of the circularly swimming cell. The cinematographic results show a trend to chaotic behavior as the temperature of the sample is increased, with concomitant decrease in overall efficiency. This is manifested by a decrease in oscillatory frequency and translational speed.     

Assessing loss of coral cover on the Great Barrier Reef: A response to Hughes et al. (2011)

Hughes et al. (Coral Reefs, 2011, in press) challenge our interpretations of the changes in coral cover observed on the Great Barrier Reef (GBR) between 1986 and 2004 (Sweatman et al. in Coral Reefs 30:521–531, 2011). They question whether we can accurately assign all causes of coral loss; we contend that this makes no difference to the observed changes. They defend the validity of historical data on coral cover from before the start of systematic large-scale monitoring and conclude that coral cover has been declining since at least 1960, but we find no trend in the early data. We remain convinced that combining data collected at different spatial scales (quadrats and transects in the past mixed with more recent whole-reef averages from manta tows) are likely to overestimate decline, because whole-reef averages will very rarely reach the high cover values that can occur at the quadrat scale. Hughes et al. (Coral Reefs, 2011, in press) state that we dismiss runoff as a cause of ecosystem degradation; we defend our interpretations and dispute some of their examples. In summary, we stand by our conclusion that coral cover on the GBR declined in the period 1986–2004 but through localised and unsynchronised changes that included recovery.     

Dynamic fluorescence quenching studies on lipid mobilities in phosphatidylcholine-cholesterol membranes

Bimolecular collision rate of 8-anilinonaphthalene-1-sulfonic acid (ANS) and the nitroxide doxyl group attached to various carbons on stearic acid spin labels (n-SASL) in phosphatidylcholine-cholesterol membranes in the fluid phase was studied by observing dynamic quenching of ANS fluorescence by n-SASL's. The excited-state lifetime of ANS and its reduction by the n-SASL doxyl group were directly measured by the time-correlated single photon counting technique to observe only dynamic quenching separately from static quenching and were analyzed by using Stern-Volmer relations. The collision rate of ANS with the n-SASL doxyl group ranges between 1 X 10(7) and 6 X 10(7), and the extent of dynamic quenching by n-SASL is in the order of 5-much much greater than 6- greater than 7- less than 9- less than 10- less than 12- less than 16-SASL (less than 5-SASL) in dimyristoylphosphatidylcholine (DMPC) membranes. Collision rate of 16-SASL is only 10% less than that of 5-SASL. Since the naphthalene ring of ANS is located in the near-surface region of the membrane, these results indicate that the methyl terminal of SASL appears in the near surface area frequently, probably due to extensive gauche-trans isomerism of the methylene chain. The presence of 30 mol% cholesterol decreases the collision rate of ANS with 12- and 16-SASL doxyl groups but not with the 5-SASL doxyl group in DMPC membranes. On the other hand, in egg-yolk phosphatidylcholine membranes, inclusion of 30 mol% cholesterol does not affect the collision of ANS with either 5-SASL or 16-SASL doxyl groups, in agreement with our previous observation that alkyl chain unsaturation moderates cholesterol effects on lipid motion in the membrane (Kusumi et al., Biochim. Biophys. Acta 854, 307-317). It is suggested that dynamic quenching of ANS fluorescence by lipid-type spin labels is a useful new monitor of membrane fluidity that reports on various lipid mobilities in the membrane; a class of motion can be preferentially observed over others by selecting a proper spin label, i.e., rotational diffusion of lipid about its long axis and translational diffusion by using 5-SASL, wobbling motion of the lipid long axis by using 7-SASL or androstane spin label, and gauche-trans isomerism by using 16-SASL.     

Model of the pathway of –1 frameshifting: Kinetics

Programmed –1 translational frameshifting is a process where the translating ribosome shifts the reading frame, which is directed by at least two stimulatory elements in the mRNA—a slippery sequence and a downstream secondary structure. Despite a lot of theoretical and experimental studies, the detailed pathway and mechanism of the –1 frameshifting remain unclear. Here, in order to understand the pathway and mechanism we consider two models to study the kinetics of the –1 frameshifting, providing quantitative explanations of the recent biochemical data of Caliskan et al. (Cell 2014, 157, 1619–1631). One model is modified from that proposed by Caliskan et al. and the other is modified from that proposed in the previous work to explain the single-molecule experimental data. It is shown that by adjusting values of some fundamental parameters both models can give quantitative explanations of the biochemical data of Caliskan et al. on the kinetics of EF-G binding and dissociation and on the kinetics of movement of tRNAs inside the ribosome. However, for the former model some adjusted parameter values deviate significantly from those determined from the available single-molecule experiments, while for the latter model all parameter values are consistent with the available biochemical and single-molecule experimental data. Thus, the latter model most likely reflects the pathway and mechanism of the –1 frameshifting.     

Necessity's sharp pinch

In a recent issue of Cell, Hughes and coworkers (Mnaimneh et al., 2004) provide a great leap forward in the analysis of essential yeast genes by constructing a strain set that expresses each essential gene from a tetracycline-regulatable promoter.     

Dscam and neuronal uniqueness

In the fruit fly Drosophila the gene encoding the cell adhesion molecule Dscam generates alternatively spliced mRNAs that can be translated into thousands of different protein isoforms. Three recent papers show that isoform-specific homophilic Dscam interactions cause dendritic branches of the same neuron to avoid each other (Hughes et al., 2007; Soba et al., 2007; Matthews et al., 2007). This process ensures the correct patterning of dendrites in the peripheral nervous system.     

More options for gene editing

Engineering precise genetic changes in a genome is powerful way to study gene function, and several recent papers describe new applications of gene-editing tools. Working with researchers at Sangamo BioSciences, Howard Hughes Medical Institute investigator Barbara Meyer and her colleagues at the University of California, Berkeley, described the first systems for making targeted genomic modifications in the roundworm Caenorhabditis elegans, a valuable model organism (Wood et al., 2011).     

Flow cytometric analysis of European flat oyster, Ostrea edulis, haemocytes using a monoclonal antibody specific for granulocytes

The importance of haemocytes in mollusc defence mechanisms can be inferred from their functions. They participate in pathogen elimination by phagocytosis (Cheng, 1981; Fisher, 1986). Hydrolytic enzymes and cytotoxic molecules produced by haemocytes contribute to the destruction of pathogenic organisms (Cheng, 1983; Leippe & Renwrantz, 1988; Charlet et al., 1996; Hubert et al., 1996; Roch et al., 1996). Haemocytes may also be involved in immunity modulation by the production of cytokines and neuropeptides (Hughes et al., 1990; Stefano et al., 1991; Ottaviani et al., 1996). As a result, the literature dealing with bivalve haemocyte studies has increased during the last two decades. Most of these publications use microscopy for morphological analysis (Seiler & Morse, 1988; Auffret, 1989; Hine & Wesney, 1994; Giamberini et al., 1996; Carballal et al., 1997; Lopez et al., 1997; Nakayama et al., 1997), and functional analysis (e.g. phagocytosis) (Hinsch & Hunte, 1990; Tripp, 1992; Mourton et al., 1992; Fryer & Bayne, 1996; Mortensen & Glette, 1996). Flow cytometry represents a rapid technique applicable to both morphological and functional studies of cells in suspension. While the measurements based on autofluorescence provide information on cell morphology, the analyses with fluorescent markers including labelled antibodies, offer data on phenotyping and cell functions. As a result, its application has greatly contributed to the investigation of immunocyte functions and differentiation in vertebrates (Stewart et al., 1986; Rothe & Valet, 1988; Ashmore et al., 1989; Koumans-van Diepen et al., 1994; Rombout et al., 1996; Caruso et al., 1997). Some authors studied oyster haemocyte populations by flow cytometry based on cellular autofluorescence (Friedl et al., 1988; Fisher & Ford, 1988; Ford et al., 1994). However, no analysis using specific monoclonal antibodies has been reported to date. In this study, a protocol for studying European flat oyster, Ostrea edulis, haemocytes by flow cytometry using a monoclonal antibody specific for granulocytes and an indirect immunofluorescence technique have been developed. European flat oysters, Ostrea edulis, 7-9 cm in shell length were obtained from shellfish farms in Marenne Oléron bay (Charente Maritime, France) on the French Atlantic coast. All individuals were purchased just before each experiment and processed without any previous treatment.     

Effect of bovine prothrombin fragment 1 on the translational diffusion of phospholipids in Langmuir-Blodgett monolayers.

Previous work has shown that bovine prothrombin fragment 1 binds to supported planar membranes composed of phosphatidylcholine and phosphatidylserine in a Ca(2+)-specific manner (Tendian et al. (1991) Biochemistry 30, 10991; Pearce et al. (1992) Biochemistry 31, 5983-5995). In the present work, fluorescence pattern photobleaching recovery has been used to examine the effect of membrane-bound fragment 1 on the translational diffusion coefficients of two fluorescent phospholipids in fluid-like phosphatidylserine/phosphatidylcholine Langmuir-Blodgett monolayers. The results show that saturating concentrations of fragment 1, in the presence of Ca2+, reduce the diffusion coefficient of nitrobenzoxadiazolyl-conjugated phosphatidylserine (NBD-PS) and nitrobenzoxadiazolyl-conjugated phosphatidylcholine (NBD-PC) by factors of approximately four and two, respectively. Ca2+ or fragment 1 alone do not have a statistically significant effect on NBD-PS or NBD-PC diffusion. In addition, a nonspecific protein (ovalbumin) does not change the diffusion coefficients of the fluorescent phospholipids either in the absence or presence of Ca2+. The fractions of the fluorescent phospholipids that are laterally mobile are approximately 0.9 for all samples. These results are interpreted with several models for possible mechanisms by which extrinsically bound proteins might retard phospholipid diffusion in membranes.     

Single molecule imaging of green fluorescent proteins in living cells: E-cadherin forms oligomers on the free cell surface

Single green fluorescent protein (GFP) molecules were successfully imaged for the first time in living cells. GFP linked to the cytoplasmic carboxyl terminus of E-cadherin (E-cad-GFP) was expressed in mouse fibroblast L cells, and observed using an objective-type total internal reflection fluorescence microscope. Based on the fluorescence intensity of individual fluorescent spots, the majority of E-cad-GFP molecules on the free cell surface were found to be oligomers of various sizes, many of them greater than dimers, suggesting that oligomerization of E-cadherin takes place before its assembly at cell-cell adhesion sites. The translational diffusion coefficient of E-cad-GFP is reduced by a factor of 10 to 40 upon oligomerization. Because such large decreases in translational mobility cannot be explained solely by increases in radius upon oligomerization, an oligomerization-induced trapping model is proposed in which, when oligomers are formed, they are trapped in place due to greatly enhanced tethering and corralling effects of the membrane skeleton on oligomers (compared with monomers). The presence of many oligomers greater than dimers on the free surface suggests that these greater oligomers are the basic building blocks for the two-dimensional cell adhesion structures (adherens junctions).