Reconstructing equations of motion for cell phenotypic transitions: integration of data science and dynamical systems theory

Dynamical systems theory has long been fruitfully applied to describe cellular processes, while a main challenge is lack of quantitative information for constraining models. Advances of quantitative approaches, especially single cell techniques, have accelerated the emergence of a new direction of reconstructing the equations of motion of a cellular system from quantitative single cell data, thus places studies under the framework of dynamical systems theories, as compared to the currently dominant statistics-based approaches. Here I review a selected number of recent studies using live- and fixed- cell data, and provide my perspective on the future development.Comment: 18 pages, 4 figure

Coupled Reversible and Irreversible Bistable Switches Underlying TGF-\beta-induced Epithelial to Mesenchymal Transition

Epithelial to mesenchymal transition (EMT) plays important roles in embryonic development, tissue regeneration and cancer metastasis. While several feedback loops have been shown to regulate EMT, it remains elusive how they coordinately modulate EMT response to TGF-\beta treatment. We construct a mathematical model for the core regulatory network controlling TGF-\beta-induced EMT. Through deterministic analyses and stochastic simulations, we show that EMT is a sequential two-step program that an epithelial cell first transits to partial EMT then to the mesenchymal state, depending on the strength and duration of TGF-\beta stimulation. Mechanistically the system is governed by coupled reversible and irreversible bistable switches. The SNAIL1/miR-34 double negative feedback loop is responsible for the reversible switch and regulates the initiation of EMT, while the ZEB/miR-200 feedback loop is accountable for the irreversible switch and controls the establishment of the mesenchymal state. Furthermore, an autocrine TGF-\beta/miR-200 feedback loop makes the second switch irreversible, modulating the maintenance of EMT. Such coupled bistable switches are robust to parameter variation and molecular noise. We provide a mechanistic explanation on multiple experimental observations. The model makes several explicit predictions on hysteretic dynamic behaviors, system response to pulsed stimulation and various perturbations, which can be straightforwardly tested.Comment: 32 pages, 8 figures, accepted by Biophysical Journa

Fluctuation-dissipation relations far from equilibrium

The fluctuation-dissipation (F-D) theorem is a fundamental result for systems near thermodynamic equilibrium, and justifies studies between microscopic and macroscopic properties. It states that the nonequilibrium relaxation dynamics is related to the spontaneous fluctuation at equilibrium. Most processes in Nature are out of equilibrium, for which we have limited theory. Common wisdom believes the F-D theorem is violated in general for systems far from equilibrium. Recently we show that dynamics of a dissipative system described by stochastic differential equations can be mapped to that of a thermostated Hamiltonian system, with a nonequilibrium steady state of the former corresponding to the equilibrium state of the latter. Her we derived the corresponding F-D theorem, and tested with several examples. We suggest further studies exploiting the analogy between a general dissipative system appearing in various science branches and a Hamiltonian system. Especially we discussed the implications of this work on biological network studies.Comment: 12 pages, 4 figures, major revision over the first versio

A non-equilibrium dynamic mechanism for the allosteric effect

Allosteric regulation is often viewed as thermodynamic in nature. However protein internal motions during an enzymatic reaction cycle can be slow hopping processes over numerous potential barriers. We propose that regulating molecules may function by modifying the nonequilibrium protein dynamics. The theory predicts that an enzyme under the new mechanism has different temperature dependence, waiting time distribution of the turnover cycle, and dynamic fluctuation patterns with and without effector. Experimental tests of the theory are proposed.Comment: accepted by Phys. Rev. Lett. Major revisions were made to fit the style. 4 pages, 2 figure

Resonant activation: a strategy against bacterial persistence

A bacterial colony may develop a small number of cells genetically identical to, but phenotypically different from other normally growing bacteria. These so-called persister cells keep themselves in a dormant state and thus are insensitive to antibiotic treatment, resulting in serious problems of drug resistance. In this paper, we proposed a novel strategy to "kill" persister cells by triggering them to switch, in a fast and synchronized way, into normally growing cells that are susceptible to antibiotics. The strategy is based on resonant activation (RA), a well-studied phenomenon in physics where the internal noise of a system can constructively facilitate fast and synchronized barrier crossings. Through stochastic Gilliespie simulation with a generic toggle switch model, we demonstrated that RA exists in the phenotypic switching of a single bacterium. Further, by coupling single cell level and population level simulations, we showed that with RA, one can greatly reduce the time and total amount of antibiotics needed to sterilize a bacterial population. We suggest that resonant activation is a general phenomenon in phenotypic transition, and can find other applications such as cancer therapy.Comment: 21 pages, 12 figures, submitte