The faster we do tasks the harder it is to do them well. For example, when we wish to judge if, say, a cup, is too hot, we first quickly withdraw our hand after touching it: we know that the cup is hot but not how much. Next we hold a finger against the cup to accurately judge its temperature. Such speed-accuracy trade-offs are studied widely in fields ranging from neuroscience to engineering, but their consequences for single cells are unknown. This is despite the fact that when cells are exposed to stress they must respond both quickly (to survive) and accurately (to reduce how many resources they consume).

One way of stressing yeast cells is to place them in a syrupy substance called sorbitol. This causes the cells to lose water, shrink in size, and launch a stress response to regain volume. If the cells respond inappropriately to the situation, they may die.

The signalling network that produces the stress response is unusual in that it has a Y-shaped structure, where the two ‘arms’ of the Y are the input pathways. Although it was known that one input pathway responds to stress faster than the other, the advantages of having two inputs in the signalling network were not understood. Granados, Crane et al. thought that the differences in speed and the Y-shaped structure could allow the cell to respond to stress with both speed and accuracy.

To investigate this theory, Granados, Crane et al. used a microscope to study individual yeast cells that had been exposed to sorbitol. Combining these results with a mathematical model of the cell signalling network revealed that a mutant yeast cell that only has one of the input pathways specializes in speed but is inaccurate, similar to a reflex-like response. In contrast, a mutant with only the other pathway specializes in accuracy, being slower but matching the level of the cell’s response to the level of stress placed on it. This trade-off is reflected in rates of cell survival: the first mutant survives best in sudden shocks of stress; the second mutant survives best in gradually increasing stress. Normal yeast cells that have both input pathways survive more often than either mutant.

Overall, the results presented by Granados, Crane et al. reveal principles behind cellular decision-making that should hold true in more complex organisms and could be exploited by synthetic biologists to programme cells with new behaviours.

Cells must adapt to changes in their environment and to do so specialise their response to the nature of the signal being detected. Improving performance in one task, however, often undermines performance in another (Pareto, 1896). In engineering, for example, it is well-known that fast responses have lower accuracy and that higher amplifications can cause overshooting and unintended oscillations (Astrom and Murray, 2008).

At the cellular level, we expect signal transduction has evolved to reduce such trade-offs because performance in, for example, both speed and accuracy are likely to be under selection (Shoval et al., 2012; Lan et al., 2012; Siggia and Vergassola, 2013). In particular, stress responses can not only be a life-and-death situation where a too slow response is fatal, but also often lead to the consumption of substantial cellular resources so that cells must accurately coordinate their response with the stress (López-Maury et al., 2008; Perkins and Swain, 2009). To maintain accuracy, we can think of cells having to continuously match the degree of activation of signalling networks with both their internal state and with the magnitude and type of extracellular signals. By doing so, cells can then correctly ‘interpret’ the environment and launch and modify the appropriate response at the appropriate level.

To understand how cells mitigate trade-offs in signalling, we turned to one of the most studied eukaryotic stress responses: hyperosmotic stress in budding yeast. Following an abrupt increase in environmental osmolarity, yeast cells can shrink in seconds (Hohmann, 2002) and must therefore respond quickly. Their response though is metabolically costly, involving the synthesis of the osmoprotectant glycerol, and inaccurate hyperactivation of the signalling network can be highly deleterious (Tao et al., 1999; Mitchell et al., 2015).

When the osmolarity of the environment increases, yeast activate a p38 kinase, Hog1, to launch the stress response. The Hyper-Osmolarity-Glycerol (HOG) network has a Y-shaped structure with two input pathways both converging on Pbs2, a MAP kinase kinase (Figure 1A). One branch of the Y, the Sln1 pathway, uses a two-component phosphorelay, analogous to those in bacteria, to propagate the signal (Posas et al., 1996; Posas and Saito, 1998); the other, the Sho1 branch, uses protein kinases, similar to signalling in higher organisms (Posas and Saito, 1997; Tatebayashi et al., 2006). Once activated, Pbs2 in turn activates Hog1 via phosphorylation (Brewster et al., 1993). Similarly to MAP kinases in mammalian cells, Hog1 can then translocate into the nucleus. Upon activation, Hog1 causes an increase in the intracellular concentration of glycerol, yeast’s main osmoprotectant, in two ways (Saito and Posas, 2012): first, through cytosolic changes, such as diverting glycolysis towards synthesizing glycerol and closing channels that export glycerol, and, second, through altering gene expression to increase the numbers of enzymes involved in glycerol synthesis. As levels of intracellular glycerol increase, water returns to the cell, and the cellular volume expands. This increase in volume reduces signalling through the HOG network and the levels of activation of Hog1.

Figure 1

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Despite these discoveries, the advantage of having two input pathways in the HOG network is still not understood (Tanaka et al., 2014; Brewster and Gustin, 2014). The two branches of the Y may sense stress differently (Reiser et al., 2003; Tanaka et al., 2014) and are known to operate at different time-scales (Maeda et al., 1995; Hersen et al., 2008): the Sln1 branch being faster than the Sho1 branch. These different response times imply that each pathway has the potential to respond distinctly to input signals (Behar et al., 2007) and hence generate distinct dynamics of volume recovery. Mutants that have only one branch of the Y have been created (Maeda et al., 1995; Reiser et al., 2003; Hersen et al., 2008; Macia et al., 2009; Schaber et al., 2012; English et al., 2015), but there is no reported phenotype for strains having only the Sln1 branch, and the Sho1 pathway is often considered redundant (Klipp et al., 2005; Muzzey et al., 2009).

We hypothesized that the Y-shaped structure could allow the cell to respond to stress with both speed and accuracy. Our approach was to characterize the behaviour of both Hog1 and cellular volume at the single-cell level in the wild-type and in mutants with only one of the input pathways. With both types of single-cell measurements, we can quantify accuracy by the statistical dependency between the dynamics of cellular volume and the dynamics of nuclear Hog1. We show that each input pathway specializes to a particular task and that by having the two pathways the wild-type is both fast and accurate over a wide range of dynamic environments.

To understand how the HOG network might mitigate trade-offs in performance, we measured the extent of cellular stress by the reduction of the cellular volume and the extent of activation of the HOG network by the degree of nuclear localization of Hog1. The nuclear level of Hog1 has long been used as a read-out of the HOG network’s response (Mettetal et al., 2008; Muzzey et al., 2009; Pelet et al., 2011; Babazadeh et al., 2013; Mitchell et al., 2015) and is strongly correlated with Hog1 phosphorylation (Reiser et al., 1999).

We measured the dynamics of Hog1 in the wild-type strain and in two established mutants (Hersen et al., 2008; English et al., 2015)—a ‘fast’ mutant with only the Sln1 branch (deletion of Ste11) and a ‘slow’ mutant with only the Sho1 branch (deletion of Ssk1)—at the same time and in stress with identical dynamics (Figure 1B) and quantified single-cell responses (Figure 1C–E). To impose osmotic stress, we use sorbitol (Hersen et al., 2008), which unlike salts does not apply any additional stress from toxic cations (Posas et al., 2000).

Mutants with just one of the input pathways have different accuracy

In steps of hyperosmotic stress, by far the most common type of input so far investigated (Saito and Posas, 2012), the fast (Sln1 only) mutant has been reported to perform almost identically to wild-type. We first verified that the two mutants, each with one of the branches of the Y, behave as expected (Maeda et al., 1995; Hersen et al., 2008; Macia et al., 2009). Indeed, in steps, the mean response of Hog1 in the fast mutants is equivalent to wild-type cells, but the slow mutant has typically longer response times and a lower maximum level of nuclear localization (Figure 2A).

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Considering the reduction in cellular volume, the wild-type and fast response are again almost identical on average, and the longer response time of the slow mutant is reflected in a slower volume recovery (Figure 2A), particularly in larger steps (Figure 2—figure supplement 1). In all strains, the mean volume and the mean level of nuclear Hog1 simultaneously go to zero (Figure 2A).

At the single-cell level, however, this picture changes (Figure 2B). We quantified the degree to which the cellular response matches the cellular volume—the accuracy of the response—by the statistical dependency (the Pearson correlation) between the time of adaptation of Hog1 and the time of adaptation of the volume. Cells differ in their internal states, for example in their intracellular levels of glycerol, and so the recovery of the volume reports the extent of the subjective stress experienced by each cell. To normalize between cells and for the magnitude of the step, the correlation is calculated for different fractions of the recovery of the volume (Figure 2C). Although the accuracy of all strains increases as the volume recovers, it is the wild-type and the slow mutant that behave similarly, and the correlation for the fast mutant remains consistently lower than the wild-type.

This discrepancy between the mean (Figure 2A) and the single-cell results (Figure 2C) implies that the Hog1 behaviour in the fast mutant during adaptation is more noisy than the wild-type. The variation can be quantified by the statistical dependency (the mutual information) between the adaptation times of Hog1 in single cells and the magnitude of the stress (Figure 2D). A higher mutual information implies that there is less overlap between the distributions of adaptation times for each stress (Figure 2—figure supplement 2) and therefore that the adaptation time of a typical Hog1 response is different for different levels of stress. As Hog1 adapts, Hog1 in the fast mutant becomes less informative on the level of stress and its distribution of adaptation times is broader than the wild-type for some stresses.

The two pathways therefore have contrasting behaviors: the slow pathway has a slower mean response of Hog1 but is almost as accurate as the wild-type at long times, and the fast pathway although responding the same as the wild-type on average is inaccurate at the single-cell level. Our results suggest that maintaining accuracy is principally addressed by the slow pathway, which best correlates the dynamics of Hog1 with the dynamics of the cellular volume in individual cells.

Sensitivity to the system’s negative integral feedback affects accuracy

The adaptation of Hog1 and the adaptation of the volume are connected by negative feedback (Muzzey et al., 2009). This feedback acts through intracellular glycerol. Higher intracellular concentration of glycerol cause water to move into the cell and the resulting increase in volume reduces the level of activation of the HOG network. The rate of increase in glycerol is expected to depend on the time-integral of nuclear Hog1 (Muzzey et al., 2009; English et al., 2015), and the feedback is therefore called integral feedback (Astrom and Murray, 2008).

We reasoned that if the slow mutant is able to gradually increase its accuracy (Figure 2C) then the slow pathway should be more sensitive to the integral feedback. Indeed, the slow pathway unlike the fast pathway is known to have multiple types of osmo-sensors (Tanaka et al., 2014) and so may better sense the increase in volume resulting from the increase in glycerol.

To determine the sensitivity of each pathway to the feedback, we exogenously perturbed the level of activation of the network to measure the extent to which each pathway can compensate for the perturbation. If Hog1 activity in the nucleus is reduced and the network is sensitive to the integral feedback, the system will compensate by increasing the time spent by Hog1 in the nucleus (Figure 3A) (Mettetal et al., 2008; Zi et al., 2010). We therefore expect the wild-type and the slow mutant, but not the fast, to maintain accuracy in compromised networks.

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By exogenously decreasing levels of the MAP kinase kinase Pbs2, which lies downstream of both pathways (Figure 3A), we perturbed the network’s activity and showed that the slow pathway is most sensitive to the integral feedback. Decreasing expression of PBS2 reduces the maximum level of Hog1 localization but increases its adaptation time in both the wild-type and slow mutant (Figure 3B and C). In contrast, for the fast pathway, there is little increase in the adaptation time (Figure 3D). Similarly, there is a corresponding change in the speed of the response of the slow, but not the fast, pathway indicating that the slow pathway is better coupled to the dynamics of the integral feedback. Both the ratio of adaptation time of Hog1 to the adaptation time of the volume and the accuracy decreases significantly only for the fast mutant (Figure 3D inset with p<10⁻⁶ using a two-sided Wilcoxon rank sum test for equal medians calculated by pooling distributions from single cells).

To reduce metabolic costs, cells should respond accurately to stress, matching the dynamics of their response with the dynamics of the stress and of their internal states. Our results are consistent with this task being principally performed by the slow pathway because of its stronger coupling to the system’s integral feedback.

The insensitivity of the adaptation time of Hog1 and the sensitivity of the adaptation time of the volume for the fast mutant in these experiments (Figure 3D; Figure 3—figure supplement 1) suggest the existence of a mechanism within the fast pathway that decreases signalling of Hog1 before the volume completely recovers. This additional adaptation within the pathway to a step of stress implies that the fast pathway has the potential to respond to the time-derivative of its input (Block et al., 1983; Behar et al., 2007; Alon, 2007). A derivative response, referred to as derivative action, is often used in engineering to improve performance by predicting the future behaviour of the input (Astrom and Murray, 2008).

Ramp inputs indicate derivative action within the fast pathway

A system that only senses the time-derivative of an input should continually respond to an input that ramps linearly from low to high values because such an input has a constant time-derivative (Block et al., 1983). We therefore exposed cells to inputs where stress increases gradually (Figure 4A).

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In contrast to steps, ramp inputs reveal a substantial phenotypic difference between the fast mutant and the wild-type. We observe a systematic increase in the amplitude of Hog1 in the fast mutant over that of the wild-type and the mutant responds quicker (Figure 4A and B; Figure 4—figure supplement 1). Indeed, the mean wild-type response is closer in amplitude to the slow mutant, particularly during adaptation (Figure 4A). The overshoot of the fast mutant (Figure 4C) is consistent with stronger derivative action in the fast pathway. Nevertheless, Hog1 in the fast mutant adapts despite the ramp in stress, and so the fast pathway must not only have derivative action but also respond to other aspects of the input. Indeed, linearizing a mathematical model of adaptation with negative feedback (Behar et al., 2007) shows that the network performs a time-derivative of the input in parallel with a proportional response.

We note that the wild-type response is generated by interactions between the two pathways and is not an average of their responses (Figure 4A): the maximum amplitude of the wild-type strain increases linearly with the gradient of the ramp although the response of strains with each individual pathway does not (Figure 4C).

To test further the existence of derivative action in the fast pathway, we exposed cells to fluctuating ramps, which have varying time-derivatives (Figure 4D), and determined if the response of Hog1 in each strain best correlated with either the input or the time-derivative of the input. As expected, both the fast mutant and the wild-type have the highest statistical dependency with the (smoothed) time-derivative (Figure 4E and F; Figure 4—figure supplement 1).

The cellular response to osmotic stress should be sufficiently fast to enable survival. Our results are consistent with this task being addressed principally by the fast pathway, which initiates a ‘knee-jerk’, reflex-like response, partly through derivative action, that can overshoot and be too fast in comparison to the wild-type in ramps of stress.

Interactions between the two pathways enables the wild-type response

Together our results indicate contrasting roles for the two input pathways: the slow pathway provides accuracy at the expense of speed (Figure 3); the fast pathway provides speed at the expense of accuracy (Figure 4). Further, the response to ramps of stress implies the outputs of the two pathways do not always sum to give the wild-type response (Figure 4A).

Building on previous work (Mettetal et al., 2008; Muzzey et al., 2009), we developed a modular mathematical model of the network with the aim of highlighting general principles governing how cells might balance two opposing tasks. Control theory is a natural framework to describe the modulation of cellular responses (Yi et al., 2000; El-Samad et al., 2005), and correspondingly we present the model as a block diagram (Figure 5A; Figure 5—figure supplement 1).

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Figure 5—source data 1

Parameters for the mathematical model of the HOG network.

Values for the zero-order gain and time-constants of the different components of the block diagram shown in Figure 5—figure supplement 1.

https://doi.org/10.7554/eLife.21415.013

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We modelled the Hog1 response as the output of the cell’s ’controller’ and the production of glycerol as the process being controlled. The integral feedback, which exists because glycerol affects the volume, makes the system a closed loop, and the network as whole acts to reduce the ‘error’—the difference between the intracellular osmolarity (predominately determined by glycerol) and the extracellular osmolarity (the stress or input) (Klipp et al., 2005; Muzzey et al., 2009).

The slow pathway passes the error through a low-pass filter (the time-scale of this filter is determined by the adaptation time of the pathway) and then responds proportionally to the filtered error. Low-pass filtering in this pathway has been observed previously (Hersen et al., 2008).

In contrast, the activation of the fast pathway has two sources: it both responds to the error and to the time-derivative of the input. The error passes through a low-pass filter that has a higher cut-off frequency than the filter for the slow pathway (Hersen et al., 2008). The overall (zero-frequency) gain of the pathway is higher than the gain of the slow pathway, and the response of the pathway is therefore faster.

To generate the wild-type behaviour, the two input pathways inhibit each other (Figure 5A), but the model is agnostic to the biochemical details of this inhibition. A possible mechanism is competition between the pathways for Pbs2 (both pathways activate Pbs2 via phosphorylation of the same two residues [Hohmann, 2002]). For example, each pathway may be able to sequester Pbs2 from the other. This sequestering could potentially arise either from the different spatial locations of the receptors—Sln1 is observed throughout the plasma membrane, but Sho1 localizes to sites of polarized growth (Raitt et al., 2000; Reiser et al., 2000)—or from different allosteric states of Pbs2 (Monod et al., 1965). Indeed, from our data (Figure 3B), the amount of Pbs2 is limiting because the response of Hog1 changes if the levels of Pbs2 are reduced. Nevertheless, the inhibition could also be indirect: for example, the slow pathway could positively feedback on the fast pathway, which in turn inhibits the slow pathway.

The output of this biochemical controller is Hog1, whose activation is determined by the cross-inhibition between the input pathways. Hog1 feeds into an integrator, which determines the levels of glycerol and gives the system integral feedback (Muzzey et al., 2009). This integrator could be a long-lived gene product whose transcription is activated by Hog1 and whose levels are therefore proportional to the total amount of time that Hog1 spends in the nucleus.

Finally, Hog1-independent mechanisms are know to regulate the early accumulation of glycerol (Brewster et al., 1993). For example, the Fps1 channels, which export glycerol through the plasma membrane, are not only controlled by Hog1, but also have additional regulation (Luyten et al., 1995; Ahmadpour et al., 2016). Their fast closure gives an initial boost of glycerol (Petelenz-Kurdziel et al., 2013), which is important in all three mutants because the glycerol produced from nuclear Hog1 accumulates relatively slowly, over the time-scale of the integrator. We include such mechanisms as an additional input pathway that responds proportionally to the error and directly controls glycerol (Muzzey et al., 2009). We note that if the error becomes negative, this pathway reduces intracellular glycerol and therefore partly describes the effects of open Fps1 channels.

The model captures the differences between the mutants and the wild-type we observe in both steps (Figure 5B) and ramps (Figure 5C) and provides insight into how two opposing tasks can be implemented in the network by having specialized subnetworks. Analogous specialization is believed to occur, for example, in the establishment of polarity in yeast where the speeds of activating and de-activating of the relevant signalling network are made distinct by having two separate positive feedbacks (Brandman et al., 2005).

Each input pathway favours survival in distinct dynamic environments

The two mutants perform better at different tasks, responding at different speeds and with different levels of accuracy, and if these tasks are important for the cell we expect that the mutations may come with a fitness cost, although potentially only in particular environments. We therefore measured cell viability for stress with three different types of dynamics: steps, linear ramps, and fluctuating ramps.

Bulk fitness has been previously measured in the two mutants, and growth deficiencies for the slow mutant have been observed at high osmolarity (above approximately 0.3 M salt) (Macia et al., 2009). Such bulk measurements, based on monitoring optical density in liquid media, make varying the environmental dynamics challenging and miss single-cell events. Using ALCATRAS, we measure the number of cells that either die in the stress or never restart growth over five hours once the environment has stabilized. This direct measure allows the performance of individual cells to be evaluated (Figure 6A). All strains grow similarly in rich media and any change in fitness is therefore a consequence of the osmotic stress.

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Quantifying the number of unfit cells, we find that the selective advantage of having both input pathways is revealed by exposing cells to environments with a range of different dynamics: the fast mutant outperforms the slow mutant in steps of stress and the slow mutant outperforms the fast mutant in ramps of fluctuating stress (Figure 6A; Videos 2 and 3).

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For steps, a fast response is a priority, and although the slow pathway is more accurate, the corresponding greater degree of overshoot of glycerol in the fast pathway, as expected by our model (Figure 5D), does not substantially affect survival of the fast mutant. In the model, the overshoot is counteracted by export through the Fps1 channels, and so the fast mutant pays a greater metabolic cost by exporting more glycerol. This cost does not affect survival but may change other correlates with fitness, such as lag time.

In ramps, where the environment continually changes, the derivative action in the fast pathway does not eventually decrease like it does in steps and the overshoot of glycerol correspondingly has a longer life-time in the fast mutant (Figure 5E) and is therefore likely to be more deleterious. An indication of deleterious effects in higher gradients can be seen in the amplitude of Hog1 (Figure 4C): although the amplitude of the wild-type Hog1 increases linearly with the gradient of the ramp and is therefore likely to be informative about this gradient, the saturating response of the fast mutant implies that its amplitude of Hog1 will often be similar, at least for inputs with higher gradients. Individual cells in the fast mutant may not then be able to match their response to the magnitude of the stress.

In the fluctuating ramps, accuracy is a priority. In the fast mutant, the derivative action depends only on the current value of the input and so the fast mutant responds almost anew each time the stress increases regardless of the cell’s internal state (levels of glycerol). The resulting overshooting of glycerol is therefore compounded because of the long life-times of the overshoots and the ramp’s greater duration. The slow mutant, in contrast, can modulate its response both by the cell’s internal state and by the history of the stress because of its greater sensitivity to the integral feedback. With its two input pathways, the wild-type performs both tasks and is both fast and accurate, always having the highest probability of survival.

We have thus shown that trade-offs in performance can undermine signalling in a single input pathway with either speed being sacrificed for accuracy or vice versa, but that by having two input pathways, each specializing to particular task, signalling networks can mitigate these trade-offs (Figure 6B).

In the HOG network, the Sln1 pathway is a fast reflex-like response that provides the speed necessary to survive sudden shocks but at the expense of accuracy, and alone can cause adaptation of Hog1 before recovery of the cellular volume. Consistent with this observation, Macia et al. report that fast mutants have a shorter duration of Hog1 phosphorylation compared to wild-type cells (Macia et al., 2009).

In contrast, the Sho1 pathway provides accuracy at the expense of speed and by specializing to sensing the integral feedback coming from volume recovery is more sensitive to the cell’s internal state and the history of the extracellular stress. This behaviour is consistent with earlier speculations that the Sho1 branch primarily monitors osmotic changes during normal growth (Hohmann, 2002). If the integral feedback is to allow recovery of the volume, the network must remember the cellular volume before the stress (Astrom and Murray, 2008), and the Sho1 pathway interacts with the actin cytoskeleton (Tanaka et al., 2014), which might allow information from cell morphology and growth to be integrated with activation of Hog1.

The two input pathways have been reported to have different thresholds of activation (Macia et al., 2009), but our data and modelling points towards a re-interpretation in terms of different gains for the pathways. For all the steps and ramps of stress that we consider, we observe a response from both mutants, and so any differences in thresholds must be small (less than 0.2 M sorbitol in steps and 0.03 M min${}^{-1}$ in ramps). The advantage of multiple thresholds might be to increase the network’s dynamic range, but given that both thresholds can only be small, such an increase is unlikely to be substantial in the HOG network. Our data points towards it being the interaction between the two pathways that increases the dynamic range: we observe that only the wild-type response increases linearly with the gradient of a ramp of stress (Figure 4C).

A potentially alternative architecture of the HOG signalling network is to have a single fast input pathway controlling the integral feedback. Such a network, however, would not only have structural instabilities in its dynamics because of the high gain necessary for high speed, but also would be more likely to become insensitive to the cell’s internal state for sufficiently high stress. In large stress, all Hog1 molecules can become activated and the output of the HOG controller is then saturated. This saturation will happen for shocks of smaller magnitude for systems with high gain and causes a loss of accuracy because the system is then in open loop and is unable to exploit the integral feedback. Saturated activity of Hog1 should generate maximum production of glycerol and so faster recovery of cellular volume, but, once the volume has recovered, the level of glycerol synthesis will be too high for the level of stress and there will be a fitness cost. Having a slow pathway that inhibits the fast pathway helps prevent saturation of Hog1 activity and so increases sensitivity to the integral feedback for higher levels of stress.

We have developed a block diagram model of the HOG network, but a caveat is that, although the model is therefore modular, it is also agnostic to the biochemical details of both the interaction between the two input pathways and the mechanism allowing the fast pathway to respond to the time-derivative of the input. Competing for Pbs2 is one possible means of cross-inhibition between the pathways, but multiple feedbacks, both positive and negative, exist within the HOG network (Hao et al., 2007; Macia et al., 2009; Sharifian et al., 2015; English et al., 2015), and a feedback-based interaction is possible. That biochemistry can be used to measure a time-derivative on a time-scales as fast as seconds is well established (Block et al., 1983), and, in analogy with bacterial chemotaxis, we expect that upstream signalling in the fast pathway encodes a short-term memory of the level of the input to allow comparison of the current level to a value in the past.

More generally, our results confirm the importance of using inputs with varying dynamics to uncover the logic behind cellular signalling (Nurse, 2008; Alexander et al., 2009). In the wild, organisms are exposed to signals with a wider range of temporal behaviours then the constant inputs typically studied in the laboratory (López-Maury et al., 2008), and signal transduction is likely to have evolved to allow organisms to differentiate between such signals or at least between classes of signals (Bowsher and Swain, 2014; Tkačik and Bialek, 2016). Although such work is still in its infancy, dynamic inputs have been successfully used to understand signalling responses in, for example, bacteria (Young et al., 2013), yeast (Hao et al., 2013), and mammalian cells (Kellogg and Tay, 2015), and, with the ease of use of microfluidics (Bennett and Hasty, 2009), we believe should become commonplace.

In conclusion, we have shown that cellular signalling is vulnerable to fundamental trade-offs in performance, but that these vulnerabilities can be overcome by distributing tasks to different parts of the network and integrating together the outputs of this division of labour. We therefore expect such improvements in performance by the specialization of subnetworks to different tasks to exist broadly within cellular signal transduction.

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Author details

1. Alejandro A Granados

   1. SynthSys - Synthetic and Systems Biology, University of Edinburgh, Edinburgh, United Kingdom
   2. Department of Bioengineering, Imperial College London, London, United Kingdom

   Contribution

   AAG, Conceptualization, Formal analysis, Investigation, Visualization, Methodology, Writing—original draft, Writing—review and editing

   Contributed equally with

   Matthew M Crane

   Competing interests

   The authors declare that no competing interests exist.

2. Matthew M Crane

   1. SynthSys - Synthetic and Systems Biology, University of Edinburgh, Edinburgh, United Kingdom
   2. School of Biological Sciences, University of Edinburgh, Edinburgh, United Kingdom

   Contribution

   MMC, Conceptualization, Formal analysis, Investigation, Visualization, Methodology, Writing—review and editing

   Contributed equally with

   Alejandro A Granados

   Competing interests

   The authors declare that no competing interests exist.

3. Luis F Montano-Gutierrez

   1. SynthSys - Synthetic and Systems Biology, University of Edinburgh, Edinburgh, United Kingdom
   2. School of Biological Sciences, University of Edinburgh, Edinburgh, United Kingdom

   Contribution

   LFM-G, Resources, Methodology

   Competing interests

   The authors declare that no competing interests exist.

4. Reiko J Tanaka

   Department of Bioengineering, Imperial College London, London, United Kingdom

   Contribution

   RJT, Supervision, Writing—review and editing

   Competing interests

   The authors declare that no competing interests exist.

   "This ORCID iD identifies the author of this article:" 0000-0002-0769-9382

5. Margaritis Voliotis

   Department of Mathematics and Living Systems Institute, College of Engineering, Mathematics, and Physical Sciences, University of Exeter, Exeter, United Kingdom

   Contribution

   MV, Conceptualization, Formal analysis, Investigation, Visualization, Writing—review and editing

   Competing interests

   The authors declare that no competing interests exist.

   "This ORCID iD identifies the author of this article:" 0000-0001-6488-7198

6. Peter S Swain

   1. SynthSys - Synthetic and Systems Biology, University of Edinburgh, Edinburgh, United Kingdom
   2. School of Biological Sciences, University of Edinburgh, Edinburgh, United Kingdom

   Contribution

   PSS, Conceptualization, Formal analysis, Funding acquisition, Visualization, Writing—original draft, Writing—review and editing

   For correspondence

   peter.swain@ed.ac.uk

   Competing interests

   The authors declare that no competing interests exist.

   "This ORCID iD identifies the author of this article:" 0000-0001-7489-8587

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