Alexandra Pokhilko

The clock gene circuit in Arabidopsis includes a repressilator with additional feedback loops

Circadian clocks synchronise biological processes with the day/night cycle, using molecular mechanisms that include interlocked, transcriptional feedback loops. Recent experiments identified the evening complex (EC) as a repressor that can be essential for gene expression rhythms in plants. Integrating the EC components in this role significantly alters our mechanistic, mathematical model of the clock gene circuit. Negative autoregulation of the EC genes constitutes the clocks evening loop, replacing the hypothetical component Y. The EC explains our earlier conjecture that the morning gene PSEUDO‐RESPONSE REGULATOR 9 was repressed by an evening gene, previously identified with TIMING OF CAB EXPRESSION1 (TOC1). Our computational analysis suggests that TOC1 is a repressor of the morning genes LATE ELONGATED HYPOCOTYL and CIRCADIAN CLOCK ASSOCIATED1 rather than an activator as first conceived. This removes the necessity for the unknown component X (or TOC1mod) from previous clock models. As well as matching timeseries and phase‐response data, the model provides a new conceptual framework for the plant clock that includes a three‐component repressilator circuit in its complex structure.

Mapping the Core of the Arabidopsis Circadian Clock Defines the Network Structure of the Oscillator

Tic TOC1 Plant Clock The molecular clocks intertwined with cellular physiology regulate daily cycles. In plants, these circadian rhythms affect processes as diverse as carbon metabolism and leaf orientation. Huang et al. (p. 75, published online 8 March) have now analyzed the interactions driven by a key element of the circadian clock in plants, TOC1 (“TIMING OF CAB EXPRESSION 1”). TOC1 helps to coordinate responses of the morning and evening cycles, functioning to repress activity of other clock components. Morning and evening components of circadian rhythms are coordinated and stabilized by a repressor. In many organisms, the circadian clock is composed of functionally coupled morning and evening oscillators. In Arabidopsis, oscillator coupling relies on a core loop in which the evening oscillator component TIMING OF CAB EXPRESSION 1 (TOC1) was proposed to activate a subset of morning-expressed oscillator genes. Here, we show that TOC1 does not function as an activator but rather as a general repressor of oscillator gene expression. Repression occurs through TOC1 rhythmic association to the promoters of the oscillator genes. Hormone-dependent induction of TOC1 and analysis of RNA interference plants show that TOC1 prevents the activation of morning-expressed genes at night. Our study overturns the prevailing model of the Arabidopsis circadian clock, showing that the morning and evening oscillator loops are connected through the repressing activity of TOC1.

Dynamics of Cdc42 network embodies a Turing-type mechanism of yeast cell polarity

Complex biochemical networks can be understood by identifying their principal regulatory motifs and mode of action. We model the early phase of budding yeast cellular polarization and show that the biochemical processes in the presumptive bud site comprise a Turing‐type mechanism. The roles of the prototypical activator and substrate are played by GTPase Cdc42 in its active and inactive states, respectively. We demonstrate that the nucleotide cycling of Cdc42 converts cellular energy into a stable cluster of activated Cdc42. This energy drives a continuous membrane‐cytoplasmic exchange of the cluster components to counteract diffusive spread of the cluster. This exchange explains why only one bud forms per cell cycle, because the winner‐takes‐all competition of candidate sites inevitably selects a single site.

Temporal repression of core circadian genes is mediated through EARLY FLOWERING 3 in Arabidopsis

Summary The circadian clock provides robust, ∼24 hr biological rhythms throughout the eukaryotes. The clock gene circuit in plants comprises interlocking transcriptional feedback loops, reviewed in [1], whereby the morning-expressed transcription factors CIRCADIAN CLOCK-ASSOCIATED 1 (CCA1) and LATE ELONGATED HYPOCOTYL (LHY) repress the expression of evening genes, notably TIMING OF CAB EXPRESSION 1 (TOC1). EARLY FLOWERING 3 (ELF3) has been implicated as a repressor of light signaling to the clock [2, 3] and, paradoxically, as an activator of the light-induced genes CCA1 and LHY [4, 5]. We use cca1-11 lhy-21 elf3-4 plants to separate the repressive function of ELF3 from its downstream targets CCA1 and LHY. We further demonstrate that ELF3 associates physically with the promoter of PSEUDO-RESPONSE REGULATOR 9 (PRR9), a repressor of CCA1 and LHY expression, in a time-dependent fashion. The repressive function of ELF3 is thus consistent with indirect activation of LHY and CCA1, in a double-negative connection via a direct ELF3 target, PRR9. This mechanism reconciles the functions of ELF3 in the clock network during the night and points to further effects of ELF3 during the day.

Data assimilation constrains new connections and components in a complex, eukaryotic circadian clock model

Circadian clocks generate 24‐h rhythms that are entrained by the day/night cycle. Clock circuits include several light inputs and interlocked feedback loops, with complex dynamics. Multiple biological components can contribute to each part of the circuit in higher organisms. Mechanistic models with morning, evening and central feedback loops have provided a heuristic framework for the clock in plants, but were based on transcriptional control. Here, we model observed, post‐transcriptional and post‐translational regulation and constrain many parameter values based on experimental data. The models feedback circuit is revised and now includes PSEUDO‐RESPONSE REGULATOR 7 (PRR7) and ZEITLUPE. The revised model matches data in varying environments and mutants, and gains robustness to parameter variation. Our results suggest that the activation of important morning‐expressed genes follows their release from a night inhibitor (NI). Experiments inspired by the new model support the predicted NI function and show that the PRR5 gene contributes to the NI. The multiple PRR genes of Arabidopsis uncouple events in the late night from light‐driven responses in the day, increasing the flexibility of rhythmic regulation.

Quantitative analysis of regulatory flexibility under changing environmental conditions

The circadian clock controls 24‐h rhythms in many biological processes, allowing appropriate timing of biological rhythms relative to dawn and dusk. Known clock circuits include multiple, interlocked feedback loops. Theory suggested that multiple loops contribute the flexibility for molecular rhythms to track multiple phases of the external cycle. Clear dawn‐ and dusk‐tracking rhythms illustrate the flexibility of timing in Ipomoea nil. Molecular clock components in Arabidopsis thaliana showed complex, photoperiod‐dependent regulation, which was analysed by comparison with three contrasting models. A simple, quantitative measure, Dusk Sensitivity, was introduced to compare the behaviour of clock models with varying loop complexity. Evening‐expressed clock genes showed photoperiod‐dependent dusk sensitivity, as predicted by the three‐loop model, whereas the one‐ and two‐loop models tracked dawn and dusk, respectively. Output genes for starch degradation achieved dusk‐tracking expression through light regulation, rather than a dusk‐tracking rhythm. Model analysis predicted which biochemical processes could be manipulated to extend dusk tracking. Our results reveal how an operating principle of biological regulators applies specifically to the plant circadian clock.

Modelling the widespread effects of TOC1 signalling on the plant circadian clock and its outputs

Background24-hour biological clocks are intimately connected to the cellular signalling network, which complicates the analysis of clock mechanisms. The transcriptional regulator TOC1 (TIMING OF CAB EXPRESSION 1) is a founding component of the gene circuit in the plant circadian clock. Recent results show that TOC1 suppresses transcription of multiple target genes within the clock circuit, far beyond its previously-described regulation of the morning transcription factors LHY (LATE ELONGATED HYPOCOTYL) and CCA1 (CIRCADIAN CLOCK ASSOCIATED 1). It is unclear how this pervasive effect of TOC1 affects the dynamics of the clock and its outputs. TOC1 also appears to function in a nested feedback loop that includes signalling by the plant hormone Abscisic Acid (ABA), which is upregulated by abiotic stresses, such as drought. ABA treatments both alter TOC1 levels and affect the clock’s timing behaviour. Conversely, the clock rhythmically modulates physiological processes induced by ABA, such as the closing of stomata in the leaf epidermis. In order to understand the dynamics of the clock and its outputs under changing environmental conditions, the reciprocal interactions between the clock and other signalling pathways must be integrated.ResultsWe extended the mathematical model of the plant clock gene circuit by incorporating the repression of multiple clock genes by TOC1, observed experimentally. The revised model more accurately matches the data on the clock’s molecular profiles and timing behaviour, explaining the clock’s responses in TOC1 over-expression and toc1 mutant plants. A simplified representation of ABA signalling allowed us to investigate the interactions of ABA and circadian pathways. Increased ABA levels lengthen the free-running period of the clock, consistent with the experimental data. Adding stomatal closure to the model, as a key ABA- and clock-regulated downstream process allowed to describe TOC1 effects on the rhythmic gating of stomatal closure.ConclusionsThe integrated model of the circadian clock circuit and ABA-regulated environmental sensing allowed us to explain multiple experimental observations on the timing and stomatal responses to genetic and environmental perturbations. These results crystallise a new role of TOC1 as an environmental sensor, which both affects the pace of the central oscillator and modulates the kinetics of downstream processes.

Computational model explains high activity and rapid cycling of Rho GTPases within protein complexes.

Formation of multiprotein complexes on cellular membranes is critically dependent on the cyclic activation of small GTPases. FRAP-based analyses demonstrate that within protein complexes, some small GTPases cycle nearly three orders of magnitude faster than they would spontaneously cycle in vitro. At the same time, experiments report concomitant excess of the activated, GTP-bound form of GTPases over their inactive form. Intuitively, high activity and rapid turnover are contradictory requirements. How the cells manage to maximize both remains poorly understood. Here, using GTPases of the Rab and Rho families as a prototype, we introduce a computational model of the GTPase cycle. We quantitatively investigate several plausible layouts of the cycling control module that consist of GEFs, GAPs, and GTPase effectors. We explain the existing experimental data and predict how the cycling of GTPases is controlled by the regulatory proteins in vivo. Our model explains distinct and separable roles that the activating GEFs and deactivating GAPs play in the GTPase cycling control. While the activity of GTPase is mainly defined by GEF, the turnover rate is a sole function of GAP. Maximization of the GTPase activity and turnover rate places conflicting requirements on the concentration of GAP. Therefore, to achieve a high activity and turnover rate at once, cells must carefully maintain concentrations of GEFs and GAPs within the optimal range. The values of these optimal concentrations indicate that efficient cycling can be achieved only within dense protein complexes typically assembled on the membrane surfaces. We show that the concentration requirement for GEF can be dramatically reduced by a GEF-activating GTPase effector that can also significantly boost the cycling efficiency. Interestingly, we find that the cycling regimes are only weakly dependent on the concentration of GTPase itself.

Stochastic properties of the plant circadian clock

Circadian clocks are gene regulatory networks whose role is to help the organisms to cope with variations in environmental conditions such as the day/night cycle. In this work, we explored the effects of molecular noise in single cells on the behaviour of the circadian clock in the plant model species Arabidopsis thaliana. The computational modelling language Bio-PEPA enabled us to give a stochastic interpretation of an existing deterministic model of the clock, and to easily compare the results obtained via stochastic simulation and via numerical solution of the deterministic model. First, the introduction of stochasticity in the model allowed us to estimate the unknown size of the system. Moreover, stochasticity improved the description of the available experimental data in several light conditions: noise-induced fluctuations yield a faster entrainment of the plant clock under certain photoperiods and are able to explain the experimentally observed dampening of the oscillations in plants under constant light conditions. The model predicts that the desynchronization between noisy oscillations in single cells contributes to the observed damped oscillations at the level of the cell population. Analysis of the phase, period and amplitude distributions under various light conditions demonstrated robust entrainment of the plant clock to light/dark cycles which closely matched the available experimental data.

Ubiquitin ligase switch in plant photomorphogenesis: A hypothesis.

The E3 ubiquitin ligase COP1 (CONSTITUTIVE PHOTOMORPHOGENIC1) plays a key role in the repression of the plant photomorphogenic development in darkness. In the presence of light, COP1 is inactivated by a mechanism which is not completely understood. This leads to accumulation of COP1’s target transcription factors, which initiates photomorphogenesis, resulting in dramatic changes of the seedling’s physiology. Here we use a mathematical model to explore the possible mechanism of COP1 modulation upon dark/light transition in Arabidopsis thaliana based upon data for two COP1 target proteins: HY5 and HFR1, which play critical roles in photomorphogenesis. The main reactions in our model are the inactivation of COP1 by a proposed photoreceptor-related inhibitor I and interactions between COP1 and a CUL4 (CULLIN4)-based ligase. For building and verification of the model, we used the available published and our new data on the kinetics of HY5 and HFR1 together with the data on COP1 abundance. HY5 has been shown to accumulate at a slower rate than HFR1. To describe the observed differences in the timecourses of the “slow” target HY5 and the “fast” target HFR1, we hypothesize a switch between the activities of COP1 and CUL4 ligases upon dark/light transition, with COP1 being active mostly in darkness and CUL4 in light. The model predicts a bi-phasic kinetics of COP1 activity upon the exposure of plants to light, with its restoration after the initial decline and the following slow depletion of the total COP1 content. CUL4 activity is predicted to increase in the presence of light. We propose that the ubiquitin ligase switch is important for the complex regulation of multiple transcription factors during plants development. In addition, this provides a new mechanism for sensing the duration of light period, which is important for seasonal changes in plant development.