Models of membrane-bound signaling molecules exhibiting diffusion, state transitions and membrane dissociation.

<p>(A) Schematic view of the three principle models. (B,D,F) The probability density function (PDF) of molecular position at <i>t</i> = 0.033, 0.3 and 1 (B) or 0.033, 0.3 and 3 (D,F). (C,E,G) The membrane residence probability, <i>R</i>(<i>t</i>) (<i>black</i>), and the subpopulation probability, <i>Q</i>(<i>t</i>), for state 1 (<i>green</i>) and state 2 (<i>orange</i>). (insets in E and G) Time series of the subpopulation ratios. (B,C) Model S1. The PDFs before (<i>dotted lines</i>) and after (<i>solid lines</i>) incorporating the measurement error are shown. <i>D</i> = 0.01, <i>λ</i> = 1.00 and <i>ε</i> = 0.04. (D,E) Model S2. <i>D</i>₁ = 0.01, <i>D</i>₂ = 0.10, <i>λ</i>₁ = 0.10, <i>λ</i>₂ = 1.00, <i>q</i>₁ = 0.20 and <i>ε</i> = 0.04. (F,G) Model S3. <i>D</i>₁ = 0.01, <i>D</i>₂ = 0.10, <i>λ</i>₁ = 0.10, <i>λ</i>₂ = 1.00, <i>k</i>₁₂ = 0.10, <i>k</i>₂₁ = 0.50, <i>q</i>₁ = 0.20 and <i>ε</i> = 0.04. <i>D</i>, µm²s⁻¹; <i>λ</i>, <i>k</i>, s⁻¹; <i>ε</i>, µm. PDFs for Models S2 and S3 incorporate the measurement error. See also Figures S1.</p

Asymmetric PTEN Distribution Regulated by Spatial Heterogeneity in Membrane-Binding State Transitions

<div><p>The molecular mechanisms that underlie asymmetric PTEN distribution at the posterior of polarized motile cells and regulate anterior pseudopod formation were addressed by novel single-molecule tracking analysis. Heterogeneity in the lateral mobility of PTEN on a membrane indicated the existence of three membrane-binding states with different diffusion coefficients and membrane-binding lifetimes. The stochastic state transition kinetics of PTEN among these three states were suggested to be regulated spatially along the cell polarity such that only the stable binding state is selectively suppressed at the anterior membrane to cause local PTEN depletion. By incorporating experimentally observed kinetic parameters into a simple mathematical model, the asymmetric PTEN distribution can be explained quantitatively to illustrate the regulatory mechanisms for cellular asymmetry based on an essential causal link between individual stochastic reactions and stable localizations of the ensemble.</p> </div

Effect of actin filaments on PTEN hopping.

<p>(A) Hopping lifetimes of PTEN₄ in the absence (blue) and presence (red) of Latrunculin A. (B) Spatial distribution of the rebinding probability of PTEN₄ in the absence (blue) and presence (red) of Latrunculin A. (C) Temporal changes in the rebinding probability of PTEN₄ in the absence (blue) and presence (red) of Latrunculin A. Data are mean +/− SD.</p

Phenotype of wild-type PTEN and PTEN<i>_i</i> mutants (<i>i</i> = 1,2,…,7).

<p>(A) Human PTEN crystal structure (residues 14–351) <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003817#pcbi.1003817-Lee1" target="_blank">[8]</a>. PTEN<i>_i</i> mutants had different positive charges in the cα2 helix. Regions colored in green and blue show the C2 domain and phosphatase domain, respectively. The red, yellow, and orange regions show the cα2 helix, T1 loop, and CBR3 loop, respectively. The PBM at the N-terminus (residues 1–13) and 24 residues in the C2 domain (residues 282–312) are not shown. The upper side of the structure faces the membrane. (B) Fluorescence images of <i>Dictyostelium discoideum</i> cells expressing wild-type PTEN or PTEN mutants. PTEN was labeled with TMR via HaloTag (PTEN-Halo-TMR). Images were captured by confocal microscopy. Scale bar, 5 µm. (C) The ratio of the plasma membrane and cytoplasm fluorescence intensities. (D) Images of fruiting bodies formed by wild-type cells or <i>pten</i>-null cells expressing wild-type PTEN or PTEN mutants. Scale bar, 500 µm (E) The diameter of the sorus in the fruiting bodies. Data are mean +/− SD.</p

Single-molecule imaging of wild-type PTEN and PTEN<i>_i</i> mutants.

<p>(A) Images of cells expressing wild-type PTEN or PTEN<i>_i</i> mutants labeled with TMR captured under TIRFM. Scale bar, 5 µm. (B) The numbers of PTEN-Halo-TMR and PTEN<i>_i</i>-Halo-TMR molecules that remained bound to the membrane are plotted against time after membrane association. Lines are three-component exponential fits (<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003817#pcbi.1003817.e001" target="_blank">Eq. 1</a>). The cumulative plots were obtained from 16,088 molecules in 8 cells (wild-type PTEN), 12,164 molecules in 8 cells (PTEN₁), 9,022 molecules in 7 cells (PTEN₂), 11,386 molecules in 8 cells (PTEN₃), 12,406 molecules in 8 cells (PTEN₄), 11,079 molecules in 8 cells (PTEN₅), 10,822 molecules in 7 cells (PTEN₆) and 20,683 molecules in 8 cells (PTEN₇). (C, D) Dissociation constants <i>k</i>_1–3 (C) and frequencies <i>A</i>_1–3/<i>k</i>_1–3 (D) of PTEN<i>_i</i> mutants obtained from the fitting in (B). Estimated parameters are shown in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003817#pcbi-1003817-t002" target="_blank">Table 2</a>. (E) Frequency of slow, moderate and fast diffusion mobility states, <i>a_i</i>, from the displacement distribution analysis in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003817#pcbi.1003817.s003" target="_blank">Fig. S3</a>.</p

Heterogeneities in PTEN molecules on the membrane of polarized cells.

<p>(A) Fluorescent images of <i>Dictyostelium discoideum</i> cells expressing PTEN-Halo (<i>top</i>) and PTEN_G129E-Halo (<i>bottom</i>) labeled with TMR-conjugated HaloTag ligand. Cells moved leftward. Scale bar, 5 µm. (B) Asymmetric distribution of PTEN_G129E-Halo on the membrane upon stimulation with a cAMP gradient. The cell was treated with 5 µM Latrunculin A (<i>top</i>). The asterisk indicates the position of the pipette tip containing 1 µM cAMP (<i>bottom</i>). Scale bar, 5 µm. (C) Single molecules of PTEN_G129E bound to the membrane of a migrating cell. The arrow indicates the direction of movement. Scale bar, 5 µm. (D) Typical trajectories of single PTEN_G129E molecules observed at the pseudopod (<i>left</i>) and tail (<i>right</i>). (E) Dissociation curves of PTEN_G129E molecules observed at the pseudopod and tail. Fitting curves are from Eq. S11 using the parameter values described in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002862#pcbi-1002862-t001" target="_blank">Table 1</a>. (F) Distributions of displacement during 33 ms of observation at the pseudopod and tail. Fitting curves are from <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002862#pcbi.1002862.e011" target="_blank">Eq.11</a> assuming a three-state model. Diffusion coefficients and their proportions are described in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002862#pcbi-1002862-t001" target="_blank">Table 1</a> and <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002862#pcbi-1002862-g005" target="_blank">Fig. 5C</a>. (G) The time series of displacement of a PTEN_G129E molecule over a 33 ms window (excerpted from the whole trajectory observed at the tail). (H) Autocorrelation function calculated from the time series of displacements for 10 molecules observed at the tail. The fitting function is <i>y</i> = <i>a</i>*exp(−<i>Kt</i>)+<i>b</i> with <i>K</i> = 1.64 s⁻¹. See also Movie S1.</p

Simulations of the intracellular distribution.

<p>(A) Estimation of membrane association frequencies that a single cytoplasmic molecule associates with the membrane during 1 sec via three states. (B) The density of membrane bound molecules in the absence or presence of cellular polarity. (C) A temporal change in the density on the membrane (molecules/µm²) and the concentration in the cytosol (molecules/µm³) as <i>μ</i>₁ approaches 0 during <i>t</i> = 2 to 15 sec.</p

Single exponential fitting parameters for hopping lifetimes in Fig. 6C.

<p>Single exponential fitting parameters for hopping lifetimes in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003817#pcbi-1003817-g006" target="_blank">Fig. 6C</a>.</p

Diffusion constants of wild-type PTEN and PTEN mutants in the three-component model.

<p>Parameters obtained from fitting the data in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003817#pcbi.1003817.s003" target="_blank">Fig. S3</a> with <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003817#pcbi.1003817.e002" target="_blank">Eq. 2</a> (<i>n</i> = 3). The observable lowest <i>D</i> was <i>ε</i>²/Δ<i>t</i>, where <i>ε</i> is the standard deviation of the measurement error calculated from the mean square displacement of the trajectories <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003817#pcbi.1003817-Matsuoka1" target="_blank">[20]</a>.</p><p>Diffusion constants of wild-type PTEN and PTEN mutants in the three-component model.</p

The analysis method for hopping molecules proposed in this study.

<p>(A) Two coordinate systems are introduced. In the global coordinate system, <i>O</i>(<i>X</i>,<i>Y</i>,<i>T</i>), the time origin is the initial frame and the spatial origin is the lower-left corner of the image. In the coordinate system about the <i>j</i>-th molecule, <i>o_j</i>(<i>x_j</i>,<i>y_j</i>,<i>t_j</i>), the time origin is the vanished time and the spatial origin is the vanished position of the molecule. (B) Membrane-associating molecules are classified into two types: those rebinding to the membrane after hopping (hopping molecule) and those recruited from the cytoplasm (recruited molecule). (C) The spatial distribution of wild-type PTEN trajectories (blue) observed in a single cell. Scale bar, 5 µm. (D) The number of molecules appeared in a single cell after excitation of the fluorophore. Time interval, 1.666 sec. (E) Schematics of the simulation of hopping molecules. (F) Results of the rebinding probability estimated from simulated molecules. Data are mean +/− SD.</p