BACKGROUND
the high-osmolarity glycerol  pathway  of the budding yeast saccharomyces cerevisiae mediates cellular response to increased external osmolarity  <cit> .
a key component of the hog pathway is a mitogen-activated protein  kinase cascade.
within the kinase cascade, the map3ks ssk <dig> and ssk <dig> phosphorylate the map2k pbs <dig>  which in turn phosphorylates the map kinase hog <dig>  phospho-hog <dig> then regulates transcriptional and metabolic changes that increase production and accumulation of the compatible solute glycerol.
mounting a rapid response to increased osmolarity is essential to yeast survival  <cit> .
accordingly, s. cerevisiae can activate the hog pathway within one minute of experiencing an osmotic shock  <cit> .
yeast can also effectively respond to rapid periodic oscillations  between low and high external osmolyte concentrations  <cit> .figure  <dig>
structure of the sln1-ypd1-ssk <dig> relay and the hog mapk pathway.
under normal growth conditions, sln <dig> activates ypd <dig>  which in turn inhibits ssk <dig>  increased osmolarity inhibits sln <dig>  resulting in activation of ssk <dig> and of the map kinase hog <dig> through the upstream map3ks ssk <dig> and ssk <dig> and the map2k pbs <dig>  activated hog <dig> regulates transcriptional and metabolic changes within the cell that increase production and retention of glycerol.
despite its importance during periods of increased osmolarity, unintended activation of the hog pathway during growth in normal osmolarity conditions is severely deleterious  <cit> .
the sln1-ypd1-ssk <dig> three-component phospho-relay is responsible for maintaining inactivation of the hog pathway under normal conditions.
this three-component phospho-relay is a variant of the two-component signaling systems used by many prokaryotes for osmoregulation, chemotaxis, and other key cellular processes.
sln <dig> is active in vivo as a membrane-bound dimer  <cit> .
under normal osmolarity conditions, sln <dig> autophosphorylates on a histidine residue and then irreversibly transfers the phosphate to an aspartate in its response regulator  domain .
aspartate-phosphorylated sln <dig> binds to the histidine-containing phospho-transfer  protein ypd <dig> and reversibly transfers its phosphate to ypd <dig> .
finally, phospho-ypd <dig> transfers its phosphate to dimeric ssk <dig>  preventing it from interacting with ssk <dig>  and inhibiting hog pathway activity  <cit> .
the sequence of phosphate transfers in the three-component relay is summarized in figure 2a.
in response to osmotic shock, the phospho-relay is inactivated, and ssk <dig> is rapidly dephosphorylated through an as-yet unknown mechanism.
unphosphorylated ssk <dig> then activates ssk <dig> and ssk <dig>  leading to induction of the hog pathway  <cit> .
it is thus the essential controller of hog pathway activity, and variations in its concentration could compromise fitness.figure  <dig>
biochemically realistic model of the hog pathway three-component phospho-relay in
s. cerevisiae
.
a cartoon diagram of the phospho-relay indicating the quaternary structure of each component and the four relevant phosphorylation sites.
phospho-transfer proceeds from sln <dig>  to ypd <dig> to ssk <dig>  as indicated by the numbers in circles.
b crystal structure of ypd <dig>  in complex with the response regulator domain of sln <dig> .
drawn from data presented in  <cit> .
c reaction network diagram describing our model of the phospho-relay.
the network includes nearly all possible interactions between the three proteins subject to the biochemical assumptions outlined in the main text.
for clarity, the reaction network is color-coded to indicate the groups of reactions involved in each phosphorylation event.
s denotes sln <dig>  y denotes ypd <dig>  and k denotes ssk <dig>  phosphorylated residues are denoted by p, unphosphorylated residues by o. d directed graph describing the subnetwork involving phosphorylation and dephosphorylation of ssk <dig>  the graph contains four loops that are connected as a branched tree.
there is limited existing experimental evidence that the phospho-relay is able to maintain robust phosphorylation of ssk <dig> and inactivation of the hog pathway despite changes in the levels of some pathway components  <cit> .
we undertook a comprehensive characterization of the sensitivity of hog pathway activation to changes in the expression levels of the phospho-relay proteins sln <dig>  ypd <dig>  and ssk <dig>  we systematically under- and overexpressed the three proteins using the gev artificial induction system, which allows for rapid and nearly gratuitous induced expression of individual yeast genes  <cit> .
we found that the phospho-relay maintains inactivation of the hog pathway even after moderate perturbation of sln <dig>  ypd <dig>  and ssk <dig>
we developed a detailed, biochemically realistic mathematical model of the hog pathway three-component phospho-relay to elucidate the mechanism underlying this robustness .
our model incorporates extensive structural and mechanistic information about the phospho-relay and considers nearly all possible interactions between the three relay proteins.
we used mass-action kinetics and algebraic calculations to characterize the steady-state behavior of the model.
steady-state algebraic models are a useful alternative to existing computational models of the hog pathway for understanding robust behavior  <cit> .
unlike numerical simulations  <cit> , algebraic manipulations can be done without ever assigning specific values to the parameters , many of which are difficult or impossible to measure experimentally  <cit> .
this advantage enabled us to design and analyze a more biochemically realistic model.
a steady-state approximation is appropriate because previous studies have shown that activation of the hog pathway does not vary under normal growth conditions  <cit> .
our steady-state analysis predicted that relative levels of dephosphorylated ssk <dig> depend solely on ypd <dig> levels and that robustness is achieved by maintaining ypd <dig> in large excess.
we experimentally tested this prediction by perturbing protein expression levels so as to deplete this buffering pool of ypd <dig>  all such perturbations compromised the ability of the phospho-relay to inhibit the hog pathway, leading to hyperactivation in normal osmolarity conditions.
the presence of a large buffering pool of an intermediate phospho-relay component is a previously underappreciated mechanism for robustness and suggests a possible advantage of a three-component relay over a two-component system.
RESULTS
inhibition of hog pathway signaling is robust to moderate overexpression of phospho-relay components
inappropriate hog pathway activation during normal osmolarity growth unnecessarily alters transcription and metabolism  <cit> .
to assess the robustness of hog pathway inhibition by the three-component phospho-relay, we created strains capable of overexpressing sln <dig>  ypd <dig>  and ssk <dig> in response to β-estradiol.
for these overexpression experiments, we used diploid strains homozygous for the gev artificial transcription factor  <cit> .
gev consists of the gal <dig> dna-binding domain, the estrogen receptor, and the vp <dig> activation domain.
upon treatment with the hormone β-estradiol, gev rapidly translocates to the nucleus, where it activates transcription from promoters containing the gal <dig> dna-binding target sequence.
the gev system enables rapid induction of individual yeast genes with limited off-target effects  <cit> .
to make a given phospho-relay gene gev-inducible, we placed it under the control of the gal <dig> promoter , as described previously  <cit> .
inappropriate activation of the hog pathway is known to cause a growth defect  <cit> .
we therefore measured growth of these gev strains after induction with β-estradiol at a range of concentrations to screen for hog pathway hyperactivity.
a strain carrying an inducible allele of pbs <dig>  was used as a control because pbs <dig> overexpression is known to cause severe growth defects from inappropriate activation of the hog pathway  <cit> .
as shown in figure 3a, strains overexpressing pbs <dig> exhibited a measurable growth defect, while strains overexpressing components of the phospho-relay  showed no significant change.figure  <dig>
moderate overexpression of phospho-relay components does not activate the hog pathway.
a homozygous gev diploid strains with a single inducible copy of a phospho-relay gene were grown to saturation in different concentrations of β-estradiol.
the optical density  after  <dig> hours of growth is plotted.
overexpression of pbs <dig> caused a growth defect at higher concentrations of β-estradiol, while no significant growth defects were observed following overexpression of relay components .
each point represents the mean and standard deviation over four replicates.
b we assayed for hog <dig> phosphorylation using an antibody specific to doubly phosphorylated hog <dig> to confirm that moderate overexpression of phospho-relay components does not lead to activation of the hog pathway.
overexpression of phospho-relay components using a saturating dose  of β-estradiol did not lead to hog <dig> phosphorylation.
overexpression of the positive controls ssk <dig>  ssk <dig>  and pbs <dig>  however, led to clear upregulation of hog <dig> phosphorylation after  <dig> minutes of induction.
total hog <dig> is shown as a loading control.
we also assayed for hog <dig> phosphorylation following gev induction of phospho-relay components to obtain direct evidence that moderate overexpression does not cause hog pathway hyperactivation.
we used overexpression of pbs <dig> and ssk <dig>  as positive controls.
after  <dig> minutes of gev induction, there was no detectable increase in hog <dig> phosphorylation in strains overexpressing phospho-relay components .
in contrast, pbs <dig> and ssk <dig> overexpression caused phosphorylation of hog <dig>  interestingly, overexpression of the ssk <dig> homolog ssk <dig> had the strongest effect on hog <dig> phosphorylation.
we then constructed diploid strains with a single inducible copy of the hog phospho-relay gene of interest and a single p stl1-yfp reporter to assay for hog pathway transcriptional activity in response to overexpression of relay components.
stl <dig> is a glycerol/h + symporter whose expression is strongly upregulated in response to osmotic shock  <cit> .
we overexpressed all three relay components, pbs <dig>  and ssk <dig>  here we used ssk <dig> as a control instead of ssk <dig> because it showed a strong effect on hog <dig> phosphorylation in the previous experiment.
after  <dig> minutes of induction with  <dig> μm β-estradiol, ssk <dig> and pbs <dig> overexpression led to hog-dependent transcription from the stl <dig> promoter, as indicated by an increase in yfp fluorescence .
over the same period of time, overexpression of the phospho-relay components  caused almost no transcription from the stl <dig> promoter.
after  <dig> hours, overexpression of ssk <dig> and sln <dig> did increase expression of yfp from the pstl1-yfp reporter.
these effects on longer time scales may have been due to factors beyond ssk <dig> and sln <dig> overexpression, however, as there was a population expressing yfp even in the control strain at  <dig> hours.figure  <dig>
moderate overexpression of phospho-relay components causes mild activation of hog pathway transcriptional targets on long timescales.
stl <dig> is a gene induced in response to active hog <dig>  we replaced one copy of the stl <dig> gene with yevenus in homozygous gev strains to create a p stl1-yevenus transcriptional reporter of hog pathway activity.
we used flow cytometry to analyze yevenus expression in cells at the start of the experiment and at  <dig> hours and  <dig> hours after induction with  <dig> μm β-estradiol.
pbs <dig> and ssk <dig> overexpression caused the strongest activation of the hog pathway transcriptional reporter.
cell counts are plotted against the natural log of their fluorescence signal .
construction of a biochemically realistic model of the hog pathway phospho-relay
growth, phosphorylation, and transcriptional measurements of hog pathway activity all indicated that hog pathway activation is robust to fluctuations in the sln1-ypd1-ssk <dig> phospho-relay components.
these results prompted us to investigate the mechanistic basis of this robustness using a biochemical model.
the reaction network underlying our model  has  <dig> nodes and involves  <dig> species.
in this section we discuss the biochemical justification for key assumptions in the model.
there exist high-resolution crystal structures of ypd <dig> alone and in complex with the sln <dig> receiver domain   <cit> .
genetic and biochemical evidence suggest that sln <dig> forms an obligate homodimer and that ypd <dig> can interact with either half of the dimer  <cit> , which implies that formation of a ypd1-sln1-ypd <dig> ternary complex is possible.
accordingly, we include sln <dig> in the reaction network as a dimer with four relevant phosphorylation sites.
the sln <dig> dimer is referred to as sh1d1h2d <dig>  where h <dig> and d <dig> denote the phosphorylatable histidine and aspartate residues in one half of the dimer and h <dig> and d <dig> denote the corresponding residues in the other half.
the dimer is allowed to autophosphorylate on either histidine residue.
phospho-transfer from the histidine to the aspartate in the rr domain is treated as irreversible.
a reverse reaction is included with all histidine autophosphorylation steps to account for possible hydrolysis of the phosphate prior to transfer  <cit> .
each half of the dimer is assumed to be independent from the other.
coincident phosphorylation events  are therefore considered to be unlikely and are excluded from the model.
following these assumptions, the model includes nine different forms of free sln <dig> that are interconverted as shown in the reaction network.
in the second leg of the phospho-relay, any sln <dig> phospho-form with at least one phosphorylated aspartate is allowed to reversibly associate with unphosphorylated monomeric ypd <dig>  to form a series of binary complexes .
sln1-ypd <dig> phospho-transfer has been shown to be reversible  <cit> .
as such, all reactions that produce phospho-ypd <dig>  are treated as reversible.
no assumption is made about which half ypd <dig> binds to in the ysopop binary complex because the halves of the sln <dig> dimer are considered to be indistinguishable.
accordingly, the ysopop complex is allowed to form from either yp+sooop or yp+sopoo.
additionally, ysopop can bind to a second y molecule to form a ternary complex  that produces yp using either of the sln <dig> phospho-aspartate residues.
phospho-ypd <dig> then binds to and phosphorylates ssk <dig>  which is modeled as a dimer with two phosphorylation sites   <cit> .
the two monophosphorylated forms of ssk <dig>  which are known to be fully inactive  <cit> , are assumed to be identical .
yp can form a complex with koo, leading to the production of kop, and in turn yp can bind to kop and transfer a phosphate to produce kpp.
the network includes one further interaction between ypd <dig> and ssk <dig> deduced from kinetic data.
the half-life of phospho-ssk <dig> in vitro has been measured to be dramatically different with and without the presence of ypd <dig> , suggesting that ypd <dig> binds to kop and kpp to prevent hydrolysis of the phosphate  <cit> .
accordingly, the reaction network includes the reversible formation of dead-end complexes between ypd <dig> and phospho-ssk <dig>  finally, unstabilized kpp and kop are allowed to lose phosphates via spontaneous hydrolysis.
inclusion of these hydrolysis reactions ensures that there is a complete cycle for ssk <dig> modification/demodification and that the system can reach a stable steady state.
we emphasize, however, that spontaneous hydrolysis of complexed ssk <dig> is likely not the mechanism for rapid dephosphorylation of large quantities of ssk <dig> in response to osmotic shock.
the mechanism for this rapid activation remains unknown but is irrelevant for our model, which is restricted to yeast growing in steady-state normal osmolarity conditions.
derivation of the key invariant
robust inactivation of the hog pathway requires that only a small fraction of total ssk <dig>  be in the active  modification form at steady state.
the goal of this section is to derive a simple steady-state expression  for the ratio of active to total ssk <dig>  we find an invariant of the form   kt=11+1γα+β2+α′+β′ <dig>
where the coefficients are combinations of the rate constants.
in this section we derive eq.
<dig>  and in the following section we discuss experimental tests of its predictions.
the subnetwork involving ssk <dig> contains four loops, which are linked in a branched tree .
it is a general feature of such networks that, at steady state, each individual loop is at steady state, irrespective of any other loops in which the components participate  <cit> .
if each individual loop is at steady state, then the forward flux through each loop must be balanced by the backward flux, which yields the following four equations:   k51kop=k43ypkook52kpp=k48ypkopk45ykop=k44ykopk50ykpp=k49ykpp.
because the intermediate complexes ypkoo and ypkop are also at steady state, we can write  k43ypkoo=k41ypkoo−k42ypkook48ypkop=k46ypkop−k47ypkop.
from which we deduce that   ypkoo=k41k42+k43ypkooypkop=k46k47+k48ypkop.
substituting eq.
<dig> into eq.
<dig>  we obtain expressions for kop, kpp, ykop, and ykpp in terms of koo, y, and yp.
from eq.
<dig> we already have expressions for ypkoo and ypkop in terms of koo and yp.
as such, we are able to calculate the total amount of ssk <dig>  in terms of just koo, y, and yp.
we have  kt=koo+kop+kpp+ypkoo+ypkop+ykop+ykpp.
substituting for the individual terms, we obtain  kt=koo1+1γα+β2+α′+β′ <dig>   where  α=k41k45k50k52β=k41k43k45k46k50α′=k41k43k44k50k52β′=k41k43k45k46k48k49γ=k45k50k51k <dig>
the relative concentration of koo is thus given by the invariant in eq.
<dig>
the tree of loops structure of the ssk <dig> network has an important consequence.
it implies that the steady-state ratio of active to total ssk <dig> is independent of the upstream biochemistry  as long as some process exists to generate positive levels of y and yp.
in that case, the ratio will always be given by eq.
<dig>  although the numerical value will of course differ depending on steady-state concentrations of y and yp.
the implications of this result, including its suggestion that robustness in the hog pathway is independent of putative sln <dig> bifunctionality, are considered in the conclusion.
breakdown of robustness due to depletion of the ypd <dig> pool
the invariant derived from our mathematical model  suggests that ypd <dig> levels are critical to robustness.
the denominator of the invariant is quadratic in the concentration of free yp and linear in the concentration of free y. provided that the upstream network favors production of yp over y and that there is substantially more ypd <dig> than ssk <dig>  the denominator of eq.
<dig> will be large, and the relative concentration of koo will be maintained at a low level.
this situation allows for considerable under- or overexpression of pathway components without spurious activation of the hog pathway, in agreement with our experimental findings.
the invariant predicts that massive overexpression of ypd <dig> should not cause phosphorylation of hog <dig>  in fact, additional ypd <dig> would drive the kt ratio even closer to zero, lowering the amount of unphophorylated ssk <dig> required for hog pathway activation.
in contrast, ypd <dig> underexpression should increase the ratio, potentially compromising fitness due to inappropriate activation of the hog pathway.
similarly, massive overexpression of ssk <dig> should deplete free y and yp due to increased levels of the four intermediate complexes .
under the assumption of tight binding between ypd <dig> and ssk <dig> in each of these complexes, which is well-supported by existing kinetic data  <cit> , very little free ypd <dig> will be present at steady state if there is much more ssk <dig> than ypd <dig>  as such, eq.
<dig> predicts that the ratio will be higher following massive overexpression of ssk <dig> than under wild-type conditions.
we experimentally validated these three predictions.
the gev system can achieve at most a 10-fold increase in protein expression from a single inducible allele  <cit> .
we created haploid gev yeast strains carrying high-copy  <dig> μ plasmids with a gev-inducible allele  of a gene of interest, which allowed us to test the model prediction that massive overexpression of ssk <dig>  but not of ypd <dig>  should lead to inappropriate hog pathway activation.
these high-copy yeast plasmids are estimated to be present at 15- <dig> copies per cell  <cit> .
we measured the growth of these strains in different concentrations of β-estradiol to assay for growth defects that might be due to hog pathway hyperactivation.
massive overexpression of both sln <dig> and ssk <dig> caused a growth defect over a range of β-estradiol concentrations, but the strain with ypd <dig> overexpressed grew as well as a wild-type strain carrying only the empty vector  .
examination of growth over a finer range of β-estradiol concentrations indicated that overexpression of ssk <dig> caused a more severe growth defect than overexpression of sln <dig> .
these defects were also visible on solid media .
as such, extreme overexpression of ssk <dig> compromises fitness.figure  <dig>
massive overexpression of phospho-relay components leads to growth defects.
a haploid gev strains carrying a high-copy plasmid with an inducible hog pathway gene were grown in different concentrations of β-estradiol.
the od  <dig> after  <dig> hours of growth is plotted as a function of β-estradiol concentration.
each point represents the mean and standard deviation of four replicates.
overexpression of sln <dig> and ssk <dig>  caused a growth defect.
b the same strains were grown over a finer titration of β-estradiol concentrations.
the od  <dig> after  <dig> hours is plotted.
at this resolution, it is clear that the growth defect from ssk <dig> overexpression is more severe than the growth defect from sln <dig> overexpression at low β-estradiol concentrations.
c the same strains were frogged onto plates containing different concentrations of β-estradiol.
massive overexpression of sln <dig> and ssk <dig> again caused a growth defect comparable to that from overexpression of pbs <dig>  in all experiments, the parent strain carrying the empty vector plasmid [ <dig> μ
p
gal <dig> scura3] was used as a negative control.
we again assayed phospho-hog <dig> levels to check if overexpression of sln <dig> and ssk <dig> causes activation of the hog pathway in normal osmolarity conditions .
we measured hog <dig> phosphorylation levels after gev-induction of relay components and of the positive controls pbs <dig> and ssk <dig> from a multi-copy plasmid.
overexpression of pbs <dig>  ssk <dig>  and ssk <dig> caused a significant change in hog <dig> phosphorylation after  <dig> minutes .
although some hog <dig> phosphorylation was observed after overexpression of sln <dig>  the increase was insignificant.
interestingly, overexpression of ypd <dig> did not cause an increase in the level of phosphorylated hog <dig>  in fact, levels of hog <dig> phosphorylation were reduced in the ypd <dig> overexpression strain .figure  <dig>
growth defects following massive overexpression of phospho-relay components are due to activation of the hog pathway.
a we assayed for hog <dig> phosphorylation after overexpression of relay components  and positive controls .
the parental strain carrying the empty plasmid vector was used as a negative control.
b we quantified the amount of phosphorylated hog <dig>  in five biological replicates of this experiment.
error bars represent the standard error.
pbs <dig>  ssk <dig>  and ssk <dig> caused a significant  change in hog <dig> phosphorylation levels after overexpression for  <dig> minutes .
hog <dig> phosphorylation levels were also significantly lower in the ypd <dig> overexpression strain .
we could not perform underexpression experiments in a ypd <dig> Δ background because deletion of ypd <dig> is lethal.
to underexpress ypd <dig>  we instead sporulated the diploid strain  containing a wild-type copy of ypd <dig> and a single copy under the control of p gal <dig> onto media containing  <dig> nm β-estradiol.
we reasoned that  <dig> nm β-estradiol would give sufficient expression of ypd <dig> for cell growth, which was confirmed by observation of four viable spores.
we then grew these spores on media containing a range of β-estradiol concentrations .
ypd <dig> underexpression caused a clear growth defect compared to the wild-type control on  <dig> nm and  <dig> nm β-estradiol, indicating that ypd <dig> underexpression is toxic.
in contrast, underexpression of sln <dig> and ssk <dig> did not cause a growth defect .figure  <dig>
underexpression of ypd <dig> causes a severe growth defect.
a diploid homozygous gev strain carrying one inducible allele of ypd <dig>  was sporulated onto  <dig> nm β-estradiol, and individual spores were frogged onto plates containing different concentrations of β-estradiol.
at low concentrations of β-estradiol, spores carrying the inducible allele  exhibited a growth defect due lower levels of ypd <dig> and hyperactivation of the hog pathway.
spores carrying the wild-type allele  showed no growth defect.
the growth defect following sln <dig> overexpression is only partially due to hog pathway activation
as discussed above, we observed a slight but non-significant increase in hog <dig> phosphorylation following massive overexpression of sln <dig> .
we therefore investigated whether the growth defect in response to sln <dig> overexpression is only partially due to hog pathway activation by creating yeast strains null for ssk <dig>  activation of the hog cascade through the sln <dig> branch requires ssk <dig>  so in ssk <dig> Δ strains it is not possible for sln <dig> overexpression to activate the hog pathway.
overexpression of sln <dig> from a  <dig> μ plasmid using gev was still detrimental to growth in the ssk <dig> Δ strain , indicating that the growth defect due to sln <dig> overexpression is only partially due to hog pathway activation.
this result held both for growth in liquid cultures  and on solid media .
it is consistent with sln <dig> overexpression causing a smaller effect on hog <dig> phosphorylation levels .figure  <dig>
growth defects following sln <dig> overexpression are not completely due to hog pathway activation.
a we assayed growth in wild-type and ssk <dig> Δ strains overexpressing sln <dig> in response to β-estradiol or carrying an empty p gal <dig> vector control.
deletion of ssk <dig>  which prevented hog pathway activation by sln <dig>  partially alleviated the growth defect due to sln <dig> overexpression.
b growth of cells on plates containing  <dig> μm β-estradiol indicated that ssk <dig> Δ reduced the toxicity of sln <dig> overexpression.
CONCLUSIONS
robustness of the sln1-ypd1-ssk <dig> phospho-relay is essential to prevent spurious activation of the hog pathway, which severely compromises yeast fitness.
we established that the phospho-relay is robust to perturbations in the concentrations of the three relay components.
a theoretical analysis suggested that a large pool of the intermediate component ypd <dig> can buffer fluctuations in other pathway components to maintain robustness.
this suggestion was consistent with earlier published measurements indicating that ypd <dig> is at least  <dig> times more abundant than ssk <dig> at normal expression levels  <cit> .
although ypd <dig> may also bind to the protein skn <dig>  combined levels of ssk <dig> and skn <dig> have been measured to be below total ypd <dig> levels  <cit> .
our subsequent experiments confirmed that depletion of this buffering pool of ypd <dig> leads to inappropriate activation of the hog pathway.
the differential expression of ypd <dig> and ssk <dig> enables phosphorylation of excess ssk <dig> and stabilization of the new phospho-ssk <dig>  buffering hog pathway activation to fluctuations in ssk <dig> levels.
this novel mechanism of robustness suggests an advantage of a three-component architecture over a two-component one.
in particular, the implementation of an analogous buffering strategy in a two-component system would be difficult because it would require expressing the sensor histidine kinase at very high levels.
this situation might lead to imprecise sensing and various other off-target effects.
in contrast, the use of an intermediate transfer protein enables robust buffering with both the sensor and response regulator expressed at comparable levels.
our work has thus identified a potential mechanism for circumventing a trade-off between efficient sensing and robust control.
there are other possible advantages for a three-component architecture, including combinatorial control of response regulators by sensor proteins through a common phosphotransfer protein or segregation of sensing and activation functions between the nucleus and cytoplasm.
intriguingly, deletion of ypd <dig> has recently been shown to cause constitutive activation of the hog pathway in candida albicans, suggesting that its buffering capacity might also be important in this organism  <cit> .
robustness in real biological systems is necessarily approximate and apt to be compromised at extreme expression levels of cellular components.
in many systems, however, it has proven difficult to characterize where robustness breaks down and to reconcile such results with mathematical models, which often predict exact robustness  <cit> .
our combined theoretical and experimental results specify a single condition  for robust regulation of the hog pathway.
the link between bifunctionality and robustness is well-established  <cit> , and it is known that bifunctionality of envz is essential to robustness in escherichia coli osmoregulation  <cit> .
as such, it is intriguing that our model suggests that robustness in s. cerevisiae osmoregulation is not dependent on bifunctionality of sln <dig>  it is important to emphasize, however, that bifunctionality would not compromise robustness.
rather, the model indicates that any upstream process that produces non-zero levels of y and yp should enable the same fundamental behavior predicted by eq.
<dig>  the possibility that sln <dig> exhibits phosphatase activity warrants further experimental investigation.

 the high-osmolarity glycerol pathway of the budding yeast saccharomyces cerevisiae mediates cellular response to increased external osmolarity. a key component of the hog pathway is a mitogen-activated protein kinase cascade. within the kinase cascade, the map3ks ssk and ssk phosphorylate the map2k pbs which in turn phosphorylates the map kinase hog phospho-hog then regulates transcriptional and metabolic changes that increase production and accumulation of the compatible solute glycerol. mounting a rapid response to increased osmolarity is essential to yeast survival. accordingly, s. cerevisiae can activate the hog pathway within one minute of experiencing an osmotic shock. yeast can also effectively respond to rapid periodic oscillations between low and high external osmolyte concentrations.figure structure of the sln1-ypd1-ssk relay and the hog mapk pathway. under normal growth conditions, sln activates ypd which in turn inhibits ssk increased osmolarity inhibits sln resulting in activation of ssk and of the map kinase hog through the upstream map3ks ssk and ssk and the map2k pbs activated hog regulates transcriptional and metabolic changes within the cell that increase production and retention of glycerol. despite its importance during periods of increased osmolarity, unintended activation of the hog pathway during growth in normal osmolarity conditions is severely deleterious. the sln1-ypd1-ssk three-component phospho-relay is responsible for maintaining inactivation of the hog pathway under normal conditions. this three-component phospho-relay is a variant of the two-component signaling systems used by many prokaryotes for osmoregulation, chemotaxis, and other key cellular processes. sln is active in vivo as a membrane-bound dimer. under normal osmolarity conditions, sln autophosphorylates on a histidine residue and then irreversibly transfers the phosphate to an aspartate in its response regulator domain. aspartate-phosphorylated sln binds to the histidine-containing phospho-transfer protein ypd and reversibly transfers its phosphate to ypd. finally, phospho-ypd transfers its phosphate to dimeric ssk preventing it from interacting with ssk and inhibiting hog pathway activity. the sequence of phosphate transfers in the three-component relay is summarized in figure 2a. in response to osmotic shock, the phospho-relay is inactivated, and ssk is rapidly dephosphorylated through an as-yet unknown mechanism. unphosphorylated ssk then activates ssk and ssk leading to induction of the hog pathway. it is thus the essential controller of hog pathway activity, and variations in its concentration could compromise fitness.figure biochemically realistic model of the hog pathway three-component phospho-relay in s. cerevisiae. a cartoon diagram of the phospho-relay indicating the quaternary structure of each component and the four relevant phosphorylation sites. phospho-transfer proceeds from sln to ypd to ssk as indicated by the numbers in circles. b crystal structure of ypd in complex with the response regulator domain of sln. drawn from data presented in. c reaction network diagram describing our model of the phospho-relay. the network includes nearly all possible interactions between the three proteins subject to the biochemical assumptions outlined in the main text. for clarity, the reaction network is color-coded to indicate the groups of reactions involved in each phosphorylation event. s denotes sln y denotes ypd and k denotes ssk phosphorylated residues are denoted by p, unphosphorylated residues by o. d directed graph describing the subnetwork involving phosphorylation and dephosphorylation of ssk the graph contains four loops that are connected as a branched tree. there is limited existing experimental evidence that the phospho-relay is able to maintain robust phosphorylation of ssk and inactivation of the hog pathway despite changes in the levels of some pathway components. we undertook a comprehensive characterization of the sensitivity of hog pathway activation to changes in the expression levels of the phospho-relay proteins sln ypd and ssk we systematically under- and overexpressed the three proteins using the gev artificial induction system, which allows for rapid and nearly gratuitous induced expression of individual yeast genes. we found that the phospho-relay maintains inactivation of the hog pathway even after moderate perturbation of sln ypd and ssk we developed a detailed, biochemically realistic mathematical model of the hog pathway three-component phospho-relay to elucidate the mechanism underlying this robustness. our model incorporates extensive structural and mechanistic information about the phospho-relay and considers nearly all possible interactions between the three relay proteins. we used mass-action kinetics and algebraic calculations to characterize the steady-state behavior of the model. steady-state algebraic models are a useful alternative to existing computational models of the hog pathway for understanding robust behavior. unlike numerical simulations, algebraic manipulations can be done without ever assigning specific values to the parameters, many of which are difficult or impossible to measure experimentally. this advantage enabled us to design and analyze a more biochemically realistic model. a steady-state approximation is appropriate because previous studies have shown that activation of the hog pathway does not vary under normal growth conditions. our steady-state analysis predicted that relative levels of dephosphorylated ssk depend solely on ypd levels and that robustness is achieved by maintaining ypd in large excess. we experimentally tested this prediction by perturbing protein expression levels so as to deplete this buffering pool of ypd all such perturbations compromised the ability of the phospho-relay to inhibit the hog pathway, leading to hyperactivation in normal osmolarity conditions. the presence of a large buffering pool of an intermediate phospho-relay component is a previously underappreciated mechanism for robustness and suggests a possible advantage of a three-component relay over a two-component system.  inhibition of hog pathway signaling is robust to moderate overexpression of phospho-relay components inappropriate hog pathway activation during normal osmolarity growth unnecessarily alters transcription and metabolism. to assess the robustness of hog pathway inhibition by the three-component phospho-relay, we created strains capable of overexpressing sln ypd and ssk in response to β-estradiol. for these overexpression experiments, we used diploid strains homozygous for the gev artificial transcription factor. gev consists of the gal dna-binding domain, the estrogen receptor, and the vp activation domain. upon treatment with the hormone β-estradiol, gev rapidly translocates to the nucleus, where it activates transcription from promoters containing the gal dna-binding target sequence. the gev system enables rapid induction of individual yeast genes with limited off-target effects. to make a given phospho-relay gene gev-inducible, we placed it under the control of the gal promoter, as described previously. inappropriate activation of the hog pathway is known to cause a growth defect. we therefore measured growth of these gev strains after induction with β-estradiol at a range of concentrations to screen for hog pathway hyperactivity. a strain carrying an inducible allele of pbs was used as a control because pbs overexpression is known to cause severe growth defects from inappropriate activation of the hog pathway. as shown in figure 3a, strains overexpressing pbs exhibited a measurable growth defect, while strains overexpressing components of the phospho-relay showed no significant change.figure moderate overexpression of phospho-relay components does not activate the hog pathway. a homozygous gev diploid strains with a single inducible copy of a phospho-relay gene were grown to saturation in different concentrations of β-estradiol. the optical density after hours of growth is plotted. overexpression of pbs caused a growth defect at higher concentrations of β-estradiol, while no significant growth defects were observed following overexpression of relay components. each point represents the mean and standard deviation over four replicates. b we assayed for hog phosphorylation using an antibody specific to doubly phosphorylated hog to confirm that moderate overexpression of phospho-relay components does not lead to activation of the hog pathway. overexpression of phospho-relay components using a saturating dose of β-estradiol did not lead to hog phosphorylation. overexpression of the positive controls ssk ssk and pbs however, led to clear upregulation of hog phosphorylation after minutes of induction. total hog is shown as a loading control. we also assayed for hog phosphorylation following gev induction of phospho-relay components to obtain direct evidence that moderate overexpression does not cause hog pathway hyperactivation. we used overexpression of pbs and ssk as positive controls. after minutes of gev induction, there was no detectable increase in hog phosphorylation in strains overexpressing phospho-relay components. in contrast, pbs and ssk overexpression caused phosphorylation of hog interestingly, overexpression of the ssk homolog ssk had the strongest effect on hog phosphorylation. we then constructed diploid strains with a single inducible copy of the hog phospho-relay gene of interest and a single p stl1-yfp reporter to assay for hog pathway transcriptional activity in response to overexpression of relay components. stl is a glycerol/h + symporter whose expression is strongly upregulated in response to osmotic shock. we overexpressed all three relay components, pbs and ssk here we used ssk as a control instead of ssk because it showed a strong effect on hog phosphorylation in the previous experiment. after minutes of induction with μm β-estradiol, ssk and pbs overexpression led to hog-dependent transcription from the stl promoter, as indicated by an increase in yfp fluorescence. over the same period of time, overexpression of the phospho-relay components caused almost no transcription from the stl promoter. after hours, overexpression of ssk and sln did increase expression of yfp from the pstl1-yfp reporter. these effects on longer time scales may have been due to factors beyond ssk and sln overexpression, however, as there was a population expressing yfp even in the control strain at hours.figure moderate overexpression of phospho-relay components causes mild activation of hog pathway transcriptional targets on long timescales. stl is a gene induced in response to active hog we replaced one copy of the stl gene with yevenus in homozygous gev strains to create a p stl1-yevenus transcriptional reporter of hog pathway activity. we used flow cytometry to analyze yevenus expression in cells at the start of the experiment and at hours and hours after induction with μm β-estradiol. pbs and ssk overexpression caused the strongest activation of the hog pathway transcriptional reporter. cell counts are plotted against the natural log of their fluorescence signal. construction of a biochemically realistic model of the hog pathway phospho-relay growth, phosphorylation, and transcriptional measurements of hog pathway activity all indicated that hog pathway activation is robust to fluctuations in the sln1-ypd1-ssk phospho-relay components. these results prompted us to investigate the mechanistic basis of this robustness using a biochemical model. the reaction network underlying our model has nodes and involves species. in this section we discuss the biochemical justification for key assumptions in the model. there exist high-resolution crystal structures of ypd alone and in complex with the sln receiver domain. genetic and biochemical evidence suggest that sln forms an obligate homodimer and that ypd can interact with either half of the dimer, which implies that formation of a ypd1-sln1-ypd ternary complex is possible. accordingly, we include sln in the reaction network as a dimer with four relevant phosphorylation sites. the sln dimer is referred to as sh1d1h2d where h and d denote the phosphorylatable histidine and aspartate residues in one half of the dimer and h and d denote the corresponding residues in the other half. the dimer is allowed to autophosphorylate on either histidine residue. phospho-transfer from the histidine to the aspartate in the rr domain is treated as irreversible. a reverse reaction is included with all histidine autophosphorylation steps to account for possible hydrolysis of the phosphate prior to transfer. each half of the dimer is assumed to be independent from the other. coincident phosphorylation events are therefore considered to be unlikely and are excluded from the model. following these assumptions, the model includes nine different forms of free sln that are interconverted as shown in the reaction network. in the second leg of the phospho-relay, any sln phospho-form with at least one phosphorylated aspartate is allowed to reversibly associate with unphosphorylated monomeric ypd to form a series of binary complexes. sln1-ypd phospho-transfer has been shown to be reversible. as such, all reactions that produce phospho-ypd are treated as reversible. no assumption is made about which half ypd binds to in the ysopop binary complex because the halves of the sln dimer are considered to be indistinguishable. accordingly, the ysopop complex is allowed to form from either yp+sooop or yp+sopoo. additionally, ysopop can bind to a second y molecule to form a ternary complex that produces yp using either of the sln phospho-aspartate residues. phospho-ypd then binds to and phosphorylates ssk which is modeled as a dimer with two phosphorylation sites. the two monophosphorylated forms of ssk which are known to be fully inactive, are assumed to be identical. yp can form a complex with koo, leading to the production of kop, and in turn yp can bind to kop and transfer a phosphate to produce kpp. the network includes one further interaction between ypd and ssk deduced from kinetic data. the half-life of phospho-ssk in vitro has been measured to be dramatically different with and without the presence of ypd, suggesting that ypd binds to kop and kpp to prevent hydrolysis of the phosphate. accordingly, the reaction network includes the reversible formation of dead-end complexes between ypd and phospho-ssk finally, unstabilized kpp and kop are allowed to lose phosphates via spontaneous hydrolysis. inclusion of these hydrolysis reactions ensures that there is a complete cycle for ssk modification/demodification and that the system can reach a stable steady state. we emphasize, however, that spontaneous hydrolysis of complexed ssk is likely not the mechanism for rapid dephosphorylation of large quantities of ssk in response to osmotic shock. the mechanism for this rapid activation remains unknown but is irrelevant for our model, which is restricted to yeast growing in steady-state normal osmolarity conditions. derivation of the key invariant robust inactivation of the hog pathway requires that only a small fraction of total ssk be in the active modification form at steady state. the goal of this section is to derive a simple steady-state expression for the ratio of active to total ssk we find an invariant of the form kt=11+1γα+β2+α′+β′ where the coefficients are combinations of the rate constants. in this section we derive eq. and in the following section we discuss experimental tests of its predictions. the subnetwork involving ssk contains four loops, which are linked in a branched tree. it is a general feature of such networks that, at steady state, each individual loop is at steady state, irrespective of any other loops in which the components participate. if each individual loop is at steady state, then the forward flux through each loop must be balanced by the backward flux, which yields the following four equations: k51kop=k43ypkook52kpp=k48ypkopk45ykop=k44ykopk50ykpp=k49ykpp. because the intermediate complexes ypkoo and ypkop are also at steady state, we can write k43ypkoo=k41ypkoo−k42ypkook48ypkop=k46ypkop−k47ypkop. from which we deduce that ypkoo=k41k42+k43ypkooypkop=k46k47+k48ypkop. substituting eq. into eq. we obtain expressions for kop, kpp, ykop, and ykpp in terms of koo, y, and yp. from eq. we already have expressions for ypkoo and ypkop in terms of koo and yp. as such, we are able to calculate the total amount of ssk in terms of just koo, y, and yp. we have kt=koo+kop+kpp+ypkoo+ypkop+ykop+ykpp. substituting for the individual terms, we obtain kt=koo1+1γα+β2+α′+β′ where α=k41k45k50k52β=k41k43k45k46k50α′=k41k43k44k50k52β′=k41k43k45k46k48k49γ=k45k50k51k the relative concentration of koo is thus given by the invariant in eq. the tree of loops structure of the ssk network has an important consequence. it implies that the steady-state ratio of active to total ssk is independent of the upstream biochemistry as long as some process exists to generate positive levels of y and yp. in that case, the ratio will always be given by eq. although the numerical value will of course differ depending on steady-state concentrations of y and yp. the implications of this result, including its suggestion that robustness in the hog pathway is independent of putative sln bifunctionality, are considered in the conclusion. breakdown of robustness due to depletion of the ypd pool the invariant derived from our mathematical model suggests that ypd levels are critical to robustness. the denominator of the invariant is quadratic in the concentration of free yp and linear in the concentration of free y. provided that the upstream network favors production of yp over y and that there is substantially more ypd than ssk the denominator of eq. will be large, and the relative concentration of koo will be maintained at a low level. this situation allows for considerable under- or overexpression of pathway components without spurious activation of the hog pathway, in agreement with our experimental findings. the invariant predicts that massive overexpression of ypd should not cause phosphorylation of hog in fact, additional ypd would drive the kt ratio even closer to zero, lowering the amount of unphophorylated ssk required for hog pathway activation. in contrast, ypd underexpression should increase the ratio, potentially compromising fitness due to inappropriate activation of the hog pathway. similarly, massive overexpression of ssk should deplete free y and yp due to increased levels of the four intermediate complexes. under the assumption of tight binding between ypd and ssk in each of these complexes, which is well-supported by existing kinetic data, very little free ypd will be present at steady state if there is much more ssk than ypd as such, eq. predicts that the ratio will be higher following massive overexpression of ssk than under wild-type conditions. we experimentally validated these three predictions. the gev system can achieve at most a 10-fold increase in protein expression from a single inducible allele. we created haploid gev yeast strains carrying high-copy μ plasmids with a gev-inducible allele of a gene of interest, which allowed us to test the model prediction that massive overexpression of ssk but not of ypd should lead to inappropriate hog pathway activation. these high-copy yeast plasmids are estimated to be present at 15- copies per cell. we measured the growth of these strains in different concentrations of β-estradiol to assay for growth defects that might be due to hog pathway hyperactivation. massive overexpression of both sln and ssk caused a growth defect over a range of β-estradiol concentrations, but the strain with ypd overexpressed grew as well as a wild-type strain carrying only the empty vector. examination of growth over a finer range of β-estradiol concentrations indicated that overexpression of ssk caused a more severe growth defect than overexpression of sln. these defects were also visible on solid media. as such, extreme overexpression of ssk compromises fitness.figure massive overexpression of phospho-relay components leads to growth defects. a haploid gev strains carrying a high-copy plasmid with an inducible hog pathway gene were grown in different concentrations of β-estradiol. the od after hours of growth is plotted as a function of β-estradiol concentration. each point represents the mean and standard deviation of four replicates. overexpression of sln and ssk caused a growth defect. b the same strains were grown over a finer titration of β-estradiol concentrations. the od after hours is plotted. at this resolution, it is clear that the growth defect from ssk overexpression is more severe than the growth defect from sln overexpression at low β-estradiol concentrations. c the same strains were frogged onto plates containing different concentrations of β-estradiol. massive overexpression of sln and ssk again caused a growth defect comparable to that from overexpression of pbs in all experiments, the parent strain carrying the empty vector plasmid [ μ p gal scura3] was used as a negative control. we again assayed phospho-hog levels to check if overexpression of sln and ssk causes activation of the hog pathway in normal osmolarity conditions. we measured hog phosphorylation levels after gev-induction of relay components and of the positive controls pbs and ssk from a multi-copy plasmid. overexpression of pbs ssk and ssk caused a significant change in hog phosphorylation after minutes. although some hog phosphorylation was observed after overexpression of sln the increase was insignificant. interestingly, overexpression of ypd did not cause an increase in the level of phosphorylated hog in fact, levels of hog phosphorylation were reduced in the ypd overexpression strain.figure growth defects following massive overexpression of phospho-relay components are due to activation of the hog pathway. a we assayed for hog phosphorylation after overexpression of relay components and positive controls. the parental strain carrying the empty plasmid vector was used as a negative control. b we quantified the amount of phosphorylated hog in five biological replicates of this experiment. error bars represent the standard error. pbs ssk and ssk caused a significant change in hog phosphorylation levels after overexpression for minutes. hog phosphorylation levels were also significantly lower in the ypd overexpression strain. we could not perform underexpression experiments in a ypd Δ background because deletion of ypd is lethal. to underexpress ypd we instead sporulated the diploid strain containing a wild-type copy of ypd and a single copy under the control of p gal onto media containing nm β-estradiol. we reasoned that nm β-estradiol would give sufficient expression of ypd for cell growth, which was confirmed by observation of four viable spores. we then grew these spores on media containing a range of β-estradiol concentrations. ypd underexpression caused a clear growth defect compared to the wild-type control on nm and nm β-estradiol, indicating that ypd underexpression is toxic. in contrast, underexpression of sln and ssk did not cause a growth defect.figure underexpression of ypd causes a severe growth defect. a diploid homozygous gev strain carrying one inducible allele of ypd was sporulated onto nm β-estradiol, and individual spores were frogged onto plates containing different concentrations of β-estradiol. at low concentrations of β-estradiol, spores carrying the inducible allele exhibited a growth defect due lower levels of ypd and hyperactivation of the hog pathway. spores carrying the wild-type allele showed no growth defect. the growth defect following sln overexpression is only partially due to hog pathway activation as discussed above, we observed a slight but non-significant increase in hog phosphorylation following massive overexpression of sln. we therefore investigated whether the growth defect in response to sln overexpression is only partially due to hog pathway activation by creating yeast strains null for ssk activation of the hog cascade through the sln branch requires ssk so in ssk Δ strains it is not possible for sln overexpression to activate the hog pathway. overexpression of sln from a μ plasmid using gev was still detrimental to growth in the ssk Δ strain, indicating that the growth defect due to sln overexpression is only partially due to hog pathway activation. this result held both for growth in liquid cultures and on solid media. it is consistent with sln overexpression causing a smaller effect on hog phosphorylation levels.figure growth defects following sln overexpression are not completely due to hog pathway activation. a we assayed growth in wild-type and ssk Δ strains overexpressing sln in response to β-estradiol or carrying an empty p gal vector control. deletion of ssk which prevented hog pathway activation by sln partially alleviated the growth defect due to sln overexpression. b growth of cells on plates containing μm β-estradiol indicated that ssk Δ reduced the toxicity of sln overexpression.  robustness of the sln1-ypd1-ssk phospho-relay is essential to prevent spurious activation of the hog pathway, which severely compromises yeast fitness. we established that the phospho-relay is robust to perturbations in the concentrations of the three relay components. a theoretical analysis suggested that a large pool of the intermediate component ypd can buffer fluctuations in other pathway components to maintain robustness. this suggestion was consistent with earlier published measurements indicating that ypd is at least times more abundant than ssk at normal expression levels. although ypd may also bind to the protein skn combined levels of ssk and skn have been measured to be below total ypd levels. our subsequent experiments confirmed that depletion of this buffering pool of ypd leads to inappropriate activation of the hog pathway. the differential expression of ypd and ssk enables phosphorylation of excess ssk and stabilization of the new phospho-ssk buffering hog pathway activation to fluctuations in ssk levels. this novel mechanism of robustness suggests an advantage of a three-component architecture over a two-component one. in particular, the implementation of an analogous buffering strategy in a two-component system would be difficult because it would require expressing the sensor histidine kinase at very high levels. this situation might lead to imprecise sensing and various other off-target effects. in contrast, the use of an intermediate transfer protein enables robust buffering with both the sensor and response regulator expressed at comparable levels. our work has thus identified a potential mechanism for circumventing a trade-off between efficient sensing and robust control. there are other possible advantages for a three-component architecture, including combinatorial control of response regulators by sensor proteins through a common phosphotransfer protein or segregation of sensing and activation functions between the nucleus and cytoplasm. intriguingly, deletion of ypd has recently been shown to cause constitutive activation of the hog pathway in candida albicans, suggesting that its buffering capacity might also be important in this organism. robustness in real biological systems is necessarily approximate and apt to be compromised at extreme expression levels of cellular components. in many systems, however, it has proven difficult to characterize where robustness breaks down and to reconcile such results with mathematical models, which often predict exact robustness. our combined theoretical and experimental results specify a single condition for robust regulation of the hog pathway. the link between bifunctionality and robustness is well-established, and it is known that bifunctionality of envz is essential to robustness in escherichia coli osmoregulation. as such, it is intriguing that our model suggests that robustness in s. cerevisiae osmoregulation is not dependent on bifunctionality of sln it is important to emphasize, however, that bifunctionality would not compromise robustness. rather, the model indicates that any upstream process that produces non-zero levels of y and yp should enable the same fundamental behavior predicted by eq. the possibility that sln exhibits phosphatase activity warrants further experimental investigation. 
we then developed a biochemically realistic mathematical model of the phospho-relay, which suggested that robustness is due to buffering by a large excess pool of ypd we confirmed experimentally that depletion of the ypd pool results in inappropriate activation of the hog pathway. we identified buffering by an intermediate component in excess as a novel mechanism through which a phospho-relay can achieve robustness. the hog pathway is rapidly activated under conditions of elevated osmolarity and regulates transcriptional and metabolic changes within the cell. under normal growth conditions, however, a three-component phospho-relay consisting of the histidine kinase sln the transfer protein ypd and the response regulator ssk represses hog pathway activity by phosphorylation of ssk this inhibition of the hog pathway is essential for cellular fitness in normal osmolarity. nevertheless, the extent to and mechanisms by which inhibition is robust to fluctuations in the concentrations of the phospho-relay components has received little attention. we established that the sln1-ypd1-ssk phospho-relay is robust—it is able to maintain inhibition of the hog pathway even after significant changes in the levels of its three components. hog pathwayosmotic stresshistidine kinaserobustnessmathematical modelinginvariantsissue-copyright-statement© the author 2015
 the yeast saccharomyces cerevisiae relies on the high-osmolarity glycerol signaling pathway to respond to increases in external osmolarity. the hog pathway is rapidly activated under conditions of elevated osmolarity and regulates transcriptional and metabolic changes within the cell. under normal growth conditions, however, a three-component phospho-relay consisting of the histidine kinase sln the transfer protein ypd and the response regulator ssk represses hog pathway activity by phosphorylation of ssk this inhibition of the hog pathway is essential for cellular fitness in normal osmolarity. nevertheless, the extent to and mechanisms by which inhibition is robust to fluctuations in the concentrations of the phospho-relay components has received little attention.  we established that the sln1-ypd1-ssk phospho-relay is robust—it is able to maintain inhibition of the hog pathway even after significant changes in the levels of its three components. we then developed a biochemically realistic mathematical model of the phospho-relay, which suggested that robustness is due to buffering by a large excess pool of ypd we confirmed experimentally that depletion of the ypd pool results in inappropriate activation of the hog pathway.  we identified buffering by an intermediate component in excess as a novel mechanism through which a phospho-relay can achieve robustness. this buffering requires multiple components and is therefore unavailable to two-component systems, suggesting one important advantage of multi-component relays. electronic supplementary material the online version of this article contains supplementary material, which is available to authorized users. keywords hog pathwayosmotic stresshistidine kinaserobustnessmathematical modelinginvariantsissue-copyright-statement© the author 2015 