Atomistic and Continuum Reinvestigation of Protein Membrane Interactions

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The phenomenological theory of elasticity, which encompasses the classical Helfrich- Canham model of a lipid membrane, is used to calculate the deformation energy of a membrane in the presence of inclusions such as proteins. However, the effective proper- ties calculated using this model does not incorporate the specificity of protein and membrane. In this dissertation, we argue that each protein has a unique mechanical signature based on its interaction with the surrounding lipid bilayer membrane and cannot be treated as a non- specific rigid object. We modify the classical Helfrich-Canham theory of curvature elasticity to incorporate protein-membrane specificity. Experimental observations perplexingly appear to show that rigid proteins may either soften or harden membranes even though conventional wisdom only suggests stiffening. Based on the hypothesis of our modified Helfrich-Canham model, we have carried out atomistic simulations to investigate peptide-membrane interactions. Together with a continuum model, we reconcile contrast- ing experimental data in the literature including the case of HIV-fusion peptide induced softening. We conclude that the structural rearrangements of the lipids around the inclusions cause the softening or stiffening of the biological membranes. We also discuss the estimation of the new model parameters via atomistic simulations. Furthermore, we use our modified Helfrich-Canham model to reinvestigate the membrane curvature mediated long ranged force between two transmembrane proteins. The classical linearized Helfrich- Canham Hamiltonian based derivations reveal the nature of the force between a pair of proteins to be repulsive in the zero-temperature limit and the interaction potential is inversely proportional to the fourth power of the distance separating the inclusions. A key observation regarding this widely-quoted result is that any two (mechanically rigid) proteins will experience an identical force; this is because the protein membrane specificity is not taken into account in the existing models. We find that the incorporation of protein- specificity can reduce the interaction force by several orders of magnitude. Our result may provide at least one plausible reason behind why in some computational and experimental studies, a net attractive force between proteins is in evidence.

Membrane proteins, Simulations
Portions of this document appear in: Agrawal, Himani, Matthew Zelisko, Liping Liu, and Pradeep Sharma. "Rigid proteins and softening of biological membranes—with application to HIV-induced cell membrane softening." Scientific reports 6 (2016): 25412. And in: Agrawal, Himani, Liping Liu, and Pradeep Sharma. "Revisiting the curvature-mediated interactions between proteins in biological membranes." Soft matter 12, no. 43 (2016): 8907-8918.