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

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Negative feedback prediction

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y = B + A![ ]

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a AkA

ka

kAB,nAB

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kb

kBa,nBa

d A[ ]dt

= 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:

KA=A[ ]

s.s.

a[ ]s.s.

=kA+ k

!A![ ]

n!A

ka+ k

BaB[ ]

nBa

KB=B[ ]

s.s.

b[ ]s.s.

=kB+ k

ABA[ ]

nAB

kb

steady-state activities:

A[ ]s.s.

=K

A

1+ KA

B[ ]s.s.

=K

B

1+ KB

non-cooperativecooperative

bette

r fit

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optimizationα A B C D α A B C D

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WT Fus3 (F)∆Kss1 (P)∆Sst2 (P)∆Fus3 (P)WT PRM1 (P)

α R G F P

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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)

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ydata

ymodelrescaling dose axis simplifies result:

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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

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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.