It is widely accepted that signaling pathways are capable of transmitting quantitative information about their surrounding environment. While the importance of transient versus sustained signaling has been recognized for some time 
, most previous investigations have focused on information transfer using amplitude encoding without considering the temporal aspects of signal transduction 
. Here we demonstrate that dose-to-duration encoding provides cells with an alternative mechanism for processing and transmitting quantitative information about their surrounding environment. The ability of signaling pathways to convert stimulus strength into signal duration results directly from the nonlinear nature of these systems and emphasizes the importance of considering the dynamic properties of signaling pathways when characterizing their behavior. Taken together, our computational and experimental results suggest that dose-to-duration encoding occurs in the pheromone response pathway of yeast and underlies the developmental switch from chemotropic growth to mating.
One important advantage of dose-to-duration encoding is that it has the potential to increase the dynamic range of signaling pathways. One way this can occur is if feedback regulation allosterically modifies the receptor's affinity for the ligand. Dynamically regulating the Kd
of the receptor has the interesting effect of shifting the EC50
of the cellular response to the right of the receptor occupancy curve (). Depending on the response of downstream components, the dose-response curve for the system is not only shifted but also stretched. This highlights the important point that receptor occupancy curves are potentially time-dependent quantities and need to be interpreted with care. Interestingly, Kd
values determined in vitro or in reconstituted systems usually differ from those obtained in vivo, and this discrepancy is often attributed to an abnormal conformation of the receptor in the artificial environment. The analysis presented here suggests that even when there is correspondence between the microenvironment of an in vitro experiment and the macroenvironment of a cell culture, the results of ligand binding assays might differ due to dynamic regulation of the receptor in vivo. For example, this could happen if a downstream element of the signaling pathway has been disrupted in the in vitro experiment, thereby breaking the negative feedback loop. Interactions between receptors, in particular G-protein coupled receptors (GPCRs), and cytosolic proteins have been shown to affect receptor-ligand affinity 
. Most GPCR's are known to undergo biochemical modifications, such as phosphorylation, and to interact with a number of signaling proteins, including G proteins, arrestins, kinases, RGS proteins, and to form oligomers, all of which could affect affinity for the ligand. Therefore dynamic regulation of a receptor as a mechanism for dose-to-duration encoding seems quite plausible.
Dose-to-duration encoding may also provide a more robust transmission mechanism than amplitude-encoding in multilevel networks. This is because accurate transfer of information using amplitude encoding requires that the input-output characteristics of the individual components be well matched 
. Note that dose-to-duration encoding does not have to function throughout the whole pathway. It is likely that multiple information processing strategies coexist at different levels (or even under different conditions) in a single pathway. In fact, the use of multiple information processing strategies may provide signaling networks with more flexibility when responding to changing environmental conditions. Another potential advantage of dose-to-duration encoding arises from the need to prevent spurious activation of pathways that share components. Recently we proposed “kinetic insulation” 
as a strategy for achieving pathway specificity. Kinetic insulation relies solely on the temporal profiles of the propagated signals to ensure signal fidelity. It requires that at least one of the pathways responds transiently. Because signal duration is a natural strategy for pathways with transient activity to encode information, signaling systems with shared components are potential candidates for dose-to-duration encoding. Consistent with these ideas, the yeast pheromone response pathway contains several signaling proteins (e.g., Ste11 and Ste7) that are known to also participate in the hyper-osmotic shock 
and filamentous growth 
Our modeling results and experimental data provide compelling evidence for dose-to-duration encoding by the yeast pheromone response pathway. A key question is then what is the molecular mechanism responsible for transducing stimulus dose into signal duration? We have demonstrated that a scenario in which feedback regulation acts at the level of the receptor is consistent with our experimental data for MAP kinase activity. Our motivation for considering such a mechanism came from data suggesting that yeast continue to respond in a dose-dependent manner to pheromone concentrations well beyond the reported value for the receptor dissociation constant. As we have shown, by dynamically altering the affinity of the receptor for pheromone, our model provides an explanation for this phenomenon of signaling beyond saturation. Modulation of the receptor affinity in yeast might occur by interactions with other receptors (receptor dimers) 
, the G-protein 
, or the RGS protein Sst2 
. Similarly, affinity could be altered through receptor phosphorylation or ubiquitination 
. GTP-dependent changes in the pheromone receptor affinity attributed to the interaction with the G protein have been reported 
. Although the physiological relevance of this effect has not been clearly established in yeast, this is an example of a phenomenon observed for many mammalian GPCR's in vitro.
We note that interpreting dose-response data for the pheromone pathway is complicated by the presence of the protease Bar1 
. In fact, a mechanism based solely on Bar1 degradation of pheromone is in theory sufficient to achieve the dose-to-duration transformation. However, our recent experiments performed in a bar1Δ
mutant show cells responding to lower pheromone doses, but with time courses of MAPK activity that are consistent with dose-to-duration encoding (Supplemental Data 
). These results argue against a mechanism involving Bar1 alone. It should be emphasized that dose-to-duration encoding does not require the negative feedback to act at the level of the receptor. For example, induction of the negative regulator Sst2 
, feedback phosphorylation of an upstream pathway component 
, or receptor endocytosis could also accomplish this transformation, although they would not account for the observed shift in the EC50
. Thus, it is clear more work is necessary to unambiguously identify the mechanisms responsible for information transfer in the pheromone response pathway. However, the remarkable agreement between our modeling results and experimental data offers strong evidence in support of dose-to-duration encoding and provides a foundation for interpreting future experimental results.
Interestingly, the combination of fast and slow kinetics exhibited by the two MAP kinases, Kss1 and Fus3, has the potential to form a feed-forward adaptive system. It has been demonstrated that pheromone-induced degradation of the transcriptional activator Ste12 requires Fus3, but not Kss1 
. Ste12 might also play a role in generating the second peak of Kss1 activity observed at high pheromone concentrations, a possibility that we are now investigating. In the absence of pheromone, Kss1 acts as a transcriptional repressor by forming a complex with Ste12 and the proteins Dig1 and Dig2 (also known as Rst1/2) 
. It is possible that pheromone-stimulated release of Kss1 from this complex 
generates a second pool of Kss1 and this pool is responsible for the second peak of activity. However, at this point we cannot rule out alternative explanations including transcriptional induction, re-localization, or positive feedback.
Dose-to-duration encoding is not restricted to yeast. For example the intensity of light (number of photons) impinging on photoreceptors in rod cells is encoded as the duration of G protein-mediated activity of the pathway 
. It has been shown recently that the RGS protein RGS9 plays a particularly important role in determining the duration of the signal 
. Furthermore, switches based on transient versus sustained signals, like the ones arising from transitions between the regimes of , have been proposed to underlie cell fate decision process in a number of systems 
. The recent discovery that different temporal profiles of IκB kinase (IKK) activity in the NF-kB signaling module selectively activate different groups of target genes, further supports the notion that dose-to-duration encoding plays a significant regulatory role in determining cellular responses. In this case, stimulation of murine embryonic fibroblasts with tumor necrosis factor-α produces a short transient peak of IKK activity whereas stimulation with polysaccharides results in a slower and more sustained IKK response 
. The fact that each profile affects the expression of different groups of genes illustrates how the temporal dynamics of a signaling pathway can play a role in determining pathway specificity.
Finally, it is remarkable that the simple pathway architectures considered here can generate such a variety of responses depending on the strength of the stimulus (). These systems not only function as amplitude and dose-to-duration encoders, but also can act as biochemical switches that transition from transient to sustained outputs potentially generating different physiological responses 
. Typical signaling pathways involve multiple levels of regulation that in general should lead to even more complex behavior. Our results demonstrate how quantitative measurements of the temporal patterns of pathway activity when combined with mathematical modeling can be used to discover the design principles upon which signaling networks operate and decipher the code used by these systems to transmit information.