NFAT

and

NFκB

Activation

in

T

Lymphocytes

A

Model

of

Differential

Activation

of

Gene

Expression

Mathematical

models

for

the

regulation

of

the

dependent

transcription

factors

NFAT

and

NFκB

that

are

involved

in

the

activation

of

the

immune

and

inflammatory

responses

in

T

lymphocytes

have

been

developed

These

pathways

are

important

targets

for

drugs

which

act

as

powerful

immunosuppressants

by

suppressing

activation

of

NFAT

and

NFκB

in

T

cells

The

models

simulate

activation

and

deactivation

over

physiological

concentrations

of

diacyl

glycerol

-LRB-

DAG

-RRB-

and

PKCθ

using

single

and

periodic

step

increases

The

model

suggests

the

following

-LRB-

-RRB-

the

activation

NFAT

does

not

occur

at

low

frequencies

as

NFAT

requires

calcineurin

activated

by

to

remain

dephosphorylated

and

in

the

nucleus

-LRB-

-RRB-

NFκB

is

activated

at

lower

oscillation

frequencies

than

NFAT

as

IκB

is

degraded

in

response

to

elevations

in

allowing

free

NFκB

to

translocate

into

the

nucleus

and

-LRB-

-RRB-

the

degradation

of

IκB

is

essential

for

efficient

translocation

of

NFκB

to

the

nucleus

Through

sensitivity

analysis

the

model

also

suggests

that

the

largest

controlling

factor

for

NFAT

activation

is

the

dissociation/reassociation

rate

of

the

NFAT

calcineurin

complex

and

the

translocation

rate

of

the

complex

into

the

nucleus

and

for

NFκB

is

the

degradation/resynthesis

rate

of

IκB

and

the

import

rate

of

IκB

into

the

nucleus

Introduction

Nuclear

factor

of

activated

T

cells

-LRB-

NFAT

-RRB-

and

nuclear

factor

κB

-LRB-

NFκB

-RRB-

are

dependent

and

PKCθ-dependent

transcription

factors

that

mediate

the

immune

response

in

T

lymphocytes

-LRB-

T

cells

-RRB-

In

resting

cells

both

NFAT

and

NFκB

reside

primarily

in

the

cytoplasm

NFAT

in

its

phosphorylated

form

and

NFκB

bound

to

the

inhibitor

IκB

T

cell

receptor

stimulation

initiates

a

cascade

of

intracellular

reactions

causing

an

increase

in

the

cytosolic

calcium

concentration

and

a

resulting

translocation

of

both

NFAT

and

NFκB

to

the

nucleus

Both

NFAT

and

NFκB

may

bind

to

promoter

regions

of

DNA

and

in

concert

with

other

transcription

factors

allow

expression

of

genes

responsible

for

the

production

of

the

interleukins

by

and

by

NFκB

In

the

NFAT

pathway

-LRB-

Fig.

-RRB-

activates

the

phosphatase

calcineurin

which

binds

to

and

dephosphorylates

NFAT

Dephosphorylation

exposes

nuclear

localization

signals

resulting

in

rapid

translocation

of

the

NFAT-calcineurin

complex

to

the

nucleus

where

it

can

participate

in

promoting

gene

transcription

The

cytoplasm-to-nucleus

translocation

is

opposed

by

kinases

such

as

and

possibly

protein

kinase

A

that

block

the

calcineurin

dephosphorylation

of

NFAT

in

the

cytoplasm

or

that

rephosphorylate

free

NFAT

in

the

nucleus

Association

of

NFAT

with

activated

calcineurin

inhibits

the

kinase

activity

in

the

absence

of

activated

calcineurin

dephosphorylated

NFAT

in

the

nucleus

is

rephosphorylated

and

exported

This

futile

shuttling

of

NFAT

into

and

out

of

the

nucleus

results

in

little

gene

transcription

thus

gene

expression

activated

by

NFAT

requires

continuously

active

calcineurin

Figure

-LRB-

a

-RRB-

Schematic

diagram

of

the

mechanism

of

action

of

NFAT

At

rest

NFAT

is

in

its

phosphorylated

form

-LRB-

NFAT

Pi

-RRB-

and

located

mainly

in

the

cytosol

Upon

activation

a

rise

in

-LSB-

Ca

-RSB-

i

activates

calcineurin

-LRB-

C

-RRB-

which

binds

NFAT

Pi

and

dephosphorylates

it

allowing

its

import

into

the

nucleus

where

it

can

act

on

the

DNA

-LRB-

b

-RRB-

Schematic

diagram

of

the

mechanism

of

action

of

NFκB

At

rest

NFκB

is

bound

to

its

inhibitor

IκB

mainly

in

the

cytosol

-LRB-

NFκB

IκB

-RRB-

Activation

of

calcineurin

-LRB-

C

-RRB-

synergizes

with

PKCα

activating

an

early

phase

of

the

kinase

IKK

and

activation

of

PKCθ

activates

a

later

phase

of

IKK

which

phosphorylates

IκB

It

then

dissociates

from

NFκB

allowing

NFκB

to

be

imported

into

the

nucleus

where

it

can

act

on

the

DNA

In

contrast

to

NFAT

NFκB

is

retained

in

the

cytoplasm

-LRB-

Fig.

-RRB-

not

by

phosphorylation

but

by

association

with

the

inhibitory

IκB

proteins

In

resting

cells

NFκB

and

IκB

can

dissociate

in

the

cytoplasm

and

translocate

to

the

nucleus

Reassociation

of

NFκB

and

IκB

masks

nuclear

localization

signals

on

both

species

resulting

in

nuclear

export

NFκB

has

little

opportunity

to

bind

to

DNA

during

this

shuttling

and

so

little

transcription

occurs

Stimulation

of

the

T

cell

receptor

however

initiates

a

cascade

of

reactions

proceeding

through

and

that

results

in

activation

of

the

IκB

kinase

IKK

IKK

phosphorylates

IκB

associated

with

NFκB

allowing

the

IκB

to

dissociate

from

NFκB

and

marking

the

IκB

for

subsequent

polyubiquitination

and

degradation

by

the

proteasome

NFκB

is

freed

by

this

degradation

nuclear

localization

signals

on

NFκB

are

exposed

and

it

is

translocated

to

the

nucleus

where

it

can

bind

to

DNA

and

promote

gene

transcription

IκB

is

resynthesized

when

the

calcium

and

PKCθ

concentration

decrease

Newly

formed

IκB

translocates

to

the

nucleus

where

it

binds

to

NFκB

and

masks

its

nuclear

localization

signals

The

NFκB

IκB

complex

is

then

exported

to

the

cytoplasm

thus

completing

the

activation-deactivation

cycle

Recently

Hoffman

and

co-workers

showed

that

oscillations

in

the

IκB

concentration

are

observed

experimentally

and

modeled

its

mechanism

In

many

cells

interplay

of

the

sources

and

sinks

of

results

in

oscillations

in

the

intracellular

calcium

concentration

when

surface

receptors

are

stimulated

by

agonist

In

particular

T

cells

display

calcium

oscillations

in

response

to

T

cell

receptor

activation

The

transcription

factors

NFAT

and

NFκB

respond

in

different

ways

to

the

frequency

of

these

oscillations

thus

differentiating

the

activation

of

NFAT

and

NFκB

In

this

way

differential

transcription

factor

activation

and

consequent

gene

expression

is

conferred

through

a

ubiquitous

second

messenger

namely

Calcium

oscillations

have

also

been

shown

to

increase

the

level

of

NFAT

activation

at

low

levels

of

stimulation

over

a

steady

rise

in

increasing

the

efficiency

of

low-level

signal

detection

Furthermore

overexpression

of

calcineurin

partially

replaces

the

calcium

requirement

for

NFAT

activation

as

does

the

expression

of

constitutively

active

calcineurin

Defects

in

the

activation

of

NFAT

and

NFκB

and

expression

of

and

respectively

have

been

implicated

in

a

number

of

human

diseases

and

conditions

In

several

patients

failure

to

activate

NFAT

was

shown

to

cause

severe

combined

immunodeficiency

disease

SCID

Overexpression

of

can

cause

psoriasis

and

rheumatoid

arthritis

Other

conditions

related

to

defects

in

NFAT

and

NFκB

activation

include

asthma

allergy

inflammation

and

septic

shock

These

pathways

also

contain

an

important

target

for

drugs

such

as

cyclosporin

A

and

which

act

as

powerful

immunosuppressants

by

blocking

the

activation

of

calcineurin

's

phosphatase

activity

thereby

suppressing

activation

of

NFAT

and

NFκB

in

T

cells

Furthermore

the

PKCθ

inhibitor

rottlerin

can

block

PKCθ

translocation

to

the

immunological

synapse

-LRB-

IS

-RRB-

which

suppresses

the

activation

of

NFκB

in

T

cells

These

properties

make

these

drugs

useful

not

only

in

combating

immune

system

diseases

but

also

in

preventing

the

rejection

of

transplanted

tissues

But

the

general

immune

system

suppression

that

results

with

cyclosporin

A

and

leads

to

severe

side

effects

such

as

secondary

tumors

and

opportunistic

infections

and

progressive

loss

of

renal

function

and

neurotoxicity

Additionally

inhibition

of

transcription

factor

activation

in

other

types

of

cells

can

have

unintended

and

undesirable

consequences

To

understand

better

how

signal

transduction

pathways

function

to

help

find

therapies

and

cures

for

immune

system

diseases

and

to

find

better

ways

to

control

the

immune

system

in

transplant

patients

it

would

be

useful

to

understand

the

NFAT

and

NFκB

pathways

in

a

quantitative

fashion

Models

and

Mechanisms

We

have

developed

mathematical

models

for

the

action

of

NFAT

and

NFκB

that

simulate

the

activation

and

deactivation

of

each

factor

by

changes

in

intracellular

calcium

concentration

Two

separate

models

have

been

developed

one

for

NFAT

and

one

for

NFκB

We

required

both

models

to

incorporate

experimentally

determined

reaction

pathways

and

to

simulate

activation

and

deactivation

of

the

transcription

factors

through

experimentally

determined

intermediates

and

over

physiological

calcium

concentrations

Both

models

use

parameters

derived

as

much

as

possible

from

experimental

observations

-LRB-

Tables

-RRB-

We

required

the

models

to

be

capable

of

simulating

the

system

response

to

calcium

concentration

oscillations

and

in

line

with

experimental

observations

to

show

a

different

response

in

the

activation

of

NFAT

and

NFκB

to

changes

in

the

frequency

of

the

oscillations

We

expect

the

NFAT

model

to

show

that

oscillations

in

the

concentration

of

calcium

enhance

the

activity

of

NFAT

at

low

calcium

concentrations

and

that

overexpression

of

calcineurin

replaces

the

requirement

for

calcium

in

the

activation

of

NFAT

For

both

the

NFAT

and

NFκB

models

we

expect

the

models

to

require

sustained

calcium

signaling

for

gene

expression.TABLE

NFAT

rate

constants.Rate

s

s

et

al.

s

s

s

et

al.

s

et

al.

s

s

s

s

μM

s

to

control

rate

of

activation

observed

by

Shaw

et

al.

s

to

control

rate

of

deactivation

observed

by

Beals

et

al.

s

agree

with

similar

reactions

given

by

Klee

et

al.

s

et

al.

s

to

control

rate

of

deactivation

observed

by

Beals

et

al.

μM

to

control

rate

of

activation

observed

by

Shaw

et

al.

s

and

s

and

μM

et

al.

Kakalis

et

al.

s

et

al.

Kakalis

et

al.

s

and

adjusted

relative

to

to

give

equal

calcium

ion

concentrations

in

nucleus

and

s

Concentration

and

volume

parameters.ParameterValueSourceCell

nMEstimate

-LRB-

Alberts

et

al.

-RRB-

Nucleus

nMEstimate

-LRB-

Alberts

et

al.

-RRB-

Nucleus

volume

-LRB-

vn

-RRB-

volume

-LRB-

vc

-RRB-

cell

-LSB-

-RSB-

nMAlberts

et

al.

cell

-LSB-

-RSB-

nMAlberts

et

al.

calcineurin

NFκB

nMCarlotti

et

al.

NFAT

nMEstimateTotal

IκB

nMCarlotti

et

al.

calcium

ions

required

to

activate

each

calcineurin

et

al.

PKCθ

nMEstimateTotal

PKCα

nMEstimateTABLE

PKCα

membrane-binding

parameters.ParameterDefinitionValueSourceKCaDissociation

μMNalefski

et

al.

binding

Nalefski

et

al.

mol/molNalefski

et

al.

nMAnanthanarayanan

et

al.

-LSB-

DAG

-RSB-

Diacyl

glycerol

nMMogami

et

al.

constitutive

mRNA

μM

s

et

al.

inducible

mRNA

2μ

M

s

et

al.

mRNA

s

et

al.

NFκB

rate

constants.Rate

s

et

al.

s

et

al.

μM

et

al.

Kakalis

et

al.

s

et

al.

Kakalis

et

al.

s

and

adjusted

relative

to

to

give

equal

calcium

ion

concentrations

in

nucleus

and

s

μM

s

et

al.

Huang

et

al.

s

et

al.

s

to

control

rate

of

activation/deactivation

observed

by

Dolmetsch

et

al.

μM

s

to

control

rate

of

activation/deactivation

observed

by

Dolmetsch

et

al.

s

Carlotti

et

al.

s

from

Birbach

et

al.

s

Carlotti

et

al.

s

s

s

s

s

s

to

agree

with

Trushin

et

al.

s

to

agree

with

Trushin

et

al.

s

to

agree

with

Trushin

et

al.

s

to

agree

with

Trushin

et

al.

s

to

agree

with

Trushin

et

al.

s

to

agree

with

Trushin

et

al.

s

to

agree

with

Yang

et

al.

s

to

agree

with

Yang

et

al.

Estimated

from

Trushin

et

al.

Estimated

from

Trushin

et

al.

NFAT

Model

A

schematic

diagram

of

the

mechanism

for

the

action

of

NFAT

is

shown

in

Fig.

A

rise

in

the

cytosolic

calcium

concentration

leads

to

an

increased

calcium

calmodulin

concentration

which

activates

calcineurin

-LRB-

denoted

by

C

-RRB-

Calcineurin

binds

to

and

dephosphorylates

the

cytosolic

species

NFAT

Pi

the

phosphorylated

form

of

NFAT

Without

calmodulin

the

phosphatase

activity

of

calcineurin

is

much

reduced

The

dephosphorylated

NFAT-calcineurin

complex

-LRB-

NFAT

C

-RRB-

translocates

to

the

nucleus

where

it

may

bind

to

promoter

regions

of

DNA

and

assist

in

initiation

of

gene

transcription

A

lowering

of

the

calcium

concentration

results

in

deactivation

of

calcineurin

and

its

dissociation

from

the

NFAT-calcineurin

complex

Free

nuclear

NFAT

may

then

be

phosphorylated

by

ubiquitous

kinases

masking

nuclear

localization

signals

and

resulting

in

translocation

from

the

nucleus

to

the

cytoplasm

Thus

rising

and

falling

calcium

ion

concentrations

result

in

activation

and

deactivation

of

the

transcription

factor

NFAT

There

are

several

simplifying

assumptions

made

in

the

model

for

NFAT

activation

-LRB-

-RRB-

the

total

cellular

concentration

of

NFAT

remains

constant

that

is

the

degradation

and

synthesis

rates

are

balanced

-LRB-

-RRB-

dephosphorylated

NFAT

bound

to

calcineurin

in

the

nucleus

is

the

transcriptionally

active

form

of

NFAT

-LRB-

-RRB-

calcineurin

dephosphorylates

NFAT

in

one

composite

dephosphorylation

site

-LRB-

i.e.

all

sites

are

treated

as

one

-RRB-

-LRB-

-RRB-

The

cytosolic

and

nuclear

free

calcium

concentrations

are

equal

and

are

controlled

by

a

calcium

clamp

protocol

simulating

the

procedure

used

by

Dolmetsch

et

al.

-LRB-

-RRB-

calcineurin

binds

three

calcium

ions

to

become

active

and

-LRB-

-RRB-

NFAT

and

calcineurin

clearly

bind

to

other

molecules

in

the

cell

however

these

interactions

are

ignored

for

simplicity

A

reaction

scheme

consistent

with

this

mechanism

is

given

in

Fig.

Here

nuclear

species

are

shown

in

the

lower

half

of

the

figure

and

given

the

subscript

n.

Cytosolic

species

are

shown

in

the

upper

half

of

the

figure

and

given

the

subscript

c

At

the

low

calcium

concentrations

present

in

the

resting

cell

the

dominant

NFAT-containing

species

is

phosphorylated

NFAT

in

the

cytoplasm

designated

-LRB-

NFAT

Pi

-RRB-

c

-LRB-

Fig.

dark

gray

box

at

left

-RRB-

At

the

high

calcium

concentrations

present

in

the

activated

cell

the

dominant

species

is

NFAT

associated

with

activated

calcineurin

in

the

nucleus

-LRB-

NFAT

C

-RRB-

n

-LRB-

Fig.

light

gray

box

at

right

-RRB-

The

model

treats

cytosolic

and

nuclear

entities

as

distinct

and

thus

includes

separate

chemical

species

and

cytosolic

and

nuclear

Ca.

The

arrows

between

species

represent

forward

and

reverse

chemical

reactions

or

nuclear

import

and

export

The

rates

of

reaction

and

of

import

and

export

are

represented

by

the

rate

constants

designated

to

Figure

-LRB-

a

-RRB-

Reaction

scheme

for

the

NFAT

mechanism

The

activation

path

for

NFAT

is

shown

by

the

light

gray

arrows

An

increasing

calcium

concentration

activates

calcineurin

-LRB-

C

-RRB-

which

binds

to

and

dephosphorylates

NFAT

Pi

-LRB-

dark

gray

box

-RRB-

The

NFAT-activated

calcineurin

complex

NFAT

C

is

imported

to

the

nucleus

where

it

may

be

transcriptionally

active

-LRB-

light

gray

box

-RRB-

The

deactivation

path

for

NFAT

is

shown

by

the

dark

gray

arrows

A

decreasing

calcium

concentration

allows

dissociation

of

NFAT

and

activated

calcineurin

-LRB-

NFAT

C

-RRB-

in

the

nucleus

-LRB-

light

gray

box

-RRB-

Free

NFAT

is

phosphorylated

and

exported

to

the

cytoplasm

-LRB-

dark

gray

box

-RRB-

-LRB-

b

-RRB-

Reaction

scheme

for

the

NFκB

mechanism

The

activation

path

for

NFκB

is

shown

by

light

gray

arrows

An

increase

in

the

calcium

ion

concentration

activates

calcineurin

in

synergy

with

PKCα

which

through

a

sequence

of

reactions

activates

an

early

phase

of

the

kinase

IKK

Activation

of

PKCθ

leads

to

activation

of

a

later

phase

of

IKK

IKK

phosphorylates

the

NFκB

IκB

complex

-LRB-

dark

gray

box

-RRB-

which

then

dissociates

The

phosphorylated

IκB

is

degraded

and

the

free

NFκB

imported

into

the

nucleus

to

be

the

transcriptionally

active

form

-LRB-

light

gray

-RRB-

The

deactivation

path

for

NFκB

is

shown

by

dark

gray

arrows

A

decrease

in

the

calcium

ion

concentration

allows

resynthesis

of

IκB

Pi

which

enters

the

nucleus

and

associates

with

NFκB

The

resulting

complex

dephosphorylates

and

is

exported

from

the

nucleus

Using

the

law

of

mass

action

this

reaction

scheme

yields

a

system

of

coupled

first

order

differential

equations

describing

the

change

in

concentration

with

time

for

each

of

the

distinct

chemical

species

-LRB-

Appendix

A

-RRB-

The

parameters

in

the

equations

include

the

rate

constants

and

the

number

of

calcium

ions

required

to

activate

the

phosphatase

activity

of

each

calcineurin

molecule

designated

by

m

in

the

figure

The

time

course

for

the

concentrations

of

each

of

the

chemical

species

from

a

given

initial

condition

is

determined

by

numerical

solution

of

the

system

using

a

standard

fourth

order

Runge

Kutta

technique

Table

lists

the

rate

constants

used

in

the

NFAT

model

They

may

be

loosely

divided

into

three

groups

-LRB-

-RRB-

calculated

from

published

data

-LRB-

-RRB-

estimated

from

published

data

and

-LRB-

-RRB-

adjusted

to

fall

within

expected

physiological

ranges

in

order

to

make

the

model

conform

to

published

experimental

data

NFkB

Model

A

schematic

diagram

of

the

mechanism

of

action

of

NFκB

is

shown

in

Fig.

As

previous

studies

have

shown

PKCθ

and

calcineurin

act

as

co-activators

of

the

transcription

factor

NFκB

A

high

calcium

concentration

activates

calcineurin

and

PKCα

which

through

a

sequence

of

reactions

co-activates

the

IKK

complex

with

PKCθ

activation

leads

to

the

translocation

of

PKCθ

to

the

immunological

synapse

-LRB-

IS

-RRB-

and

activation

leads

to

PKCθ

migration

to

the

central

supramolecular

activation

cluster

-LRB-

cSMAC

-RRB-

in

the

IS

IKK

phosphorylates

IκB

in

the

complex

NFκB

IκB

leading

to

immediate

recognition

of

IκB

by

the

F-box/WD-domain

protein

polyubiquitination

of

the

and

subsequent

degradation

of

the

IκB

by

the

proteasome

Our

model

does

not

explicitly

include

the

polyubiquitination

but

includes

it

in

the

degradation

rate

of

IκB

which

is

essential

for

NFκB

translocation

and

hence

for

gene

transcription

Once

freed

of

IκB

NFκB

translocates

to

the

nucleus

where

it

may

bind

to

DNA

and

promote

gene

transcription

When

the

calcium

concentration

falls

to

resting

levels

newly

synthesized

IκB

rapidly

translocates

to

the

nucleus

where

it

combines

with

NFκB

masking

nuclear

localization

signals

on

both

species

The

NFκB

IκB

complex

is

then

exported

from

the

nucleus

to

the

cytoplasm

There

are

several

simplifying

assumptions

used

to

render

the

model

computationally

tractable

-LRB-

-RRB-

the

total

cellular

NFκB

concentration

is

constant

due

to

a

balance

between

its

synthesis

and

degradation

processes

-LRB-

-RRB-

IκB

production

is

enhanced

by

activated

NFκB

as

described

by

Hoffman

et

al.

-LRB-

-RRB-

the

cytosolic

and

nuclear

free

calcium

concentrations

are

equal

and

are

controlled

by

a

calcium

clamp

protocol

simulating

the

procedure

used

by

Dolmetsch

et

al.

-LRB-

-RRB-

the

IKK

kinases

are

lumped

into

one

reaction

-LRB-

-RRB-

in

the

model

IκB

represents

IκBα

-LRB-

-RRB-

the

amount

of

free

NFκB

in

the

nucleus

is

used

as

a

measure

of

the

activation

of

the

transcription

factor

-LRB-

-RRB-

calcineurin

binds

calcium

ions

to

become

active

and

-LRB-

-RRB-

the

binding

of

calcineurin

IκB

and

NFκB

to

other

molecules

in

the

cell

clearly

occurs

but

is

not

included

in

the

model

for

simplicity

A

reaction

scheme

consistent

with

this

schematic

diagram

is

shown

in

Fig.

As

in

the

reaction

scheme

for

NFAT

nuclear

species

are

shown

in

the

lower

half

of

the

figure

and

given

the

subscript

n.

Cytosolic

species

are

shown

in

the

upper

half

of

the

figure

and

given

the

subscript

c

In

the

resting

cell

the

dominant

NFκB

containing

species

is

NFκB

IκB

in

the

cytoplasm

-LRB-

Fig.

dark

gray

box

at

right

-RRB-

In

the

active

cell

the

dominant

species

is

NFκBn

-LRB-

Fig.

light

gray

box

at

left

-RRB-

The

NFκB

model

has

different

chemical

species

with

the

nuclear

and

cytosolic

concentrations

represented

separately

As

in

the

NFAT

model

the

arrows

between

species

represent

forward

and

reverse

chemical

reactions

or

nuclear

import

and

export

The

rates

of

reaction

and

of

import

and

export

are

represented

by

the

rate

constants

designated

and

and

to

Note

that

represents

the

rate

of

degradation

of

IκB

and

the

rate

of

its

resynthesis

From

the

NFκB

reaction

scheme

a

system

of

coupled

first

order

differential

equations

may

be

written

one

for

the

change

in

concentration

with

time

of

each

of

the

distinct

chemical

species

-LRB-

Appendix

B

-RRB-

Given

the

initial

concentration

of

each

species

numerical

integration

of

the

system

yields

the

time

course

of

the

concentration

for

each

species

Results

and

Discussion

A

number

of

simulations

were

performed

to

duplicate

experimental

results

to

validate

the

model

In

all

simulations

the

parameters

listed

in

Tables

were

used

unless

stated

in

the

figure

legends

The

only

difference

in

the

simulated

results

was

the

calcium

clamp

protocol

used

NFAT

Model

Results

Using

the

parameter

values

in

Tables

and

the

model

was

allowed

to

come

to

steady

state

at

rest

-LRB-

-LSB-

Ca

-RSB-

i

μM

-RRB-

The

resting

state

concentrations

are

shown

in

Table

These

concentrations

were

used

as

initial

values

when

simulating

the

evolution

of

the

concentration

of

each

species

during

a

transition

from

the

resting

state

-LRB-

-LSB-

Ca

-RSB-

i

μM

-RRB-

to

the

active

state

-LRB-

-LSB-

Ca

-RSB-

i

μM

-RRB-

The

results

are

shown

in

Fig.

The

high

calcium

concentration

activates

calcineurin

which

associates

with

and

dephosphorylates

NFAT

Pi

in

the

cytoplasm

the

concentration

of

NFAT

Pi

in

the

cytoplasm

falls

rapidly

Only

a

small

amount

of

NFAT

Pi

C

is

formed

in

the

cytoplasm

when

activated

calcineurin

associates

with

NFAT

Pi

because

it

is

rapidly

dephosphorylated

to

NFAT

C

which

in

turn

is

rapidly

translocated

to

the

nucleus

where

it

is

transcriptionally

active

Note

in

this

figure

that

the

change

in

concentration

of

the

nuclear

species

appears

large

relative

to

the

concentrations

of

the

cytosolic

species

because

the

volume

of

the

nucleus

is

smaller

than

the

volume

of

the

cytoplasm

by

a

factor

of

about

The

light

gray

arrows

in

Fig.

show

the

NFAT

activation

pathway

on

the

reaction

scheme

for

NFAT

Calcineurin

associates

with

calcium

ion

activating

calcineurin

The

activated

calcineurin

associates

with

phosphorylated

NFAT

and

dephosphorylates

it

The

NFAT

C

resulting

from

this

dephosphorylation

is

rapidly

imported

to

the

nucleus

where

it

is

transcriptionally

active

Figure

-LRB-

a

-RRB-

Activation

of

NFAT

from

the

resting

state

-LRB-

b

-RRB-

Deactivation

of

NFAT

from

the

active

state

The

reaction

paths

-LRB-

Fig.

-RRB-

for

the

activation

and

deactivation

of

NFAT

are

determined

by

observing

the

sequence

of

the

formation

of

the

various

species

in

the

reaction

scheme

TABLE

NFAT

resting

steady-state

concentrations

Species

Concentration

-LRB-

nM

-RRB-

NFATn

NFATc

C

n

C

c

-LRB-

NFAT

Pi

-RRB-

n

-LRB-

NFAT

Pi

-RRB-

c

-LRB-

NFAT

Pi

C

-RRB-

n

-LRB-

NFAT

Pi

C

-RRB-

c

-LRB-

NFAT

C

-RRB-

n

-LRB-

NFAT

C

-RRB-

c

Cn

Cc

A

simulation

of

the

deactivation

of

the

activated

state

is

shown

in

Fig.

Here

the

initial

concentrations

were

those

of

the

activated

steady

state

and

the

calcium

ion

concentration

was

set

to

μM

Figure

shows

that

the

concentration

of

the

transcriptionally

active

species

-LRB-

NFAT

C

-RRB-

n

falls

rapidly

as

NFAT

and

calcineurin

dissociate

Consequently

the

concentration

of

NFATn

rises

as

NFAT

is

freed

by

the

dissociation

and

then

falls

as

it

is

phosphorylated

The

concentration

of

the

phosphorylated

species

-LRB-

NFAT

Pi

-RRB-

n

never

rises

very

high

because

this

species

is

rapidly

exported

from

the

nucleus

The

dark

gray

arrows

in

Fig.

show

the

NFAT

deactivation

pathway

on

the

reaction

scheme

for

NFAT

After

-LRB-

NFAT

C

-RRB-

n

dissociates

free

NFAT

is

phosphorylated

and

exported

from

the

nucleus

Dolmetsch

et

al.

suggest

that

non-linearity

in

the

response

of

NFAT

to

calcium

ion

concentration

is

important

in

determining

how

the

activity

of

NFAT

depends

on

oscillations

in

the

calcium

ion

concentration

Their

experiments

show

that

oscillation

frequency

is

the

critical

factor

in

differentiating

the

response

of

NFAT

and

NFκB

Our

models

for

both

NFAT

and

NFκB

simulate

the

effect

of

calcium

ion

concentration

oscillations

on

the

activation

of

the

transcription

factors

One

such

simulation

for

NFAT

is

shown

in

Fig.

The

initial

concentrations

of

the

species

were

those

of

the

resting

state

and

the

oscillation

period

of

the

calcium

ion

concentration

was

s

The

calcium

ion

concentration

was

fixed

at

μM

during

the

initial

s

and

μM

during

the

final

s

of

each

oscillation

Figure

shows

that

the

concentration

of

the

transcriptionally

active

-LRB-

NFAT

C

-RRB-

n

rises

rapidly

during

the

high

calcium

concentration

pulse

and

then

decays

more

slowly

during

the

low

calcium

concentration

portion

of

the

period

The

concentration

of

-LRB-

NFAT

Pi

-RRB-

c

follows

the

reverse

trend

decreasing

rapidly

when

the

calcium

ion

concentration

is

high

and

increasing

slowly

when

the

concentration

is

low

A

fraction

of

the

NFAT

exists

as

free

NFAT

in

the

nucleus

oscillating

between

the

form

NFATn

and

-LRB-

NFAT

C

-RRB-

n

as

calcineurin

associates

with

and

dissociates

from

NFAT

We

can

easily

see

that

in

the

absence

of

constant

signaling

the

concentration

of

transcriptionally

active

-LRB-

NFAT

C

-RRB-

n

would

soon

fall

to

resting

state

levels

This

is

shown

in

Fig.

where

at

s

the

calcium

ion

concentration

is

set

to

μM

The

concentration

of

the

transcriptionally

active

-LRB-

NFAT

C

-RRB-

n

falls

and

that

of

-LRB-

NFAT

Pi

-RRB-

c

rises

both

approaching

their

resting

levels

as

time

increases

Figure

-LRB-

a

-RRB-

Activation

of

NFAT

by

oscillations

in

the

calcium

ion

concentration

During

each

period

the

calcium

concentration

was

high

-LRB-

μM

-RRB-

for

s

and

low

-LRB-

μM

-RRB-

for

s

At

s

the

calcium

concentration

was

set

to

the

resting

state

value

-LRB-

μM

-RRB-

and

the

system

returned

to

the

resting

state

-LRB-

b

-RRB-

The

percent

of

NFAT

in

the

active

state

is

plotted

as

a

function

of

calcium

ion

oscillation

period

-LRB-

c

-RRB-

The

percent

of

NFAT

in

the

active

state

is

plotted

as

a

function

of

average

calcium

ion

concentration

for

steady

state

and

oscillating

calcium

ion

concentrations

The

percent

of

NFAT

in

the

active

steady

state

decreases

below

μM

when

the

calcium

concentration

is

constant

The

percent

of

NFAT

in

the

active

state

persists

at

a

high

level

to

less

than

μM

average

concentration

when

the

calcium

concentration

oscillates

To

study

how

the

degree

of

NFAT

activation

varies

with

oscillation

frequency

we

simulated

calcium

concentration

oscillations

using

s

intervals

of

high

concentration

and

varying

intervals

of

low

concentration

with

the

total

period

ranging

from

to

s

-LRB-

Fig.

-RRB-

Because

the

concentration

of

the

transcriptionally

active

-LRB-

NFAT

C

-RRB-

n

varies

throughout

the

period

a

sufficient

number

of

periods

was

simulated

to

reach

a

stable

state

then

the

lowest

value

of

-LRB-

NFAT

C

-RRB-

n

during

the

last

period

was

chosen

to

calculate

the

percent

of

NFAT

in

the

transcriptionally

active

form

We

reasoned

here

that

NFAT

involved

in

shuttling

in

and

out

of

the

active

form

was

not

likely

to

bind

to

DNA

and

assist

in

initiation

of

transcription

thus

the

lowest

value

of

the

concentration

of

the

active

form

was

justified

In

this

way

the

fraction

of

NFAT

in

the

transcriptionally

active

form

was

found

as

a

function

of

the

oscillation

period

Figure

shows

that

the

percent

of

NFAT

that

is

transcriptionally

active

is

almost

with

a

s

period

and

that

this

fraction

falls

to

less

than

with

a

s

period

These

results

agree

qualitatively

with

the

results

presented

by

Dolmetsch

et

al.

in

their

Fig.

for

the

percent

of

gene

expression

as

a

function

of

oscillation

period

Their

data

shows

gene

expression

with

a

s

oscillation

with

the

percent

expression

falling

to

zero

for

periods

of

s

or

more

The

quantitative

differences

between

our

simulated

results

and

the

experimental

observations

by

Dolmetsch

et

al.

possibly

occur

because

they

have

determined

percent

gene

expression

while

we

calculate

percent

of

NFAT

that

is

transcriptionally

active

There

might

be

additional

non-linearity

or

cooperativity

introduced

in

transcription

factor

binding

to

DNA

and

transcription

For

example

as

mentioned

earlier

Fiering

et

al.

observed

that

the

binding

of

NFAT

molecules

to

a

constructed

promoter

on

a

DNA

strand

produced

cooperativity

of

transcription

They

also

suggested

a

similar

requirement

for

NFκB

activation

of

gene

expression

While

inclusion

of

these

factors

would

result

in

a

more

quantitatively

accurate

reproduction

of

the

reporter

gene

expression

data

we

chose

to

simplify

the

model

to

emphasize

the

mechanisms

for

activation

of

the

transcription

factors

Dolmetsch

et

al.

show

that

the

percent

of

cells

expressing

a

lacZ

reporter

gene

sensitive

to

transcriptionally

active

NFAT

decreased

when

the

steady-state

calcium

concentration

fell

below

about

μM

But

if

the

calcium

concentration

exhibited

oscillations

the

gene

expression

persisted

to

an

average

calcium

concentration

at

least

as

low

as

μM

The

model

displays

similar

behavior

-LRB-

Fig.

-RRB-

To

simulate

oscillations

s

periods

of

high

calcium

concentration

and

s

periods

of

low

calcium

concentration

were

used

The

low

calcium

concentration

was

fixed

at

μM

and

the

concentration

during

the

high

calcium

intervals

was

fixed

in

each

of

several

tests

to

produce

a

set

of

experiments

each

having

a

different

average

calcium

concentration

Model

data

for

the

steady

state

was

obtained

following

the

protocol

described

previously

Figure

shows

that

simulating

oscillations

does

indeed

enhance

the

activity

of

NFAT

at

low

calcium

concentrations

relative

to

the

activity

at

a

constant

calcium

concentration

The

shape

of

the

curves

representing

steady

state

and

oscillating

calcium

concentration

behavior

are

quite

similar

to

those

shown

by

Dolmetsch

et

al.

in

their

Fig.

The

two

calculated

curves

meet

at

a

calcium

concentration

of

μM

very

close

to

the

μM

shown

in

the

experimental

work

This

corresponds

to

a

period

of

approximately

s

If

the

period

is

longer

than

s

-LRB-

the

average

calcium

is

lower

than

μM

-RRB-

then

the

oscillations

are

more

potent

than

steady-state

calcium

with

the

same

average

at

activating

NFAT

If

higher

the

opposite

is

true

The

model

data

shows

enhanced

NFAT

activity

down

to

about

μM

below

which

the

activity

decreases

rapidly

Finally

the

NFAT

model

was

tested

to

determine

if

it

correctly

simulates

the

observation

that

overexpression

of

calcineurin

partially

replaces

the

requirement

for

calcium

as

reported

by

Luo

et

al.

These

simulations

were

carried

out

by

holding

the

calcium

ion

concentration

fixed

at

the

resting

state

value

μM

and

varying

the

calcineurin

concentration

followed

by

calculating

the

degree

of

activation

of

the

NFAT

Figure

shows

the

results

obtained

when

the

calcineurin

concentration

was

increased

as

much

as

a

factor

of

times

above

the

baseline

concentration

The

percent

of

NFAT

in

the

transcriptionally

active

form

does

indeed

increase

when

the

calcineurin

concentration

increases

and

high

levels

of

activation

are

achieved

with

high

calcineurin

concentrations

Figure

Percent

active

NFAT

as

a

function

of

calcineurin

concentration

at

fixed

low

calcium

ion

concentration

The

calcium

concentration

was

fixed

at

a

level

characteristic

of

the

resting

state

-LRB-

μM

-RRB-

and

the

calcineurin

concentration

increased

to

simulate

overexpression

of

calcineurin

Each

data

point

shows

the

steady

state

concentration

of

transcriptionally

active

NFAT

at

a

fixed

calcineurin

concentration

Overexpression

of

calcineurin

replaces

the

requirement

for

calcium

at

fixed

low

calcium

concentration

NFκB

Model

Results

The

NFκB

model

was

characterized

in

a

manner

similar

to

that

for

the

NFAT

model

Using

the

parameters

from

Tables

the

calcium

concentration

was

fixed

at

μM

and

the

time

evolution

of

the

concentration

of

each

species

calculated

until

steady

state

values

were

observed

These

concentrations

were

taken

to

be

those

of

the

steady

state

at

rest

-LRB-

Table

-RRB-

TABLE

NFκB

resting

steady-state

concentrations.SpeciesConcentration

-LRB-

nM

-RRB-

-LRB-

IκB

Pi

-RRB-

-LRB-

IκB

Pi

-RRB-

-LRB-

NFκB

IκB

Pi

-RRB-

-LRB-

NFκB

IκB

Pi

-RRB-

-LRB-

NFκB

IκB

-RRB-

-LRB-

NFκB

IκB

-RRB-

C

C

Figure

shows

the

concentrations

of

species

in

the

NFκB

model

during

a

transition

from

the

resting

to

active

states

Starting

with

the

resting

steady

state

concentrations

the

calcium

ion

concentration

was

fixed

at

μM

and

the

time

evolution

of

the

concentration

of

each

species

calculated

The

high

calcium

concentration

activates

calcineurin

which

in

synergy

with

PKCα

and

PKCθ

co-activates

the

kinase

IKK

The

activated

kinase

phosphorylates

IκB

associated

with

NFκB

in

the

cytoplasm

Subsequent

polyubiquitination

and

IκB

degradation

result

in

a

decrease

in

the

cytoplasmic

NFκB

IκB

Pi

concentration

a

dissociation

of

NFκB

and

IκB

and

rapid

translocation

of

NFκB

into

the

nucleus

The

concentration

of

cytosolic

NFκB

never

rises

very

high

because

of

its

rapid

nuclear

import

therefore

the

concentration

of

this

species

is

not

shown

in

Fig.

The

light

gray

arrows

in

Fig.

show

the

NFκB

activation

pathway

on

the

reaction

scheme

for

NFκB

A

rise

in

the

calcium

concentration

activates

calcineurin

which

through

a

sequence

of

reactions

and

in

synergy

with

PKCα

activates

an

early

phase

of

the

kinase

IKK

activate

PKCθ

leading

to

activation

of

a

later

phase

of

IKK

Activated

IKK

phosphorylates

the

NFκB

IκB

complex

in

the

cytoplasm

After

dissociation

the

phosphorylated

IκB

is

polyubiquitinated

and

degraded

and

free

NFκB

is

imported

to

the

nucleus

where

it

may

be

transcriptionally

active

Figure

-LRB-

a

-RRB-

Activation

of

NFκB

from

the

resting

state

-LRB-

b

-RRB-

Deactivation

of

NFκB

from

the

active

state

The

sequence

of

events

depicted

in

Fig.

can

be

determined

by

observing

the

time

evolution

of

the

concentration

of

the

different

reaction

species

Deactivation

of

the

activated

state

of

NFκB

is

shown

in

Fig.

The

initial

concentrations

were

those

of

the

activated

state

at

equilibrium

and

the

calcium

ion

concentration

was

fixed

at

μM

The

most

important

step

in

deactivation

is

synthesis

of

new

IκB

which

is

rapidly

translocated

to

the

nucleus

forming

the

phosphorylated

complex

with

NFκB

This

complex

is

dephosphorylated

and

rapidly

translocated

into

the

cytoplasm

The

result

is

an

overall

increase

in

concentration

of

NFκB

IκB

in

the

cytoplasm

as

the

concentration

of

NFκB

in

the

nucleus

decreases

The

dark

gray

arrows

in

Fig.

show

the

pathway

for

deactivation

on

the

reaction

scheme

for

NFκB

Newly

synthesized

IκB

is

imported

to

the

nucleus

where

it

associates

with

NFκB

The

resulting

complex

dephosphorylates

and

the

NFκB

IκB

complex

is

exported

to

the

cytoplasm

As

for

NFAT

Dolmetsch

et

al.

have

studied

the

degree

of

gene

expression

caused

by

NFκB

as

a

function

of

steady-state

calcium

ion

concentration

In

their

paper

Fig.

shows

that

NFAT

and

NFκB

behave

in

a

similar

manner

they

exhibit

a

highly

non-linear

sigmoidal

dependence

with

very

little

gene

expression

at

calcium

ion

concentrations

of

μM

or

less

a

rapid

rise

in

gene

expression

at

calcium

concentrations

between

μM

and

μM

and

near

gene

expression

at

calcium

concentrations

over

μM

Since

we

follow

the

calcium

clamp

protocols

used

by

Dolmetsch

and

co-workers

which

does

not

involve

or

activation

and

hence

does

not

involve

activation

of

PKCθ

we

do

not

activate

PKCθ

in

these

simulations

Figure

shows

our

simulated

results

for

NFκB

without

PKCθ

activation

with

the

percent

of

NFκB

that

is

transcriptionally

active

plotted

as

a

function

of

the

calcium

ion

concentration

These

results

were

obtained

by

setting

the

calcium

ion

concentration

to

the

desired

value

then

calculating

the

concentration

of

transcriptionally

active

NFκB

as

a

function

of

time

until

a

steady

state

was

reached

There

is

good

agreement

between

our

simulated

behavior

and

the

experimental

results

of

Dolmetsch

et

al.

Both

show

activation

of

NFκB

over

the

physiological

range

of

calcium

ion

concentrations

with

little

activity

at

low

concentrations

and

full

activity

at

high

concentrations

The

sigmoidal

shape

of

the

calculated

curve

agrees

with

the

experimental

results

Figure

Dependence

of

the

percent

active

NFκB

on

the

steady-state

calcium

concentration

For

each

data

point

the

calcium

ion

concentration

was

fixed

at

the

indicated

value

As

was

done

for

the

NFAT

model

the

NFκB

model

will

simulate

the

system

response

to

calcium

oscillations

An

example

of

NFκB

activation

by

calcium

concentration

oscillations

is

shown

in

Fig.

The

initial

concentrations

were

those

of

the

resting

steady

state

and

the

oscillation

period

was

s

The

calcium

ion

concentration

was

fixed

at

μM

during

the

initial

s

of

each

period

and

at

μM

for

the

remaining

s

of

each

period

When

the

calcium

concentration

is

high

the

concentration

of

NFκB

IκB

in

the

cytoplasm

falls

rapidly

and

when

the

calcium

concentration

is

low

the

concentration

of

this

species

increases

slowly

The

concentration

of

NFκB

in

the

nucleus

follows

the

reverse

trend

increasing

rapidly

during

the

periods

of

high

calcium

concentration

and

falling

more

slowly

when

calcium

concentration

is

low

Figure

-LRB-

a

-RRB-

Activation

of

NFκB

by

oscillations

in

the

calcium

ion

concentration

During

each

period

the

calcium

concentration

was

high

-LRB-

μM

-RRB-

for

s

and

low

-LRB-

μM

-RRB-

for

s

The

concentration

of

the

NFκB

IκB

complex

in

the

cytoplasm

falls

rapidly

during

periods

of

high

calcium

concentration

The

concentration

of

the

phosphorylated

NFκB

IκB

complex

first

rises

then

falls

as

IκB

is

degraded

Free

NFκB

is

imported

to

the

nucleus

steadily

increasing

the

concentration

of

the

transcriptionally

active

nuclear

NFκB

-LRB-

b

-RRB-

Differentiation

of

the

activity

of

NFAT

and

NFκB

by

calcium

ion

oscillation

period

The

activity

of

NFκB

decreases

as

the

oscillation

period

increases

-LRB-

upper

curve

-RRB-

but

not

as

much

as

for

NFAT

-LRB-

lower

curve

-RRB-

the

percent

active

NFκB

is

greater

than

that

of

NFAT

for

a

given

calcium

concentration

oscillation

period

This

dissimilarity

in

behavior

differentiates

the

response

of

NFAT

and

NFκB

to

calcium

concentration

oscillations

During

the

calcium

oscillations

the

concentration

of

the

transcriptionally

active

nuclear

NFκB

rises

showing

little

oscillation

because

of

the

relatively

slow

rate

of

the

polyubiquitination

and

IκB

degradation

steps

In

the

absence

of

constant

signaling

the

concentrations

of

the

species

return

to

their

resting

levels

In

Fig.

the

concentration

of

is

set

to

μM

at

s

after

which

the

concentration

of

nuclear

NFκB

falls

and

that

of

-LRB-

NFκB

IκB

-RRB-

c

rises

to

levels

characteristic

of

the

resting

state

We

studied

how

the

degree

of

NFκB

activation

varied

with

calcium

concentration

oscillation

period

as

we

did

for

the

NFAT

model

Figure

shows

the

results

of

simulations

with

periods

varying

from

to

s.

For

the

shortest

period

the

percent

of

active

NFκB

was

and

at

the

longest

period

the

percent

active

NFκB

was

These

results

agree

qualitatively

with

those

shown

by

Dolmetsch

et

al.

in

their

Fig.

Their

figure

shows

over

gene

expression

with

a

s

period

falling

to

less

than

gene

expression

for

an

s

period

Note

that

they

have

determined

percent

gene

expression

while

we

calculate

percent

of

transcriptionally

active

NFκB

a

difference

that

may

explain

the

quantitative

difference

in

the

results

Figure

combines

the

model

results

for

NFAT

and

NFκB

to

compare

the

effect

of

oscillation

frequency

on

activation

of

NFκB

to

the

activation

of

NFAT

by

including

the

curve

from

Fig.

Figure

shows

that

a

higher

fraction

of

the

NFκB

is

transcriptionally

active

than

that

of

NFAT

for

long

oscillation

periods

These

results

agree

qualitatively

with

those

shown

in

Dolmetsch

et

al.

Fig.

where

gene

expression

by

NFAT

declined

rapidly

with

oscillation

frequency

but

persisted

to

long

periods

for

NFκB

Figure

simulates

the

results

of

Yang

et

al.

who

studied

the

degradation

of

IκBα

with

time

in

fibroblasts

To

simulate

this

we

have

used

oscillations

with

a

period

of

s

and

assumed

that

degradation

is

the

same

for

all

members

of

the

IκB

family

and

then

plotted

the

percent

of

IκB

remaining

with

time

We

have

also

assumed

that

the

active

PKCθ

and

PKCα

concentrations

drop

after

min

based

on

the

experimental

observations

of

Szamel

et

al.

who

report

that

PKCθ

and

PKCα

translocated

rapidly

to

the

membrane

within

min

and

start

to

decline

after

min

This

was

simulated

with

the

model

by

reducing

the

amounts

of

active

PKCθ

and

PKCα

concentrations

to

resting

values

at

min

-LRB-

Fig.

-RRB-

The

simulation

shows

that

there

is

near

complete

degradation

of

IκB

in

about

min

which

agrees

with

the

experimental

results

shown

in

Yang

et

al.

in

their

Fig.

They

observed

an

increase

in

IκB

concentration

after

about

min

Figure

-LRB-

a

-RRB-

Degradation

of

IκB

with

time

during

oscillations

with

period

s.

Activation

of

PKCθ

and

PKCα

is

terminated

at

s.

-LRB-

b

-RRB-

Percent

active

NFκB

as

a

function

of

the

rate

of

degradation

of

NFκB

At

steady

state

and

at

high

calcium

concentration

the

percent

of

active

NFκB

is

sensitive

to

the

rate

of

IκB

degradation

assumed

in

the

model

As

the

degradation

rate

decreases

the

percent

of

active

NFκB

decreases

Thus

the

degradation

rate

must

be

sufficiently

high

to

obtain

significant

activation

of

NFκB

The

NFκB

model

uses

a

degradation

rate

of

s

Figure

shows

that

the

rate

of

degradation

of

IκB

is

an

essential

factor

in

the

activation

of

NFκB

Here

the

dependence

of

the

percent

active

NFκB

is

shown

as

a

function

of

the

IκB

constitutive

degradation

rate

in

the

NFκB

model

Our

NFκB

model

uses

a

degradation

rate

of

s

As

the

degradation

rate

decreases

below

this

value

the

percent

of

active

NFκB

decreases

thus

a

sufficiently

high

IκB

degradation

rate

is

required

for

efficient

NFκB

activation

Sensitivity

Analysis

To

further

characterize

the

system

a

sensitivity

analysis

was

performed

to

determine

which

steps

in

the

reaction

schemes

for

NFAT

and

NFκB

exerted

the

most

influence

on

the

activation

of

the

transcription

factors

To

this

end

each

rate

constant

was

increased

and

decreased

by

The

percent

change

of

steady-state

active

transcription

factor

at

μM

calcium

over

the

control

was

calculated

-LRB-

Fig.

-RRB-

The

sensitivity

was

calculated

by

Figure

-LRB-

a

-RRB-

Sensitivity

analysis

for

NFAT

activation

-LRB-

b

-RRB-

Sensitivity

analysis

for

NFκB

activation

In

both

cases

the

rate

constants

were

increased

and

decreased

by

The

sensitivity

of

the

steady

state

concentration

of

active

transcription

factor

at

μM

calcium

to

changes

in

the

rate

constants

is

shown

For

NFAT

-LRB-

Fig.

-RRB-

the

rate

constants

that

seem

to

exert

the

greatest

effect

on

activation

are

and

The

rate

constants

and

control

the

rate

of

nuclear

import

and

export

of

NFAT

and

the

rate

constants

and

control

the

phosphorylation

and

dephosphorylation

of

NFAT

by

calcineurin

The

sensitivities

here

suggest

that

increasing

the

binding

affinity

of

NFAT

and

calcineurin

-LRB-

and

-RRB-

will

increase

activation

of

NFAT

This

is

consistent

with

mutational

studies

that

demonstrate

that

alteration

of

the

calcineurin

binding

site

on

NFAT

decreases

activation

of

NFAT

It

is

interesting

to

note

that

even

though

the

sensitivities

of

NFAT

activation

to

changes

in

and

are

in

the

expected

directions

the

values

of

these

sensitivities

are

relatively

small

Also

increasing

the

rate

of

activation

of

calcineurin

through

calcium

binding

-LRB-

and

-RRB-

will

also

increase

activation

of

NFAT

Other

rate

constants

that

exert

a

small

but

still

significant

effect

are

and

suggesting

that

an

increase

in

the

amount

of

free

cytosolic

calcineurin

will

increase

activation

of

NFAT

This

is

consistent

with

Fig.

and

the

experiments

that

demonstrate

that

increasing

calcineurin

increases

the

activation

of

NFAT

For

NFκB

-LRB-

Fig.

-RRB-

the

rate

constants

and

exert

the

greatest

control

on

the

activation

of

NFκB

The

rate

constants

and

also

exert

a

significant

influence

on

activation

of

NFκB

The

rate

constants

and

control

the

degradation

and

synthesis

of

IκB

The

rate

constants

and

control

the

rate

of

IκB

mRNA

synthesis

and

degradation

The

importance

of

these

rate

constants

re-emphasizes

the

importance

of

the

removal

of

free

IκB

from

the

cystosol

for

activation

of

NFκB

as

indicated

by

Fig.

The

rate

constants

and

control

the

shuttling

of

IKK

between

the

cytoplasm

and

the

nucleus

The

rate

constants

and

control

the

import

of

IκB

into

the

nucleus

Preventing

the

import

of

IκB

into

the

nucleus

increases

the

activation

of

NFκB

as

it

lowers

the

amount

of

IκB

available

to

bind

NFκB

which

leads

to

its

export

from

the

nucleus

The

rate

constants

and

control

the

dissociation

of

NFκB

and

IκB

Increasing

the

dissociation

rate

increases

activation

of

NFκB

The

effect

of

the

rate

constants

and

demonstrate

that

increasing

the

rate

of

phosphorylation

of

IκB

by

IKK

increases

the

activation

of

NFκB

Finally

decreasing

the

rate

constant

for

export

of

NFκB

out

of

the

nucleus

or

increasing

the

rate

of

import

NFκB

to

the

nucleus

increases

the

amount

of

activation

of

NFκB

This

effectively

increases

the

amount

of

NFκB

in

the

nucleus

It

is

interesting

that

although

reducing

the

rate

of

phosphorylation

of

IKK

by

calcineurin

does

inhibit

NFkB

translocation

to

the

nucleus

this

is

not

one

of

the

most

sensitive

parameters

The

sensitivity

analysis

suggests

that

there

are

several

other

targets

that

will

block

NFAT

and

NFκB

translocation

For

several

of

the

targets

on

NFAT

there

is

experimental

data

to

support

the

model

predictions

about

the

sensitivities

On

the

other

hand

the

prediction

that

blocking

of

NFAT

translocation

decreases

transcription

has

yet

to

be

verified

experimentally

This

might

be

accomplished

by

developing

a

compound

that

either

binds

the

nuclear

import

site

of

NFAT

or

that

blocks

the

import

mechanism

For

NFκB

the

prediction

of

this

analysis

is

that

the

most

effective

target

would

be

to

block

IκB

degradation

or

increase

its

re-synthesis

Another

potent

target

would

be

to

block

NFκB

translocation

Other

possible

interventions

to

block

NFκB

translocation

would

be

to

introduce

compounds

that

increase

the

affinity

of

NFκB

for

IκB

or

that

increase

the

activity

of

IKK

These

are

not

the

only

possible

sites

as

many

accessory

pathways

regulate

this

system

Future

studies

that

build

on

this

model

and

explore

these

pathways

will

give

further

insight

Conclusions

We

have

developed

models

for

the

calcium

and

PKCθ

mediated

activation

and

deactivation

of

the

transcription

factors

NFAT

and

NFκB

that

incorporate

experimentally

determined

reaction

pathways

and

that

simulate

this

action

over

physiological

calcium

concentrations

The

model

reproduces

experimentally

observed

behaviors

of

both

the

NFAT

and

NFκB

systems

under

a

variety

of

conditions

Several

parameters

values

for

T

cells

were

not

available

and

therefore

were

derived

from

experimental

observations

in

cells

other

than

the

T

cell

For

the

most

part

these

choices

are

reasonable

estimates

but

should

be

examined

further

as

new

data

on

signaling

during

T

cell

activation

becomes

available

Variations

in

some

estimates

will

have

a

greater

influence

on

model

outcomes

than

the

others

For

example

the

total

concentration

of

NFκB

was

taken

from

fibroblast

data

but

this

mostly

affects

the

amount

activated

rather

than

the

percent

activated

yielding

a

small

control

coefficient

-LRB-

-RRB-

On

the

other

hand

sensitivity

analysis

indicates

that

the

degradation

rate

of

IκB

that

was

estimated

using

data

from

would

exert

a

greater

influence

on

model

results

and

thus

its

choice

is

more

critical

While

the

model

is

qualitatively

accurate

simulation

of

the

reporter

gene

levels

observed

by

Dolmetsch

and

colleagues

might

be

more

closely

approximated

by

the

inclusion

of

additional

features

to

the

model

Several

of

these

enhancements

are

obvious

and

consist

of

including

elements

both

upstream

and

downstream

of

the

system

modeled

For

example

binding

of

the

transcription

factors

to

the

DNA

might

be

added

along

with

steps

to

describe

the

expression

of

the

reporter

genes

observed

in

the

experiment

Inclusion

of

these

steps

would

require

adding

significant

complexity

to

the

model

that

might

obstruct

demonstration

of

the

mechanisms

governing

activation

of

the

calcium

dependent

transcription

factors

NFAT

and

NFκB

Thus

addition

of

these

steps

has

been

left

for

future

work

Although

this

model

is

able

to

simulate

the

calcium

clamp

in

the

in

vitro

experiments

used

by

Dolmetsch

and

co-workers

in

vivo

the

T

cell

has

more

complex

calcium

dynamics

One

aspect

of

these

dynamics

is

the

calcium

activation

of

PKC

and

its

feedback

on

phospholipase

C

-LRB-

PLC

-RRB-

Many

studies

have

indicated

that

PKC

acts

as

a

co-activator

of

the

transcription

factors

NFAT

and

NFκB

through

its

effect

on

calcineurin

According

to

Pfeifhofer

et

al.

PKCθ

is

predominately

expressed

in

T-lymphocytes

They

found

that

PKCθ

increases

NFAT

and

NF-κB

activation

by

reducing

the

intracellular

calcium

elevation

through

a

reduction

in

production

They

also

found

that

PKCα

does

this

to

a

lesser

degree

The

current

model

includes

the

activation

of

PKCθ

and

its

effect

on

IKK

complex

Future

work

might

include

any

feedback

of

PKC

on

PLC

and

possibly

the

actions

of

other

PKCs

Two

computational

models

have

been

developed

by

other

authors

to

model

the

dynamics

of

NFκB

in

T-lymphocytes

The

model

developed

by

Carlotti

et

al.

describes

the

association

and

dissociation

of

NFκB

and

IκB

and

their

translocation

into

the

nucleus

both

in

the

associated

and

dissociated

forms

Their

model

demonstrates

that

NFκB

is

localized

in

the

cytoplasm

at

rest

due

to

its

association

with

IκB

and

the

export

of

NFκB

from

the

nucleus

A

second

model

developed

by

Hoffman

and

co-workers

demonstrated

that

the

temporal

control

was

due

to

coordinated

degradation

and

resynthesis

of

IκB

and

that

IκB

provides

a

strong

negative

feedback

that

can

turn

off

the

NFκB

response

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O B O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O B O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O B O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O B O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O B O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O B O O O O O O B O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O 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