Doctor of Philosophy (PhD)


Geology & Geophysics

Document Type



High-dimensional isotope relationships describes the relationships of two or more element or position-specific (PS) elements in the same molecule or ion. It provides us more powerful tools to study reaction mechanisms and dynamics. Chapter 1 is about dual or multiple stable isotope relationship on δ-δ (or δ'-δ') space. While temporal data sampled from a closed-system can be treated by a Rayleigh Distillation Model (RDM), spatial data should be treated by a Reaction-Transport Model (RTM). Here we compare the results of a closed-system RDM to a RTM for systems with diffusional mass transfer by simulating the trajectories on nitrate's δ'18O-δ'15N space. Our results highlight the importance of linking the underlying physical model to the plotted data points before interpreting their high-dimensional isotope relationships. Chapter 2 proposed a rigorous approach that can describe isotope distribution among biomolecules and their apparent deviation from equilibrium state. Applying the concept of distance matrix in graph theory, we propose that apparent local isotope equilibrium among a subset of biomolecules can be assessed using an apparent fractionation difference (|Δα|) matrix. The application of |Δα| matrix can help us to locate potential reversible reactions or reaction networks in a complex system like a metabolic system. Chapter 3 calculated the equilibrium PS isotope composition for large organic molecules. A prevailing idea is that each of the positions can reach equilibrium with each other, if a reaction is fully reversible. However, such an equilibrium intramolecular isotope distribution (Intra-ID) can only be achieved when every carbon atom of different positions exchange with each other within a molecule. Equilibrium Intra-IDs (reduced partition function ratios, β) can serve as a fixed reference for measured Intra-ID. The analysis of calculated PS 13β factors of acetate and C16 fatty acid showed that equilibrium isotope effect can produce fatty acid with alternating Intra-ID from disequilibrium precursors.



Committee Chair

Wang, Jianwei