Micropatterns of an extracellular matrix protein with defined information content

Computing spatial information from Fourier coefficient distributions

The spatial relationships between molecules can be quantified in terms of information. In the case of membranes, the spatial organization of molecules in a bilayer is closely related to biophysically and biologically important properties. Here, we present an approach to computing spatial information based on Fourier coefficient distributions. The Fourier transform (FT) of an image contains a complete description of the image, and the values of the FT coefficients are uniquely associated with that image. For an image where the distribution of pixels is uncorrelated, the FT coefficients are normally distributed and uncorrelated. Further, the probability distribution for the FT coefficients of such an image can readily be obtained by Parseval's theorem. We take advantage of these properties to compute the spatial information in an image by determining the probability of each coefficient (both real and imaginary parts) in the FT, then using the Shannon formalism to calculate information. By using the probability distribution obtained from Parseval's theorem, an effective distance from the uncorrelated or most uncertain case is obtained. The resulting quantity is an information computed in k-space (kSI). This approach provides a robust, facile and highly flexible framework for quantifying spatial information in images and other types of data (of arbitrary dimensions). The kSI metric is tested on a 2D Ising model, frequently used as a model for lipid bilayer; and the temperature-dependent phase transition is accurately determined from the spatial information in configurations of the system.

Phase segregation of untethered zwitterionic model lipid bilayers observed on mercaptoundecanoic-acid-modified gold by AFM imaging and force mapping

Planar supported lipid bilayers (SLBs) are often studied as model cell membranes because they are accessible to a variety of surface-analytic techniques. Specifically, recent studies of lipid phase coexistence in model systems suggest that membrane lateral organization is important to a range of cellular functions and diseases. We report the formation of phase-segregated dioleoylphosphatidylcholine (DOPC)/sphingomyelin/cholesterol bilayers on mercaptoundecanoic-acid-modified (111) gold by spontaneous fusion of unilamellar vesicles, without the use of charged or chemically modified headgroups. The liquid-ordered (l(o)) and liquid-disordered (l(d)) domains are observed by atomic force microscopy (AFM) height and phase imaging. Furthermore, the mechanical properties of the bilayer were characterized by force-indentation maps. Fits of force indentation to Sneddon mechanics yields average apparent Young's moduli of the l(o) and l(d) phases of 100 +/- 2 and 59.8 +/- 0.9 MPa, respectively. The results were compared to the same lipid membrane system formed on mica with good agreement, though modulus values on mica appeared higher. Semiquantitative comparisons suggest that the mechanical properties of the l(o) phase are dominated by intermolecular van der Waals forces, while those of the fluid l(d) phase, with relatively weak van der Waals forces, are influenced appreciably by differences in surface charge density between the two substrates, which manifests as a difference in apparent Poisson ratios.