Molecular ​​time-sharing ​​through​​ dynamic ​​pulsing ​​in ​​single ​​cells

n cells, specific regulators often compete for limited amounts of a core enzymatic resource. It is typically assumed that competition leads to partitioning of core enzyme molecules among regulators at constant levels. Alternatively, however, different regulatory species could time share, or take turns utilizing, the core resource. Using quantitative time-lapse microscopy, we analyzed sigma factor activity dynamics, and their competition for RNA polymerase, in individual Bacillus subtilis cells under energy stress. Multiple alternative sigma factors were activated in ∼1-hr pulses in stochastic and repetitive fashion. Pairwise analysis revealed that two sigma factors rarely pulse simultaneously and that some pairs are anti-correlated, indicating that RNAP utilization alternates among different sigma factors. Mathematical modeling revealed how stochastic time-sharing dynamics can emerge from pulse-generating sigma factor regulatory circuits actively competing for RNAP. Time sharing provides a mechanism for cells to dynamically control the distribution of cell states within a population. Since core molecular components are limiting in many other systems, time sharing may represent a general mode of regulation

Reducing the complexity of mathematical models for the plant circadian clock by distributed delays

This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this record.A major bottleneck in the modelling of biological networks is the parameter explosion problem – the exponential increase in the number of parameters that need to be optimised to data as the size of the model increases. Here, we address this problem in the context of the plant circadian clock by applying the method of distributed delays. We show that using this approach, the system architecture can be simplified efficiently – reducing the number of parameters – whilst still preserving the core mechanistic dynamics of the gene regulatory network. Compared to models with discrete time-delays, which are governed by functional differential equations, the distributed delay models can be converted into sets of equivalent ordinary differential equations, enabling the use of standard methods for numerical integration, and for stability and bifurcation analyses. We demonstrate the efficiency of our modelling approach by applying it to three exemplar mathematical models of the Arabidopsis circadian clock of varying complexity, obtaining significant reductions in complexity in each case. Moreover, we revise one of the most up-to-date Arabidopsis models, updating the regulation of the PRR9 and PRR7 genes by LHY in accordance with recent experimental data. The revised model more accurately reproduces the LHY-induction experiments of core clock genes, compared with the original model. Our work thus shows that the method of distributed delays facilitates the optimisation and reformulation of genetic network models.Engineering and Physical Sciences Research Council (EPSRC)Japan Society for the Promotion of Science (JSPS)Gatsby Foundatio

Nitrate modulates stem cell dynamics in Arabidopsis shoot meristems through cytokinins

The shoot apical meristem (SAM) is responsible for the generation of all of the aerial parts of plants. Given its critical role, dynamical changes in SAM activity should play a central role in the adaptation of plant architecture to the environment. Using quantitative microscopy, grafting experiments and genetic perturbations, we connect the plant environment to the SAM, by describing the molecular mechanism by which cytokinins signal the level of nutrient availability to the SAM. We show that a systemic signal of cytokinin precursors mediates the adaptation of SAM size and organogenesis rate to the availability of mineral nutrients by modulating the expression of WUSCHEL, a key regulator of stem cell homeostasis. In time- lapse experiments, we further show that this mechanism allows meristems to adapt to rapid changes in nitrate concentration, and thereby modulate their rate of organ production to the availability of mineral nutrients within a few days. Our work sheds new light on the role of the stem cell regulatory network, by showing that it does not only maintain meristem homeostasis but also allows plants to adapt to rapid changes in the environment.This work is supported by the Gatsby Charitable Foundation [fellowship GAT3395/DAA (to E.M.M.), GAT3272/GLC (to J.C.W.L.), and GAT3395-PR4 (to H.J.)]. E.M.M. also acknowledges support from the Howard Hughes Medical Institute and the Gordon and Betty Moore Foundation (through Grant GBMF3406). Research in the laboratory of J.C.W.L. was made possible by the award of a European Research Council under the European Union’s Seventh Framework Programme (FP/2007-2013)/ERC Grant Agreement 338060. P.F.-J. acknowledges a postdoctoral fellowship provided by the Herchel Smith Foundation

Robustness of circadian clocks to daylight fluctuations: hints from the picoeucaryote Ostreococcus tauri

The development of systemic approaches in biology has put emphasis on identifying genetic modules whose behavior can be modeled accurately so as to gain insight into their structure and function. However most gene circuits in a cell are under control of external signals and thus quantitative agreement between experimental data and a mathematical model is difficult. Circadian biology has been one notable exception: quantitative models of the internal clock that orchestrates biological processes over the 24-hour diurnal cycle have been constructed for a few organisms, from cyanobacteria to plants and mammals. In most cases, a complex architecture with interlocked feedback loops has been evidenced. Here we present first modeling results for the circadian clock of the green unicellular alga Ostreococcus tauri. Two plant-like clock genes have been shown to play a central role in Ostreococcus clock. We find that their expression time profiles can be accurately reproduced by a minimal model of a two-gene transcriptional feedback loop. Remarkably, best adjustment of data recorded under light/dark alternation is obtained when assuming that the oscillator is not coupled to the diurnal cycle. This suggests that coupling to light is confined to specific time intervals and has no dynamical effect when the oscillator is entrained by the diurnal cycle. This intringuing property may reflect a strategy to minimize the impact of fluctuations in daylight intensity on the core circadian oscillator, a type of perturbation that has been rarely considered when assessing the robustness of circadian clocks

Global parameter search reveals design principles of the mammalian circadian clock

Background: Virtually all living organisms have evolved a circadian (~24 hour) clock that controls physiological and behavioural processes with exquisite precision throughout the day/night cycle. The suprachiasmatic nucleus (SCN), which generates these ~24 h rhythms in mammals, consists of several thousand neurons. Each neuron contains a gene-regulatory network generating molecular oscillations, and the individual neuron oscillations are synchronised by intercellular coupling, presumably via neurotransmitters. Although this basic mechanism is currently accepted and has been recapitulated in mathematical models, several fundamental questions about the design principles of the SCN remain little understood. For example, a remarkable property of the SCN is that the phase of the SCN rhythm resets rapidly after a 'jet lag' type experiment, i.e. when the light/ dark (LD) cycle is abruptly advanced or delayed by several hours. Results: Here, we describe an extensive parameter optimization of a previously constructed simplified model of the SCN in order to further understand its design principles. By examining the top 50 solutions from the parameter optimization, we show that the neurotransmitters' role in generating the molecular circadian rhythms is extremely important. In addition, we show that when a neurotransmitter drives the rhythm of a system of coupled damped oscillators, it exhibits very robust synchronization and is much more easily entrained to light/dark cycles. We were also able to recreate in our simulations the fast rhythm resetting seen after a 'jet lag' type experiment. Conclusion: Our work shows that a careful exploration of parameter space for even an extremely simplified model of the mammalian clock can reveal unexpected behaviours and non-trivial predictions. Our results suggest that the neurotransmitter feedback loop plays a crucial role in the robustness and phase resetting properties of the mammalian clock, even at the single neuron level

Evolving Sensitivity Balances Boolean Networks

We investigate the sensitivity of Boolean Networks (BNs) to mutations. We are interested in Boolean Networks as a model of Gene Regulatory Networks (GRNs). We adopt Ribeiro and Kauffman’s Ergodic Set and use it to study the long term dynamics of a BN. We define the sensitivity of a BN to be the mean change in its Ergodic Set structure under all possible loss of interaction mutations. Insilico experiments were used to selectively evolve BNs for sensitivity to losing interactions. We find that maximum sensitivity was often achievable and resulted in the BNs becoming topologically balanced, i.e. they evolve towards network structures in which they have a similar number of inhibitory and excitatory interactions. In terms of the dynamics, the dominant sensitivity strategy that evolved was to build BNs with Ergodic Sets dominated by a single long limit cycle which is easily destabilised by mutations. We discuss the relevance of our findings in the context of Stem Cell Differentiation and propose a relationship between pluripotent stem cells and our evolved sensitive networks

Listen to genes : dealing with microarray data in the frequency domain

Background: We present a novel and systematic approach to analyze temporal microarray data. The approach includes normalization, clustering and network analysis of genes. Methodology: Genes are normalized using an error model based uniform normalization method aimed at identifying and estimating the sources of variations. The model minimizes the correlation among error terms across replicates. The normalized gene expressions are then clustered in terms of their power spectrum density. The method of complex Granger causality is introduced to reveal interactions between sets of genes. Complex Granger causality along with partial Granger causality is applied in both time and frequency domains to selected as well as all the genes to reveal the interesting networks of interactions. The approach is successfully applied to Arabidopsis leaf microarray data generated from 31,000 genes observed over 22 time points over 22 days. Three circuits: a circadian gene circuit, an ethylene circuit and a new global circuit showing a hierarchical structure to determine the initiators of leaf senescence are analyzed in detail. Conclusions: We use a totally data-driven approach to form biological hypothesis. Clustering using the power-spectrum analysis helps us identify genes of potential interest. Their dynamics can be captured accurately in the time and frequency domain using the methods of complex and partial Granger causality. With the rise in availability of temporal microarray data, such methods can be useful tools in uncovering the hidden biological interactions. We show our method in a step by step manner with help of toy models as well as a real biological dataset. We also analyse three distinct gene circuits of potential interest to Arabidopsis researchers

Nitrate modulates stem cell dynamics in Arabidopsis shoot meristems through cytokinins

The shoot apical meristem (SAM) is responsible for the generation of all the aerial parts of plants. Given its critical role, dynamical changes in SAM activity should play a central role in the adaptation of plant architecture to the environment. Using quantitative microscopy, grafting experiments, and genetic perturbations, we connect the plant environment to the SAM by describing the molecular mechanism by which cytokinins signal the level of nutrient availability to the SAM. We show that a systemic signal of cytokinin precursors mediates the adaptation of SAM size and organogenesis rate to the availability of mineral nutrients by modulating the expression of WUSCHEL, a key regulator of stem cell homeostasis. In time-lapse experiments, we further show that this mechanism allows meristems to adapt to rapid changes in nitrate concentration, and thereby modulate their rate of organ production to the availability of mineral nutrients within a few days. Our work sheds light on the role of the stem cell regulatory network by showing that it not only maintains meristem homeostasis but also allows plants to adapt to rapid changes in the environment

Diurnal and Circadian Rhythms in the Tomato Transcriptome and Their Modulation by Cryptochrome Photoreceptors

BACKGROUND: Circadian clocks are internal molecular time-keeping mechanisms that provide living organisms with the ability to adjust their growth and physiology and to anticipate diurnal environmental changes. Circadian clocks, without exception, respond to light and, in plants, light is the most potent and best characterized entraining stimulus. The capacity of plants to respond to light is achieved through a number of photo-perceptive proteins including cryptochromes and phytochromes. There is considerable experimental evidence demonstrating the roles of photoreceptors in providing light input to the clock. METHODOLOGY: In order to identify genes regulated by diurnal and circadian rhythms, and to establish possible functional relations between photoreceptors and the circadian clock in tomato, we monitored the temporal transcription pattern in plants entrained to long-day conditions, either by large scale comparative profiling, or using a focused approach over a number of photosensory and clock-related genes by QRT-PCR. In parallel, focused transcription analyses were performed in cry1a- and in CRY2-OX tomato genotypes. CONCLUSIONS: We report a large series of transcript oscillations that shed light on the complex network of interactions among tomato photoreceptors and clock-related genes. Alteration of cryptochrome gene expression induced major changes in the rhythmic oscillations of several other gene transcripts. In particular, over-expression of CRY2 had an impact not only on day/night fluctuations but also on rhythmicity under constant light conditions. Evidence was found for widespread diurnal oscillations of transcripts encoding specific enzyme classes (e.g. carotenoid biosynthesis enzymes) as well as for post-transcriptional diurnal and circadian regulation of the CRY2 transcript

Effects of bursty protein production on the noisy oscillatory properties of downstream pathways

Experiments show that proteins are translated in sharp bursts; similar bursty phenomena have been observed for protein import into compartments. Here we investigate the effect of burstiness in protein expression and import on the stochastic properties of downstream pathways. We consider two identical pathways with equal mean input rates, except in one pathway proteins are input one at a time and in the other proteins are input in bursts. Deterministically the dynamics of these two pathways are indistinguishable. However the stochastic behavior falls in three categories: (i) both pathways display or do not display noise-induced oscillations; (ii) the non-bursty input pathway displays noise-induced oscillations whereas the bursty one does not; (iii) the reverse of (ii). We derive necessary conditions for these three cases to classify systems involving autocatalysis, trimerization and genetic feedback loops. Our results suggest that single cell rhythms can be controlled by regulation of burstiness in protein production