Bayesian modeling reveals metabolite-dependent ultrasensitivity in the cyanobacterial circadian clock.

Mathematical models can enable a predictive understanding of mechanism in cell biology by quantitatively describing complex networks of interactions, but such models are often poorly constrained by available data. Owing to its relative biochemical simplicity, the core circadian oscillator in Synechococcus elongatus has become a prototypical system for studying how collective dynamics emerge from molecular interactions. The oscillator consists of only three proteins, KaiA, KaiB, and KaiC, and near-24-h cycles of KaiC phosphorylation can be reconstituted in vitro. Here, we formulate a molecularly detailed but mechanistically naive model of the KaiA-KaiC subsystem and fit it directly to experimental data within a Bayesian parameter estimation framework. Analysis of the fits consistently reveals an ultrasensitive response for KaiC phosphorylation as a function of KaiA concentration, which we confirm experimentally. This ultrasensitivity primarily results from the differential affinity of KaiA for competing nucleotide-bound states of KaiC. We argue that the ultrasensitive stimulus-response relation likely plays an important role in metabolic compensation by suppressing premature phosphorylation at nighttime.

Geographically Resolved Rhythms in Twitter Use Reveal Social Pressures on Daily Activity Patterns.

Daily rhythms in human physiology and behavior are driven by the interplay of circadian rhythms, environmental cycles, and social schedules. Much research has focused on the mechanism and function of circadian rhythms in constant conditions or in idealized light-dark environments. There have been comparatively few studies into how social pressures, such as work and school schedules, affect human activity rhythms day to day and season to season. To address this issue, we analyzed activity on Twitter in >1,500 US counties throughout the 2012-2013 calendar years in 15-min intervals using geographically tagged tweets representing ≈0.1% of the total population each day. We find that sustained periods of low Twitter activity are correlated with sufficient sleep as measured by conventional surveys. We show that this nighttime lull in Twitter activity is shifted to later times on weekends relative to weekdays, a phenomenon we term "Twitter social jet lag." The magnitude of this social jet lag varies seasonally and geographically-with the West Coast experiencing less Twitter social jet lag compared to the Central and Eastern US-and is correlated with average commuting schedules and disease risk factors such as obesity. Most counties experience the largest amount of Twitter social jet lag in February and the lowest in June or July. We present evidence that these shifts in weekday activity coincide with relaxed social pressures due to local K-12 school holidays and that the direct seasonal effect of altered day length is comparatively weaker.

High protein copy number is required to suppress stochasticity in the cyanobacterial circadian clock.

Circadian clocks generate reliable ~24-h rhythms despite being based on stochastic biochemical reactions. The circadian clock in Synechococcus elongatus uses a post-translational oscillator that cycles deterministically in a test tube. Because the volume of a single bacterial cell is much smaller than a macroscopic reaction, we asked how clocks in single cells function reliably. Here, we show that S. elongatus cells must express many thousands of copies of Kai proteins to effectively suppress timing errors. Stochastic modeling shows that this requirement stems from noise amplification in the post-translational feedback loop that sustains oscillations. The much smaller cyanobacterium Prochlorococcus expresses only hundreds of Kai protein copies and has a simpler, hourglass-like Kai system. We show that this timer strategy can outperform a free-running clock if internal noise is significant. This conclusion has implications for clock evolution and synthetic oscillator design, and it suggests hourglass-like behavior may be widespread in microbes.

The cyanobacterial circadian clock follows midday in vivo and in vitro.

Circadian rhythms are biological oscillations that schedule daily changes in physiology. Outside the laboratory, circadian clocks do not generally free-run but are driven by daily cues whose timing varies with the seasons. The principles that determine how circadian clocks align to these external cycles are not well understood. Here, we report experimental platforms for driving the cyanobacterial circadian clock both in vivo and in vitro. We find that the phase of the circadian rhythm follows a simple scaling law in light-dark cycles, tracking midday across conditions with variable day length. The core biochemical oscillator comprised of the Kai proteins behaves similarly when driven by metabolic pulses in vitro, indicating that such dynamics are intrinsic to these proteins. We develop a general mathematical framework based on instantaneous transformation of the clock cycle by external cues, which successfully predicts clock behavior under many cycling environments.