Hop Diffusion Research Articles

Simulation for diffusion behaviour of molecules in nanopattern-supported lipid bilayers based on random walk theory

In both the scientific and the technological approach, molecular manipulation with microscopic obstacles is of great importance. Recently, the application of a self-spreading lipid bilayer has attracted growing interest for its ability to transport any molecule in any desired direction. In this paper, we propose a new model, which imitates a self-spreading lipid bilayer on a substrate with metallic nanobarriers, to simulate the diffusion behaviours of molecules within it based on the random walk (RW) theory. The barriers are designed as Jones Tsai's experiments. The barrier's length, width, spacing, gap and interaction energy with molecules are investigated in this paper. The mean square displacement and diffusion coefficients (D) were calculated based on our simulation results. The results show that our simulation is consistent with the experiments. Comparing with the experimental techniques, this simulation work has improved the time- and space-resolution. Furthermore, it can simulate in rather long time-scale. Our RW models are expected to provide theoretical foundation for single molecular observation of hop diffusion in a lipid bilayer with metallic nanogates.

Lipid Hop Diffusion on the Plasma Membrane - a STED-FCS Investigation

Currently two of the most important - as well as controversial - proposed membrane-organizing principles are the “lipid rafts” hypothesis, proposed by K. Simons, and the “picket-fence” model, proposed by A. Kusumi. To date, both hypotheses encounter obstacles for full acceptance due to technical limitations on the available superresolution and single molecule techniques and limitations on the correspondent probes utilized by such techniques applied to living cells.Trying to elucidate the lipid hop diffusion dilemma, which would be the underlying principle for the “picket-fence” model, we planned a series of STED-FCS experiments to probe the diffusion of phospholipids on the membrane of different cell types. The superresolution of STED microscopy allows FCS experiments to probe areas comparable in size to the compartments created by the actin cytoskeleton, arguably one of the major structures responsible for lipid and protein segregation in the cell membrane.Using STED-FCS, we were able to detect phospholipid hop diffusion in two of the cell lines studied (NRK and IA32) and free diffusion was observed for the other cell lines under consideration (Ptk2, Vero, Hela). Different treatments to deplete the actin cytoskeleton on IA32 and NRK cells resulted in the extinction or hindrance of phospholipid hop diffusion. The same result was observed in a mutant cell line Arp 2/3 depleted originated from IA32, evidencing the major role of actin cytoskeleton on the compartmentalization of lipids. Simulations connecting membrane content and actin cytoskeleton density provided insight into the reason for apparent different diffusion modes in different cells.Whereas lipid hop diffusion could still not be confirmed by SPT experiments using fluorescent tags as markers due to technical limitations, it was now for the first time evidenced by STED-FCS, which is the time-domain counterpart of that technique.

High-Speed Interferometric Scattering Microscopy of Receptor Mobility Reveals Anomalous Diffusion in Model Membranes

The diffusive behavior of membrane proteins has been reported to change with the timescale of the measurement. High-speed single-particle tracking studies have revealed that it is Brownian on time scales less than 100 μs, confined from 1 to 10 ms, and Brownian at longer times (>10 ms).1 This behavior has been interpreted as hop diffusion between submicron compartments in the plasma membrane. Due to the fundamental difficulty in achieving simultaneously high spatial and temporal resolution, these results have relied on a single experimental approach. Furthermore, attempts to use a complementary fluorescence technique to study anomalous diffusion have not reproduced the hop diffusion model.2Here we use interferometric scattering microscopy (iSCAT)3 to track the motion of the GM1 ganglioside receptor binding the B subunit of cholera toxin using 40-nm gold nanoparticle labels, in both supported lipid bilayers (SLBs) and droplet hydrogel bilayers (DHBs).4 In SLBs, in single trajectories containing >200,000 frames and providing simultaneous 10 μs temporal and sub-nm spatial precision, we observe a shift from Brownian diffusion at early time scales (30 - 100 μs) to confined diffusion (100 μs - 10 ms) back to Brownian diffusion (>10 ms). In contrast, GM1 diffusion in DHBs is Brownian at all timescales. These data suggest that the presence of a structural support on one side of the bilayer is sufficient to produce anomalous diffusion, even for diffusers that do not penetrate the membrane.1. Kusumi, A. et al. Annu. Rev. Biophys. Biomol. Struct.34, 351-378 (2005).2. Weiser, S. et al. Biophys. J. 92, 3719-3728 (2007).3. Ortega-Arroyo, J. and Kukura, P. Phys. Chem. Chem. Phys. (2012)DOI: 10.1039/c2cp41013c4. Thompson, J. R et al.Nano Lett.7, 3875-3878 (2007).

Movement on Uneven Surfaces Displays Characteristic Features of Hop Diffusion

Diffusion in cell plasma membranes is reported to be appreciably slower than diffusion in artificial membranes. We suspect that this is largely an artifact resulting from 2D interpretation of 3D movement over an uneven surface, which leads to the consequent underestimation of the net movement (1). Transient anchorage and/or confinement in domains can easily be explained by topographical trapping. The most serious flaw in the current methods of diffusion measurement is the assumption that the membrane is smooth. When the membrane is uneven, the straight-line-distance between two points requires that the particle leaves the surface, which underestimates the distance travelled. Clearly this is an illegitimate move since both lipids and proteins are restricted to movement within the plane of the membrane. We have therefore developed a new method for analyzing tracks that confines the path to the surface - the shortest within surface distance (SWSD). Simple diffusion was simulated over smooth and uneven surfaces created on a 3D orthogonal grid using an array of connected voxels starting a conditional dilation at the first location that spreads over the surface for a defined number of steps. Notably, after a few steps the diffusion coefficient was higher than after more steps - a characteristic feature of the hop diffusion. We conclude that the minimum requirement for accurate diffusion measurements on the plasma membrane is high resolution topographical images that can be used to assess the effect of local topography on simple diffusion. Only if there is a discrepancy between the measured diffusion coefficient and that expected from Brownian motion within the plane of the membrane after accounting for cell topography is it relevant to invoke anomalous diffusion.1. Adler et al. (2010) Nat. Methods 7, 170-171

Analysis of the Mobilities of Band 3 Populations Associated with Ankyrin Protein and Junctional Complexes in Intact Murine Erythrocytes

Current models of the erythrocyte membrane depict three populations of band 3: (i) a population tethered to spectrin via ankyrin, (ii) a fraction attached to the spectrin-actin junctional complex via adducin, and (iii) a freely diffusing population. Because many studies of band 3 diffusion also distinguish three populations of the polypeptide, it has been speculated that the three populations envisioned in membrane models correspond to the three fractions observed in diffusion analyses. To test this hypothesis, we characterized band 3 diffusion by single-particle tracking in wild-type and ankyrin- and adducin-deficient erythrocytes. We report that ∼40% of total band 3 in wild-type murine erythrocytes is attached to ankyrin, whereas ∼33% is immobilized by adducin, and ∼27% is not attached to any cytoskeletal anchor. More detailed analyses reveal that mobilities of individual ankyrin- and adducin-tethered band 3 molecules are heterogeneous, varying by nearly 2 orders of magnitude and that there is considerable overlap in diffusion coefficients for adducin and ankyrin-tethered populations. Taken together, the data suggest that although the ankyrin- and adducin-immobilized band 3 can be monitored separately, significant heterogeneity still exists within each population, suggesting that structural and compositional properties likely vary considerably within each band 3 complex.

High-Speed Single Quantum Dot Imaging of in Live Cells Reveal Hop Diffusion

Ultra high-speed single particle tracking (image frame rates 40-50 kHz) experiments with 40 nm gold particles has indicated that lipids and proteins in the plasma membrane undergo hop-diffusion between nanometer sized compartments (Fujiwara et al. (2002) J Cell Biol. 157:1071-81). These findings have yet to be independently confirmed. In this work, we show that high-speed single particle tracking with quantum dots (QDs) and using a standard wide-field fluorescence microscope and an EMCCD is possible at image acquisition rates of up to ∼2000 Hz. The spatial precision in these experiments is ∼40 nm (as determined from the standard deviation of repeated position measurements of an immobile QD on a cell). Using this system, we show that membrane proteins and lipids, which have been exogenously labeled with functionalized QDs, show examples of three types of motion in the plasma membrane of live mouse embryo fibroblasts, 1) approximately free diffusion, 2) confined (immobile) diffusion, and 3) hop diffusion between compartments with a size of ∼100 nm diameter, and a lifetime of ∼100-200 milliseconds. In these experiments, we have used QDs that had a hydrodynamic radius (RH) of about 12-15 nm as determined by fluorescence correlation spectroscopy (FCS). While these QDs are very large compared to fluorescent dyes, they are 25-40% smaller in radius and are at least two fold smaller in volume than the 40 nm diameter gold particles used in ultra high speed SPT.

Near-Critical Fluctuations and Cytoskeleton-Assisted Phase Separation Lead to Subdiffusion in Cell Membranes

We address the relationship between membrane microheterogeneity and anomalous subdiffusion in cell membranes by carrying out large-scale lattice-based Monte Carlo simulations of two-component lipid membranes. We study the diffusion of lipid molecules in free membranes and find that near-critical fluctuations in the membrane lead to transient subdiffusion of lipid molecules spanning several orders of magnitude in time [1, 2]. We observe that the membrane-cytoskeleton interaction strongly affects phase separation, enhances subdiffusion, and eventually leads to hop diffusion of lipids [2].

Near-Critical Fluctuations and Cytoskeleton-Assisted Phase Separation Lead to Subdiffusion in Cell Membranes

We address the relationship between membrane microheterogeneity and anomalous subdiffusion in cell membranes by carrying out Monte Carlo simulations of two-component lipid membranes. We find that near-critical fluctuations in the membrane lead to transient subdiffusion, while membrane-cytoskeleton interaction strongly affects phase separation, enhances subdiffusion, and eventually leads to hop diffusion of lipids. Thus, we present a minimum realistic model for membrane rafts showing the features of both microscopic phase separation and subdiffusion.

Direct Observation of Hop Diffusion of Lipid and Protein Molecules in the Plasma Membrane by High-Speed Single Fluorescent-Molecule Imaging

Previously, using single-particle tracking at a temporal resolution of 0.025 ms, employing a 40-nmΦ colloidal gold probe, we have shown that virtually all of the lipid and protein molecules incorporated in the plasma membrane undergo hop diffusion. Based on this and many other observations, we proposed a model in which the entire plasma membrane is parcelled up into apposed domains due to the presence of the actin-based membrane skeleton (fence) and its associated transmembrane proteins (pickets), and membrane molecules undergo short-term confined diffusion within a domain (compartment), and long-term hop diffusion between the compartments. However, due to technological limitations, the observation of hop diffusion was only possible with a 40-nmΦ-colloidal gold probe, which might artifactually induce hop diffusion. To circumvent this problem, here, we developed a new high-speed, high-sensitivity CMOS camera system, which allowed us to track single fluorescently (0.5-nmΦ)-labeled molecules at a temporal resolution of 0.1 ms, the fastest single fluorescent-molecule imaging ever made. This camera system gave the position determination accuracy for single fluorescent molecules of ≈35 nm at a 0.1-ms time resolution. Virtually, all molecules of a phospholipid (DOPE) and a transmembrane protein, transferrin receptor, were found to undergo hop diffusion over the 110-nm compartments with median residency times of 9 ms and 33 ms, respectively, in the plasma membrane of a human epithelial T24 cell line. Meanwhile, in the actin-depleted, blebbed membrane, all of the DOPE and transferrin receptor molecules exhibited simple-Brownian diffusion. These results are in an excellent agreement with the previous high-speed gold-particle tracking data, and clearly indicate the necessity for the paradigm shift for the plasma membrane structure and dynamics, from the single continuous fluid model to the partitioned fluid model.

What Can We Learn From Single-Molecule Diffusion

There is increasing interest in a detailed understanding of the structure and dynamics of the cellular plasma membrane, primarily based on recognizing its essential role for controlling cellular signaling processes. Various pictures emerged, which ascribe the plasma membrane a high degree of organization at very short length scales of tens of nanometers. We employed single molecule fluorescence microscopy to study diffusion of CD59, a GPI-anchored protein, in the plasma membrane of living T24 cells at sub-wavelength resolution, both on the cell body and on tunneling nanotubules connecting cells. By separating longitudinal and transversal mobility, we found isotropic diffusion behavior on the surface of tunneling nanotubules, rendering direct influences of the membrane skeleton unlikely. In both studies we analyzed the mean square displacement as a function of the time-lag and the distribution of displacement steps. However, a closed analytical theory for these analysis is only available for the simplest models. To address a suspected diffusion process we reasoned that a full analytical description may not be required; it may well be sufficient to compare the experimental data with Monte Carlo simulations of the process. We demonstrated the working principle for the analysis of free diffusion, hop diffusion and transient binding of the tracer molecule to slowly moving receptors. In the recent years increasing evidence was reported for an inherent heterogeneity of cell populations. Our reasoning was that mobility probes nanometer-sized properties of the moving protein and its local environment. Automated and tailored data analysis routines allowed for the analysis of the required large data sets: ∼200.000 trajectories obtained on ∼350 cells were analyzed in total. We found up to five-fold higher variability of the diffusion constant between cells compared to the uncertainty for the determination of the diffusion constant on a single cell.

2P235 1C1535 超高速1蛍光分子イメジング開発による細胞膜分子のホップ拡散の直接観察(細胞生物的課題(接着,運動,骨格,伝達,膜),第48回日本生物物理学会年会)

2P235 1C1535 超高速1蛍光分子イメジング開発による細胞膜分子のホップ拡散の直接観察(細胞生物的課題(接着,運動,骨格,伝達,膜),第48回日本生物物理学会年会)

Single Molecular Observation of Hop Diffusion in a Lipid Bilayer at Metallic Nanogates

Single molecular tracking was carried out for a lipid molecule (TR-DHPE) in a self-spreading lipid bilayer (egg-PC) on a glass substrate with and without Ag nanoarchitectures. Without Ag architectures, the mean square displacement (MSD) analyses demonstrated that lipid molecules diffuse randomly within the self-spreading lipid bilayer with a diffusion coefficient of 3.1 μm2/s, which is comparable to the value for an artificial solid supported lipid bilayer. However, in the presence of the Ag architectures, TR-DHPE molecules undergo hop diffusion between two neighboring compartments surrounded by the Ag architectures. Smaller diffusion coefficients observed for the substrates with the Ag architectures are attributable to the suppressed diffusion at the gap between the Ag architectures. The escape probability from the initial compartment to the neighboring compartment estimated from the MSD analysis agreed well with the values estimated from the compartment configuration, which proves that the Ag nanoarchitectures act as a diffusion barrier.

Glycosphingolipids and Non-Raft Phospholipids Exhibit Very Similar Dynamics in Single-Molecule Observations

The diffusion of typical raft-associated molecules, glycosphingolipids, GM1, GM3, GD1a, was observed using high-speed single-particle tracking (HS-SPT) at a temporal resolution of ∼6 μs. Each glycosphingolipid molecule was tagged with a 40-nm-gold particle conjugated by the respective Fab antibody or a Cy3-conjugated Fab antibody. At video rate, both probes exhibited the same diffusion behavior, undergoing apparent simple Brownian diffusion at the same effective diffusion coefficient (about 0.2 μm2/s). In HS-SPT observations, each glycosphingolipid molecule underwent actin-dependent hop diffusion over the membrane compartment of an average of 110 nm in diameter at an average frequency of once every 25 ms. Surprisingly, this behavior is the same as that of a typical non-raft phospholipid DOPE, qualitatively and quantitatively. These results are at variance with the previous FCS/FRAP studies. In addition, previous investigations concluded that GM1, labeled either with cholera toxin (CTX) in its headgroup or with Bodipy-FL on the alkyl chain, diffused much more slowly than non-raft phospholipid probes. Here, we found that CTX bound to GM1 in the plasma membrane diffused as fast as DOPE during the initial 0.5 s after its binding to the membrane, but slowed by a factor of 4 within 10 min after its binding. These results suggest that the slowed diffusion of GM1 found in previous observations would probably be due to the influences of CTX-induced GM1 crosslinking or of perturbation by Bodipy-FL on the alkyl chain. These results indicate that in the plasma membrane of non-stimulated cells, glycosphingolipids movements are not slowed by the possible presence of raft, further suggesting that the rafts in the steady-state cells are much smaller than the compartment size (110 nm) and/or short-lived (<<25 ms).

Versatile Analysis of Single-Molecule Tracking Data by Comprehensive Testing against Monte Carlo Simulations

We propose here an approach for the analysis of single-molecule trajectories which is based on a comprehensive comparison of an experimental data set with multiple Monte Carlo simulations of the diffusion process. It allows quantitative data analysis, particularly whenever analytical treatment of a model is infeasible. Simulations are performed on a discrete parameter space and compared with the experimental results by a nonparametric statistical test. The method provides a matrix of p-values that assess the probability for having observed the experimental data at each setting of the model parameters. We show the testing approach for three typical situations observed in the cellular plasma membrane: i), free Brownian motion of the tracer, ii), hop diffusion of the tracer in a periodic meshwork of squares, and iii), transient binding of the tracer to slowly diffusing structures. By plotting the p-value as a function of the model parameters, one can easily identify the most consistent parameter settings but also recover mutual dependencies and ambiguities which are difficult to determine by standard fitting routines. Finally, we used the test to reanalyze previous data obtained on the diffusion of the glycosylphosphatidylinositol-protein CD59 in the plasma membrane of the human T24 cell line.

Both MHC Class II and its GPI-Anchored Form Undergo Hop Diffusion as Observed by Single-Molecule Tracking

Previously, investigations using single-fluorescent-molecule tracking at frame rates of up to 65Hz, showed that the transmembrane MHC class II protein and its GPI-anchored modified form expressed in CHO cells undergo simple Brownian diffusion, without any influence of actin depolymerization with cytochalasin D. These results are at apparent variance with the view that GPI-anchored proteins stay with cholesterol-enriched raft domains, as well as with the observation that both lipids and transmembrane proteins undergo short-term confined diffusion within a compartment and long-term hop diffusion between compartments. Here, this apparent discrepancy has been resolved by reexamining the same paradigm, by using both high-speed single-particle tracking (50kHz) and single fluorescent-molecule tracking (30Hz). Both molecules exhibited rapid hop diffusion between 40-nm compartments, with an average dwell time of 1–3ms in each compartment. Cytochalasin D hardly affected the hop diffusion, consistent with previous observations, whereas latrunculin A increased the compartment sizes with concomitant decreases of the hop rates, which led to an ∼50% increase in the median macroscopic diffusion coefficient. These results indicate that the actin-based membrane skeleton influences the diffusion of both transmembrane and GPI-anchored proteins.

2S2-1 超高速1蛍光分子追跡法が明らかにしたコンパートメント化された細胞膜内でのリン脂質のホップ拡散(2S2 細胞膜とアクチン骨格との相互作用:生物物理のアプローチ,第46回日本生物物理学会年会)

2S2-1 超高速1蛍光分子追跡法が明らかにしたコンパートメント化された細胞膜内でのリン脂質のホップ拡散(2S2 細胞膜とアクチン骨格との相互作用:生物物理のアプローチ,第46回日本生物物理学会年会)

Evaluation of the Spectrin Compartment Size in Normal and Diseased Red Blood Cells by Single Particle Tracking.

In a process termed “hop diffusion”, membrane proteins diffuse randomly within a cytoskeletally-enclosed compartment over short time scales, periodically hopping from one compartment to the next. Band 3 diffuses in the erythrocyte membrane bilayer in a manner that is thought to be restricted by the size and stability of the spectrin network. Although a fraction of band 3 may exhibit reduced mobility due to its association with spectrin (mediated by proteins such as ankyrin and adducin), another subpopulation of band 3 is thought to diffuse freely within the spectrin compartments, hopping from one corral to the next by transient opening of the barrier (presumably a spectrin tetramer) separating adjacent corrals. Based on this hypothesis, measurement of the compartment size and hopping frequency of a band 3 molecule in the erythrocyte membrane can provide information on the structure and stability of the spectrin network. We have combined single particle tracking (SPT) techniques with high-speed video microscopy to determine the average compartment size and diffusion coefficient of the mobile fraction of band 3 in both normal and diseased red blood cells (RBCs). Streptavidin-linked quantum dots (525nm emission) and 40 nm fluorescent beads were attached to band 3 via a DIDS-biotin-linker, and fluorescence microscopy coupled to a high speed camera was used to determine the position of band 3 with a time resolution of 8 ms (120 fps). Labeling specificity was demonstrated by blotting with streptavidin-horseradish peroxidase, and flow cytometry studies established the binding constant of DIDS-biotin for band 3 in the intact cell of ∼1-2*10−5 M. For diffusion studies, RBCs were incubated with 10−11 M conjugate in order to attach only one or two streptavidin-quantum dots per cell. SPT data were collected on both healthy and pathologic human RBCs, including HbSS (sickle cells), HbSC (sickle cell hemoglobin C), HbSBo (sickle cell zero-beta-thalasamia), HbSB+ (sickle cell beta-plus-thalasamia), HS (hereditary spherocytosis), and HPP (hereditary pyropoikilocytosis). Movement within the observed compartments was found to be random, with an average diagonal length for the mobile fraction in healthy cells of ∼100nm and a diffusion coefficient of ∼1–2*10−10cm2/s. HbSS cells, however, displayed a comparatively smaller compartment size (∼60–80nm) with a lower diffusion coefficient (0.1−1*10−10cm2/s). In contrast, HPP cells exhibited an average compartment size of ∼133nm with a diffusion coefficient of 6*10−10cm2/s. SPT data further suggest the presence of multiple populations of band 3, exhibiting both free diffusion and restricted mobilities with different characteristics. Details of band 3 diffusion in all of the aforementioned diseased and normal blood cells will be provided, and a model accounting for the multiple populations of band 3 will be presented.

(Un)Confined Diffusion of CD59 in the Plasma Membrane Determined by High-Resolution Single Molecule Microscopy

There has been emerging interest whether plasma membrane constituents are moving according to free Brownian motion or hop diffusion. In the latter model, lipids, lipid-anchored proteins, and transmembrane proteins would be transiently confined to periodic corrals in the cell membrane, which are structured by the underlying membrane skeleton. Because this model is based exclusively on results provided by one experimental strategy—high-resolution single particle tracking—we attempted in this study to confirm or amend it using a complementary technique. We developed a novel strategy that employs single molecule fluorescence microscopy to detect confinements to free diffusion of CD59—a GPI-anchored protein—in the plasma membrane of living T24 (ECV) cells. With this method, minimum invasive labeling via fluorescent Fab fragments was sufficient to measure the lateral motion of individual protein molecules on a millisecond timescale, yielding a positional accuracy down to 22 nm. Although no hop diffusion was directly observable, based on a full analytical description our results provide upper boundaries for confinement size and strength.

Interleaflet Diffusion Coupling When Polymer Adsorbs onto One Sole Leaflet of a Supported Phospholipid Bilayer

ReceiVed October 9, 2006 ReVised Manuscript ReceiVed January 11, 2007 Introduction. Lipid mobility in fluid-phase lipid bilayers attracts much interest not just because this problem is fundamental but also because it is so closely related to biological processes such as membrane ion channel formation, ligandreceptor binding, and membrane adhesion and fusion.1-3 Here we consider lipid lateral diffusion in bilayers that are supported on a solid substrate. Literature on this general question is extensive, including various aspects such as free Brownian motion in singleand multicomponent bilayers,4,5 anomalous subdiffusion in heterogeneous bilayers,6 obstructed diffusion in phase-separated bilayers,7 and hop diffusion in compartmentalized cell membranes.8 However, the fact that any lipid bilayer is comprised of an inner leaflet and an outer leaflet raises the question of whether lipid moves synchronously in the two leafletssa problem of interleaflet coupling in phospholipid bilayers. Here we focus on discriminating between diffusion on the two sides of the bilayer. Previous studies of interleaflet coupling in phospholipid bilayers did not investigate the situation where the adsorbate was located onto one sole side. Important prior studies investigated lipid raft formation in the two leaflets due to temperature decrease or incorporated cholesterol molecules.9,10 Also, in the absence of adsorbate, lipid diffusion in the outer and inner leaflets of a planar-supported lipid bilayer was studied with the conclusion that strong coupling exists between diffusion in the inner and outer leaflets.11 We address the basic question of what happens when adsorbate is present. As adsorbate, we allow polymers to adsorb at low surface coverage to the outer leaflet, and using iodide quenching of diffusion in the outer leaflet, we discriminate between lipid diffusion in the outer and inner leaflets. Experimental Section. For study, phospholipid DLPC, 1,2dilauroyl-sn-glycero-3-phosphocholine, was purchased from Avanti Polar Lipids (Alabaster, AL), into which we doped at 10 ppm (0.001%) molar concentration DMPE, 1,2-dimyristoylsn-glycero-3-phosphoethanolamine, with polar head group labeled by rhodamine B. Supported bilayers of the mixture were formed on hydrophilic quartz using known protocols based on the fusion of small unilamellar vesicles.12 Fully quaternized poly(4-vinylpyridine), QPVP, was prepared by us from parent poly(vinylpyridine) (Polymer Source Inc., Quebec, Canada) by reaction with an excess of ethyl bromide.13 The surface coverage of QPVP on DLPC bilayers was quantified using Fourier transform infrared spectroscopy in the mode of attenuated total reflection (FTIR-ATR) using known methods.13 All measurements were made in PBS buffer (10 mM, pH 6.0). The lateral diffusion of dye-labeled lipids was measured by fluorescence correlation spectroscopy (FCS) in the two-photon excitation mode using a home-built apparatus.14 As illustrated in Figure 1, near-infrared femtosecond pulses from a Ti:sapphire laser (800 nm, 82 MHz, pulse width ∼100 fs) were directed into a water immersion objective lens (Zeiss Axiovert 135 TV, 63x, NA ) 1.2) via a dichroic mirror and focused onto the sample, giving an excitation spot whose diffraction-limited diameter was ∼0.35 μm, thus affording measurements that were spatially resolved depending on where the laser beam was focused. Fluorescence from the sample was collected by the same objective and split into two channels after passing through the dichroic mirror and the emission filter. Each channel was connected to a single photon counting module (Hamamatsu). The photon counting output was recorded by an integrated FCS data acquisition board (ISS, Champaign, IL) and was analyzed to give an autocorrelation function curve, G(τ), which one can fit to standard equations to give the translational diffusion coefficient (D).15,16 For the planar-supported phospholipid bilayer system studied here, it is appropriate to fit data of this kind to a 2-dimensional Gaussian model with two-photon excitation using the following equation17

Particle simulation approach for subcellular dynamics and interactions of biological molecules

BackgroundSpatio-temporal dynamics within cells can now be visualized at appropriate resolution, due to the advances in molecular imaging technologies. Even single-particle tracking (SPT) and single fluorophore video imaging (SFVI) are now being applied to observation of molecular-level dynamics. However, little is known concerning how molecular-level dynamics affect properties at the cellular level.ResultsWe propose an algorithm designed for three-dimensional simulation of the reaction-diffusion dynamics of molecules, based on a particle model. Chemical reactions proceed through the interactions of particles in space, with activation energies determining the rates of these chemical reactions at each interaction. This energy-based model can include the cellular membrane, membranes of other organelles, and cytoskeleton. The simulation algorithm was tested for a reversible enzyme reaction model and its validity was confirmed. Snapshot images taken from simulated molecular interactions on the cell-surface revealed clustering domains (size ~0.2 μm) associated with rafts. Sample trajectories of raft constructs exhibited "hop diffusion". These domains corralled the diffusive motion of membrane proteins.ConclusionThese findings demonstrate that our approach is promising for modelling the localization properties of biological phenomena.