  Lipid phase heterogeneity in the plasma membrane is thought to be crucial for
many aspects of cell signaling, but the physical basis of participating
membrane domains such as "lipid rafts" remains controversial. Here we consider
a lattice model yielding a phase diagram that includes several states proposed
to be relevant for the cell membrane, including microemulsion - which can be
related to membrane curvature - and Ising critical behavior. Using a neural
network-based machine learning approach, we compute the full phase diagram of
this lattice model. We analyze selected regions of this phase diagram in the
context of a signaling initiation event in mast cells: recruitment of the
membrane-anchored tyrosine kinase Lyn to a cluster of transmembrane of
IgE-Fc{\epsilon}RI receptors. We find that model membrane systems in
microemulsion and Ising critical states can mediate roughly equal levels of
kinase recruitment (binding energy ~ -0.6 kBT), whereas a membrane near a
tricritical point can mediate much stronger kinase recruitment (-1.7 kBT). By
comparing several models for lipid heterogeneity within a single theoretical
framework, this work points to testable differences between existing models. We
also suggest the tricritical point as a new possibility for the basis of
membrane domains that facilitate preferential partitioning of signaling
components.
