Abstract
Chapter 1: We present the exact solution of a microscopic statistical mechanical model for the transformation of a long polypeptide between an unstructured coil conformation and an α-helix conformation. The polypeptide is assumed to be adsorbed to the interface between a polar and a non-polar environment such as realized by water and the lipid bilayer of a membrane. The interfacial coil-helix transformation is the first stage in the folding process of helical membrane proteins. Depending on the values of model parameters, the conformation changes as a crossover, a discontinuous transition, or a continuous transition with helicity in the role of order parameter. Our model is constructed as a system of statistically interacting quasiparticles that are activated from the helix pseudo-vacuum. The particles represent links between adjacent residues in coil conformation that form a self-avoiding random walk in two dimensions. Explicit results are presented for helicity, entropy, heat capacity, and the average numbers and sizes of both coil and helix segments. Chapter 2: We investigate profiles of local attributes (densities of entropy, enthalpy, free energy, and helicity) for the backbone of long polypeptides in the heterogeneous environment of a lipid bilayer or cell membrane. From these profiles we infer landscapes of global attributes for the backbone of short peptides with given position and orientation in that environment. Our methodology interprets the broken internal H-bonds along the backbone of the polypeptide as statistically interacting quasiparticles activated from the helix reference state. The interaction depends on the local environment (ranging from polar to non-polar), in particular on the availability of external H-bonds (with H2O molecules or lipid headgroups) to replace internal H-bonds. The helicity landscape in particular is an essential prerequisite for the continuation of this part of the project with focus on the side-chain contributions to the free-energy landscapes. The full free-energy landscapes are expected to yield information on insertion conditions and likely insertion pathways. Chapter 3: We present the first part in the design of a kinetic model for the insertion of short peptides, including variants of pHLIP, into a lipid bilayer. The process under scrutiny combines a transport phenomenon and a change in protonation status of negatively charged sites near the C terminus. The two kinetic phenomena influence each other and set different time scales. Processes with a significant range of time scales, known to be a challenge for molecular dynamics simulations, are shown to be within the scope of
Highlights
Chapter 3: We present the first part in the design of a kinetic model for the insertion of short peptides, including variants of pH Low Insertion Peptide (pHLIP), into a lipid bilayer
1.5 Conclusion and outlook We have launched this project mainly for the purpose of interpreting experiments on pHLIP. In this first of three stages of analysis we have constructed a microscopic model for the pH-driven coil-helix conformational change of a long polypeptide adsorbed to a water-lipid interface
Our results include the t-dependence of the helicity, the average numbers and the average lengths of helix and coil segments, the entropy, and the heat capacity
Summary
The microscopic model that we present here is a system of statistically interacting quasiparticles with shapes. The methodology employed for its exact statistical mechanical analysis is built on the concept of fractional statistics, invented by Haldane [15], and developed by Wu [16], Isakov [17], Anghel [18], and others [19] in the context of quantum many-body systems. The adaptation of this approach to classical statistical mechanical systems of particles with shapes was developed in a recent series of studies with applications to Ising spins [20, 21, 22, 23], jammed granular matter [24, 25], lattice gases with long-range interactions [26], and DNA under tension [27]. The application to the coil-helix transition of a long polypeptide adsorbed to a water-lipid interface worked out in the following is conceptually simple but surprisingly rich in scope
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