A temporal switch model for estimating transcriptional activity in gene expression

Motivation: The analysis and mechanistic modelling of time series gene expression data provided by techniques such as microarrays, NanoString, reverse transcription–polymerase chain reaction and advanced sequencing are invaluable for developing an understanding of the variation in key biological processes. We address this by proposing the estimation of a flexible dynamic model, which decouples temporal synthesis and degradation of mRNA and, hence, allows for transcriptional activity to switch between different states. Results: The model is flexible enough to capture a variety of observed transcriptional dynamics, including oscillatory behaviour, in a way that is compatible with the demands imposed by the quality, time-resolution and quantity of the data. We show that the timing and number of switch events in transcriptional activity can be estimated alongside individual gene mRNA stability with the help of a Bayesian reversible jump Markov chain Monte Carlo algorithm. To demonstrate the methodology, we focus on modelling the wild-type behaviour of a selection of 200 circadian genes of the model plant Arabidopsis thaliana. The results support the idea that using a mechanistic model to identify transcriptional switch points is likely to strongly contribute to efforts in elucidating and understanding key biological processes, such as transcription and degradation

Robustness from flexibility in the fungal circadian clock

Background Robustness is a central property of living systems, enabling function to be maintained against environmental perturbations. A key challenge is to identify the structures in biological circuits that confer system-level properties such as robustness. Circadian clocks allow organisms to adapt to the predictable changes of the 24-hour day/night cycle by generating endogenous rhythms that can be entrained to the external cycle. In all organisms, the clock circuits typically comprise multiple interlocked feedback loops controlling the rhythmic expression of key genes. Previously, we showed that such architectures increase the flexibility of the clock's rhythmic behaviour. We now test the relationship between flexibility and robustness, using a mathematical model of the circuit controlling conidiation in the fungus Neurospora crassa. Results The circuit modelled in this work consists of a central negative feedback loop, in which the frequency (frq) gene inhibits its transcriptional activator white collar-1 (wc-1), interlocked with a positive feedback loop in which FRQ protein upregulates WC-1 production. Importantly, our model reproduces the observed entrainment of this circuit under light/dark cycles with varying photoperiod and cycle duration. Our simulations show that whilst the level of frq mRNA is driven directly by the light input, the falling phase of FRQ protein, a molecular correlate of conidiation, maintains a constant phase that is uncoupled from the times of dawn and dusk. The model predicts the behaviour of mutants that uncouple WC-1 production from FRQ's positive feedback, and shows that the positive loop enhances the buffering of conidiation phase against seasonal photoperiod changes. This property is quantified using Kitano's measure for the overall robustness of a regulated system output. Further analysis demonstrates that this functional robustness is a consequence of the greater evolutionary flexibility conferred on the circuit by the interlocking loop structure. Conclusions Our model shows that the behaviour of the fungal clock in light-dark cycles can be accounted for by a transcription-translation feedback model of the central FRQ-WC oscillator. More generally, we provide an example of a biological circuit in which greater flexibility yields improved robustness, while also introducing novel sensitivity analysis techniques applicable to a broader range of cellular oscillators

Direct measurement of transcription rates reveals multiple mechanisms for configuration of the Arabidopsis ambient temperature response

Background Sensing and responding to ambient temperature is important for controlling growth and development of many organisms, in part by regulating mRNA levels. mRNA abundance can change with temperature, but it is unclear whether this results from changes in transcription or decay rates, and whether passive or active temperature regulation is involved. Results Using a base analog labelling method, we directly measured the temperature coefficient, Q10, of mRNA synthesis and degradation rates of the Arabidopsis transcriptome. We show that for most genes, transcript levels are buffered against passive increases in transcription rates by balancing passive increases in the rate of decay. Strikingly, for temperature-responsive transcripts, increasing temperature raises transcript abundance primarily by promoting faster transcription relative to decay and not vice versa, suggesting a global transcriptional process exists that controls mRNA abundance by temperature. This is partly accounted for by gene body H2A.Z which is associated with low transcription rate Q10, but is also influenced by other marks and transcription factor activities. Conclusions Our data show that less frequent chromatin states can produce temperature responses simply by virtue of their rarity and the difference between their thermal properties and those of the most common states, and underline the advantages of directly measuring transcription rate changes in dynamic systems, rather than inferring rates from changes in mRNA abundance. Background The mechanism for ambient temperature sensing in plants is unclear. Control of transcript levels is believed to be important in responses to temperature [1-4] but affects of ambient temperature on transcription and mRNA decay rates have not been measured. According to the work of Arrhenius [5] the temperature coefficient (Q10) of biochemical reactions is expected to be 2 to 3 at biological temperatures: yet less than 2% of Arabidopsis thaliana genes have a two-fold or greater difference in expression level between 17°C and 27°C [6]. The remaining genes either have rates buffered against changing temperatures, or passive increases in transcription rate must be offset by a balanced increase in decay rate, leading to higher turnover but static steady state levels. Despite this fundamental uncertainty, steady state transcriptomic responses to ambient temperature have been used to infer a role for chromatin modifications in temperature signaling [2,7]. 4-Thiouracil (4SU) is a non-toxic base analogue that has been shown to be incorporated into mammalian and yeast mRNA during transcription [8-12]. Biotinylation and column separation allow 4SU-labeled RNA to be separated from unlabeled RNA, and transcriptomic analysis using the separated samples can be used to simultaneously calculate mRNA synthesis and decay rates [8]. Here we use 4SU labeling to measure transcription rates and determine the Q10 genome-wide of mRNA synthesis and decay rates in Arabidopsis thaliana. We show that ambient temperature has large passive effects on both mRNA synthesis and decay rates, and that where temperature controls transcript abundance it does so by regulating transcription relative to decay and not vice versa. Our analysis suggests that transcription factor binding sites and epigenetic state combine to create a complex network of temperature responses in plants. Results Cells incorporate 4SU into RNA and this has been exploited in mammalian cells [8,11,12] and in yeast [13] to measure mRNA synthesis and decay rates. In order to determine whether plants can take up 4SU we floated intact seedlings in MS medium and monitored 4SU incorporation into RNA by biotinylation and dot blot (Figure S1a in Additional file 1). This clearly showed that plants incorporate 4SU from the environment into RNA and that concentrations as low as 1 mM lead to a signal detectable above background within 1 hour (Figure 1B). The resulting RNA could be separated from unlabeled RNA by biotinylation and passage through a streptavidin column as described previously. At 1.5 mM the flow-through can be depleted of detectable 4SU-labeled RNA, whilst labeled plant RNA is highly concentrated in the fraction recovered from the column [8,13] (Figure S1c in Additional file 1). To maximize recovery we chose a low concentration of 4SU at 1.5 mM [8] as high labeling frequencies are known to lead to binding of fewer more frequently labeled transcripts to the columns and reduce recovery. At this concentration Arabidopsis plants treated with 4SU showed the same growth and survival as control plants (Figure S2a in Additional file 1), suggesting 4SU has low toxicity in plants, as in other organisms. Therefore, 4SU dynamics in Arabidopsis seedlings resemble those described for other experimental systems. Preliminary experiments showed that RNA turnover was faster at 27°C compared to 12°C (Figure S2b in Additional file 1), suggesting that temperature generally affected transcription rates

Cyclical population dynamics of automatic versus controlled processing : an evolutionary pendulum

Psychologists, neuroscientists, and economists often conceptualize decisions as arising from processes that lie along a continuum from automatic (i.e., “hardwired” or over-learned, but relatively inflexible) to controlled (less efficient and effortful, but more flexible). Control is central to human cognition, and plays a key role in our ability to modify the world to suit our needs. Given its advantages, reliance on controlled processing may seem predestined to increase within the population over time. Here, we examine whether this is so by introducing an evolutionary game theoretic model of agents that vary in their use of automatic versus controlled processes, and in which cognitive processing modifies the environment in which the agents interact. We find that, under a wide range of parameters and model assumptions, cycles emerge in which the prevalence of each type of processing in the population oscillates between two extremes. Rather than inexorably increasing, the emergence of control often creates conditions that lead to its own demise by allowing automaticity to also flourish, thereby undermining the progress made by the initial emergence of controlled processing. We speculate that this observation may have relevance for understanding similar cycles across human history, and may lend insight into some of the circumstances and challenges currently faced by our species

Cluster approximations for infection dynamics on random networks

In this paper, we consider a simple stochastic epidemic model on large regular random graphs and the stochastic process that corresponds to this dynamics in the standard pair approximation. Using the fact that the nodes of a pair are unlikely to share neighbors, we derive the master equation for this process and obtain from the system size expansion the power spectrum of the fluctuations in the quasi-stationary state. We show that whenever the pair approximation deterministic equations give an accurate description of the behavior of the system in the thermodynamic limit, the power spectrum of the fluctuations measured in long simulations is well approximated by the analytical power spectrum. If this assumption breaks down, then the cluster approximation must be carried out beyond the level of pairs. We construct an uncorrelated triplet approximation that captures the behavior of the system in a region of parameter space where the pair approximation fails to give a good quantitative or even qualitative agreement. For these parameter values, the power spectrum of the fluctuations in finite systems can be computed analytically from the master equation of the corresponding stochastic process.Comment: the notation has been changed; Ref. [26] and a new paragraph in Section IV have been adde

If cooperation is likely punish mildly: Insights from economic experiments based on the snowdrift game

Punishment may deter antisocial behavior. Yet to punish is costly, and the costs often do not offset the gains that are due to elevated levels of cooperation. However, the effectiveness of punishment depends not only on how costly it is, but also on the circumstances defining the social dilemma. Using the snowdrift game as the basis, we have conducted a series of economic experiments to determine whether severe punishment is more effective than mild punishment. We have observed that severe punishment is not necessarily more effective, even if the cost of punishment is identical in both cases. The benefits of severe punishment become evident only under extremely adverse conditions, when to cooperate is highly improbable in the absence of sanctions. If cooperation is likely, mild punishment is not less effective and leads to higher average payoffs, and is thus the much preferred alternative. Presented results suggest that the positive effects of punishment stem not only from imposed fines, but may also have a psychological background. Small fines can do wonders in motivating us to chose cooperation over defection, but without the paralyzing effect that may be brought about by large fines. The later should be utilized only when absolutely necessary.Comment: 15 pages, 6 figures; accepted for publication in PLoS ON

Benevolent characteristics promote cooperative behaviour among humans

Cooperation is fundamental to the evolution of human society. We regularly observe cooperative behaviour in everyday life and in controlled experiments with anonymous people, even though standard economic models predict that they should deviate from the collective interest and act so as to maximise their own individual payoff. However, there is typically heterogeneity across subjects: some may cooperate, while others may not. Since individual factors promoting cooperation could be used by institutions to indirectly prime cooperation, this heterogeneity raises the important question of who these cooperators are. We have conducted a series of experiments to study whether benevolence, defined as a unilateral act of paying a cost to increase the welfare of someone else beyond one's own, is related to cooperation in a subsequent one-shot anonymous Prisoner's dilemma. Contrary to the predictions of the widely used inequity aversion models, we find that benevolence does exist and a large majority of people behave this way. We also find benevolence to be correlated with cooperative behaviour. Finally, we show a causal link between benevolence and cooperation: priming people to think positively about benevolent behaviour makes them significantly more cooperative than priming them to think malevolently. Thus benevolent people exist and cooperate more

Bridging the Divide between Manual Gating and Bioinformatics with the Bioconductor Package flowFlowJo

In flow cytometry, different cell types are usually selected or “gated” by a series of 1- or 2-dimensional geometric subsets of the measurements made on each cell. This is easily accomplished in commercial flow cytometry packages but it is difficult to work computationally with the results of this process. The ability to retrieve the results and work with both them and the raw data is critical; our experience points to the importance of bioinformatics tools that will allow us to examine gating robustness, combine manual and automated gating, and perform exploratory data analysis. To provide this capability, we have developed a Bioconductor package called flowFlowJo that can import gates defined by the commercial package FlowJo and work with them in a manner consistent with the other flow packages in Bioconductor. We present this package and illustrate some of the ways in which it can be used

Sustainable institutionalized punishment requires elimination of second-order free-riders

Although empirical and theoretical studies affirm that punishment can elevate collaborative efforts, its emergence and stability remain elusive. By peer-punishment the sanctioning is something an individual elects to do depending on the strategies in its neighborhood. The consequences of unsustainable efforts are therefore local. By pool-punishment, on the other hand, where resources for sanctioning are committed in advance and at large, the notion of sustainability has greater significance. In a population with free-riders, punishers must be strong in numbers to keep the "punishment pool" from emptying. Failure to do so renders the concept of institutionalized sanctioning futile. We show that pool-punishment in structured populations is sustainable, but only if second-order free-riders are sanctioned as well, and to a such degree that they cannot prevail. A discontinuous phase transition leads to an outbreak of sustainability when punishers subvert second-order free-riders in the competition against defectors.Comment: 7 two-column pages, 3 figures; accepted for publication in Scientific Report

A Phase Front Instability in Periodically Forced Oscillatory Systems

Multiplicity of phase states within frequency locked bands in periodically forced oscillatory systems may give rise to front structures separating states with different phases. A new front instability is found within bands where $\omega_{forcing}/\omega_{system}=2n$ ($n>1$). Stationary fronts shifting the oscillation phase by $\pi$ lose stability below a critical forcing strength and decompose into $n$ traveling fronts each shifting the phase by $\pi/n$. The instability designates a transition from stationary two-phase patterns to traveling $n$-phase patterns