Xiangting Li

Welcome

Hello! My name is Xiangting Li and I am currently pursuing my Ph.D. in biomathematics at UCLA, advised by Prof. Tom Chou. My research focuses on understanding the stochastic processes that occur in biological systems, particularly diving into how DNA and proteins interact across different scales.

A recent interest of mine, inspired by the work of Anton Zilman, is to understand and evaluating nonequilibrium processes by its functions. In our paper on the stochastic kinetic proofreading (KPR) processes, we introduced a simplification, a deterministic processing time, to the classical KPR processes and obtained analytical understanding of how the whole process preserves information from input to output. While KPR has been applied to many different biological processes including replication and signaling, we highlight the differences in the biological context. Consequently, the performance metrics for KPR are different in different scenarios, which resolved the conflicts in results from Zilman’s work and previous understanding of speed-accuracy tradeoff in KPR. Our simplification to KPR allows for a generalized form of KPR with higher accuracy and speed, in which both the activation (processing) time and unbinding time are near deterministic.

Since the beginning of last century, (nonequilibrium) statistical physics has developed independently a set of tools to deal with stochastic (Langevin) processes, while the math community adopted a different set of tools for stochastic calculus. There can be some fruitful consequences of introducing existing mathematical tools, in particular, the Ito formula, to the field of stochastic thermodynamics. For example, as Manzano et al. showed in their work, the work theorem can be derived from the martingale perspective. Their proof is still based on the language of Crook’s fluctuation theorem and path integrals. However, the use of inverse paths may endanger the requirement of adaptivity in the martingale with respect to the filtration, let alone the path integral formulation is not well established in mathematics. We provide an alternative proof to the martingale property without the use of fluctuation theorem/stochastic entropy production/path integral formulation.

I also develop tools to facilitate research itself, such as citation crawler, a tool to build interactive network of papers based on citation information.

General Interests

My interest lies in dissecting the stochastic processes present in biological systems, with a special emphasis on DNA-protein interactions spanning multiple scales. My approach is a fusion of statistical physics, mathematics, and computational techniques, all aimed at elucidating the deterministic and stochastic dynamics that dictate molecular interactions from a semi-analytical perspective.

I received my B.S. in the Integrated Science Program at Peking University. The program provided me with a broad and relatively in-depth exposure to mathematics (analysis, geometry, topology, dynamical systems, and probability), physics (statistical mechanics), physical chemistry, and biology (molecular, developmental, and evolutionary biology). Beyond the training in the classroom, I managed to appreciate different research fields from perspectives of a mathematician, a physicist, and a biologist. Even for the same problem of Brownian motion and Langevin equation, the physical approach and the mathematical approach are quite different in the formalism, see my blog post A note on Langevin Equations and Stochastic Differential Equations for more details. This perspective may have profound consequences on other aspects of stochastic thermodynamics, including the stochastic work theorem.

During my undergraduate years, I worked with Prof. Zhi Qi (齐 志) on the single-molecule biophysics topics. I worked both as a theorist and an experimentalist, and developed a strong interest in the stochastic processes that occur in biological systems.

At UCLA, my work is focused on characterizing the stochastic dynamics of DNA-protein interactions. The goal is to create a link between the microscopic interactions occurring at the molecular level and the macroscopic phenomena observed in biology. In pursuit of this goal, I have explored various models of molecular biology, such as nucleosome disassembly, the coupled processes of transcription and translation, and understanding the driving forces behind viral evolution.

I am also interested in the development of computational tools to aid in the analysis of biological data, with a particular flavor on inferring first principles from experimental data using a top-down approach.

Recent Publications

* Denotes co-first authorship

Recent Talks

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