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Single molecule localization microscopy (SMLM) permits the visualization of cellular structures an order of magnitude smaller than the diffraction limit of visible light, and an accurate, objective evaluation of the resolution of an SMLM dataset is an essential aspect of the image processing and analysis pipeline. Here we present a simple method that uses the pair autocorrelation function evaluated both in space and time to measure the time-interval dependent point-spread function of SMLM images of static samples. Using this approach, we demonstrate that experimentally obtained images typically have effective point spread functions that are broader than expected from the localization precision alone, due to additional uncertainty arising from drift and drift correction algorithms. This resolution metric reports on how precisely one can measure pairwise distances between labeled objects and is complementary to the commonly used Fourier Ring Correlation metric that also considers spatial sampling. The method is demonstrated on simulated localizations, DNA origami rulers, and cellular structures labelled by dye-conjugated antibodies or fluorescent fusion proteins., Comment: 29 pages, 13 figures (including supplement)

Lateral organization in the plane of the plasma membrane is an important driver of biological processes. The past dozen years have seen increasing experimental support for the notion that lipid organization plays an important role in modulating this heterogeneity. Various biophysical mechanisms rooted in the concept of liquid-liquid phase separation have been proposed to explain diverse experimental observations of heterogeneity in model and cell membranes, with distinct but overlapping applicability. In this review, we focus on evidence for and consequences of the hypothesis that the plasma membrane is poised near an equilibrium miscibility critical point. Critical phenomena explain certain features of the heterogeneity observed in cells and model systems, but also go beyond heterogeneity to predict other interesting phenomena, including responses to composition perturbations., Comment: 49 pages, 4 Figures

Many of the processes that underly neural computation are carried out by ion channels embedded in the plasma membrane, a two-dimensional liquid that surrounds all cells. Recent experiments have demonstrated that this membrane is poised close to a liquid-liquid critical point in the Ising universality class. Here we use both exact and stochastic techniques on the lattice Ising model to explore the ramifications of proximity to criticality for proteins that are allosterically coupled to Ising composition modes. Owing to diverging generalized susceptibilities, such a protein's activity becomes strongly influenced by perturbations that influence the two relevant parameters of the critical point, especially the critical temperature. In addition, the protein's kinetics acquire a range of time scales from its surrounding membrane, naturally leading to non-Markovian dynamics., Comment: 6 pages 3 figures, and 3 page supplement

Diverse molecules induce general anesthesia with potency strongly correlated both with their hydrophobicity and their effects on certain ion channels. We recently observed that several n-alcohol anesthetics inhibit heterogeneity in plasma membrane derived vesicles by lowering the critical temperature ($T_c$) for phase separation. Here we exploit conditions that stabilize membrane heterogeneity to further test the correlation between the anesthetic potency of n-alcohols and effects on $T_c$. First we show that hexadecanol acts oppositely to n-alcohol anesthetics on membrane mixing and antagonizes ethanol induced anesthesia in a tadpole behavioral assay. Second, we show that two previously described `intoxication reversers' raise $T_c$ and counter ethanol's effects in vesicles, mimicking the findings of previous electrophysiological and behavioral measurements. Third, we find that hydrostatic pressure, long known to reverse anesthesia, also raises $T_c$ in vesicles with a magnitude that counters the effect of butanol at relevant concentrations and pressures. Taken together, these results demonstrate that $\Delta T_c$ predicts anesthetic potency for n-alcohols better than hydrophobicity in a range of contexts, supporting a mechanistic role for membrane heterogeneity in general anesthesia., Comment: 20 pages, 6 figures

A large and diverse array of small hydrophobic molecules induce general anesthesia. Their efficacy as anesthetics has been shown to correlate both with their affinity for a hydrophobic environment and with their potency in inhibiting certain ligand gated ion channels. Here we explore the effects that n-alcohols and other liquid anesthetics have on the two-dimensional miscibility critical point observed in cell derived giant plasma membrane vesicles (GPMVs). We show that anesthetics depress the critical temperature (Tc) of these GPMVs without strongly altering the ratio of the two liquid phases found below Tc. The magnitude of this affect is consistent across n-alcohols when their concentration is rescaled by the median anesthetic concentration (AC50) for tadpole anesthesia, but not when plotted against the overall concentration in solution. At AC50 we see a 4{\deg}C downward shift in Tc, much larger than is typically seen in the main chain transition at these anesthetic concentrations. GPMV miscibility critical temperatures are also lowered to a similar extent by propofol, phenylethanol, and isopropanol when added at anesthetic concentrations, but not by tetradecanol or 2,6 diterbutylphenol, two structural analogs of general anesthetics that are hydrophobic but have no anesthetic potency. We propose that liquid general anesthetics provide an experimental tool for lowering critical temperatures in plasma membranes of intact cells, which we predict will reduce lipid-mediated heterogeneity in a way that is complimentary to increasing or decreasing cholesterol. Also, several possible implications of our results are discussed in the context of current models of anesthetic action on ligand gated ion channels., Comment: 16 pages, 6 figures

Recent experiments suggest that membranes of living cells are tuned close to a miscibility critical point in the 2D Ising universality class. We propose that one role for this proximity to criticality in live cells is to provide a conduit for relatively long-ranged critical Casimir forces. Using techniques from conformal field theory we calculate potentials of mean force between membrane bound inclusions mediated by their local interactions with the composition order parameter. We verify these calculations using Monte-Carlo where we also compare critical and off-critical results. Our findings suggest that membrane bound proteins experience weak yet long range forces mediated by critical composition fluctuations in the plasma membranes of living cells., Comment: 5 pages, 3 figures

We present a minimal model of plasma membrane heterogeneity that combines criticality with connectivity to cortical cytoskeleton. Our model is motivated by recent observations of micron-sized critical fluctuations in plasma membrane vesicles that are detached from their cortical cytoskeleton. We incorporate criticality using a conserved order parameter Ising model coupled to a simple actin cytoskeleton interacting through point-like pinning sites. Using this minimal model, we recapitulate several experimental observations of plasma membrane raft heterogeneity. Small (r~20nm) and dynamic fluctuations at physiological temperatures arise from criticality. Including connectivity to cortical cytoskeleton disrupts large fluctuations, prevents macroscopic phase separation at low temperatures (T<=22{\deg}C), and provides a template for long lived fluctuations at physiological temperature (T=37{\deg}C). Cytoskeleton-stabilized fluctuations produce significant barriers to the diffusion of some membrane components in a manner that is weakly dependent on the number of pinning sites and strongly dependent on criticality. More generally, we demonstrate that critical fluctuations provide a physical mechanism to organize and spatially segregate membrane components by providing channels for interaction over large distances., Comment: 18 pages, 5 figures and 12 page Supplement (2 additional figures)

Membranes containing a wide variety of ternary mixtures of high chain-melting temperature lipids, low chain-melting temperature lipids, and cholesterol undergo lateral phase separartion into coexisting liquid phases at a miscibility transition. When membranes are prepared from a ternary lipid mixture at a critical composition, they pass through a miscibility critical point at the transition temperature. Since the critical temperature is typically on the order of room temperature, membranes provide an unusual opportunity in which to perform a quantitative study of biophysical systems that exhibit critical phenomena in the two-dimensional Ising universality class. As a critical point is approached from either high or low temperature, the scale of fluctuations in lipid composition, set by the correlation length, diverges. In addition, as a critical point is approached from low temperature, the line tension between coexisting phases decreases to zero. Here we quantitatively evaluate the temperature dependence of line tension between liquid domains and of fluctuation correlation lengths in lipid membranes in order to extract a critical exponent, nu. We obtain nu=1.2 plus or minus 0.2, consistent with the Ising model prediction nu=1. We also evaluate the probability distributions of pixel intensities in fluoresence images of membranes. From the temperature dependence of these distributions above the critical temperature, we extract an independent critical exponent beta=0.124 plus or minus 0.03 which is consistent with the Ising prediction of beta=1/8., Comment: 22 pages, 7 figures

We report diffusion coeffcients of micron-scale liquid domains in giant unilamellar vesicles of phospholipids and cholesterol. The trajectory of each domain is tracked, and the mean square displacement grows linearly in time as expected for Brownian motion. We study domain dffusion as a function of composition and temperature, and measure how diffusion depends on domain size. We find mechanisms of domain diffusion which are consistent with membrane-dominated drag in viscous Lo phases [P.G. Saffman and M. Delbruck, PNAS 72, 3111 (1975)], and bulk-dominated drag for less viscous L$_\alpha$ phases [B.D.Hughes et al., J. Fluid Mech. 110, 349 (1981)]. Where applicable, we obtain the membrane viscosity and report activation energies of diffusion., Comment: 4 pages, submitted to Phys. Rev. Lett. on 17th April 2006