BMAC Lab

Westlake University, School of Engineering xiaofangzhou@westlake.edu.cn

prof_pic.jpg

Room E1-321, Yungu Campus

600 Dunyu Road, Xihu District

Hangzhou CHINA

I’m Fang, an assistant professor in the School of Engineering at Westlake University in Xihu District, Hangzhou, CHINA, starting the biomachine architecture and control (BMAC) lab. Before this, I was a postdoctoral researcher at Suckjoon Jun group at UCSD to apply my theoretical framework in engineering to fundamental laws of bacterial survival and growth in dynamic environments. I obtained my PhD in bioengineering at Caltech in 2022, mentored by John C Doyle, and built a theoretical foundation for biocontrol in cells from gene circuits, to metabolism and physiology. My PhD thesis “Biocontrol of Biomolecular Systems: Polyhedral Constraints on Binding’s Regulation of Catalysis from Biocircuits to Metabolism” is here. Here’s my google scholar site and my CV.

My career goal is to push for the mature engineering of complex biological machines that fully realizes the unique potential of biotechnology. In order to do so, not only do we need theoretical understanding and reliable manufacturing of biological parts and components, we also need a systems theory to understand how to put parts together and what can and cannot be achieved. Examples from other engineering disciplines are Turing machines for computers, information channel for communication networks, linear input output systems for electrical circuits, and thermodynamics for heat engines.

Taking other engineering disciplines as motivations, we see system theory is important to understand what can and cannot be achieved by putting parts together into a machine.

My PhD therefore focused on developing a systems theory tailored to biomolecular systems in cells. This culminated into the following statements. See the research page for details.

Biomolecular systems are binding and catalysis reactions. Catalysis determines the direction of change, while binding regulates how the catalysis rates vary with reactant concentrations. The holistic regulatory profile can be captured by the reaction order of catalysis, which in turn is constrained in polyhedra determined by the stoichiometry of binding. In summary, since cells control catalysis by binding, cells control catalysis rates by regulating reaction orders. This also has ramifications in several directions. On metabolism, by incorporating the constraint that reaction orders of metabolic fluxes, not the fluxes themselves, are controlled, we can predict metabolism dynamics directly from network stoichiometry, e.g. glycolytic oscillations and growth arrests. On systems biology, this derives Analysis by Binding and Catalysis (ABC) that allows discovery of necessary and sufficient conditions for a circuit to function, holistic comparisons of different circuit implementations, e.g. activator versus repressor, and enables biocircuit design where we know when a design will work, and when a design will fail. On dynamics and control of biocircuits, reaction order can work as a robust basis for stability, perfect adaptation, multistability and oscillations. Lyapunov functions and dissipativity theory tailored for biomolecular systems can be constructed based on reaction order. On the mathematics of biology, it relates bioregulation to convex polyhedra, log derivative operator decompositions, and fundamental rules of calculus for positive variables.

The two figures below illustrate the system view that this promotes. For more details see the research page.

Left, for a simple binding reaction of E and S binds to complex C, the reaction order of C (with log derivative as its continuous analogue) is constrained inside the triangular polyhedron. Middle, flux exponent control (FEC) as a constraint-based modelling of metabolism that can capture metabolism dynamics, utilizing more biological constraints than flux balance analysis. Right, understanding how the holistic regulatory profile of binding reactions relate to the mathematics of log derivative operators' decomposition rules enables a technique for analysis of log derivative polyhedra called dominance decomposition tree (DDT).
Binding regulates catalysis. The reaction order polyhedron (right triangle) is the holistic space of bioregulation that the binding network E+S <=> C can have on the enzymatic catalysis. Dynamics in the system happen via production and degradation changing the total enzyme and substrate concentrations (lower left), causing movements in the reaction order space (right), which in turn determines how the catalysis fluxes would respond to the changing concentrations.
Example of how log derivative polyhedra can capture the holistic behavior of a biocircuit. This is an incoherent feedforward (IFF) circuit with disturbance intput w activating both x1 and x2, and x2 inhibits x1 by catalyzing x1's degradation. C denotes the reaction complex formed for x1's degradation catalyzed by x2. The upper right triangle is the log derivative polyhedron of C, with the red corner near (1,1) corresponding to the adaptation regime where x1 is robust to disturbance w. When the log derivative deviates away from the red corner, x1 can no longer adapt. We see this fails for disturbance w that is larger than reference.

selected publications

  1. Bacterial Replication Initiation as Precision Control by Protein Counting
    Haochen Fu* ,  Fangzhou Xiao* ,  and  Suckjoon Jun
    PRX Life, highlighted with viewpoint, Aug 2023
  2. Flux exponent control predicts metabolic dynamics from network structure
    Fangzhou Xiao ,  Jing Shuang Li ,  and  John C. Doyle
    In 2023 American Control Conference (ACC) , Aug 2023
  3. Stability and Control of Biomolecular Circuits through Structure
    Fangzhou Xiao ,  Mustafa Khammash ,  and  John C. Doyle
    In 2021 Annual American Control Conference (ACC) , Aug 2021
  4. A geometric and structural approach to the analysis and design of biological circuit dynamics: a theory tailored for synthetic biology
    John P. Marken ,  Fangzhou Xiao ,  and  Richard M. Murray
    bioRxiv, Aug 2020
  5. Proofreading through spatial gradients
    Vahe Galstyan ,  Kabir Husain ,  Fangzhou Xiao , and 2 more authors
    eLife, Dec 2020
  6. Robust Perfect Adaptation in Biomolecular Reaction Networks
    Fangzhou Xiao ,  and  John Doyle
    In 2018 IEEE Conference on Decision and Control (CDC) , Dec 2018
  7. Coupled Reaction Networks for Noise Suppression
    Fangzhou Xiao ,  Meichen Fang ,  Jiawei Yan , and 1 more author
    In 2019 American Control Conference (ACC) , Dec 2019