Correlation functions quantify super-resolution images and estimate apparent clustering due to over-counting

We present an analytical method to quantify clustering in super-resolution localization images of static surfaces in two dimensions. The method also describes how over-counting of labeled molecules contributes to apparent self-clustering and how the effective lateral resolution of an image can be determined. This treatment applies to clustering of proteins and lipids in membranes, where there is significant interest in using super-resolution localization techniques to probe membrane heterogeneity. When images are quantified using pair correlation functions, the magnitude of apparent clustering due to over-counting will vary inversely with the surface density of labeled molecules and does not depend on the number of times an average molecule is counted. Over-counting does not yield apparent co-clustering in double label experiments when pair cross-correlation functions are measured. We apply our analytical method to quantify the distribution of the IgE receptor (Fc{\epsilon}RI) on the plasma membranes of chemically fixed RBL-2H3 mast cells from images acquired using stochastic optical reconstruction microscopy (STORM) and scanning electron microscopy (SEM). We find that apparent clustering of labeled IgE bound to Fc{\epsilon}RI detected with both methods arises from over-counting of individual complexes. Thus our results indicate that these receptors are randomly distributed within the resolution and sensitivity limits of these experiments.Comment: 22 pages, 5 figure

Reconfigurable self-assembly through chiral control of interfacial tension

Author Posting. © The Author(s), 2011. This is the author's version of the work. It is posted here by permission of Nature Publishing Group for personal use, not for redistribution. The definitive version was published in Nature 481 (2012): 348–351, doi:10.1038/nature10769.From determining optical properties of simple molecular crystals to establishing preferred handedness in highly complex vertebrates, molecular chirality profoundly influences the structural, mechanical, and optical properties of both synthetic and biological matter at macroscopic lengthscales1,2. In soft materials such as amphiphilic lipids and liquid crystals, the competition between local chiral interactions and global constraints imposed by the geometry of the self-assembled structures leads to frustration and the assembly of unique materials3-6. An example of particular interest is smectic liquid crystals, where the 2D layered geometry cannot support twist, expelling chirality to the edges in a manner analogous to the expulsion of a magnetic field from superconductors7-10. Here, we demonstrate a previously unexplored consequence of this geometric frustration which leads to a new design principle for the assembly of chiral molecules. Using a model system of colloidal membranes11, we show that molecular chirality can control the interfacial tension, an important property of multi-component mixtures. This finding suggests an analogy between chiral twist which is expelled to the edge of 2D membranes, and amphiphilic surfactants which are expelled to oil-water interfaces12. Similar to surfactants, chiral control of interfacial tension drives the assembly of myriad polymorphic assemblages such as twisted ribbons with linear and circular topologies, starfish membranes, and double and triple helices. Tuning molecular chirality in situ enables dynamical control of line tension that powers polymorphic transitions between various chiral structures. These findings outline a general strategy for the assembly of reconfigurable chiral materials which can easily be moved, stretched, attached to one another, and transformed between multiple conformational states, thus enabling precise assembly and nano-sculpting of highly dynamical and designable materials with complex topologies.This work was supported by the National Science Foundation (NSF-MRSEC-0820492, NSF-DMR-0955776, NSF-MRI 0923057) and Petroleum Research Fund (ACS-PRF 50558-DNI7).2012-07-0

The noisy basis of morphogenesis: Mechanisms and mechanics of cell sheet folding inferred from developmental variability

Variability is emerging as an integral part of development. It is therefore imperative to ask how to access the information contained in this variability. Yet most studies of development average their observations and, discarding the variability, seek to derive models, biological or physical, that explain these average observations. Here, we analyse this variability in a study of cell sheet folding in the green alga Volvox, whose spherical embryos turn themselves inside out in a process sharing invagination, expansion, involution, and peeling of a cell sheet with animal models of morphogenesis. We generalise our earlier, qualitative model of the initial stages of inversion by combining ideas from morphoelasticity and shell theory. Together with three-dimensional visualisations of inversion using light sheet microscopy, this yields a detailed, quantitative model of the entire inversion process. With this model, we show how the variability of inversion reveals that two separate, temporally uncoupled processes drive the initial invagination and subsequent expansion of the cell sheet. This implies a prototypical transition towards higher developmental complexity in the volvocine algae and provides proof of principle of analysing morphogenesis based on its variability

Dynamics of a Volvox embryo turning itself inside out

Deformations of cell sheets are ubiquitous in early animal development, often arising from a complex and poorly understood interplay of cell shape changes, division, and migration. Here, we explore perhaps the simplest example of cell sheet folding: the “inversion” process of the algal genus Volvox, during which spherical embryos turn themselves inside out through a process hypothesized to arise from cell shape changes alone. We use light sheet microscopy to obtain the first three-dimensional visualizations of inversion in vivo, and develop the first theory of this process, in which cell shape changes appear as local variations of intrinsic curvature, contraction and stretching of an elastic shell. Our results support a scenario in which these active processes function in a defined spatiotemporal manner to enable inversion