Date of Award

December 2015

Degree Type


Degree Name

Doctor of Philosophy



First Advisor

Valerica Raicu

Committee Members

Daniel Agterberg, Abbas Ourmazd, Dilano Saldin, Marius Schmidt


Fractal, FRET, GPCR, Molecular Dynamics Simulation, Relaxation


One of the major challenges posed to our quantitative understanding of structure, dynamics, and function of biological macromolecules has been the high level of complexity of biological structures. In the present work, we studied interactions between G protein-coupled receptors (GPCRs), and also introduced a theoretical model of relaxation in complex systems, in order to help understand interactions and relaxation in biological macromolecules.

GPCRs are the largest and most diverse family of membrane receptors that play key roles in mediating signal transduction between outside and inside of a cell. Oligomerization of GPCRs and its possible role in function and signaling currently constitute an exciting area of research, with implications on development of therapeutic regimens. We performed molecular dynamics (MD) simulations of fluorescent proteins attached through short linkers to GPCRs, in order to obtain distances between them and orientation factors of their transition dipole moments. Used in conjunction with Förster resonance energy transfer (FRET) experiments, this information is used for determination of binding interfaces between GPCR protomers (i.e., single molecules) within an oligomer. We simulated, with coarse-grained resolution, several configurations of dimers and tetramers of the M2 muscarinic acetylcholine receptor fused to the green fluorescent protein (GFP, a donor of energy in FRET) and yellow fluorescent protein (YFP, an acceptor of energy). From simulated distances and orientation factors for oligomers with different relative orientations of the protomers, we computed apparent FRET efficiencies for mixtures of monomers, dimers and tetramers based on the simulated data, and then compared them to experimental FRET data. Comparing the fitting residuals obtained for all tested oligomer configurations, we were able to determine, for the first time, the most probable quaternary structure of the M2 muscarinic receptor in living cells.

The study of relaxation processes is still insufficiently developed for the case of complex systems. Although it is currently firmly established that the dielectric behavior of systems of coupled dipoles or systems with complex biological structures deviates markedly from classical Debye (in the frequency domain) or pure exponential decay (in the time domain), the exact ways in which these deviations occur and their significance are still debated issues. In the second part of my thesis, we use a new approach to this problem for systems that present hierarchical relationships between their parts, also known as fractals. We formulated a set of differential equations of physical quantities in the hierarchical structure and developed a method of solving it. As a test case, for which there is experimental data to relate to, we applied this method to dielectric relaxation, and successfully reproduced the Debye, and non-Debye behaviors in the frequency domain, as well as corresponding non-exponential behaviors in the time domain. The proposed approach will likely provide an adequate mathematical framework for such disparate phenomena as recombination of photodissociable molecules, distribution of income in large populations of humans, and non-exponential decay of fluorescence in systems with multiple, hierarchically organized energetic levels. This in turn could help, develop correct approaches for analyzing FRET measurements in the time domain, which currently pose many challenges.