How to Quantify the Control Exerted by a Signal over a Target

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How to Quantify the Control Exerted by a Signal
over a Target?
System Response the sensitivity (R) of the
target T to a change in the signal S
Kholodenko et al (1997) FEBS Lett. 414 430
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Ultrasensitive Response of the MAPK Cascade in
Xenopus Oocytes Extracts Is Explained by
Multiplication of the Local Responses of the
Three MAPK Levels
James E. Ferrell, Jr. TIBS 21460-466 (1996)
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Control and Dynamic Properties of the MAPK
Cascades
Cascade response R d lnERK-PP/d lnRas
Cascade with no feedback R r1 ? r2 ? r3
Kholodenko, B.N. (2000) Europ. J. Biochem. 267
1583.
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Effects of Feedback Loops on the MAPK Dynamics

• Positive Feedback Can Cause Bistability and
  Hysteresis

Kholodenko, B.N. (2000) Europ. J. Biochem. 267
1583 Multi-stability analysis Angeli Sontag,
Systems Control Letters, 2003 (in press)
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Interaction Map of a Cellular Regulatory Network
is Quantified by the Local Response Matrix
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System Responses are Determined by Local
Intermodular Interactions
Rp - r 1 ?rp F1?(dgF)?rp
RP ?x/?p system response matrix p
perturbation parameters (signals) r - local
response matrix (interaction map) F ?f/?x the
Jacobian matrix rP ?f/?p matrix of
intramodular (immediate) responses to signals
Bruggeman et al, J. theor Biol. (2002)
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Untangling the Wires Tracing Functional
Interactions in Signaling, Metabolic, and Gene
Networks
Quantitative and predictive biology the ability
to interpret increasingly complex datasets to
reveal underlying interactions
However, at steady-state the Fs can only be
determined up to arbitrary scaling factors
Scaling Fij by diagonal elements, we obtain the
network interaction matrix, r - (dgF)-1?F
Problem Network interaction map r cannot be
captured in intact cells. Only system responses
(R) to perturbations can be measured in intact
cells.
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Untangling the Wires Tracing Functional
Interactions in Signaling and Gene Networks.
Goal To Determine and Quantify Unknown Network
Connections
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Testing the Method Comparing Quantitative
Reconstruction to Known Interaction Maps
Problem To Infer Connections in the Ras/MAPK
Pathway
Solution To Simulate Global Responses to
Multiple Perturbations and Calculate the Ras/MAPK
Cascade Interaction Map
Ras
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Raf-P
Raf
MEK-PP
MEK-P
MEK

ERK
ERK-PP
ERK-P
Kholodenko et al. (2002), PNAS 99 12841.
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Step 1 Determining Global Responses to Three
Independent Perturbations of the Ras/MAPK Cascade.
a). Measurement of the differences in
steady-state variables following perturbations
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Step 2 Calculating the Ras/MAPK Cascade
Interaction Map from the System Responses
r - (dg(R-1))-1?R-1
Two interaction maps (local response matrices)
retrieved from two different system response
matrices
Raf-P MEK-PP ERK-PP
Raf-P
MEK-PP
ERK-PP
Known Interaction Map
Raf-P MEK-PP ERK-PP
Raf-P
MEK-PP
ERK-PP
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Unraveling the Wiring Using Time Series Data
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Inferring dynamic connections in MAPK pathway
successfully
MAPK pathway kinetic diagram
Sontag E. et al. (submitted)
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Oscillatory dynamics of the feedback connection
strengths is successfully deduced
Oscillations in MAPK pathway
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Unraveling the Wiring of a Gene Network
System Response Matrix
Calculated Interaction Map
Known Interaction Map
Kholodenko et al. (2002) PNAS 99 12841.
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Unraveling The Wiring When Some Genes Are
Unknown The Case of Hidden Variables
Existing Network
Kholodenko et al. (2002) PNAS 99 12841.
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Reverse engineering of dynamic gene interactions
Fij ?fi/?xj
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Effect of noise on the ability to infer network
M. Andrec R. Levy
Probability of misestimating network connections
as a function of noise level and connection
strengths
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r12
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r13
3
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Special Thanks to
Eduardo Sontag Michael Andrec Ronald Levy
(Rutgers University, NJ, USA)
Jan B. Hoek Anatoly Kiyatkin (Thomas Jefferson
University, Philadelphia)
Hans Westerhoff Frank Bruggeman (Free University,
Amsterdam)
Supported by the NIH/ NIGMS grant GM59570
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A snapshot of the retrieved dynamics of gene
activation and repression for a four-gene network
Numbers on the top (with superscript a) are the
correct theoretical values of the Jacobian
elements Fij
Numbers on the bottom (with superscript b) are
the experimental estimates deduced using
perturbations of the gene synthesis and
degradation rates