Signaling mechanisms that can yield Dose-Response Alignment · arrow rates were always set to zero....
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Signaling mechanisms that can yield Dose-Response Alignment Steven S. Andrews, Richard C. Yu, Gustavo Pesce, and Roger Brent Basic Sciences Introduction Discussion Conclusions Funding: NIH, MITRE. Results Methods dose, α (nM) normalized fractional response + – Negative feedback prediction fractional response dose, α (nM) y = B + A ! [ ] N ! [ ] N + E N α A B α k αA ,n αA a A k A k a k AB ,n AB b B k B k b k Ba , n Ba d A [ ] dt = a [] k A + k ! A ! [ ] n ! A ( ) " A [ ] k a + k Ba B [ ] n Ba ( ) d B [ ] dt = b [] k B + k AB A [ ] n AB ( ) ! B [ ] k b ( ) differential equations: a [] + A [ ] = 1 b [] + B [ ] = 1 equilibrium constants: K A = A [ ] s . s . a [] s . s . = k A + k ! A ! [ ] n ! A k a + k Ba B [ ] n Ba K B = B [ ] s . s . b [] s . s . = k B + k AB A [ ] n AB k b steady-state activities: A [ ] s . s . = K A 1 + K A B [ ] s . s . = K B 1 + K B non-cooperative cooperative better fit α A B α A B α A B α A B α A B α A B α A B α A B α A B α A B α A B α A B α A B unoptimized optimized dose, α (nM) fractional response dose, α (nM) fractional response α Receptor G-protein Fus3 PRM1 optimization α A B C D α A B C D dose, α (nM) fractional response dose: α (nM) fractional response WT receptor (R) no neg. feedback (F) WT G-protein (G) WT Fus3 (F) ∆Kss1 (P) ∆Sst2 (P) ∆Fus3 (P) WT PRM1 (P) α R G F P S K The yeast pheromone response signaling system transmits information about the extracellular pheromone (e.g. α-factor) concentration to the cell nucleus. Experiments, from Brent’s laboratory 1,2 and elsewhere 3 , investigated the system response to pheromone at several “measurement points” in the signaling pathway (colored circles in cartoon). They found: • The signaling system does not adapt over time, but functions at an essentially constant pace for >4 hours. • Dose-response behaviors of the different measurement points are graded, meaning that the responses increase smoothly with increasing pheromone dose. • Dose-response behaviors of the different measurement points are remarkably aligned. We call this phenomenon DoRA, for Dose-Response Alignment. DoRA is widely observed in other systems too, likely because it improves information transmission 1 . What mechanisms enable signaling systems to exhibit DoRA? - this is the topic of this poster Negative feedback is often used in engineered systems to control downstream responses and to improve linearity between input and output. Examples range from steam engine governors to electronics operational amplifiers. References In prior work, several of us 1 discovered a new negative feedback in the yeast pheromone response system, from far downstream to far upstream (Fus3 to Ste5). This was a “smoking gun” for the negative feedback that creates DoRA. We planned to prove its feasibility using modeling. 1. Rescale dose-response data so the y-axis gives the absolute fraction of protein that is activated, or fraction of maximal possible expression rate. These are best guesses, not hard numbers. Hill functions fit to these data became the inputs for further analysis. 2. In the modeling scheme, nodes (e.g. A, below) are in equilibrium between inactive and active states (e.g. a and A). Arrows connect the nodes; the source of each arrow enzymatically activates or deactivates the destination node. The following model performs negative feedback. logic diagram: reaction diagram: A B A B A B A B At “ from ” end ( A ) signal from “active” state signal from “inactive” state this is a “low-true” arrow d = 100 y m ! y d ( ) 2 c d dy d d" + c m dy m d" # $ % & ’ ( d" !) ) * c d = 1 2 y d ! ( ) " y d 0 () c m = 1 2 y m ! ( ) " y m 0 () d = 100 c d y m ! y d ( ) 2 dy d y d 0 () y d " ( ) # + c m y m ! y d ( ) 2 dy m y m 0 () y m " ( ) # dose, α (nM) normalized response, y y data model rescaling dose axis simplifies result: y model y data y model y data At “ to ” end ( B ) activate destination deactivate destination 3. Computationally optimize model parameters to get the best fit between model and experimental dose-responses. Fit errors are quantified with a new “slope-weighted RMS difference” metric. 4. See what models can or cannot fit experimental data. The modeling scheme is not mechanistically accurate. Its results are meaningful if the model has the same capabilities and constraints as real signaling systems. Both model and reality can exhibit any Hill function, and are essentially limited to Hill functions, which suggests the model is valid. 1. A linear network architecture fit the data poorly. α Receptor G-protein Fus3 PRM1 Model dose-response amplitudes and EC 50 s invariably decreased. This agreed with prior results 4 . 2. Negative feedback never improved fits, whether alone or in combination. Upon optimization, negative feedback arrow rates were always set to zero. 3. A survey of all possible two-node networks showed two mechanisms that can enable DoRA. • A low-true negative feedforward (or low-true negative feedsame, which is similar), called “push-pull”. • Enzymatic cooperativity, in which the rate equation exponents could be ≠1. Shown with blue bars. 4. Push-pull mechanisms enable a substantially better fit. Here, the normal arrow activates the downstream node while the low-true arrow deactives it. α A B α k αA ,n αA a A k A k a k AB ,n AB b B k B k b k ab , n ab 5. Enzymatic cooperativity enables a nearly perfect fit. α Receptor G-protein Fus3 PRM1 parameter value n α,Receptor 1.0 n Receptor,G-protein 2.3 n G-protein,Fus3 0.3 n Fus3,PRM1 6.3 6. The model scheme, with push-pull mechanisms and cooperativity, fit 7 experimental yeast dose-response data sets well using a single set of parameters. An 8th data set did not fit, likely due to other consequences of the mutation. Push-pull mechanisms may arise in the yeast system from (i) parallel and complementary Fus3 and Kss1 pathways, (ii) a newly discovered G-protein activation mechanism 5 . Cooperativity may arise from (i) multiple phosphorylation in the kinase cascade, (ii) allosteric interactions in the Ste5 scaffold and other protein complexes. The observed Dose-Response Alignment (DoRA) in the yeast pheromone response signaling system likely does not arise from negative feedback. Instead, it likely arises from novel push-pull mechanisms and/or cooperativity. These are biologically plausible. 1. Yu, Pesce, Colman-Lerner, Lok, Pincus, Serra, Holl, Benjamin, Gordon, and Brent, “Negative feedback that improves information transmission in yeast signaling” Nature 456:755-761, 2008. 2. Colman-Lerner, Gordon, Serra, Chin, Resnekov, Endy, Pesce, and Brent, “Regulated cell-to-cell variation in a cell-fate decision system” Nature 437, 699-706, 2005. 3. Yi, Kitano, and Simon, “A quantitative characterization of the yeast heterotrimeric G protein cycle” Proc. Nat. Acad. Sci. USA 100, 10764-10769, 2003. 4. Black and Leff, “Operational models of pharmacological agonism” Proc. R. Soc. Lond. B 220:141-162, 1983. 5. Bush, Colman-Lerner, In preparation, 2012.
Transcript of Signaling mechanisms that can yield Dose-Response Alignment · arrow rates were always set to zero....
Signaling mechanisms that can yield Dose-Response AlignmentSteven S. Andrews, Richard C. Yu, Gustavo Pesce, and Roger Brent
Basic Sciences
Introduction
Discussion
Conclusions
Funding: NIH, MITRE.
ResultsMethods
dose, α (nM)
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Negative feedback prediction
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= a[ ] kA + k!A ![ ]n!A( ) " A[ ] ka + kBa B[ ]
nBa( )
d B[ ]dt
= b[ ] kB + kAB A[ ]nAB( ) ! B[ ] kb( )
differential equations:
a[ ] + A[ ] = 1 b[ ] + B[ ] = 1
equilibrium constants:
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!A![ ]
n!A
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BaB[ ]
nBa
KB=B[ ]
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kb
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The yeast pheromone response signaling systemtransmits information about the extracellular pheromone(e.g. α-factor) concentration to the cell nucleus.Experiments, from Brent’s laboratory1,2 and elsewhere3,investigated the system response to pheromone atseveral “measurement points” in the signaling pathway(colored circles in cartoon). They found:• The signaling system does not adapt over time, butfunctions at an essentially constant pace for >4 hours.• Dose-response behaviors of the different measurementpoints are graded, meaning that the responses increasesmoothly with increasing pheromone dose.• Dose-response behaviors of the different measurementpoints are remarkably aligned. We call this phenomenonDoRA, for Dose-Response Alignment.
DoRA is widely observed in other systems too, likelybecause it improves information transmission1.
What mechanisms enable signaling systems toexhibit DoRA? - this is the topic of this poster
Negative feedback is often used in engineered systemsto control downstream responses and to improve linearitybetween input and output. Examples range from steamengine governors to electronics operational amplifiers.
References
In prior work, several of us1
discovered a new negativefeedback in the yeastpheromone response system,from far downstream to farupstream (Fus3 to Ste5). Thiswas a “smoking gun” for thenegative feedback that createsDoRA. We planned to prove itsfeasibility using modeling.
1. Rescale dose-response data sothe y-axis gives the absolutefraction of protein that is activated,or fraction of maximal possibleexpression rate. These are bestguesses, not hard numbers. Hillfunctions fit to these data becamethe inputs for further analysis.
2. In the modeling scheme, nodes (e.g. A, below) are inequilibrium between inactive and active states (e.g. a andA). Arrows connect the nodes; the source of each arrowenzymatically activates or deactivates the destinationnode. The following model performs negative feedback.
logic diagram:
reaction diagram:
A BA BA BA B
At “from” end (A) signal from “active” state signal from “inactive” state
this is a “low-true” arrow
d = 100 ym ! yd( )2
cddyd
d"+ cm
dym
d"#$%
&'(d"
!)
)
*cd =
1
2 yd !( ) " yd 0( )cm=
1
2 ym!( ) " ym 0( )
d = 100 cd ym ! yd( )2
dydyd 0( )
yd "( )
# + cm ym ! yd( )2
dymym 0( )
ym "( )
#
dose, α (nM)
norm
aliz
ed re
spon
se, y
ydata
ymodelrescaling dose axis simplifies result:
y mod
el
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ymodel
ydata
At “to” end (B) activate destination deactivate destination
3. Computationally optimize model parameters to get thebest fit between model and experimental dose-responses.Fit errors are quantified with a new “slope-weighted RMSdifference” metric.
4. See what models can or cannot fit experimental data.The modeling scheme is not mechanistically accurate.Its results are meaningful if the model has the samecapabilities and constraints as real signaling systems.Both model and reality can exhibit any Hill function, andare essentially limited to Hill functions, which suggeststhe model is valid.
1. A linear network architecture fitthe data poorly.
α Receptor G-protein Fus3 PRM1
Model dose-response amplitudesand EC50s invariably decreased.This agreed with prior results4.
2. Negative feedback never improved fits, whether aloneor in combination. Upon optimization, negative feedbackarrow rates were always set to zero.
3. A survey of all possible two-node networks showedtwo mechanisms that can enable DoRA.• A low-true negative feedforward (or low-true negativefeedsame, which is similar), called “push-pull”.• Enzymatic cooperativity, in which the rate equationexponents could be ≠1. Shown with blue bars.
4. Push-pull mechanisms enable a substantially better fit.Here, the normal arrow activates the downstream nodewhile the low-true arrow deactives it.
α
A
B
α
kαA,nαA
a AkA
ka
kAB,nAB
b BkB
kb
kab,nab
5. Enzymatic cooperativityenables a nearly perfect fit.α Receptor G-protein Fus3 PRM1
parameter valuenα,Receptor 1.0nReceptor,G-protein 2.3nG-protein,Fus3 0.3nFus3,PRM1 6.3
6. The model scheme, with push-pull mechanisms andcooperativity, fit 7 experimental yeast dose-responsedata sets well using a single set of parameters. An 8thdata set did not fit, likely due to other consequences ofthe mutation.
Push-pull mechanisms may arise inthe yeast system from (i) paralleland complementary Fus3 and Kss1pathways, (ii) a newly discoveredG-protein activation mechanism5.
Cooperativity may arise from (i)multiple phosphorylation in thekinase cascade, (ii) allostericinteractions in the Ste5 scaffold andother protein complexes.
The observed Dose-Response Alignment (DoRA) in theyeast pheromone response signaling system likely doesnot arise from negative feedback. Instead, it likely arisesfrom novel push-pull mechanisms and/or cooperativity.These are biologically plausible.
1. Yu, Pesce, Colman-Lerner, Lok, Pincus, Serra, Holl,Benjamin, Gordon, and Brent, “Negative feedback thatimproves information transmission in yeast signaling” Nature456:755-761, 2008.
2. Colman-Lerner, Gordon, Serra, Chin, Resnekov, Endy, Pesce,and Brent, “Regulated cell-to-cell variation in a cell-fatedecision system” Nature 437, 699-706, 2005.
3. Yi, Kitano, and Simon, “A quantitative characterization of theyeast heterotrimeric G protein cycle” Proc. Nat. Acad. Sci.USA 100, 10764-10769, 2003.
4. Black and Leff, “Operational models of pharmacologicalagonism” Proc. R. Soc. Lond. B 220:141-162, 1983.
5. Bush, Colman-Lerner, In preparation, 2012.
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