Date of Award


Degree Type


Degree Name

Doctor of Philosophy in Physics



First Advisor

Gerhard Müller


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 the kinetic modeling presented here, which is based on interlocking Markov chain processes. The two processes governing protonation status and transport are run individually and then in combination. This makes it possible to investigate feedback mechanisms between the two component processes.



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