Amphiphilic Morphology: Lipids, Proteins, and Entropy

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This project develops new mathematical models of the interactions of multicomponent lipid membranes with oils and proteins. Lipid membranes are fundamental building blocks of cellular structure forming the separating walls, the plumbing, and the assembly points for many proteins. The work will be conducted by an interdisciplinary team of mathematicians and plant biologists and will focus on validating experimental observations of lipid droplets against predictions of the multicomponent lipid models. Lipid droplets are of significance to public health for their role as a signal of the onset of metabolic syndrome, which has a correlation with the development of small fatty inclusions (lipid droplets) within the liver. Lipid droplets are being pursed in oil seeds and algae as energy storage compartments to improve the energy content of the biomass. The mathematical elements of the proposal identify key bottlenecks within the rearrangement of lipid structures with the creation and destruction of minimal energy pathways within a higher dimensional system, these pathways correspond to optimal packings of lipids and oil that contribute to the observed self-assembled structures. The project presents a detailed analysis of the structure of the free energy governing the low energy connections that represent amphiphilic morphologies and high energy barriers that are the minimal cost of reorganization. The PI and his collaborators investigate the central thesis that the dominant manifestation of the entropy of packing of amphiphilic molecules lies in the structure of this connection problem. Packing-based energy landscapes are strongly nonlinear, and fundamentally distinct from the more weakly nonlinear mixture-based models built upon the Cahn Hilliard framework. The packing-based energy will be validated against in-vitro experiments on lipid droplets, the prototypical example of a two-fluid amphiphilic system driven by interfacial competition, and are compared with entropic descriptions derived from short- chain limits of self-consistent mean field theory models. Specifically, the proposal uses spatial dynamics and singular perturbation techniques to develop robust pearling inhibition that stabilizes the pearling modes of connections, and tunes the existence and persistence of connections and barriers within factored Melnikov structure via piecewise defined and singularly perturbed dynamical system approaches. The two fluid model of lipid droplet formation will be used to investigate pinch-off and merging events while one fluid models address phase separation (rafting) and localized pearling. The models will be validated by comparison to entropic effects extracted from self-consistent mean field models of amphiphilic blends, to in-vitro experimental morphology of lipid droplets, and to the bifurcation diagram for castings of synthetic amphiphilic polymers.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.