Understanding the Biochemical Origin of Sigmoidal Dose ...
Transcript of Understanding the Biochemical Origin of Sigmoidal Dose ...
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Understanding the Biochemical Origin of Sigmoidal Dose Responses: Ultrasensitive Response Motifs
September 5, 2017
Qiang Zhang, M.D., Ph.D.
Department of Environmental Health Rollins School of Public HealthEmory UniversityAtlanta, GA
Dose
Res
pons
e
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Sigmoidal Dose Response1. Sigmoidal response is a common type of dose response observed
in biological systems
2. These sigmoidal curves are often approximated empirically, among others, by Hill equations
3. Steep sigmoidal responses can mediate switch-like, threshold effects
4. Cooperativity is the often-cited mechanism for sigmoidal responses
5. Diverse biochemical mechanisms other than cooperativity can generate sigmoidal responses
6. As chemical toxicity testing is increasingly based on in vitro cell assays, understanding the mechanisms becomes ever important
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Outline
1. Sigmoidal dose response, Hill function, and ultrasensitivity
2. Common ultrasensitive response motifs (URM)
3. MAPK: an example of URM combination
4. Role of signal amplification thru URM in cellular dynamics
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Cellular System
Physical/chemical stressor
Response X Response Y Response Z
Perturbation
(Response: metabolism, gene expression, proliferation, apoptosis, carcinogenesis……)
Biochemical circuits/networks mediate cellular responses
Resp
onse
Stressor
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Bottom-up approach to understanding molecular circuits
Part list MAPK Nrf2 PHD
ERCycBCdk Cdh1
APCp53 CAT
Network motifs MAPKMAPK
MAPK Kinase
P
Phosphatase
P
CycB
Cdh1
p53
Mdm2
C/EBPα PPARγ
PU.1GATA-1
Nrf2Keap1ROS
Circuits / networks
G1
Cdh1
SynthesisSynthesisCycB
Cdk
Ø DegradationØ Degradation
APCAPCCdh1APC
PCdh1APCAPC
P
(active) (inactive)
Cell massCell mass
Cdc20SynthesisSynthesis
ØØ
(inactive)
Cdc20(active)
Cdc20(active)
IE(inactive)
IE(inactive)
IE P
(active)IE P
(active)
Degradation
IgBcl-6 Pax5Blimp-1
TCDD
AhR
LPS
AP-1
Bach2
p53A
p53A
p53A
ΦΦSignal
DNAdamage
(ATM) Signal
DNAdamage
(ATM)
Φ
p53I
Φ
p53I
p53I
Φ
Mdm2
Φ
Mdm2
Inhibitor
(Wip1)
Φ
Inhibitor
(Wip1)
Φ
ΦΦ
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Network MotifNetwork motifs are relatively simple building blocks that frequently appear in complex molecular circuits and possess specific signaling properties.
Important common motifs:
YX
I. Ultrasensitive motif
X Y Z
X Y Z
II. Positive or double-negative feedback motif
ZYX
III. Negative feedback motif
IV. Feedforward motif
Y
Z
X
Y
Z
X
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Ultrasensitive response motifsUltrasensitivity refers to a (steady-state) stimulus-response that is
significantly steeper than the hyperbolic, Michaelis-Menten form such that it appears globally as a sigmoid curve on a linear scale.
0 1 2 3 4 5 60
0.2
0.4
0.6
0.8
1.0
X
Y
hyperbolic
sigmoid
(x1, y1)
(x2, y2)
ΔxΔy 1
xxyy
1
1 >∆∆
for ultrasensitive response
• Ultrasensitive response allows amplification of percentagechange locally.
• The steepness of the globally sigmoid curve is usually approximated by Hill function.
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0 1 2 3 4 5 60
0.2
0.4
0.6
0.8
1.0
X
Y
Hill Function
nn
n
XKXY+
=
Hill Function
Hill coefficient
1.0
9.0ln
81ln
XXn =
X0.9X0.1
0.1
0.9
• The Hill coefficient measures globally how steep the sigmoid curve is by using the Michaelis-Menten formalism as reference.
• An ultrasensitive response, when approximated by Hill function, has n significantly greater than 1.
hyperbolic
sigmoid
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X0.9/X0.1 n81 19 2
4.33 33 4
Hill Function
nn
n
XKXY+
=
Hill Function
Hill coefficient
1.0
9.0ln
81ln
XXn =
• The higher the Hill coefficient (n), the steeper the sigmoid curve.
• When n=1, the Hill function reduces to the Michaelis-Menten function.
0 1 2 3 4 5 60
0.2
0.4
0.6
0.8
1.0
X
Y
n=1n=4n=3n=2
n=1
n=4n=3n=2
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Common ultrasensitive motifs and the biochemical basis of sigmoidal responses
X
R XR
X
XRXXRRX
X
R XR
XR
XY
WZ
RX XRXII
(1) Positive cooperative binding (2) Homo-multimerization
(3) Multi-step signaling (4) Molecular titration
(5) Zero-order covalent modification cycle (6) Positive feedback
+X Y
X
Y YaZ
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(1) Positive cooperative binding
Hemoglobin
O2
k1
k2
k3
k4
k5
k6
k7
k8
TF
2X response element
TF
TFTF TF
TF
TF
TFTF TFk1
k2 TF TF
TF TF
TFk3
k4
* Positive cooperative binding occurs when 12
34
56
78
kk
kk
kk
kk
<<<
* Positive cooperative binding occurs when 12
34
kk
kk
<
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XRk1
k2
X + R X2Rk3
k4
+ X
nn
ntotal
bound XKXRR
][][][
+=
Approximated by Hill function
n: Hill coefficient
X3Rk5
k6
+ X X4Rk7
k8
+ X
• When
n=112
34
56
78
kk
kk
kk
kk
===
• When
the affinity for subsequent binding is greater than that for previous binding,
n=1~4
12
34
56
78
kk
kk
kk
kk
<<<
(1) Positive cooperative binding
O2 partial pressure (mmHg)26.8 40 80 120
% O
2-bo
und
hem
oglo
bin
50
100
0
n≈2.8
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XRk1
k2
X + R X2Rk3
k4
+ X
nn
ntotal
bound XKXRR
][][][
+=
Approximated by Hill function
n: Hill coefficient
X3Rk5
k6
+ X X4Rk7
k8
+ X
• When
n=112
34
56
78
kk
kk
kk
kk
===
• When
the affinity for subsequent binding is greater than that for previous binding,
n=1~4
12
34
56
78
kk
kk
kk
kk
<<<
(1) Positive cooperative binding
Adapted from Schaeffer et al, PNAS 1999 and Gregor et al, Cell 2007
Drosophila embryo anterior-posterior axis patterning by morphogen Bicoid
Bicoid
PA
Hunchback
PA
Bicoid
Hunc
hbac
k
Multiple response elements
Bicoid BicoidBicoid
Bicoid
Bicoid
Bicoid
Bicoid
Hunchback
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(2) Homo-multimerization
Estrogen target genes
ERE
ER ER
Estrogen
ER ER
CAT
CATCAT
Catalase mononer
CATCAT
CATCATFull
Catalase
H2O2 H2O
CAT
ARE
Nrf2 Maf
OxidativeStress
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XRk1
k2
X + R X2R2
k3
k4
+ XR
]RX[k]XR[kdt
]RX[d224
23
22 −=
at steady state
2
4
322 ]XR[
kk]RX[ =
0 1 2 3 4 50
0.2
0.4
0.6
0.8
1.0
X
monomerdimertrimertetramer
% M
ultim
er
(2) Homo-multimerization
and when X is at low concentrations, [XR] is approximately linear to [X], so…
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(2) Homo-multimerization
Park CS et al, JBC 2003
n=1.55n=1
• Binging of PDGF receptor (PDGFR) by its ligand PDGF leads to receptor dimerization and autophosphorylation.
• Data shows results of tyrosine phosphorylation of PDGFβR in NIH 3T3 fibroblasts stimulated by human recombinant PDGF-BB as ligand.
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(3) Multi-step signaling
MAPK
MAPK Kinase
MAPKP
MAPKPP
Antioxidant genes
Nrf2
Keap1
ROS
↑ n
ucle
ar im
port
ing
↑ Nrf2 stability
Target gene
Antihypoxic genes
↑ coactivator-recruiting ability
HIF-1α
↑ HIF-1α stability FIH
O2
PHD
(a) MAPK signaling
(b) Antioxidant response (c) Hypoxic response
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Y
X
Z
][][
][][][
32
max
YKY
XKXZZ
++=
][][][
1
max
XKXYY
+=
Assume at steady-state
][][][][ 22
2
XKXKXKZ
ba
c
++=
max3
321
YKKKKKa +
=3
2
max
21
KK
YKKKb +
+=
max3
maxmax
YKYZKc +
=( where )
0 5 100
0.2
0.4
0.6
0.8
1.0
Actual responseHill function (n=1)Hill function (n=2)
X
Z+
+
+
(3) Multi-step signaling
For multi-step signaling to generate ultrasensitivity, the converging paths have to act on processes that are synergistic rather than additive. The former denotes multiplication in mathematical term.
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(3) An example of multi-step signaling ultrasensitivity
Hardie et al, Biochem J 1999
ZMP: an AMP mimicAM
PK-P nH = 2.5
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RR
DD DDDD DD DDRR
A
L
R
D
Ligand
Cognate receptor
Decoy receptor R
T
A
Transcription factor
Activator
Repressor
T AT A
T RT R
B
R
T A
T RT R
T RT RT RT R
T RT R
S
I
P
E
Substrate
Inhibitor
Enzyme
Product
S
I
P
EES EE
EEI EE
C
(4) Molecular titration
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L R+ RL
(Active)
k1
k2L RR+ RRL
(Active)
k1
k2
(4) Molecular titration• Ultrasensitivity occurs when binding affinity between L
and D (stoichiometric inhibitor) is much greater than that between L and R. The higher the former, the steeper the response is.
• At low concentrations, L is mostly soaked up by D. When total L increases to a level where all Ds are nearly used up, any further addition of L into the system will be all available for R. This is the point at which the abrupt change occurs.
• Note the input is the total amount of L not free L.
2
1
4
3kk
kk
>DR
+
DR
Inactive
DR
DR
L
k3 k4
DRD
DRDInactive
DRD
DRD
L
k3 k4
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(4) An example of molecular titration ultrasensitivity
Buchler and Cross, Mol Sys Biol 2009
A: CEBPα-RFP
YFP
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(5) Covalent modification cycle
Lipase
Glucagon
LipaseP
Insulin
Triacylglycerol fatty acid + glycerol
MAPKMAPK
MAPK Kinase
P
Phosphatase
Target gene
P
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0 1 2 3 4 50
0.2
0.4
0.6
0.8
1.0
Yp
Ytotal
X
Yp
X
YZ
0 20 40 60 80 10010 30 50 70 900
0.5
1
1.5
2
0.25
0.75
1.25
1.75
Yp
rate
100 80 60 40 20 090 70 50 30 10
Y
Phosphorylation rateDephosphorylation rate
X=1
X=0.5
X=0.25
X=2X=4
Ytotal=100Ytotal=10Ytotal=1
When Ytotal=100>>Km(x), Km(z)
]Y[K]Y][Z[k
]Y[K]Y][X[k
dt]Y[d
p)z(m
p2
)x(m
1p
+−
+=
])Y[]Y[Y( ptotal +=
Phosphorylation rate Dephosphorylation rate
)1]Z[KKkk( )z(m)x(m21 =====
(5) Covalent modification cycle (zero-order ultrasensitivity)
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GlycogenPhosphorylase
(5) An example of zero-order ultrasensitivity
GlycogenPhosphorylase
Phosphorylase kinase
P
Protein phosphatase-1
Glycogen Glucose-1-phosphateMeinke et al, PNAS 1986
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(6) Positive feedback
Nrf2 Maf
OxidativeStress
ARE
CAT,GPx,SOD,GR,GCL……other antioxidant genes
ARE
Nrf2
Kinase
Pro Pro *
Gene auto-regulation Auto-catalysis
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X
Y+
X
Y+
ZR
X R
RX
% RX
The ultrasensitive response can not be satisfyingly fitted with Hill function of any Hill coefficient.
0 2 4 6 8 100
0.2
0.4
0.6
0.8
1
X
Actual responseHill function (n=1)Hill function (n=2)
(6) Positive feedback
Ultrasensitivity arises even when every activation step in the feedback loop is linear.
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Combinations of Ultrasensitive Motifs
Motif A
Motif B
Motif C
Motif D
MAPK
MKK
MKKK
HRE
Heat shock protein
HSF
HSF
HSF
HSF
Heat
Homo-trimerization
Cooperative binding
Multi-step signaling, zero-order ultrasensitivity
Multi-step signaling, zero-order ultrasensitivity
A number of slightly ultrasensitive motifs can be linked in sequence to give rise to an overall steeply sigmoid, or switch-like response.
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Adapted from Johnson and Lapadat, Science 2002
Cell cycle, differentiation, apoptosis, stress response, metabolism, etc
MAPK cascade, motif, and function
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JNK ultrasensitivity in mammalian cells
Bagowski et al, Current Biology 2003
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MAPK cascade outputs increasing degree of ultrasensitivity
INPUT
MKKKP
MKKP
MKP
OUTPUT
Input
MKKK*MKKK MKKK*
MKK MKKP
MKKP
P
MAPK MAPKP
MAPKP
P
MKKP
MKP
MKKpp
Input
MAPKpp
Input
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MKKK*
MKKK*
MKK MKKP
MKKP
P
MKK
MKKK*
MKKMKKK
*MKK
P
MKKK*
MKKPP
MKKK*
MKKP
MKKK*
MKKP
MKKK*
MKKPP
MKKK*
MKK
MKKK*
MKKMKKK
*MKK
P
MKKK*
MKKPP
MKKK*
MKKPP
Scenario 1:
Scenario 2:
one collision (processive)
two collisions (nonprocessive, multi-step signaling ultrasensitivity)
Origin of MAPK ultrasensitivity (I): multi-step signaling• Scenario 2 is what actually happens with dual-
phosphorylation of MKK.• Two separate collisions mean MKKK will appear
(twice) as a non-linear term for the rate of dual-phosphorylation of MKK. This is a form of multi-step signaling, one of the sources for ultrasensitivity.
• Dual-phosphorylation of MAPK also proceeds similarly via two collisions.
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Origin of MAPK ultrasensitivity (II): zero-order ultrasensitivity
INPUT
MKKKP
MKKP
MKP
MKKK MKKK*
MKK MKKP
MKKP
P
MAPK MAPKP
MAPKP
P
MKKP
MKP
• In the MAPK cascade, each kinase is phosphorylated by its upstream kinase and dephosphorylated by a phosphatase. This covalent modification cycle may generate ultrasensitivity if the amount of the kinase, as a substrate, is comparable or greater than the Michaelis-Menten constants for its phosphorylation and dephosphorylation.
• There are at least four phosphorylation/dephosphorylation cycles in the cascade, and each could be a potential source for some degree of zero-order ultrasensitivity.
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Origin of MAPK ultrasensitivity (III): layered arrangement
INPUT
MKKKP
MKKP
MKP
MKKK MKKK*
MKK MKKP
MKKP
P
MAPK MAPKP
MAPKP
P
MKKP
MKP
• With multi-step signaling and zero-order ultrasensitivity, each layer of the MAPK cascade could have some degree of ultrasensitive response of its own, e.g., MKKpp vs. MKKK*, and MAPKpp vs. MKKpp.
• When two ultrasensitive layers are linked in tandem into a cascade, it is possible that the cascade as a whole is more ultrasensitive than each individual layer alone. This is analogous to feeding the output of one amplifier into another amplifier, together they generate a much greater output than each individual amplifier can do.
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MAPK
MKK
MKKK
TF
Hormone, growth factor, stress, etc
Target gene
+, - +
-
Ultr
asen
sitiv
e m
otif
MAPK cascade is embedded in larger networks
•Positive feedback
1. Switch-like response
2. Bistability (irreversible cell fate commitment)
•Negative feedback
1. Cellular homeostasis
2. Adaptation and signal desensitization
3. History-dependent response
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Ultrasensitive response motifsUltrasensitivity refers to a (steady-state) stimulus-response that is
significantly steeper than the hyperbolic, Michaelis-Menten form such that it appears globally as a sigmoid curve on a linear scale.
0 1 2 3 4 5 60
0.2
0.4
0.6
0.8
1.0
X
Y
hyperbolic
sigmoid
(x1, y1)
(x2, y2)
ΔxΔy 1
xxyy
1
1 >∆∆
for ultrasensitive response
• Ultrasensitive response allows amplification of percentagechange locally.
• The steepness of the globally sigmoid curve is usually approximated by Hill function.
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Invention of the vacuum tube triode and later the transistor – both of which can amplify electrical signals – heralded the age of modern electronics
+Vcc
0v
Signal Input
Signal Output
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Ultrasensitivity is required for complex dynamics
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Summary
•Ultrasensitive motifs transfer signal in a sigmoid manner such that they amplify the percentage changes in the input signal.
•Motifs that may generate ultrasensitivity include positive cooperative binding, homo-multimerization, multi-step signaling, molecular titration, zero-order covalent modification cycle, and positive feedback.
•Ultrasensitive motifs can be linked in sequence to generate steeply sigmoid, or even switch-like response.
•The MAPK cascade transfers signal in an ultrasensitive manner.
•Ultrasensitive motifs are required to generate more complex behaviors, including bistability, robust homeostasis, oscillation, and others.