PMC

Flip-bucket types for the testing: (a) continuous bucket (CB) and (b) tongue-shaped bucket (TB) (θ represents the bucket angles, l₁ represents the length of the flip bucket, b represents the width of the flip bucket, l₂ represents the sidewall length of the TB, and r represents the radius of the TB).

Actual (solid thin line) and approximated (dotted line) coverable regions for bucket 1 under: a. m = 1; b. m = 2; and c. m = 3. Outer solid lines represent the theoretical bucket 1 region. All arrowed line segments are drawn from the centers to the corresponding arcs with radius p

Centrifuge equipment that consists of (a) a 9.1 m radius geotechnical centrifuge, (b) a tsunami-generation container installed in the bucket of (a), and (c) a soil-specimen box installed in (b). Two pneumatic actuators seen in (b) are used to lift the discharge gates to initiate the runup phase and the subsequent drawdown phase. The angled mirror and the observation window next to the soil specimen box are seen in (c) on the right-hand side of the image. Schematic drawings of the container (1.93 m long, 0.94 m wide and 0.58 m deep) are depicted in (d) plan view and (e) elevation view: filled dots represent the location of water-pressure transducer to measure the flow depth. Placement of the soil-specimen box (c) (0.520 m long, 0.345 m wide, 0.230 m deep) is marked with the dashed line in both (d,e).

(a) is the target color scene, i.e., a printed film of the CIE 1931 color space. (b) is the spectral modulation film used in our setup. The rainbow spectrum is converged along the radius of the film, thus different wavelength bands are modulated with different sinusoidal periods as the film rotates. (c) shows an exemplar recorded 1D measurement sequence corresponding to a specific spatial pattern. (d) is the Fourier decomposition of the measurements, which exhibits several dominant frequencies. The coefficients of these dominant frequencies are exactly the response signals’ strengths of corresponding wavelength bands. (e) shows the decomposed sequences of different spectrum bands, and (f) presents the final reconstructed multispectral images (each owning 64 × 64 pixels) corresponding to 10 narrow bands ranging from 450 nm to 650 nm.

a Roots of 5-day-old wild type, long haired 35S::RSL4, root hair overproducing wer myb23, sporadic and short haired rsl4-1, and hairless cpc try seedlings. Scale bar =1 mm. b A schematic of the Arabidopsis centrifugation root–gel adhesion assay to illustrate the centrifuge rotor and swinging bucket containing an inverted Petri plate. Ten seedlings/plate were grown on the surface of the gel medium and as the centrifuge rotates, the bucket swings out so that the plate is perpendicular to the rotor. Over a period of ~10 min, the plates are exposed to 1-min pulses of increasing centrifugal forces and the proportion of detached seedlings are scored between each speed setting. Illustration not to scale. c Survival curves showing the proportion of seedlings that remained adhered to the gel at increasing centrifugal force for 87 wild type (black); 88 cpc try (red); 94 rsl4-1 (pink); 87 wer myb23 (light blue); and 91 35S::RSL4 (dark blue) 5-day-old seedlings. The angular velocity (ω) and diameter of the centrifuge, together with the aerial tissue weight of each seedling are used to calculate the centrifugal force (mass × radius × ω2 = Fc, kg m s⁻²) resisted by each seedling. The seedlings with more and longer root hairs were able to remain attached to the medium over the course of the experiment compared to wild type, while the seedlings with fewer or no root hairs did not. Black crosses represent plants that remained adhered to the gel medium after the maximum centrifugal speed (1611 RPM). Results are from one representative experiment of at least two independent batches, which each included over 70 biological replicates for each genotype.

(a) Simulation results for variance-matched Gaussian noise (orange dots) do not mimic data from 77 controls over 4 experimental conditions (blue) (also see ). These simulation data represent alterations in the length of exposure to stimuli, and thus relate to the psychological process of judgment regarding how long to keypress for a stimulus. The minimal overlap between real data and simulated noise is underscored by statistical parametric mapping (i.e., bucket statistics (b)). When the Gaussian noise is injected into the real data, a new manifold is produced (orange dots), which is shifted past the manifold for the Gaussian noise (c). Depending on the noise distributions used for injection into experimental data, one can observe a range of central tendencies for the manifolds resulting from data plus noise, which share features with receiver operating characteristic (ROC) curves (i)–(iv) in (d). The cartoon in (d) can also be compared to , where (i) represents the theoretical internal boundary for the trade-off manifold when subjects either keypress to approach or avoid; the central tendency of the experimental data would be (ii), while the outer border with Gaussian noise data would be (iii), and the new manifold due to injected noise would be (iv). The Pflip analysis shown in (e) and (f) allows one to assess the effects of inserting noise into the decision-making process. It specifically alters the valence or polarity of the decision-making shown by experimental subjects for their existing trace profiles in a parametric fashion (i.e., flipping 10%, 20%, 30%, 40%, 50%, etc. of the decisions from approach to avoidance, and vice versa). The graphical effect of this parametric flipping of the valence of decision-making can then be assessed by overlaying graphical representations of existing subject data with representations altered by this decision-making perturbation. In the preference trade-off graph (e), this flipping leads to data convergence toward the midpoint of the theoretical central tendency of the manifold as one goes from 0% flipping to 50% flipping. With 60% to 100% flipping one observes the manifold being stretched back out along its central tendency (i.e., the black line; data not shown). As one goes from 0% to 100% flipping, one effectively reverses the manifold so that it is rotated along the radius line of 45 degrees. In (f), we see that the radial spectra of the Pflip analysis are superimposed and similar across flipping perturbations. The manifold is thus robust to perturbation of the decision-making.

Proton flux into vesicles containing Hv channels at various protein to lipid ratios. (A) Fluorescence-based H⁺ flux assay for vesicles containing a decreasing number of Hv channels. Protein to lipid ratios of 1:100 (dark blue, n = 5), 1:500 (pink, n = 2), 1:1000 (orange, n = 3), 1:5000 (yellow, n = 3), 1:10,000 (cyan, n = 4), 1:20,000 (light green, n = 3), 1:40,000 (green, n =4), 1:60,000 (violet, n = 3) and empty vesicles (red squares, n = 4) are plotted (error bars represent the standard error of the mean, range of mean for 1:500). Protein and vesicles were prepared as described in the legend. (B) Sucrose cushion of vesicles containing Hv channels. Numbers denote the fractions collected from top to bottom. Lipid vesicles containing Hv1, with protein to lipid ratio 1: 100 (wt:wt), were layered on a sucrose gradient (From top to bottom, 140 µl sample plus 60 µl dialysis buffer, 600 µl 7 % sucrose, and 1 ml 27 % sucrose in dialysis buffer). The gradients were then centrifuged at 135,000 × g in a Sorvall RP55-S swinging bucket rotor for 2 hours and then fractionated into 8 × 225 µl fractions. A 15 µl sample of each fraction was then mixed with 15 µl 2x running buffer and run on a 12% gel (SDS-PAGE) and stained with Coomassie blue. (C) Determination of the fraction of functional Hv channels. Plot of μ versus the ratio of fluorescence decay contributed by Hv containing vesicles over the total fluorescence decay by addition of CCCP where μ is the ratio of the number of channels over number of vesicles calculated with where g_Hv and g_L are the grams of Hv channel and lipid added, r is the estimated average radius of a vesicle (100 nm), M_L is the molecular weight of the average lipid molecule (754 Da), σ is the estimated area per lipid molecule (63 Ų ) and M_Hv is the molecular mass of the Hv channel dimer (70,000 Da). Protein to lipid ratios are as in , 1:100 (μ = 43.0, n = 5), 1:500 (μ = 8.59, n = 2), 1:1000 (μ = 4.30, n = 3), 1:5000 (μ = 0.86, n = 3), 1:10,000 (μ = 0.43, n = 4), 1:20,000 (μ = 0.21, n = 3), 1:40,000 (μ = 0.11, n =4), 1:60,000 (μ = 0.07, n = 3) error bars represent the standard error of the mean (range of mean for 1:500). The two curves are derived from with φ (fraction of functional Hv) = 1.0, θ (fraction of reconstitution deficient vesicles) = 0.15 (red) and ϕ = 0.5, θ = 0.15 (green). The inset is a close-up view along the x-axis indicating that the fit is superior with a curve corresponding to ϕ = 1.0, θ = 0.15.

(A) Polarity and displacement of Talin N- and C-termini: All clear single molecule pairs in a field of view over time are analyzed. Each molecule contributes length and angle information for a single count in the histogram in each time frame. Fast changing molecules hence contribute different lengths and orientation information at different times. We used an average of 10 time steps for these observations. The polarity histogram segments the full circle into 24 sectors of 15 degrees each, and the number of vectors that fall in a given direction is represented in the length of the vector. This coarse version of a scatter plot is chosen because it is robust against small angular variations due to the error when estimating the direction. The direction is measured relative to the previously established orientation of the actin flow. The displacement distribution counts how many vectors fall in each length range of 20 nm width. The 10 nm “bucket” ranges from 0 to 20 nm, the 30 nm ranges from 20 to 40 nm. etc. (B) Polarity and displacement of EGFP-FAK and mCherry-Paxillin control: In a cell where there was roughly equal expression of EGFP and mCherry, there was weak orientation of the EGFP-mCherry vector, and the histogram plot of the separation distance rose linear with radius as expected for unlinked molecules. The likelihood to find a partner at a distance is proportional to the area at that distance and the observation corroborates this. These conclusions only hold for the low expression case. In and , we add simulator data to show how the algorithm assesses that the measurement falls within a valid range. (C) Effect of myosin inhibition on polarity and displacement: Myosin inhibition with blebbistatin resulted in a relatively uniform molecular orientation histogram, although adhesions in blebbistatin had a clear orientation over the observation period. The displacement histogram has a clear, non-zero peak at about 50–60 nm. After inhibition of Rho kinase with Y-27632, the N- to C-terminal vectors are oriented, and the displacement histogram has peaks at 50–60 and 110 nm. (B) Without inhibitors, the orientation becomes much clearer and the stretching longer. (D) Dynamic stretch cycle of a single talin observation: In specimens with low background, excitation energy can be kept low and observations over several frames are possible, allowing for insight into the repetitive stretching cycle of Talin. Most of the traces—i.e., a single molecule that was observable over several frames—live between 4 and 15 frames but we found red-green pairs being stable for more than 30 frames (with a current score of 67 frames). At 2 s observation intervals, this allows for the plots shown here. Not all molecules can be tracked reliably in all frames, which leads to dropouts which are also shown here. In nearly all observed cases, the EGFP tags here are at rest within the accuracy of the method, whereas the mCherry signal exhibits motion. In the specimen we investigated, between 2% and 30% of all pairs evolve over time and can hence be used for stretching observations. We do not know what causes high and low yield in terms of observable stretch. Specimen more at rest were easier to observe and kept focus tough. The interesting feature here is the highly regular oscillating moving pattern that suggests a rapid relaxation as well as stretching of the molecule.