Cost-effective circadian mechanism: rhythmic degradation of circadian proteins spontaneously emerges without rhythmic post-translational regulation

Enlightening the blind spot of the Michaelis-Menten rate law: The role of relaxation dynamics in molecular complex formation

The century-long Michaelis-Menten rate law and its modifications in the modeling of biochemical rate processes stand on the assumption that the concentration of the complex of interacting molecules, at each moment, rapidly approaches an equilibrium (quasi-steady state) compared to the pace of molecular concentration changes. Yet, in the case of actively time-varying molecular concentrations with transient or oscillatory dynamics, the deviation of the complex profile from the quasi-steady state becomes relevant. A recent theoretical approach, known as the effective time-delay scheme (ETS), suggests that the delay from the relaxation time of molecular complex formation contributes to the substantial breakdown of the quasi-steady state assumption. Here, we systematically expand this ETS and inquire into the comprehensive roles of relaxation dynamics in complex formation. Through the modeling of rhythmic protein-protein and protein-DNA interactions and the mammalian circadian clock, our analysis reveals the effect of the relaxation dynamics beyond the time delay, which extends to the dampening of changes in the complex concentration with a reduction in the oscillation amplitude compared to the quasi-steady state. Interestingly, the combined effect of the time delay and amplitude reduction shapes both qualitative and quantitative oscillatory patterns such as the emergence and variability of the mammalian circadian rhythms. These findings highlight the downside of the routine assumption of quasi-steady states and enhance the mechanistic understanding of rich time-varying biomolecular processes.

Circadian period is compensated for repressor protein turnover rates in single cells

Most mammalian cells have molecular circadian clocks that generate widespread rhythms in transcript and protein abundance. While circadian clocks are robust to fluctuations in the cellular environment, little is known about the mechanisms by which the circadian period compensates for fluctuating metabolic states. Here, we exploit the heterogeneity of single cells both in circadian period and a metabolic parameter-protein stability-to study their interdependence without the need for genetic manipulation. We generated cells expressing key circadian proteins (CRYPTOCHROME1/2 (CRY1/2) and PERIOD1/2 (PER1/2)) as endogenous fusions with fluorescent proteins and simultaneously monitored circadian rhythms and degradation in thousands of single cells. We found that the circadian period compensates for fluctuations in the turnover rates of circadian repressor proteins and uncovered possible mechanisms using a mathematical model. In addition, the stabilities of the repressor proteins are circadian phase dependent and correlate with the circadian period in a phase-dependent manner, in contrast to the prevailing model.

40S Ribosomal protein S6 kinase integrates daylength perception and growth regulation in Arabidopsis thaliana

Plant growth occurs via the interconnection of cell growth and proliferation in each organ following specific developmental and environmental cues. Therefore, different photoperiods result in distinct growth patterns due to the integration of light and circadian perception with specific Carbon (C) partitioning strategies. In addition, the TARGET OF RAPAMYCIN (TOR) kinase pathway is an ancestral signaling pathway that integrates nutrient information with translational control and growth regulation. Recent findings in Arabidopsis (Arabidopsis thaliana) have shown a mutual connection between the TOR pathway and the circadian clock. However, the mechanistical network underlying this interaction is mostly unknown. Here, we show that the conserved TOR target, the 40S ribosomal protein S6 kinase (S6K) is under circadian and photoperiod regulation both at the transcriptional and post-translational level. Total S6K (S6K1 and S6K2) and TOR-dependent phosphorylated-S6K protein levels were higher during the light period and decreased at dusk especially under short day conditions. Using chemical and genetic approaches, we found that the diel pattern of S6K accumulation results from 26S proteasome-dependent degradation and is altered in mutants lacking the circadian F-box protein ZEITLUPE (ZTL), further strengthening our hypothesis that S6K could incorporate metabolic signals via TOR, which are also under circadian regulation. Moreover, under short days when C/energy levels are limiting, changes in S6K1 protein levels affected starch, sucrose and glucose accumulation and consequently impacted root and rosette growth responses. In summary, we propose that S6K1 constitutes a missing molecular link where day-length perception, nutrient availability and TOR pathway activity converge to coordinate growth responses with environmental conditions.

Generalized Michaelis-Menten rate law with time-varying molecular concentrations

The Michaelis-Menten (MM) rate law has been the dominant paradigm of modeling biochemical rate processes for over a century with applications in biochemistry, biophysics, cell biology, systems biology, and chemical engineering. The MM rate law and its remedied form stand on the assumption that the concentration of the complex of interacting molecules, at each moment, approaches an equilibrium (quasi-steady state) much faster than the molecular concentrations change. Yet, this assumption is not always justified. Here, we relax this quasi-steady state requirement and propose the generalized MM rate law for the interactions of molecules with active concentration changes over time. Our approach for time-varying molecular concentrations, termed the effective time-delay scheme (ETS), is based on rigorously estimated time-delay effects in molecular complex formation. With particularly marked improvements in protein-protein and protein-DNA interaction modeling, the ETS provides an analytical framework to interpret and predict rich transient or rhythmic dynamics (such as autogenously-regulated cellular adaptation and circadian protein turnover), which goes beyond the quasi-steady state assumption.

A circadian clock translational control mechanism targets specific mRNAs to cytoplasmic messenger ribonucleoprotein granules

Phosphorylation of Neurospora crassa eukaryotic initiation factor 2 α (eIF2α), a conserved translation initiation factor, is clock controlled. To determine the impact of rhythmic eIF2α phosphorylation on translation, we performed temporal ribosome profiling and RNA sequencing (RNA-seq) in wild-type (WT), clock mutant Δfrq, eIF2α kinase mutant Δcpc-3, and constitutively active cpc-3c cells. About 14% of mRNAs are rhythmically translated in WT cells, and translation rhythms for ∼30% of these mRNAs, which we named circadian translation-initiation-controlled genes (cTICs), are dependent on the clock and CPC-3. Most cTICs are expressed from arrhythmic mRNAs and contain a P-body (PB) localization motif in their 5' leader sequence. Deletion of SNR-1, a component of cytoplasmic messenger ribonucleoprotein granules (cmRNPgs) that include PBs and stress granules (SGs), and the PB motif on one of the cTIC mRNAs, zip-1, significantly alters zip-1 rhythmic translation. These results reveal that the clock regulates rhythmic translation of specific mRNAs through rhythmic eIF2α activity and cmRNPg metabolism.

Backward simulation for inferring hidden biomolecular kinetic profiles

Our backward simulation (BS) is an approach to infer the dynamics of individual components in ordinary differential equation (ODE) models, given the information on relatively downstream components or their sums. Here, we demonstrate the use of BS to infer protein synthesis rates with a given profile of protein concentrations over time in a circadian system. This protocol can also be applied to a wide range of problems with undetermined dynamics at the upstream levels.

For complete details on the use and execution of this protocol, please refer to Lim et al. (2021).

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Inference of upstream dynamics with information on the downstream profile

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Applies to infer protein synthesis rates with a given circadian protein profile

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Widely applicable to systems biology models with known downstream profiles

A framework of artificial light management for optimal plant development for smart greenhouse application

Smart greenhouse farming has emerged as one of the solutions to global food security, where farming productivity can be managed and improved in an automated manner. While it is known that plant development is highly dependent on the quantity and quality of light exposure, the specific impact of the different light properties is yet to be fully understood. In this study, using the model plant Arabidopsis, we systematically investigate how six different light properties (i.e., photoperiod, light offset, intensity, phase of dawn, duration of twilight and period) would affect plant development i.e., flowering time and hypocotyl (seedling stem) elongation using an established mathematical model of the plant circadian system relating light input to flowering time and hypocotyl elongation outputs for smart greenhouse application. We vary each of the light properties individually and then collectively to understand their effect on plant development. Our analyses show in comparison to the nominal value, the photoperiod of 18 hours, period of 24 hours, no light offset, phase of dawn of 0 hour, duration of twilight of 0.05 hour and a reduced light intensity of 1% are able to improve by at least 30% in days to flower (from 32.52 days to 20.61 days) and hypocotyl length (from 1.90 mm to 1.19mm) with the added benefit of reducing energy consumption by at least 15% (from 4.27 MWh/year to 3.62 MWh/year). These findings could provide beneficial solutions to the smart greenhouse farming industries in terms of achieving enhanced productivity while consuming less energy.