robustness is an intrinsic feature of life as all cellular systems have to maintain functionality in the face of naturally occurring external and internal fluctuations . the resilience of cellular genetic networks lets the cell tolerate a certain level of environmental or mutational perturbations . this robustness can be achieved either by maintaining the cellular status stable against various fluctuations , or by adapting to external changes by triggering a series of cellular responses ( kitano , 2004 ; stelling et al , 2004 ) . the decision to respond and adapt is relayed via signal transduction systems , which , upon activation by specific stimuli , produce distinct regulatory signals in the form of changes in levels of activated signal - pathway components . a critical aspect of such processes is distinguishing a genuine signal from stochastic fluctuations in protein levels and activity , as misinterpretation of these has potentially disastrous fitness consequences . thus , the robustness of cells to maintain such a function despite variations in dosage of the components is of primary importance for survival . despite their importance for viability and fitness , little is known about how signalling systems distinguish between signals and natural fluctuations , or to what extent such fluctuations are tolerated . here , we approach this issue through a system - wide robustness study of the hog pathway of saccharomyces cerevisiae , which is one of the most extensively studied eukaryotic signal - transduction cascades . the signalling pathway , which is depicted in figure 1 , consists of a map kinase ( mapk ) core module , upon which two independent upstream branches converge . the first of these consists of a phosphotransfer module , including the histidine kinase and presumed osmosensor sln1p , the phosphotransfer protein ypd1p and the response regulator ssk1p . when active , this module keeps ssk1p phosphorylated and inactive . when the module is inactive , dephosphorylated ssk1p binds to and activates the mapk kinase kinases ssk2p and ssk22p ( saito and tatebayashi , 2004 ) . two mucin - like proteins msb2p and hkr1p were recently suggested as putative osmosensors of the second input branch ( tatebayashi et al , 2007 ) . on activation , the transmembrane protein sho1p is believed to receive signals from these sensors and convey these signals to the interior of the cell . sho1p also assembles the mapk kinase pbs2p and the mapk kinase kinase ste11p through its cytoplasmic domain . the sho branch also requires cdc42p and ste20p for the transmission of the signal . once active , ste11p , ssk2p and ssk22p are each able to phosphorylate pbs2p , which also acts as a scaffold for the mapk module . pbs2p in turn phosphorylates and activates the mapk hog1p , which has numerous targets , including the cytoplasmic kinase rck2p and several transcription factors such as hot1p , sko1p and smp1p . active hog1p accumulates in the nucleus and partakes in transcription ( hohmann , 2002 ) . the methodology used here links the expression of each target gene of interest to that of a defective allele of a metabolic gene . this allele , leu2-d , has a defective promoter and needs to be present in a high copy number to support high leu2p levels and thus unperturbed growth in the absence of leucine ( schneider and guarente , 1991 ) . by placing a target gene of interested on the same episomal plasmid as leu2-d , the copy number and thus the expression level of this target gene can be controlled via the leucine concentration in the media . the gene in question is still under the control of its normal promoter , allowing expression that is regulated but increases proportionally with the increase in copy number ( moriya et al , 2006 ; torres et al , 2007 ) . if the increase in target gene product interferes with cellular function , a negative pressure on plasmid copy number will balance the positive pressure conferred by the metabolic gene , resulting in a genetic tug - of - war ( gtow ; supplementary figure s1 ) . such a compromise will result in a decrease in cellular fitness , which can be measured precisely using high - resolution microcultivation ( warringer et al , 2003 ) . on applying the gtow methodology to investigate the hog - pathway robustness , we found a high prevalence of negative impacts from gene dosage perturbations within the hog pathway ( figure 1a ) . we used three physiological  windows ' to assess the robustness ; growth rate , growth adaptation time and growth efficiency . growth rate was considered the primary readout because of its strong correlation to plasmid copy number ( moriya et al , 2006 ) . adaptation defects ( prolonged growth lag ) turned out to be similar to growth - rate defects , although even more pronounced and frequent ( supplementary figure s2a ) . altogether , overexpression of 22 out of 29 hog - pathway components caused a significant defect in at least one of these three growth variables ( p<0.001 , see supplementary information ) . these phenotypes were strongly linked to leucine starvation and thus to selective pressure for high plasmid copy numbers ( figure 1b ) . they were also observed for all protein classes , and for both positive and negative regulators of the pathway ( figure 1c ) . the negative effects from increases in gene dosage were emphasized by a complete lack of positive fitness effects mediated by any of the gtow constructs . the highest frequency and strength of defects were observed during adaptation , which may reflect the delicate balance of signal transmission in initiating proliferation . the high frequency ( 76% ) of hog - pathway gtow - imposed defects stands in stark contrast to the cell - cycle system , for which only 2530% of the gtow constructs caused a clear growth retardation ( moriya et al , 2006 ) , and to a global gal1 promoter - driven overexpression study using galactose induction in which a mere 15% of the targets conferred detectable growth defects ( sopko et al , 2006 ) . interestingly , little correlation in terms of cellular toxicity was found between the gtow- and galactose - driven overexpressions of the same , but gst tagged proteins , even on galactose ( supplementary figure s3 ) . the lack of correlation may be explained by the varying absolute levels of overexpressions ( supplementary figure s3e ) in the different screens and by the influence of the gst tag on protein function . the high prevalence of nodes of fragility within the hog pathway may be partly explained by the very nature of signal transduction , as overexpression defects are enriched among components that transduce adaptation signals , that is kinases , phosphatases and transcription factors ( sopko et al , 2006 ) . however , the high fraction of such components in the hog pathway can not be the sole reason for the high frequency of fitness defects , as the system is also sensitive to overexpression of more than half of the components , which do not partake in ( de)phosphorylation or transcription . in fact , each such component that does not impair normal growth when overexpressed is either known or presumed to be a targeting or activating partner of catalytic components within the pathway , that is nbp2p for ptc1p , ste50p for ste11p and opy2p for ste50p / ste11p ( posas et al , 1998 ; mapes and ota , 2004 ; wu et al , 2006 ) . overexpression of their catalytic partners , ste11p and ptc1p , also failed to cause significant growth defects ( p>0.001 ; see supplementary information ) . overall , these paired components are more robust against overexpression ( p=0.022 , fisher 's exact test ) . the gtow targets ' phenotypes vary much more than the corresponding deletion mutants ' phenotypes . four of the genes included here are essential ( cdc24 , cdc42 , sln1 and ypd1 ) , but the twenty - five viable deletion strains show at the most mild growth defects during normal conditions . only in the presence of nacl stress does deletion of those genes cause strong but viable phenotypes . however , these deletion phenotypes have little in common with those caused by overexpression ( supplementary figure s4 ) . the strongest gtow phenotype is caused by pbs2p , which is well known to be highly important for growth on salt as well as severely toxic when overexpressed . hog1p is likewise important for osmotic tolerance but , unlike pbs2p , not toxic when overexpressed . in addition , ssk1p is severely toxic when overexpressed , but dispensable for osmotic tolerance . although their roles in the osmotic stress response are well known , the toxicity mechanisms of ssk1p and pbs2p overexpression remain to be mechanistically resolved . however , both activate hog1p constitutively and are suppressed by the deletion of hog1 , indicating that most , if not all , of the toxicity stems from the downstream pathway hyperactivation ( figure 1d and e ) . in order to gain more insight into the mechanisms of toxicity of the two main nodes of fragility , ssk1p and pbs2p , we compared the observed in vivo sensitivity profiles with the in silico sensitivities with respect to nuclear , dually phosphorylated hog1p predicted by the hog model by klipp et al ( 2005 ) ( figure 2a ) . as the in vivo differences in fragility between ssk1p and ssk2p and the fragility of the pbs2p node can not be captured using the original model , we studied seven variants with alternative motifs of regulation involving ssk1p and pbs2p ( supplementary figure s5 ) and scored the relative improvements of each in the light of our data on overexpression ( figure 2c ) . we found that the in silico sensitivity of ssk1p is enhanced most when the dimerization of ssk1p with ssk2p is required for the phosphorylation and activation of ssk2p ( figure 2d and e ) . in addition , explicit modelling of pbs2p 's function as a scaffold best improves its performance regarding the fragility of the pbs2p node ( figure 2f and g ) . however , we observed no improvement of the in silico robustness through the implementation of the known dimerization of ssk1p alone ( supplementary figure s5 ; m1 ) , suggesting that it is unlikely to contribute to the robustness pattern . if in vivo toxicity stemmed from the indiscriminate interaction between protein pairs , we would expect the effect of overexpression to be roughly symmetrical for transient interactions or biased towards the component with lower expression levels in case of sustained interactions . here , we see neither . ssk1p has both a much stronger phenotype and higher basal expression level than ssk2p ( supplementary figure s6a ) . ssk22p is even less abundant and the effect of ssk1p overexpression is suppressed in ssk2 ( supplementary figure s6d ) . as the phosphorylated , inactive state of ssk1p has been reported to be stabilized by ypd1p ( janiak - spens et al , 2000 ) , and the gtow overexpression brings ssk1p into parity with ypd1p levels ( supplementary figure s6b ) , it may be the depletion of the stabilizing ypd1p that leads to an accumulation of dephosphorylated and active ssk1p ( supplementary figure s7 ) . consistently , deletion of either sln1 or ypd1 is lethal owing to the resulting constitutive activity of ssk1p / ssk2p and the hog pathway . although this toxicity may stem from a disrupted balance with negative regulators , such as the nbp2p ptc1p phosphatase complex , the high basal abundance of pbs2p argues against the depletion of nbp2ptc1 as the sole source of toxicity ( supplementary figure s6a ) . however , the toxicity stems from the amplification of an existing residual signal , as it can be suppressed by deletion of the upstream kinase ssk2p ( supplementary figure s6d ) . as for ssk1p , it leads to hyperactivation of hog1p ( figure 1e ) and this is the source of its toxicity ( figure 1d ) . in contrast to ssk1p and pbs2p , the phenotype caused by the phosphatase ptc2p is not mediated through the activation of the hog pathway and can not be suppressed by the deletion of hog1 ( figure 1d ) , as would be expected because its overexpression phenotype is stronger than the deletion phenotype of hog1p ( supplementary figure s4b ) . instead , the mechanism of its toxicity should be found outside the context of the hog pathway . to determine whether the hog - pathway robustness is dependent on pathway activation status , we probed the hog - pathway robustness during nacl stress , which is known to activate the pathway , and superoxide stress ( paraquat addition ) , which does not activate the pathway . both stresses were applied in doses causing a similar ( 4050% ) reduction in reference strain growth rate . interestingly , the relative gtow sensitivity patterns during these two stresses were very similar to that observed during unstressed conditions , indicating that the nodes of fragility remain regardless of pathway activation . the phenotypic correlations between these growth conditions ranged from 0.57 to 0.81 ( figure 3 ; r for lsc rate ) . the impact of the hog gtow perturbations were significantly stronger under normal growth conditions than under either nacl or paraquat stress ( p=0.005 and 7.4  10 , respectively , paired t - test of lsc rate ) . apart from this general dampening effect , which is observed under different stress conditions , robustness is largely independent of pathway activation by environmental perturbations . however , we see an indication of interaction between the genetic and environmental perturbations . although paraquat and nacl stress give similar trends in the dampening of the phenotypes , the variance around this trend seems higher under nacl ( supplementary figure s8 ) . an appealing interpretation would be conditional alleviation or aggravation , which would be expected if the effect of the genetic and environmental perturbation cancel out or act synergistically , respectively . we find it interesting that the targets furthest from the trend line under nacl stress are sln1 , sko1 and ptp3 , all known negative regulators of the osmotic stress response , on the negative side and hog1 and ptc3 on the positive side . , we used the gtow method to qualitatively capture nodes of fragility from overexpression within the hog pathway . the quantitative correlation to the level of overexpression is more difficult to assess due to additional levels of gene , mrna and protein regulation . however , previous results by moriya et al show a correlation between growth phenotype , plasmid copy number and relative protein overexpression . here the system robustness against overexpression is heavily dependent on the target component and neighbouring nodes show very different fragility . in the hog pathway , overexpression of pbs2p and ssk1p yield the strongest effects , whereas none of their neighbours ; ssk2p , ste11p or hog1p , are similarly sensitive . the in silico analysis of model variants clearly shows that model structure has a strong impact on the fragility of different nodes . ssk2p dimer and pbs2p 's scaffold function contribute to the fragility of their respective nodes . although robustness information alone can not be used to reject model structures , it provides information complementary to dynamic data that can be used to discriminate models , and should prove a valuable tool in any modelling endeavour . on applying the gtow methodology to investigate the hog - pathway robustness , we found a high prevalence of negative impacts from gene dosage perturbations within the hog pathway ( figure 1a ) . we used three physiological  windows ' to assess the robustness ; growth rate , growth adaptation time and growth efficiency . growth rate was considered the primary readout because of its strong correlation to plasmid copy number ( moriya et al , 2006 ) . adaptation defects ( prolonged growth lag ) turned out to be similar to growth - rate defects , although even more pronounced and frequent ( supplementary figure s2a ) . altogether , overexpression of 22 out of 29 hog - pathway components caused a significant defect in at least one of these three growth variables ( p<0.001 , see supplementary information ) . these phenotypes were strongly linked to leucine starvation and thus to selective pressure for high plasmid copy numbers ( figure 1b ) . they were also observed for all protein classes , and for both positive and negative regulators of the pathway ( figure 1c ) . the negative effects from increases in gene dosage were emphasized by a complete lack of positive fitness effects mediated by any of the gtow constructs . the highest frequency and strength of defects were observed during adaptation , which may reflect the delicate balance of signal transmission in initiating proliferation . the high frequency ( 76% ) of hog - pathway gtow - imposed defects stands in stark contrast to the cell - cycle system , for which only 2530% of the gtow constructs caused a clear growth retardation ( moriya et al , 2006 ) , and to a global gal1 promoter - driven overexpression study using galactose induction in which a mere 15% of the targets conferred detectable growth defects ( sopko et al , 2006 ) . interestingly , little correlation in terms of cellular toxicity was found between the gtow- and galactose - driven overexpressions of the same , but gst tagged proteins , even on galactose ( supplementary figure s3 ) . the lack of correlation may be explained by the varying absolute levels of overexpressions ( supplementary figure s3e ) in the different screens and by the influence of the gst tag on protein function . the high prevalence of nodes of fragility within the hog pathway may be partly explained by the very nature of signal transduction , as overexpression defects are enriched among components that transduce adaptation signals , that is kinases , phosphatases and transcription factors ( sopko et al , 2006 ) . however , the high fraction of such components in the hog pathway can not be the sole reason for the high frequency of fitness defects , as the system is also sensitive to overexpression of more than half of the components , which do not partake in ( de)phosphorylation or transcription . in fact , each such component that does not impair normal growth when overexpressed is either known or presumed to be a targeting or activating partner of catalytic components within the pathway , that is nbp2p for ptc1p , ste50p for ste11p and opy2p for ste50p / ste11p ( posas et al , 1998 ; mapes and ota , 2004 ; wu et al , 2006 ) . overexpression of their catalytic partners , ste11p and ptc1p , also failed to cause significant growth defects ( p>0.001 ; see supplementary information ) . overall , these paired components are more robust against overexpression ( p=0.022 , fisher 's exact test ) . the gtow targets ' phenotypes vary much more than the corresponding deletion mutants ' phenotypes . four of the genes included here are essential ( cdc24 , cdc42 , sln1 and ypd1 ) , but the twenty - five viable deletion strains show at the most mild growth defects during normal conditions . only in the presence of nacl stress does deletion of those genes cause strong but viable phenotypes . however , these deletion phenotypes have little in common with those caused by overexpression ( supplementary figure s4 ) . the strongest gtow phenotype is caused by pbs2p , which is well known to be highly important for growth on salt as well as severely toxic when overexpressed . hog1p is likewise important for osmotic tolerance but , unlike pbs2p , not toxic when overexpressed . in addition , ssk1p is severely toxic when overexpressed , but dispensable for osmotic tolerance . although their roles in the osmotic stress response are well known , the toxicity mechanisms of ssk1p and pbs2p overexpression remain to be mechanistically resolved . however , both activate hog1p constitutively and are suppressed by the deletion of hog1 , indicating that most , if not all , of the toxicity stems from the downstream pathway hyperactivation ( figure 1d and e ) . in order to gain more insight into the mechanisms of toxicity of the two main nodes of fragility , ssk1p and pbs2p , we compared the observed in vivo sensitivity profiles with the in silico sensitivities with respect to nuclear , dually phosphorylated hog1p predicted by the hog model by klipp et al ( 2005 ) ( figure 2a ) . as the in vivo differences in fragility between ssk1p and ssk2p and the fragility of the pbs2p node can not be captured using the original model , we studied seven variants with alternative motifs of regulation involving ssk1p and pbs2p ( supplementary figure s5 ) and scored the relative improvements of each in the light of our data on overexpression ( figure 2c ) . we found that the in silico sensitivity of ssk1p is enhanced most when the dimerization of ssk1p with ssk2p is required for the phosphorylation and activation of ssk2p ( figure 2d and e ) . in addition , explicit modelling of pbs2p 's function as a scaffold best improves its performance regarding the fragility of the pbs2p node ( figure 2f and g ) . however , we observed no improvement of the in silico robustness through the implementation of the known dimerization of ssk1p alone ( supplementary figure s5 ; m1 ) , suggesting that it is unlikely to contribute to the robustness pattern . if in vivo toxicity stemmed from the indiscriminate interaction between protein pairs , we would expect the effect of overexpression to be roughly symmetrical for transient interactions or biased towards the component with lower expression levels in case of sustained interactions . here ssk1p has both a much stronger phenotype and higher basal expression level than ssk2p ( supplementary figure s6a ) . ssk22p is even less abundant and the effect of ssk1p overexpression is suppressed in ssk2 ( supplementary figure s6d ) . as the phosphorylated , inactive state of ssk1p has been reported to be stabilized by ypd1p ( janiak - spens et al , 2000 ) , and the gtow overexpression brings ssk1p into parity with ypd1p levels ( supplementary figure s6b ) , it may be the depletion of the stabilizing ypd1p that leads to an accumulation of dephosphorylated and active ssk1p ( supplementary figure s7 ) . consistently , deletion of either sln1 or ypd1 is lethal owing to the resulting constitutive activity of ssk1p / ssk2p and the hog pathway . pbs2p likewise stands out as being much more sensitive than its neighbours . although this toxicity may stem from a disrupted balance with negative regulators , such as the nbp2p ptc1p phosphatase complex , the high basal abundance of pbs2p argues against the depletion of nbp2ptc1 as the sole source of toxicity ( supplementary figure s6a ) . however , the toxicity stems from the amplification of an existing residual signal , as it can be suppressed by deletion of the upstream kinase ssk2p ( supplementary figure s6d ) . as for ssk1p , it leads to hyperactivation of hog1p ( figure 1e ) and this is the source of its toxicity ( figure 1d ) . in contrast to ssk1p and pbs2p , the phenotype caused by the phosphatase ptc2p is not mediated through the activation of the hog pathway and can not be suppressed by the deletion of hog1 ( figure 1d ) , as would be expected because its overexpression phenotype is stronger than the deletion phenotype of hog1p ( supplementary figure s4b ) . instead , the mechanism of its toxicity should be found outside the context of the hog pathway . to determine whether the hog - pathway robustness is dependent on pathway activation status , we probed the hog - pathway robustness during nacl stress , which is known to activate the pathway , and superoxide stress ( paraquat addition ) , which does not activate the pathway . both stresses were applied in doses causing a similar ( 4050% ) reduction in reference strain growth rate . interestingly , the relative gtow sensitivity patterns during these two stresses were very similar to that observed during unstressed conditions , indicating that the nodes of fragility remain regardless of pathway activation . the phenotypic correlations between these growth conditions ranged from 0.57 to 0.81 ( figure 3 ; r for lsc rate ) . the impact of the hog gtow perturbations were significantly stronger under normal growth conditions than under either nacl or paraquat stress ( p=0.005 and 7.4  10 , respectively , paired t - test of lsc rate ) . apart from this general dampening effect , which is observed under different stress conditions , robustness is largely independent of pathway activation by environmental perturbations . however , we see an indication of interaction between the genetic and environmental perturbations . although paraquat and nacl stress give similar trends in the dampening of the phenotypes , the variance around this trend seems higher under nacl ( supplementary figure s8 ) . an appealing interpretation would be conditional alleviation or aggravation , which would be expected if the effect of the genetic and environmental perturbation cancel out or act synergistically , respectively . we find it interesting that the targets furthest from the trend line under nacl stress are sln1 , sko1 and ptp3 , all known negative regulators of the osmotic stress response , on the negative side and hog1 and ptc3 on the positive side . , we used the gtow method to qualitatively capture nodes of fragility from overexpression within the hog pathway . the quantitative correlation to the level of overexpression is more difficult to assess due to additional levels of gene , mrna and protein regulation . previous results by moriya et al show a correlation between growth phenotype , plasmid copy number and relative protein overexpression . here the system robustness against overexpression is heavily dependent on the target component and neighbouring nodes show very different fragility . in the hog pathway , overexpression of pbs2p and ssk1p yield the strongest effects , whereas none of their neighbours ; ssk2p , ste11p or hog1p , are similarly sensitive . the in silico analysis of model variants clearly shows that model structure has a strong impact on the fragility of different nodes . ssk2p dimer and pbs2p 's scaffold function contribute to the fragility of their respective nodes . although robustness information alone can not be used to reject model structures , it provides information complementary to dynamic data that can be used to discriminate models , and should prove a valuable tool in any modelling endeavour . this file includes : supplementary material and methods , supplementary figures s1-s8 , supplementary tables si - sii this table contains lsc values for all constructs and growth conditions , together with standard deviation ( sd ) and standard error ( sem )
cellular signalling networks integrate environmental stimuli with the information on cellular status . 
 these networks must be robust against stochastic fluctuations in stimuli as well as in the amounts of signalling components . here , we challenge the yeast hog signal - transduction pathway with systematic perturbations in components ' expression levels under various external conditions in search for nodes of fragility . we observe a substantially higher frequency of fragile nodes in this signal - transduction pathway than that has been observed for other cellular processes . 
 these fragilities disperse without any clear pattern over biochemical functions or location in pathway topology and they are largely independent of pathway activation by external stimuli 
 . however , the strongest toxicities are caused by pathway hyperactivation . in silico analysis 
 highlights the impact of model structure on in silico robustness , and suggests complex formation and scaffolding as important contributors to the observed fragility patterns . 
 thus , in vivo robustness data can be used to discriminate and improve mathematical models .