Soliton driven relaxation dynamics and protein collapse in the villin headpiece.

Protein collapse from a random chain to the native state involves a dynamical phase transition. During the process, new scales and collective variables become excited while old ones recede and fade away. The presence of different phases and many scales causes formidable computational bottle-necks in approaches that are based on full atomic scale scrutiny.

Solitons and collapse in the λ-repressor protein.

The enterobacteria lambda phage is a paradigm temperate bacteriophage. Its lysogenic and lytic life cycles echo competition between the DNA binding λ-repressor (CI) and CRO proteins. Here we scrutinize the structure, stability, and folding pathways of the λ-repressor protein, which controls the transition from the lysogenic to the lytic state.

Correlation between protein secondary structure, backbone bond angles, and side-chain orientations.

We investigate the fine structure of the sp3 hybridized covalent bond geometry that governs the tetrahedral architecture around the central C(α) carbon of a protein backbone, and for this we develop new visualization techniques to analyze high-resolution x-ray structures in the Protein Data Bank. We observe that there is a correlation between the deformations of the ideal tetrahedral symmetry and the local secondary structure of the protein. We propose a universal coarse-grained energy function to describe the ensuing side-chain geometry in terms of the C(β) carbon orientations.

Protein loops, solitons, and side-chain visualization with applications to the left-handed helix region.

Folded proteins have a modular assembly. They are constructed from regular secondary structures like α helices and β strands that are joined together by loops. Here we develop a visualization technique that is adapted to describe this modular structure.

Discrete Frenet frame, inflection point solitons, and curve visualization with applications to folded proteins.

We develop a transfer matrix formalism to visualize the framing of discrete piecewise linear curves in three-dimensional space. Our approach is based on the concept of an intrinsically discrete curve. This enables us to more effectively describe curves that in the limit where the length of line segments vanishes approach fractal structures in lieu of continuous curves.

Elastic energy and phase structure in a continuous spin Ising chain with applications to chiral homopolymers.

We present a numerical Monte Carlo analysis of the phase structure in a continuous spin Ising chain that describes chiral homopolymers. We find that depending on the value of the Metropolis temperature, the model displays the three known nontrivial phases of polymers: At low temperatures the model is in a collapsed phase, at medium temperatures it is in a random walk phase, and at high temperatures it enters the self-avoiding random walk phase. By investigating the temperature dependence of the specific energy we confirm that the transition between the collapsed phase and the random walk phase is a phase transition, while the random walk phase and self-avoiding random walk phase are separated from each other by a crossover transition.

Gauge field theory of chirally folded homopolymers with applications to folded proteins.

We combine the principle of gauge invariance with extrinsic string geometry to develop a lattice model that can be employed to theoretically describe properties of chiral, unbranched homopolymers. We find that in its low temperature phase the model is in the same universality class with proteins that are deposited in the Protein Data Bank, in the sense of the compactness index. We apply the model to analyze various statistical aspects of folded proteins.