  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.
