Xiangting Li

Research Interests

My research integrates principles of statistical physics, stochastic processes, and biological insights to elucidate complex molecular dynamics in living systems. The focus is on distilling complex interactions into understandable models that predict biological behaviors under both equilibrium and nonequilibrium conditions.

DNA-Protein Interactions and Dynamics

The first part of my study focuses on a mechanistic understanding of peculiar biological phenomena, in particular, modeling of multiple protein-DNA interactions.

In these systems, the nucleic acids including DNA and RNA provides a scaffold for various interactions between them and proteins. In traditional biochemical and structural studies, specific binding sites or interactions are of the most interest. However, there are tens of thousands of different types of macromolecules inside the cell. The most prominent interaction between two random proteins is the nonspecific volume exclusion interactions. Despite its simplicity, volume exclusion can have profound consequences, especially when combined with specific interactions.

My previous work demonstrated simple mathematical law governing volume exclusion can contribute to selective DNA/RNA accessibility to different proteins based on their size and shape, when the DNA/RNA is covered by protective proteins such as histones or RPA.

Nonspecific volume exclusion interactions also influences the dynamics of nonequilibrium transport, such as the transcription and translation processes. I also studied how transcription-translation coupling in prokaryotes, a specific interaction, interacts with volume exclusion to alter the fluxes of RNA polymerase and ribosomes.

Nonequilibrium Molecular Processes

The second part of my work is the interest to understand the nonequilibrium nature of life systems from a functional perspective. It is well known that living forms utilize external energy to drive the molecular processes out of equilibrium. However, the function and mechanism of nonequilibrium processes for living forms are not very clear. In a recent work we submitted to PLoS CB, we revisit a well-known nonequilibrium process in cells, the kinetic proofreading. Our observation is that the energy consuming steps of KPR allows a non-exponential waiting time to activation. This non-exponential waiting time carries memory of the history, enabling an enhanced sensitivity to the binding affinity between the substrate and ligand. This perspective also allows us to identify a generalized form of kinetic proofreading that could be both more accurate and faster compared to the traditional proofreading scheme.

Stochastic Thermodynamics

While it is well-known that statistical physics is established on statistical or probabilistic methods, it has diverged from the modern probability theory. A most heated topic between mathematicians and physicists is the definition of path integrals, a method originally proposed by Feynman to quantum mechanics, but also central to some of the most important results in nonequilibrium statistical physics, including the Crooks fluctuation theorem and their applications such as the Jarzynski equality (also known as the work theorem). My interest is to bridge the gap between the two fields, and to provide a more rigorous foundation for the stochastic thermodynamics. For example, the work theorem can be proved using tools from the theory of stochastic processes, or It\^o calculus, with no reference to the path integral. In addition, a mathematical path integral method can be developed more rigorously to justify the Crooks fluctuation theorem, which highlights the asymmetry between forward and backward processes that is absent in the classical or ``physical’’ path integral approach.