Comparison between negative cooperativity and different sites at equilibrium conditions.

<p>Eqs <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0146043#pone.0146043.e002" target="_blank">2</a>–<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0146043#pone.0146043.e006" target="_blank">6</a> were numerically solved using the following kinetic coefficients <i>k</i>₁ = <i>k</i>₂ = 0.55 (μM^-1s^-1) and <i>k</i>_-1 = <i>k</i>_-2 = 1 (s^-1) and ω = 0.33058 for the case of two identical sites for a ligand with negative cooperativity and <i>k</i>₁ = <i>k</i>₁₍₂₎ = 1 (μM^-1s^-1); <i>k</i>₂ = <i>k</i>₂₍₁₎ = 0.1 (μM^-1s^-1) and <i>k</i>_-1 = <i>k</i>_-1(2) = <i>k</i>_-2 = <i>k</i>_-2(1) = 1 (s^-1) for two classes of binding sites without interactions. Total concentration of macromolecule was in all cases 1 (μM) and the concentrations of ligand were varied from 0.01 to 300 (μM). The average number of occupied sites (〈<i>n</i>〉) was calculated using <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0146043#pone.0146043.e007" target="_blank">Eq 7</a> and equilibrium values of 〈<i>n</i>〉 and [<i>L</i>] were obtained from each curved and plotted as a binding isotherm. The binding isotherms of two identical sites for a ligand with negative cooperativity (black triangles) and two classes of binding sites without interactions (white circles) are shown. Inset shows a zoom of the main plot at low ligand concentrations.</p

Saturation curves for the three characteristic types of interactions between sites.

<p>The fractional saturation of a macromolecule by a ligand was simulated using <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0146043#pone.0146043.e001" target="_blank">Eq 1</a> for identical and independent sites (green line), positive cooperativity (orange line) and negative cooperativity (blue line). Panel A shows a detail of the curves at low ligand concentrations, whereas Panel B includes saturation values for a wide range of ligand concentration in a logarithmic scale</p

Comparison between negative cooperativity and different sites in pre-equilibrium conditions.

<p>(A) Time course of site occupation for a macromolecule with two identical sites for negative cooperativity (continuous lines) and two classes of binding sites without interactions (dash-dotted lines) for the following initial ligand concentrations (μM): 300 (red), 100 (orange), 50 (green), 25 (turquoise), 10 (blue) and 5 (violet). Time courses simulations were obtained under the same conditions as described in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0146043#pone.0146043.g005" target="_blank">Fig 5</a>. (B) The difference Δ〈<i>n</i>〉 = 〈<i>n</i>〉_coop—〈<i>n</i>〉_{diff sites} was calculated for each ligand concentration and represented as a function of time. For clarity reasons only 6 representative time courses traces that gave rise to the equilibrium data points of <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0146043#pone.0146043.g005" target="_blank">Fig 5</a> are shown.</p

Dependence of the Hill coefficient on the interaction and association free energies.

<p>The Hill coefficient was calculated as described in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0146043#pone.0146043.g003" target="_blank">Fig 3</a> from the binding isotherms obtained for identical sites with <i>K</i>_o = 1 (μM^-1) and different values of the cooperativity factor ω (main plot) and for identical sites with <i>K</i>_o varying from 0.01 to 100 (μM^-1) and a fixed value of the cooperativity factor ω = 8 (inset). <i>ΔG</i>^o_int (main plot) and <i>ΔG</i>^o_assoc (inset), were calculated using Eqs <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0146043#pone.0146043.e010" target="_blank">10</a> and <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0146043#pone.0146043.e009" target="_blank">9</a> respectively. Continuous lines are the graphical representation of polynomial functions fitted to the simulated data.</p

Super-Resolution Imaging of Bacteria in a Microfluidics Device

<div><p>Bacteria have evolved complex, highly-coordinated, multi-component cellular engines to achieve high degrees of efficiency, accuracy, adaptability, and redundancy. Super-resolution fluorescence microscopy methods are ideally suited to investigate the internal composition, architecture, and dynamics of molecular machines and large cellular complexes. These techniques require the long-term stability of samples, high signal-to-noise-ratios, low chromatic aberrations and surface flatness, conditions difficult to meet with traditional immobilization methods. We present a method in which cells are functionalized to a microfluidics device and fluorophores are injected and imaged sequentially. This method has several advantages, as it permits the long-term immobilization of cells and proper correction of drift, avoids chromatic aberrations caused by the use of different filter sets, and allows for the flat immobilization of cells on the surface. In addition, we show that different surface chemistries can be used to image bacteria at different time-scales, and we introduce an automated cell detection and image analysis procedure that can be used to obtain cell-to-cell, single-molecule localization and dynamic heterogeneity as well as average properties at the super-resolution level.</p></div

The two stage model for lipid modulation of the enzyme activity.

<p>The scheme shows the transition between low and high activity states of PMCA. In the first stage the enzyme selects a particular lipidic microenvironment among the available amphiphiles according to their relative affinities. The interaction of the protein with specific phospholipids induces, in a second stage, a conformational change at the transmembrane region which is further propagated towards the catalytic domain.</p

Systems with strong negative cooperativity can mask binding sites.

<p>Biding isotherms obtained from kinetic simulations of a macromolecule with two binding sites and high negative cooperativity (ω = 0.02 and <i>K</i>_o = 1 (μM^-1)) for ligand concentrations up to 6 μM (A) or 300 mM (B). Insets show the simulated time courses used to generate the binding isotherms shown in both panels. Arrows indicate increasing ligand concentration. Notice the change in the kinetic behavior for high ligand concentrations in panel B.</p

smSRM of bacteria in agarose pads.

<p><b> A. smSRM imaging of bacteria in agarose pads.</b> (i) A double-side adhesive o-ring was placed on a coverslip and melted agarose was added to create an adhering surface for the bacteria. (ii) Bacterial cells, previously stained with the membrane dye FM4-64 mixed with fiducial marks, were deposited on agarose and the pad was sealed with a clean coverslip. The sample was finally fixed on an Attofluor cell (Invitrogen) to avoid bacterial motion during microscopy. (iii–iv) Sequential imaging of bacterial membrane and SpoIIIE (iii) Epi-fluorescence image of the cell membrane was collected by exiting at 532 nm. (iv) smSRM images were collected by using continuous excitation with a 532 nm laser and by applying regular pulses of photo-activation with a 405 nm laser. <b>B–C. Lateral drift during smSRM acquisition in agarose pads.</b> Lateral drift over the full acquisition period was assessed by plotting the trajectories of fluorescent beads in <i>x</i> (B) and <i>y</i> (C) coordinates over time. Each colored trajectory corresponds to a single fluorescent bead. <b>D–E. Alignment correction in smSRM experiments in agarose pads.</b> Distortion arising from chromatic aberrations was quantified from the distance between the same fluorescent beads observed in two different emission channels (D) and corrected by using a linear transformation procedure (E) (see Materials and Methods). Each dot represents a different bead and the abcissa represents the <i>x</i> coordinate of each bead. Error bars represent the precision of localization before (D) and after (E) drift and alignment correction. <b>F–G. Bleed-through of the membrane staining agent FM4-64 during smSRM imaging in agarose pads. (i)</b> Image of a cell in the SpoIIIE-PA (SpoIIIE-eosFP) (F) and FM4-64 (G) channels. (ii) Line scans of the fluorescence signal across a <i>B. subtilis</i> cell (white dotted line in panels F-i and G-i) in the two observation channels (green and red lines, respectively). For comparison, the line scan of the fluorescence intensity emitted by a single SpoIIIE-PA protein was overlapped in F-ii (black dotted line). As expected, the signal-to-noise ratio and contrast in the red channel are adequate (SNR = 40/contrast = 2.3, panel G-ii). However, even at low dye concentrations the fluorescence signal from FM4-64 bleeds into the SpoIIIE-PA channel (SNR = 8/contrast = 1.3, panel F-ii), compromising single-molecule detection, lowering the localization precision, and often leading to false positive localizations. For comparison, in the single-molecule trace shown in F-ii the signal to noise ratio is 30, and the contrast is 3. <b>H. SpoIIIE localization observed by smSRM in agarose pads.</b> Pointillist representation of SpoIIIE-PA localization in <i>B. subtilis</i> at different cell stages. Each green dot represents a single fluorescent event detected in a single frame during the smSRM acquisition. False positive localizations can be observed scattered homogeneously over the cell membrane.</p

Minimal model best fit parameter values.

<p>Minimal model best fit parameter values.</p

Model parameters estimated by global fitting.

<p>Model parameters estimated by global fitting.</p