Understanding the Biochemical Origin of Sigmoidal Dose ...

The Hamner Institutes for Health Sciences | Copyright 2014 May not be reproduced without permission 1SRA DRSG Teleseminar, September 5, 2017 1

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


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


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


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


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


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


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.


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


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


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


(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

<


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

<<<


O2 partial pressure (mmHg)26.8 40 80 120

% O

2-bo

und

hem

oglo

bin

50

100

0

n≈2.8


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

<<<


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

http://www.pnas.org/content/96/8/4461/F3.large.jpg

http://www.pnas.org/content/96/8/4461/F3.large.jpg


(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


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


and when X is at low concentrations, [XR] is approximately linear to [X], so…



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.


(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


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.


(3) An example of multi-step signaling ultrasensitivity

Hardie et al, Biochem J 1999

ZMP: an AMP mimicAM

PK-P nH = 2.5


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


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


(4) An example of molecular titration ultrasensitivity

Buchler and Cross, Mol Sys Biol 2009

A: CEBPα-RFP

YFP


(5) Covalent modification cycle

Lipase

Glucagon

LipaseP

Insulin

Triacylglycerol fatty acid + glycerol

MAPKMAPK

MAPK Kinase

P

Phosphatase

Target gene

P


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)


GlycogenPhosphorylase

(5) An example of zero-order ultrasensitivity

GlycogenPhosphorylase

Phosphorylase kinase

P

Protein phosphatase-1

Glycogen Glucose-1-phosphateMeinke et al, PNAS 1986


(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


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.


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.


Adapted from Johnson and Lapadat, Science 2002

Cell cycle, differentiation, apoptosis, stress response, metabolism, etc

MAPK cascade, motif, and function



JNK ultrasensitivity in mammalian cells

Bagowski et al, Current Biology 2003


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


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.


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.


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.


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


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.


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


Ultrasensitivity is required for complex dynamics


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.

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