Information Processing and Chaos

The framework of dynamical systems offers a powerful lens for understanding biological behavior not merely by cataloging molecular components and their interactions, but by identifying dynamical states and the transitions between them. In another word, it offers a distinct conceptual basis for dimensionality reduction in complex biological systems.

In our studies of mast cells, we observed diverse dynamical phenomena on the cortex, including excitability, oscillations, periodic traveling waves, standing waves, period doubling, and mixed-mode oscillations. We found that phosphoinositide signaling acts as essential control for all states. Phosphoinositides are key signaling lipids located on the plasma membrane. By recruiting a wide array of effector proteins, they regulate receptor signaling and influence nearly all aspects of cell physiology, including proliferation, apoptosis, and differentiation. How a small number of chemical lipids achieve such complexity is not known.

We propose that the nonlinear dynamics embedded within the phosphoinositide network are fundamental to understanding how the plasma membrane processes information. Small changes in kinetic parameters within this network can drive rapid transitions between distinct attractor states, allowing the cell to generate different functional responses.

In antigen-activated mast cells, phosphoinositide fluxes precisely regulate the frequency of periodic traveling waves (Xiong et al., Nature Chemical Biology, 2016). Using real-time imaging, lipid biosensors, optogenetics, and biochemical assays, we identified a local negative feedback loop in which Phosphatidylinositol (3,4,5)-trisphosphate [PI(3,4,5)P3] is degraded by SHIP1 while being regenerated by PI3-kinase. This circuit produces pulsatile oscillations of PI(3,4,5)P3 and PI(3,4)P2. Because the oscillation frequency scales with PI3-kinase activity, this work demonstrated for the first time that PI3-kinase activity can be encoded as a frequency inside the cell.

We also discovered two forms of waves, traveling waves and standing waves. Standing waves are specifically coupled to calcium oscillations, which has important implications for the synchronized activation of ion channels (Wu et al., PNAS, 2013; Xiong et al., bioRxiv 2022 , 2025). In addition, oscillations of cortical endoplasmic reticulum that regulate PI4P flux can tune the amplitude of calcium oscillations (Xiong et al., bioRxiv).

Phosphoinositide fluxes also explain the high variability of Rho pulses that control cell contractility (Tong et al., Cell Reports, 2023). We found that these seemingly simple Rho pulses depend critically on phosphoinositide fluxes organized as coupled nonlinear circuits that operate on two time scales. The lipid transport protein E-Syt regulates the separation of these time scales. Coupling a fast circuit based on lipid metabolism with a slow circuit based on lipid transport produces period doubling and mixed-mode oscillations in the GTPase signaling network that drives contractility. Mixed-mode oscillations consist of large-amplitude events interspersed with multiple small-amplitude events. The fast oscillation has a relatively constant cycle time of about 30 seconds, whereas the slow cycle is more variable, with a major period between 1 and 5 minutes. Mathematically, the key is the separation of time scales in circuits that modulate one another. For example, the phase or amplitude of the slow oscillator can modulate the input flux that drives the fast oscillator, causing the fast oscillator to adjust each cycle and generate longer, more complex periodic or aperiodic trajectories. Put simply, the variable duration can be viewed as overlapping bursts with different numbers of repeating units. These principles from dynamical systems show how small kinetic changes can yield qualitatively distinct dynamics. Although our study focused on Rho activation, the higher-order coupled networks provide a general framework for understanding temporal control in signal transduction.

Review