Projects

Protein Folding and Function

Proteins are large organic molecules composed of tens, hundreds, or even thousands of amino acid residues bound together by peptide bonds into a necklace like structure. Unlike other organic molecules, there are a large number of different conformations any one protein molecule can take. These structures are determined by a large number of conflicting and largely canceling forces exerted on the protein residues by the surrounding solvent and other residues in the protein chain. In one type of protein, the globular protein, the protein molecule folds spontaneously and reproducibly to a compact, well defined structure.

In the strictest sense we know that there cannot be a single pathway by which a protein folds. Consider this: if an ensemble of denatured proteins all must pass through a single narrow pathway in their phase space, then there must be a large reduction in entropy upon entering this path. This step would consequently be very unlikely and rate limiting. It is much more likely that proteins fold via many different pathways. Such a mechanism would allow analysis of protein folding dynamics through general equilibrium and non-equilibrium statistical mechanics.

This picture of protein folding dynamics, while yielding results mathematically similar to classical transition state theory, is somewhat different in spirit. In this picture of two state systems, the barrier is a free energy barrier: an energetic barrier does not exist. Thus the transition state is composed of a broad ensemble of structures rather than one particular structure. This does not mean of course that the transition state is completely random. The transition state may be characterised by partial structure in the form of stable pieces of secondary structure or partially correct backbone shape.

So protein folding can be given a lower order description as a quasi-static evolution of an ensemble of equilibrium structures from the denatured state to the native state over a relatively modest free energy barrier. The energy landscape theory based on the principle of minimal frustration describes protein folding as a process of an ensemble of converging pathways on a landscape biased towards the native state. So called Go-models are used to investigate protein folding on such a smooth energy landscape.

Electron Transfer

Electron transfer (ET) reactions play a key role in living systems, particularly in bioenergetic pathways. Most of these reactions involve large separations between donors and acceptors (5-20 A°), and they occur in the non-adiabatic limit. As so, their rates are described by the Fermi Golden Rule, and they are proportional to a product of the square of the tunneling matrix element between the donor and the acceptor and the Franck-Condon factor, which accounts for the nuclear control of the energy gap.

While the FC factor is reasonably well described by Marcus theory and its semi-classical and quantum modifications, effects of the protein environment on the effective coupling still need a better understanding. About a decade ago, David Beratan and José Onuchic have developed the Pathways model, which has since then become the standard theoretical tool utilized by experimentalists to estimate the effective coupling and to understand the tunneling mechanism. The Pathways assumes that tunneling occurs via a dominant tube inside the protein and that the tunneling decay through this tube can be quantified as a product of contributions from covalent bonds, hydrogen bonds and through space jumps. Being an empirical method, however, the Pathways has serious limitations:

Our major goal has been to explore how these issues control the effective coupling in biopolymers. For this purpose, we have developed a framework, which included analytical methods and software tools. A Dyson's equations based analysis of electronic interference in model bridges was performed and complemented by numerical simulations, providing a connection between simple Pathway-like Hamiltonians and quantum chemical models. This analysis elucidated effects of the tunneling energy, length of interactions among orbitals, side groups, boundaries and nonorthogonality of the orbital basis on the effective coupling. Sensitivity of the coupling to the pathway interference regime and the dynamics was investigated for a number of organic bridges and oligopeptides. To apply our framework to proteins, a software package bet has been developed, which performs interpreting PDB files, building an extended Huckel level electronic Hamiltonian (in the atomic, hybrid or bond/antibond orbital basis set), interactive examining and/or changing the Hamiltonian, and calculating the electronic eigenstates and the effective coupling using the Green's function method. Using combined molecular dynamics and electronic structure calculations, bet provides means to identify the dominant pathways, analyze the interference among them and explore dynamical control of the effective coupling. We have explored these effects in photosynthetic reaction centers , azurin and cytochrome C oxidase .

Molecular Motors

Recent progress in molecular biology using real time visualization of cellular process at a single molecule level have revealed much more elaborate and sophisticated nature of biological system than we had understood decades ago. Similar to the machine invented by human, biological system has an architecture composed of a large number of heterogeneous components whose interactions are orchestrated under the well-designed mechanism. The cellular functions, such as transcription, translation, cell division and etc, result from the coordination and regulation between the biological components in response to the environmental (chemical, mechanical) changes. Among biological components, extensive interest has recently been drawn to the molecular motors that play pivotal roles in cellular processes by performing mechanical work using the energy-driven conformational changes. DNA polymerase, kinesin, myosin, F1-ATPase, and GroEL belong to such a class that undergoes a series of small and large conformational changes during the mechanochemical cycle of ATP binding, hydrolysis, and the subsequent release of Gamma-P(i) where the structure of molecular motors is directly coupled to the chemical state of ligand. Following are the key questions being inquired in the study of molecular motors.

Using structure-based simplified modeling, we try to understand the working principle of molecular motors.