Protein diffusion on charged membranes: A dynamic mean-field model describes time evolution and lipid reorganization

¹ Weill Medical College of Cornell University
² The Hebrew University

^* To whom correspondence should be addressed. E-mail: gek2009{at}med.cornell.edu.

Submitted on August 26, 2007
Revised on October 18, 2007
Accepted on 26 November 2007

	Abstract

As charged macromoleculules adsorb and diffuse on cell membranes in a large variety of cell signaling processes, they can attract or repel oppositely charged lipids. This results in lateral membrane rearrangement and affects the dynamics of protein function. To address such processes quantitatively we introduce a dynamic mean-field scheme that allows self-consistent calculations of the equilibrium state of membrane-protein complexes following such lateral reorganization of the membrane components, and serves to probe kinetic details of the process. Applicable to membranes with heterogeneous compositions containing several types of lipids, this comprehensive method accounts for mobile salt ions and charged macromolecules in three dimensions, as well as for lateral demixing of charged and net-neutral lipids in the membrane plane. In our model, the mobility of membrane components is governed by the diffusion-like Cahn-Hilliard equation, while the local electrochemical potential is based on non-linear Poisson-Boltzmann theory. We illustrate the method by applying it to the adsorption of the anionic polypeptide poly-Lysine on negatively charged lipid membranes composed of binary mixtures of neutral and monovalent lipids, or onto ternary mixtures of neutral, monovalent, and multivalent lipids. Consistent with previous calculations and experiments, our results show that at steady state multivalent lipids (such as PIP₂), but not monovalent lipid (such as PS), will segregate near the adsorbing macromolecules. To address the corresponding diffusion of the adsorbing protein in the membrane plane, we couple lipid mobility with the propagation of the adsorbing protein through a dynamic Monte Carlo scheme. We find that due to their higher mobility dictated by the electrochemical potential, multivalent lipids such as PIP₂ more quickly segregate near oppositely charged proteins than do monovalent lipids, even though their diffusion constants may be similar. The segregation, in turn, slows protein diffusion, as lipids introduce an effective drag on the motion of the adsorbate. In contrast, monovalent lipids such as PS only weakly segregate, and the diffusions of protein and lipid remain largely uncorrelated.

Key Words: Cahn-Hilliard, PIP2 lipids, Poisson-Boltzmann theory, diffusion, lipid sequestration, natively unstructured proteins