Noise reduction in the intracellular pom1p gradient by a dynamic clustering mechanism

Abstract

Chemical gradients can generate pattern formation in biological systems. In the fission yeast Schizosaccharomyces pombe, a cortical gradient of pom1p (a DYRK-type protein kinase) functions to position sites of cytokinesis and cell polarity and to control cell length. Here, using quantitative imaging, fluorescence correlation spectroscopy, and mathematical modeling, we study how its gradient distribution is formed. Pom1p gradients exhibit large cell-to-cell variability, as well as dynamic fluctuations in each individual gradient. Our data lead to a two-state model for gradient formation in which pom1p molecules associate with the plasma membrane at cell tips and then diffuse on the membrane while aggregating into and fragmenting from clusters, before disassociating from the membrane. In contrast to a classical one-component gradient, this two-state gradient buffers against cell-to-cell variations in protein concentration. This buffering mechanism, together with time averaging to reduce intrinsic noise, allows the pom1p gradient to specify positional information in a robust manner.

Figure 1. Pom1p forms a dynamic and noisy gradient along the cell cortex

A. Confocal image of wildtype cells expressing pom1-tomato in a medial focal plane. See also Supplemental Movie 1. Scale bar = 2 μm. B. Left: Measuring cortical intensities. A cortical mask (red) superimposed on a cell is used for measuring cortical intensities. d is defined as the distance along the cortex from the center of a cell tip. Right: Mean pom1-tomato intensity profile. Mean pom1p intensities are derived from 196 profiles from 98 cells, with each profile obtained from time lapse images acquired over 90 s. Mean maximal intensity normalized to unity. Error bars are standard deviation. Inset: Same profile but on logarithmic intensity scale. Red line is a fit to an exponentially decay curve. C. Distribution of total number of pom1-GFP molecules per cell (number of cells analyzed=82), estimated from fluorescence intensities (see Supplemental Methods). D. Pom1p intensity is variable; total, but not tip-region, levels correlate with cell length. Using medial slice, summed pom1-tomato intensities in cortical tip region (from tip to d=±1 μm; blue circles) and from the whole cell including cytoplasm (red squares) are plotted against cell length (n=98 for both). Each data set is normalized to maximum value independently. Data for each point is from images acquired over 90 s. For cell of length L, best fit for normalized total intensity = 0.05L, with r² = 0.32 (dotted red line). Best linear fit for normalized tip intensity = 0.51 + 0.005L, with r² = 0.002 (dotted blue line). E. The decay length of the gradients does not correlate with cell length. Decay length λ was derived by fitting individual pom1p profiles imaged over 90 s to an exponential decay function. Fitted profiles with r²<0.9 excluded, giving n=161 from 98 cells. F. Comparison of pom1p cortical cell tip region intensities (from tip to d=±1 μm) on the two cell tips in the same cell (n=98). The dashed line corresponds to equal tip intensities. G. Time averaging can significantly decrease the effects of dynamic pom1p fluctuations. Left: single 0.5 s exposure of cell expressing pom1-tomato. Adjacent graph shows four separately normalized pom1p cortical intensity profiles from 0.5 s exposures taken 15 s apart in same cell. Right: Summed time-lapse images of the same cell taken with overall 25 s exposure time. Adjacent graph shows corresponding normalized pom1p intensity profile. Scale bar: 2 μm. See also Figure S1.

Figure 2. The pom1p gradient could be formed by diffusion

A. Pom1-tomato was imaged in cells treated with 25 μg/ml MBC (a microtubule inhibitor), 200 μM Latrunculin A (F-actin inhibitor), or DMSO (control), and in an end4Δ cell (endocytosis mutant). Graphs show mean cortical intensity profiles, with maximum normalized to unity, as function of distance d (data from 16 profiles for each condition, each imaged over 25 s); error bars: standard error of mean. Scale bar = 2 μm. B. Whole-tip region FRAP of pom1-tomato. Left: photo-bleached area is outlined. Right: Graph shows recovery of mean tip-region fluorescence intensity in 13 cells over time. Blue circles are experimental data, and dashed black line is a fit to c₀(1-(1/2)^t/τ), with τ =30 s. Error bars are standard deviation. C. Half-tip region FRAP of pom1-tomato. Left: photo-bleached area is outlined. Right: Graph shows recovery of mean half-tip region fluorescence intensity in 14 cells. Blue circles are experimental data, and dashed black line is fit to c₁(1-(1/2)^t/τ), with τ =8 s. Error bars are standard deviation. D. Movement of pom1p on cell surface contributes to fluorescence recovery. Pom1-tomato on half a cell tip was photo-bleached at 0 s. Images every 0.3 s are shown. Graph shows pom1p intensity changes at different positions in the tip region. Note that the fluorescence in region 3 recovers faster than that in region 4, and conversely, fluorescence in region 2 loses intensity faster than region 1. See also Supplemental Movie 2. See also Figure S2.

Figure 3. Pom1p forms dynamic clusters on the plasma membrane

A. Confocal image of a cortical section along top of a cell expressing pom1-tomato (0.5 s exposure; see also Supplemental Movie 3). B. Time-lapse images showing the behavior of a single pom1p cluster. Graph shows intensity tracings over time of representative clusters (normalized by maximum intensity value measured). C. Distribution of individual cluster lifetimes (198 clusters analyzed from 7 cells). D. Tracks of cluster movements. Top: Outline of cell with 9 cluster tracks shown. Scale bar =1 μm Bottom: Magnified view of tracks. Times mark start and finish of each track in seconds. Scale bar =0.25 μm E. Histogram of cluster displacements (198 clusters tracked from 7 cells). Red line: predicted distribution of cluster displacements from simple diffusion (see Supplemental Information). F. Estimated diffusion constant (extracted from overall mean square displacement) from clusters with different average intensities (116 clusters analyzed from 6 cells), showing that brighter clusters diffuse more slowly. Error bars: standard error of mean. See also Figure S3.

Figure 4. Fluorescence correlation spectroscopy analysis reveals multiple species

A. Autocorrelation curves of pom1-GFP. FCS measurements were made at multiple sites within wild-type cells. Each curve represents the average of six measurements in one cell. Measurements in the cell interior show rapid decay of the autocorrelation function, which can be fit to a three-dimensional diffusion model, with a cytoplasmic pom1p diffusion coefficient D₁=1.5 μm²s^-1 (Species S1). Measurements at the cell surface show slower decay in the autocorrelation function corresponding to increased residence time in the FCS volume. These results reveal the presence of membrane-associated species whose relative abundance changes as the probe is moved towards a cell tip. B. Summary of pom1-GFP species detected by FCS. See also Figure S4.

Figure 5. Two state mathematical model of pom1p gradient formation

A. Pictorial summary of the two-state (TS) model of pom1p gradient formation. Also shown are the TS model reactions, equations, parameter values (together with the experiments from which the values were extracted) and the Gaussian form of the membrane association function f. B. Fit of TS model to normalized mean pom1p intensity profile (experimental data from Figure 1B). Inset: same profile but on logarithmic intensity scale. C. Contribution of pom1p clusters to the total cortical pom1p intensity as a function of linear distance from tip (see Supplemental Information). Data from 9 profiles from 9 cells. Red profile is fit from TS model. D. Full-tip FRAP recovery data (as in Figure 2B) but with fit from TS model (red line). E. Half-tip FRAP recovery data (as in Figure 2C) but with fit from 1d TS model (red line), see Supplemental Information. See also Figure S5.

Figure 6. The two state (TS) model buffers against cell-to-cell variations

A. The TS model predicts that gradients with higher membrane association will have a steeper decay. Left: schematic picture of how I_a-λ anti-correlation is generated through cluster dynamics. Right: Demonstration of the effects of this anti-correlation on gradient profiles. Two in silico exponential profiles, with I_a=0.5 and λ=1.7 μm (blue) and I_a=1 and λ=1.2 μm (dashed red). B. TS model anti-correlation between pom1p peak concentrations and λ (red circles) from 100 simulated profiles. Shown are effects of fluctuations in pom1p association (relative standard deviation 20%) and diffusion, aggregation, fragmentation, disassociation (all with relative standard deviation 10%). Pom1p concentration normalized to unity at smallest value of λ. Error bars: standard deviation. C. In vivo pom1p profiles exhibit I_a-λ anti-correlation. Three representative profiles with different pom1p peak intensities (imaged over 90 s) are shown. Pom1p intensity is normalized to the highest peak. Note decay length of the gradient changes with these different peak intensities. D. Experimentally measured anti-correlation between fitted values of I_a and λ (profiles used in fitting were time-averaged for 90 s). Error bars: standard deviation. Fitted profiles with r²<0.9 were excluded, giving 90 profiles analyzed from 90 cells. E. Standard deviation in pom1p intensity divided by mean intensity, as derived from experimentally measured I_a and λ from 90 fitted profiles from 90 cells (blue line), compared to case where each I_a is paired with a randomly chosen λ (red dashed line). Inset: normalized mean pom1p profile unchanged between two data sets. See also Figure S6.

Figure 7. Effects of noise on the overall positional precision of the pom1p gradient

A. Standard deviation in pom1p intensity due to intrinsic fluctuations (arbitrary units) as function of averaging time at different positions along the gradient (196 gradients analyzed from 98 cells). Red curves are fit from time-averaging theory (see Supplemental Information). B. Relative contribution of cell-to-cell fluctuations to total observed variation in pom1p intensity as a function of averaging time (196 gradients analyzed from 98 cells). Lines correspond to different distances d away from a tip. C. Top: An example of a noisy pom1p intensity profile acting as a morphogen-like gradient. With little time-averaging, at a given threshold intensity (set here at 2250 in arbitrary intensity units, solid line), a noisy gradient determines position of a boundary (dashed lines; mean threshold intercept position at 3.5 μm). Bottom: Effect of time-averaging for 3 s (blue) and 90 s (red) on positional precision (standard deviation of threshold intercept positions) of the gradient for different thresholds, and therefore different mean intercept positions (188 gradients analyzed from 94 cells). D. Top: An example showing how pom1p might act as a tip-excluder with a minimum threshold intensity (solid line). Bottom: effect of time averaging on the probability of being able to distinguish cortical pom1p intensity from cytoplasmic pom1p intensity as a function of distance d (188 gradients analyzed from 94 cells). See also Figure S7.