(387c) Protein-Mediated Membrane Phase Behavior: Calculation of Free Energies Associated with Membrane Deformations

We present a computational methodology for incorporating thermal effects and calculation of free energies for elastic fluid membranes subject to intrinsic curvature fields using the method of thermodynamic integration. Based on a simple model for the intrinsic curvature imposed by the clathrin coat on the membrane, we employ thermodynamic integration to calcuate free energy change as a function increasing strength of the intrinsic curvature field and a thermodynamic cycle to compute free energy changes for different sizes of the clathrin coat. Through analysis of a simplified one-dimensional analog of the fluid-membrane, we show that the membrane stiffness increases with increasing intrinsic membrane curvature field, thereby renormalizing the membrane bending rigidity. In particular, the stiffness of the membrane for non-zero intrinsic curvature is greater than that for the membrane with zero intrinsic curvature, leading to a reduction in the quasiharmonic entropy. We have confirmed these trends by explicitly computing the free energy changes using thermodynamic integration and by quantifying the loss of entropy accompanied with increasing membrane deformation. One of the main conclusions of this work is that the entropy of a membrane decreases with increasing size of the clathrin coat. However, the contribution of the enrtopic effects to the overall change in the bending free energy is small (∼ 5%). We also show that the Fourier modes are not the natural basis when the membrane is subject to an intrinsic curvature field, and the degree of mode-mixing depends on the strength of the intrinsic curvature function. Our results help quantify the free energy change when a planar membrane deforms under the influence of curvature inducing proteins at a finite temperature, and the role of membrane entropy in mediating membrane-induced interactions between curvature-inducing proteins. The thermodynamic integration approach offers a promising avenue for quantifying thermal effects in protein-mediated membrane processes, which are ubiquitous in intracellular signaling and trafficking mechanisms.