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Graduate Student Supervision
Doctoral Student Supervision (Jan 2008 - Nov 2020)
We use classical density functional theory to investigate the interactions between solvents and proteins. We examine a diverse experimental literature to establish thermodynamic properties of protein-cosolute interaction, particularly the compensation between transfer entropy and transfer enthalpy. We develop a method of analysing the uncertainties in such measurements and use the method to resolve a long-standing debate over entropy-enthalpy compensation. We develop a classical density functional theory for interactions between proteins and cosolutes. The theory developed here ignores the solvent-solvent interaction but is nonetheless quite accurate. We use this approach to reproduce transfer free energies reported elsewhere, and show that the cDFT model captures the desolvation barrier and the temperature dependence of the transfer free energy. We use experimental values that we have analyzed to define the parameter space of a model density functional theory approach. We then extend the classical density functional theory to capture protein-water interactions, thus developing a new implicit solvent model. Along the way we give a proof that the free energy of a bath of particles in a finite external potential is independent of the external potential in the isothermal-isobaric ensemble. We finally discuss the challenges remaining in implementing our implicit solvent model.
This thesis is divided into three chapters. Chapter 1 is a study of statistical models of graphs, in order to explore possible realizations of emergent manifolds. Graphs with given numbers of vertices and edges are considered, governed by a Hamiltonian that favors graphs with near-constant valency and local rotational symmetry. The model is simulated numerically in the canonical ensemble. It is found that the model exhibits a first-order phase transition, and that the low energy states are almost triangulations of two dimensional manifolds. The resulting manifold shows topological "handles" and surface intersections in a higher embedding space as well as non-trivial fractal dimension. The model exhibits a phase transition temperature of zero in the bulk limit. We explore the effects of adding long-range interactions to the model, which restore a finite transition temperature in the bulk limit.In Chapter 2, aspects of Chern-Simons theory are studied. The relations between Chern-Simons theory, a model known as BF theory named after the fields that appear in the actions, and 3D gravity, are explored and generalized to the case of non-orientable spacetime manifolds. U(1) Chern-Simons theory is quantized canonically on orientable manifolds, and U(1) BF theory is similarly quantized on non-orientable manifolds. By requiring the quantum states to form a representation of the deformed holonomy group and the deformed large gauge transformation group, we find that the mapping class group of the spacetime manifold can be consistently represented, provided the prefactor k of the Chern-Simon action satisfies quantization conditions which in general are non-trivial. We also find a k 1/k duality for the representations. Motivated by open questions about interpreting the finite size results from Chapter 1, models of finite size scaling for systems with a first-order phase transition are discussed in Chapter 3. Three physics models -- the Potts model, the Go model for protein folding, and the graph model in Chapter 1 -- are simulated. Several finite size scaling models, including three functional forms to fit the energy distributions, and a capillarity model, are compared with simulations of the corresponding physics models.
The Euclidean distance, D, between two points is generalized to the distance between strings or polymers. The problem is of great mathematical beauty and very rich in structure even for the simplest of cases. The necessary and sufficient conditions for finding minimal distance transformations are presented. Locally minimal solutions for one-link and two-link chains are discussed, and the large N limit of a polymer is studied. Applications of D to protein folding and structural alignment are explored, in particular for finding minimal folding pathways. Non-crossing constraints and the resulting untangling moves in folding pathways are discussed as well. It is observed that, compared to the total distance, these extra untangling moves constitute a small fraction of the total movement. The resulting extra distance from untangling movements (Dnx ) are used to distinguish different protein classes, e.g. knotted proteins from unknotted proteins. By studying the ensembles of untangling moves, dominant folding pathways are constructed for three proteins, in particular a knotted protein. Finally, applications of D, and related metrics to protein folding rate prediction are discussed. It is seen that distance metrics are good at predicting the folding rates of 3-state folders.
Protein misfolding diseases represent a large burden to human health for which only symptomatictreatment is generally available. These diseases, such as Creutzfeldt-Jakob disease, amyotrophiclateral sclerosis, and the systemic amyloidoses, are characterized by conversion of globular, nativelyfoldedproteins into pathologic β-sheet rich protein aggregates deposited in affected tissues. Understandingthe thermodynamic and kinetic details of protein misfolding on a molecular level dependson accurately appraising the free energies of the folded, partially unfolded intermediate,and misfolded protein conformers. There are multiple energetic and entropic contributions to thetotal free energy, including nonpolar, electrostatic, solvation, and configurational terms. To accuratelyassess the electrostatic contribution, a method to calculate the spatially-varying dielectricconstant in a protein/water system was developed using a generalization of Kirkwood Frohlich theoryalong with brief all-atom molecular dynamics simulations. This method was combined withpreviously validated models for nonpolar solvation and configurational entropy in an algorithm tocalculate the free energy change on partial unfolding of contiguous protein subsequences. Resultswere compared with those from a minimal, topologically-based Gō model and direct calculationof free energies by steered all-atom molecular dynamics simulations. This algorithm was appliedto understand the early steps in the misfolding mechanism for β₂-microglobulin, prion protein,and superoxide dismutase 1 (SOD1). It was hypothesized that SOD1 misfolding may follow atemplate-directed mechanism like that discovered previously for prion protein, so misfolding ofSOD1 was induced in cell culture by transfection with mutant SOD1 constructs and observed tostably propagate intracellularly and intercellularly much like an infectious prion. A defined minimalassay with recombinant SOD protein demonstrated the sufficiency of mutant SOD1 aloneto trigger wtSOD1 misfolding, reminiscent of the “protein-only” hypothesis of prion spread. Finally,protein misfolding as a feature of disease may extend beyond neurodegeneration and amyloidformation to cancer, in which derangement of protein folding quality control may lead to antibodyrecognizablemisfolded protein present selectively on cancer cell surfaces. The evidence for thishypothesis and possible therapeutic targets are discussed as a future direction.
Living cells are composed of a variety of biological macromolecules such as nucleic acid, metabolites, proteins and cytoskeletal filaments as well as other particles. The fraction of the cellular interior volume that is taken by these biomolecules is about 30%, leading to a highly crowded environment. Biomolecules present in an extremely dense environment inside a cell have a completely different set of kinetic and thermodynamic behavior than in a test tube. Therefore comprehending the effect of crowding conditions on biological molecules is crucial to broad research fields such as biochemical, medical and pharmaceutical sciences. Experimentally, we are able to mimic such crowded environments; which are of more physiological relevance, by adding high concentrations of synthetic macromolecules into uncrowded buffers. Theoretically, very little attention has been paid to the effects of the dense cellular cytoplasm on biological reactions. The purpose of this work is to investigate analytically the effects of crowding agents on protein folding and stability. We present a new parameter as the measure of the polymer size, which will substitute the traditional measurements of the radius of gyration of the polymer and the end to end distance of a polymeric chain. Using this quantity we derive an expression for the free energy of the polymer which can easily be generalized to provide the free energy of a protein. This mechanism enables us to study the effect of crowding on folding and stability of a protein. The stabilization effects of the crowding particles depend on the concentration and the size of the crowders and also the type of the crowding particles that are present in the system. In our calculations the type of the crowders is controlled by the energetic parameter between the protein and surrounding macromolecules.