A design principle for posttranslational chaotic oscillators

Periodicity, mixed-mode oscillations, and multiple timescales in a phosphoinositide-Rho GTPase network

While rhythmic contractile behavior is commonly observed at the cellular cortex, the primary focus has been on excitable or periodic events described by simple activator-delayed inhibitor mechanisms. We show that Rho GTPase activation in nocodazole-treated mitotic cells exhibits both simple oscillations and complex mixed-mode oscillations. Rho oscillations with a 20- to 30-s period are regulated by phosphatidylinositol (3,4,5)-trisphosphate (PIP3) via an activator-delayed inhibitor mechanism, while a slow reaction with period of minutes is regulated by phosphatidylinositol 4-kinase via an activator-substrate depletion mechanism. Conversion from simple to complex oscillations can be induced by modulating PIP3 metabolism or altering membrane contact site protein E-Syt1. PTEN depletion results in a period-doubling intermediate, which, like mixed-mode oscillations, is an intermediate state toward chaos. In sum, this system operates at the edge of chaos. Small changes in phosphoinositide metabolism can confer cells with the flexibility to rapidly enter ordered states with different periodicities.

Machine learning alternative to systems biology should not solely depend on data

In recent years, artificial intelligence (AI)/machine learning has emerged as a plausible alternative to systems biology for the elucidation of biological phenomena and in attaining specified design objective in synthetic biology. Although considered highly disruptive with numerous notable successes so far, we seek to bring attention to both the fundamental and practical pitfalls of their usage, especially in illuminating emergent behaviors from chaotic or stochastic systems in biology. Without deliberating on their suitability and the required data qualities and pre-processing approaches beforehand, the research and development community could experience similar 'AI winters' that had plagued other fields. Instead, we anticipate the integration or combination of the two approaches, where appropriate, moving forward.

Elucidation of master allostery essential for circadian clock oscillation in cyanobacteria

Spatiotemporal allostery is the source of complex but ordered biological phenomena. To identify the structural basis for allostery that drives the cyanobacterial circadian clock, we crystallized the clock protein KaiC in four distinct states, which cover a whole cycle of phosphor-transfer events at Ser⁴³¹ and Thr⁴³². The minimal set of allosteric events required for oscillatory nature is a bidirectional coupling between the coil-to-helix transition of the Ser⁴³¹-dependent phospho-switch in the C-terminal domain of KaiC and adenosine 5'-diphosphate release from its N-terminal domain during adenosine triphosphatase cycle. An engineered KaiC protein oscillator consisting of a minimal set of the identified master allosteric events exhibited a monophosphorylation cycle of Ser⁴³¹ with a temperature-compensated circadian period, providing design principles for simple posttranslational biochemical circadian oscillators.

Overall structure of fully assembled cyanobacterial KaiABC circadian clock complex by an integrated experimental-computational approach

In the cyanobacterial circadian clock system, KaiA, KaiB and KaiC periodically assemble into a large complex. Here we determined the overall structure of their fully assembled complex by integrating experimental and computational approaches. Small-angle X-ray and inverse contrast matching small-angle neutron scatterings coupled with size-exclusion chromatography provided constraints to highlight the spatial arrangements of the N-terminal domains of KaiA, which were not resolved in the previous structural analyses. Computationally built 20 million structural models of the complex were screened out utilizing the constrains and then subjected to molecular dynamics simulations to examine their stabilities. The final model suggests that, despite large fluctuation of the KaiA N-terminal domains, their preferential positionings mask the hydrophobic surface of the KaiA C-terminal domains, hindering additional KaiA-KaiC interactions. Thus, our integrative approach provides a useful tool to resolve large complex structures harboring dynamically fluctuating domains.

The revealed full KaiA₁₂B₆C₆ complex is assembled including the dynamic and asynchronous KaiA N-terminal domains that have been missing in cryo-EM structures.

A design principle of spindle oscillations in mammalian sleep

Neural oscillations are mainly regulated by molecular mechanisms and network connectivity of neurons. Large-scale simulations of neuronal networks have driven the population-level understanding of neural oscillations. However, cell-intrinsic mechanisms, especially a design principle, of neural oscillations remain largely elusive. Herein, we developed a minimal, Hodgkin-Huxley-type model of groups of neurons to investigate molecular mechanisms underlying spindle oscillation, which is synchronized oscillatory activity predominantly observed during mammalian sleep. We discovered that slowly inactivating potassium channels played an essential role in characterizing the firing pattern. The detailed analysis of the minimal model revealed that leak sodium and potassium channels, which controlled passive properties of the fast variable (i.e., membrane potential), competitively regulated the base value and time constant of the slow variable (i.e., cytosolic calcium concentration). Consequently, we propose a theoretical design principle of spindle oscillations that may explain intracellular mechanisms behind the flexible control over oscillation density and calcium setpoint.

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A minimal, Hodgkin-Huxley-type model of spindle oscillations is developed

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The property of delayed rectifier K⁺ channels characterizes spindle oscillations

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The combination of bifurcations specifies spindle oscillations

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Spindle oscillations are controlled by the balance of inward and outward currents

Live imaging approach of dynamic multicellular responses in ERK signaling during vertebrate tissue development

The chemical and mechanical responses of cells via the exchange of information during growth and development result in the formation of biological tissues. Information processing within the cells through the signaling pathways and networks inherent to the constituent cells has been well-studied. However, the cell signaling mechanisms responsible for generating dynamic multicellular responses in developing tissues remain unclear. Here, I review the dynamic multicellular response systems during the development and growth of vertebrate tissues based on the extracellular signal-regulated kinase (ERK) pathway. First, an overview of the function of the ERK signaling network in cells is provided, followed by descriptions of biosensors essential for live imaging of the quantification of ERK activity in tissues. Then adducing four examples, I highlight the contribution of live imaging techniques for studying the involvement of spatio-temporal patterns of ERK activity change in tissue development and growth. In addition, theoretical implications of ERK signaling are also discussed from the viewpoint of dynamic systems. This review might help in understanding ERK-mediated dynamic multicellular responses and tissue morphogenesis.