Development

of

a

kinetic

metabolic

model

application

to

Catharanthus

roseus

hairy

root

A

kinetic

metabolic

model

describing

Catharanthus

roseus

hairy

root

growth

and

nutrition

was

developed

The

metabolic

network

includes

glycolysis

pentose-phosphate

pathway

TCA

cycle

and

the

catabolic

reactions

leading

to

cell

building

blocks

such

as

amino

acids

organic

acids

organic

phosphates

lipids

and

structural

hexoses

The

central

primary

metabolic

network

was

taken

at

pseudo-steady

state

and

metabolic

flux

analysis

technique

allowed

reducing

from

metabolic

fluxes

to

independent

pathways

Hairy

root

specific

growth

rate

was

described

as

a

function

of

intracellular

concentration

in

cell

building

blocks

Intracellular

transport

and

accumulation

kinetics

for

major

nutrients

were

included

The

model

uses

intracellular

nutrients

as

well

as

energy

shuttles

to

describe

metabolic

regulation

Model

calibration

was

performed

using

experimental

data

obtained

from

batch

and

medium

exchange

liquid

cultures

of

C.

roseus

hairy

root

using

a

minimal

medium

in

Petri

dish

The

model

is

efficient

in

estimating

the

growth

rate

Introduction

In

vitro

plant

biotechnology

offers

a

controlled

environment

and

has

been

widely

studied

for

phyto-pharmaceuticals

and

recombinant

proteins

production

However

the

low

productivity

and

the

poor

reproducibility

of

the

cultures

are

still

limiting

the

economical

feasibility

of

such

in

vitro

bioprocesses

Moreover

the

lack

of

reproducibility

of

the

cultures

significantly

complicates

process

validation

and

acceptance

by

the

regulatory

agencies

and

thus

the

potential

to

rapidly

put

a

product

to

market

Different

approaches

have

succeeded

in

decreasing

the

technological

risk

associated

with

in

vitro

plant

biotechnology

The

introduction

of

elicitors

such

as

chitin

-LSB-

-RSB-

and

jasmonic

acid

-LSB-

-RSB-

has

shown

to

enhance

significantly

the

production

level

for

many

plant

species

cultured

as

cell

suspensions

and

hairy

roots

The

use

of

an

extractive

phase

allowed

the

simplification

of

harvesting

procedures

-LSB-

-RSB-

More

recently

cell

engineering

studies

have

shown

its

potential

in

improving

cell

catalytic

capacity

towards

the

production

of

secondary

metabolites

-LSB-

-RSB-

and

in

in

vitro

molecular

farming

for

recombinant

human

proteins

-LSB-

-RSB-

However

high

variability

levels

in

cell

growth

and

production

of

biomolecules

of

interest

are

still

observed

The

genetic

flexibility

of

plant

cells

may

partly

explain

these

phenomena

-LSB-

-RSB-

and

inadequate

culture

management

may

also

be

involved

A

plant

cell

has

the

ability

to

accumulate

nutrients

and

metabolites

which

are

involved

in

the

regulation

of

its

metabolic

pathways

The

key

for

improving

plant

cell

culture

reproducibility

may

thus

rely

on

a

better

understanding

of

the

links

that

are

exerting

between

a

plant

cell

physiological

state

and

its

potential

towards

growth

and

production

of

a

biomolecule

of

interest

This

understanding

-LRB-

following

that

of

Bailey

-LSB-

-RSB-

-RRB-

could

take

the

form

of

a

descriptive

and

predictive

metabolic

model

Such

structured

model

may

then

be

either

useful

to

enhance

our

understanding

of

cell

behaviour

in

identifying

possible

regulatory

roles

-LSB-

-RSB-

as

well

as

being

a

tool

for

defining

adequate

controlled

culture

conditions

Metabolic

modelling

has

been

applied

to

plant

cells

for

studying

specific

metabolic

sub-networks

such

as

photosynthesis

-LSB-

-RSB-

respiration

-LSB-

-RSB-

cellulose

biosynthesis

-LSB-

-RSB-

and

lipid

biosynthesis

-LSB-

-RSB-

These

studies

have

clearly

showed

the

importance

of

the

energy

shuttles

on

the

control

of

the

metabolic

pathways

In

addition

some

nutrients

are

known

to

be

involved

in

the

regulation

of

the

cell

metabolism

Intracellular

inorganic

phosphate

-LRB-

Pi

-RRB-

plays

a

central

role

in

the

regulation

of

enzymes

activity

through

phosphorylation/dephosphorylation

processes

ATP/ADP

concentration

ratio

starch

synthesis

and

storage

and

in

the

flux

distribution

between

the

glycolysis

and

the

pentose-phosphate

pathway

-LRB-

PPP

-RRB-

Intracellular

nitrate

and

ammonium

are

known

to

affect

amino

acid

-LRB-

AA

-RRB-

production

The

large

capacity

of

plant

cells

for

nutrient

and

metabolite

accumulation

plays

a

crucial

role

in

cell

growth

and

biomolecule

production

as

observed

for

Daucus

carota

hairy

root

-LSB-

-RSB-

and

Eschscholtzia

californica

suspension

cells

-LSB-

-RSB-

Recently

we

have

developed

a

kinetic

model

based

on

intracellular

nutrients

such

as

inorganic

phosphate

nitrate

and

sugars

which

showed

to

be

efficient

in

simulating

carrot

hairy

root

growth

for

different

culture

media

composition

-LSB-

-RSB-

Therefore

the

aim

of

this

work

was

to

include

the

description

of

metabolic

pathways

to

the

nutritional

model

in

order

to

describe

plant

cells

behaviour

from

the

estimation

of

the

cells

physiological

state

including

nutritional

and

metabolic

states

Catharanthus

roseus

was

studied

as

a

model

biological

system

Cell

nutritional

state

in

Pi

nitrogen

-LRB-

and

-RRB-

and

carbohydrates

-LRB-

sucrose

fructose

glucose

and

starch

-RRB-

is

described

The

hypothesis

of

a

central

primary

metabolism

at

steady

state

has

been

proposed

based

on

literature

-LSB-

-RSB-

Using

the

metabolic

flux

analysis

-LRB-

MFA

-RRB-

approach

a

model

reduction

-LSB-

-RSB-

was

applied

on

the

central

primary

metabolism

network

and

resulted

in

independent

pathways

A

second

network

includes

transient

fluxes

such

as

for

nutrient

uptake

and

storage

energy

shuttles

management

and

root

cells

growth

Metabolic

regulation

of

the

fluxes

from

energy

shuttles

and

nutrients

is

included

The

hairy

root

specific

growth

rate

is

described

as

a

function

of

the

content

in

cell

building

blocks

such

as

amino

acids

-LRB-

including

proteins

-RRB-

lipids

-LRB-

LIP

-RRB-

organic

acids

-LRB-

ORA

-RRB-

organic

phosphates

-LRB-

OP

-RRB-

-LRB-

including

nucleic

acids

-RRB-

and

structural

hexoses

-LRB-

STH

-RRB-

Batch

and

medium

exchange

cultures

of

C.

roseus

hairy

root

were

performed

and

the

experimental

data

were

used

for

model

calibration

Model

general

structure

The

model

has

been

first

developed

by

Tikhomiroff

-LSB-

-RSB-

The

cell

metabolic

network

-LRB-

Fig.

-RRB-

is

divided

into

two

interlinked

sub-networks

as

the

stationary

-LRB-

SPMP

-RRB-

-LRB-

Fig.

-RRB-

and

the

transient

-LRB-

TPMP

-RRB-

primary

metabolic

pathways

-LRB-

Fig.

-RRB-

The

SPMP

includes

glycolysis

PPP

the

TCA

cycle

and

the

catabolic

reactions

leading

to

the

cell

building

blocks

The

cell

building

blocks

are

amino

acids

and

peptides

which

were

taken

as

a

unique

pool

of

AA

ORA

OP

LIP

and

STH

The

TPMP

network

is

linked

to

the

SPMP

network

and

describes

cells

growth

and

nutrient

transport

between

medium

and

intracellular

volumes

Compartmentalization

of

nutrients

and

metabolites

among

the

cytosol

the

vacuole

and

other

organelles

is

not

included

in

the

model

and

a

single

cell

population

was

considered

to

describe

the

hairy

root

cells

pools

This

simplification

already

showed

to

be

efficient

to

model

hairy

root

growth

and

nutrition

-LSB-

-RSB-

The

secondary

metabolism

is

simplified

to

fluxes

leading

to

two

pools

one

accounting

for

the

global

pool

in

secondary

metabolites

derived

from

tryptamin

-LRB-

TRYSM

-RRB-

and

one

accounting

for

the

global

pool

in

secondary

metabolites

derived

from

secologanin

-LRB-

SECSM

-RRB-

The

model

is

thus

composed

of

interlinked

metabolic

networks

that

are

at

steady

-LRB-

SPMP

-RRB-

and

transient

-LRB-

TPMP

-RRB-

states

and

is

described

by

a

mass

balance

using

the

stoichiometric

matrix

and

the

hairy

root

specific

growth

rate

where

S

is

the

stoichiometric

matrix

Φ

is

a

vector

containing

reaction

fluxes

μ

is

the

hairy

root

specific

growth

rate

and

M

is

a

vector

containing

the

concentration

in

cellular

metabolites

and

nutrients

Root

mass

with

time

can

then

be

estimated

both

kinetically

and

from

a

mass

balance

on

all

cell

constituents.Fig

metabolic

model

global

structure

Fluxes

in

the

transient

primary

metabolic

pathways

-LRB-

TPMP

-RRB-

Flux

numbers

refer

to

the

stoichiometric

biochemical

reactions

of

Table

Kinetic

description

of

the

resulting

fluxes

is

presented

in

Table

in

the

stationary

primary

metabolic

pathways

-LRB-

SPMP

-RRB-

Flux

numbers

refer

to

the

stoichiometric

biochemical

reactions

of

Table

Stationary

primary

metabolic

pathways

The

pseudo-steady-state

assumption

for

the

central

metabolism

was

based

on

observations

from

Rontein

et

al.

-LSB-

-RSB-

and

Stitt

and

Fernie

-LSB-

-RSB-

and

proposed

to

simplify

the

model

development

The

original

SPMP

metabolic

network

has

fluxes

-LRB-

Fig.

Table

-RRB-

which

were

reduced

to

independent

pathways

-LRB-

Fig.

Table

-RRB-

using

the

method

proposed

by

Simpson

et

al.

-LSB-

-RSB-

and

Stephanopoulos

et

al.

-LSB-

-RSB-

and

the

following

simplifications

Briefly

the

minimal

number

of

independent

feasible

metabolic

pathways

is

determined

with

a

group

of

metabolites

assumed

at

steady

state

CHO

PEP

PYR

A-CoA

OXO

and

OAA

The

N

matrix

-LRB-

-RRB-

is

first

constructed

from

the

biochemical

reactions

and

the

metabolites

at

steady

state

The

determination

of

the

independent

pathways

then

requires

the

knowledge

of

the

kernel

matrix

K

-LRB-

number

of

independent

pathways

-RRB-

which

describe

each

pathway

as

a

linear

combination

of

the

biochemical

reactions

of

the

SPMP

This

matrix

is

the

non-trivial

solution

of

the

equation

Since

this

equation

has

an

infinite

number

of

solutions

both

N

and

K

matrices

are

decomposed

each

into

two

matrices

with

and

selected

as

square

invertible

matrices

Starting

using

identity

matrix

for

can

then

be

determined

by

modifying

such

that

possible

independent

pathways

can

be

identified

Using

the

complete

matrix

K

we

can

build

the

independent

pathways

presented

in

Fig.

In

this

work

the

size

of

this

matrix

is

The

complete

method

to

obtain

the

pathways

can

be

found

in

Ref

-LSB-

-RSB-

Table

reactions

of

the

stationary

primary

metabolic

pathwaysFluxν

-LRB-

-RRB-

a

cν

-LRB-

-RRB-

a

cν

-LRB-

-RRB-

aν

-LRB-

-RRB-

aν

-LRB-

-RRB-

bν

-LRB-

-RRB-

bν

-LRB-

-RRB-

a

cν

-LRB-

-RRB-

aν

-LRB-

-RRB-

aν

-LRB-

-RRB-

bν

-LRB-

-RRB-

aν

-LRB-

-RRB-

bν

-LRB-

-RRB-

aν

-LRB-

-RRB-

a

cν

-LRB-

-RRB-

aν

-LRB-

-RRB-

a

cν

-LRB-

-RRB-

c

dν

-LRB-

-RRB-

a

cν

-LRB-

-RRB-

c

dν

-LRB-

-RRB-

a

cν

-LRB-

-RRB-

eν

-LRB-

-RRB-

bν

-LRB-

-RRB-

bν

-LRB-

-RRB-

aν

-LRB-

-RRB-

bν

-LRB-

-RRB-

eν

-LRB-

-RRB-

ν

-LRB-

-RRB-

ν

-LRB-

-RRB-

dν

-LRB-

-RRB-

aν

-LRB-

-RRB-

da

-LSB-

-RSB-

b

-LSB-

-RSB-

c

-LSB-

-RSB-

d

-LSB-

-RSB-

e

-LSB-

-RSB-

f

-LSB-

-RSB-

Fig.

independent

biochemical

pathways

from

the

SPMP

Pathway

numbers

refer

to

the

stoichiometric

biochemical

reactions

of

Table

Kinetic

description

of

the

resulting

fluxes

is

presented

in

Table

The

independent

biochemical

pathways

were

obtained

from

the

biochemical

reactions

of

the

SPMP

described

in

Fig.

and

Table

using

the

reduction

method

of

Simpson

et

al.

-LSB-

-RSB-

and

Stephanopoulos

et

al.

-LSB-

-RSB-

as

described

in

Sect.

fluxes

of

the

SPMPs

after

pathways

reduction

using

MFA

approachFluxaν

-LRB-

-RRB-

ν

-LRB-

-RRB-

ν

-LRB-

-RRB-

ν

-LRB-

-RRB-

ν

-LRB-

-RRB-

ν

-LRB-

-RRB-

ν

-LRB-

-RRB-

ν

-LRB-

-RRB-

ν

-LRB-

-RRB-

ν

-LRB-

-RRB-

ν

-LRB-

-RRB-

ν

-LRB-

-RRB-

ν

-LRB-

-RRB-

ν

-LRB-

-RRB-

ν

-LRB-

-RRB-

ν

-LRB-

-RRB-

ν

-LRB-

-RRB-

ν

-LRB-

-RRB-

ν

-LRB-

-RRB-

ν

-LRB-

-RRB-

aThe

biochemical

reactions

are

denoted

with

an

r

to

indicate

that

they

are

obtained

from

pathways

reduction

The

nutrient

concentrations

described

are

glucose

-LRB-

GLC

-RRB-

fructose

-LRB-

FRU

-RRB-

sucrose

-LRB-

SUC

-RRB-

ammonium

-LRB-

-RRB-

and

inorganic

phosphate

-LRB-

Pi

-RRB-

The

anaplerotic

pathways

are

simplified

to

the

transformation

of

phosphoenolpyruvate

-LRB-

PEP

-RRB-

into

oxaloacetate

-LRB-

OAA

-RRB-

The

metabolite

pools

resulting

from

the

SPMP

are

starch

-LRB-

STA

-RRB-

STH

-LRB-

cell

wall

and

membrane

constituents

-RRB-

OP

-LRB-

nucleotides

phospholipids

nucleic

acids

-RRB-

total

AA

including

that

of

peptides

ORA

pools

from

tryptamin

-LRB-

TRYSM

-RRB-

and

from

secologanin

-LRB-

SECSM

-RRB-

Starch

biosynthesis

-LRB-

flux

v

-LRB-

-RRB-

in

Table

-RRB-

and

catabolism

-LRB-

v

-LRB-

-RRB-

-RRB-

are

included

AA

-LRB-

v

-LRB-

-RRB-

-RRB-

are

assumed

to

be

synthesized

from

oxoglutarate

since

it

is

the

site

for

ammonium

fixation

and

thus

the

initiation

step

in

the

AA

biosynthesis

-LSB-

-RSB-

even

though

there

are

AA

synthesized

from

other

pathways

Tryptamin

-LRB-

TRYSM

-RRB-

biosynthesis

-LRB-

v

-LRB-

-RRB-

-RRB-

has

been

explicitly

described

because

this

AA

is

a

precursor

with

secologanin

-LRB-

SECSM

-RRB-

-LRB-

v

-LRB-

-RRB-

and

v

-LRB-

-RRB-

-RRB-

to

the

formation

of

the

secondary

metabolites

OP

biosynthesis

-LRB-

v

-LRB-

-RRB-

-RRB-

has

been

simplified

as

illustrated

in

Fig.

and

is

accounting

for

the

four

nucleotides

The

biosynthesis

of

STH

results

from

multiple

biochemical

reactions

-LSB-

-RSB-

but

it

is

simplified

to

the

condensation

of

with

-LRB-

v

-LRB-

-RRB-

-RRB-

The

biosynthesis

-LRB-

v

-LRB-

-RRB-

-RRB-

and

catabolism

-LRB-

v

-LRB-

-RRB-

-RRB-

of

LIP

is

linked

to

acetyl-coenzyme

A

-LSB-

-RSB-

as

for

ORA

biosynthesis

-LRB-

v

-LRB-

-RRB-

-RRB-

and

catabolism

-LRB-

v

-LRB-

-RRB-

-RRB-

The

kinetic

expressions

of

the

fluxes

are

described

in

the

next

section

Transient

primary

metabolic

pathways

The

TPMP

network

includes

the

biochemical

reactions

that

can

not

satisfy

the

pseudo-steady-state

hypothesis

These

include

nutrients

transport

and

accumulation

root

cells

growth

and

energy

shuttles

dynamics

The

general

structure

of

the

TPMP

and

its

interactions

with

the

SPMP

are

illustrated

in

Figs.

and

The

stoichiometric

mass

balances

are

presented

in

Table

and

the

kinetic

terms

used

in

fluxes

regulation

are

described

in

Table

Extracellular

nutrients

such

as

sucrose

-LRB-

ESUC

-RRB-

glucose

-LRB-

EGLC

-RRB-

fructose

-LRB-

EFRU

-RRB-

ammonium

-LRB-

-RRB-

nitrate

-LRB-

-RRB-

and

Pi

-LRB-

EPi

-RRB-

are

included

Sucrose

is

hydrolysed

into

fructose

and

glucose

extracellularly

by

apoplastic

invertases

-LRB-

Table

v

-LRB-

-RRB-

-RRB-

or

intracellularly

as

described

in

the

SPMP

-LRB-

Table

v

-LRB-

-RRB-

-RRB-

It

should

be

noted

that

sucrose

biosynthesis

-LRB-

Table

v

-LRB-

-RRB-

-RRB-

is

not

included

into

the

model

because

there

are

no

evidence

that

hairy

roots

have

active

chloroplasts

v

-LRB-

-RRB-

then

represents

the

net

flux

of

sucrose

hydrolysis

Alternative

glycolytic

pathways

-LSB-

-RSB-

are

described

and

the

carbohydrate

sources

include

sucrose

glucose

fructose

and

starch

However

since

all

the

biosynthesis

pathways

of

the

SPMP

are

defined

with

glucose

as

precursor

all

available

intracellular

carbon

sources

have

first

to

be

converted

into

glucose

Fructose

conversion

-LRB-

v

-LRB-

-RRB-

-RRB-

starch

catabolism

-LRB-

v

-LRB-

-RRB-

-RRB-

and

sucrose

hydrolysis

-LRB-

v

-LRB-

-RRB-

-RRB-

processes

are

thus

feeding

the

intracellular

glucose

pool

Plant

cell

adaptation

mechanism

to

Pi

deficiency

is

described

with

the

fluxes

for

the

degradation

of

pyrophosphate

-LRB-

v

-LRB-

-RRB-

-RRB-

and

OP

-LRB-

v

-LRB-

-RRB-

-RRB-

into

Pi

The

plant

cell

storage

capacity

for

sugars

Pi

and

cell

building

blocks

is

described

Respiration

is

described

-LRB-

v

-LRB-

-RRB-

-RRB-

however

oxygen

is

assumed

to

be

non-limiting

as

discussed

below

Energy

loss

associated

with

maintenance

and

other

reactions

that

are

not

included

into

the

SPMP

is

contained

in

flux

v

-LRB-

-RRB-

Table

reactions

of

the

transient

primary

metabolic

pathwaysFluxaν

-LRB-

-RRB-

ν

-LRB-

-RRB-

ν

-LRB-

-RRB-

ν

-LRB-

-RRB-

ν

-LRB-

-RRB-

ν

-LRB-

-RRB-

ν

-LRB-

-RRB-

ν

-LRB-

-RRB-

ν

-LRB-

-RRB-

ν

-LRB-

-RRB-

ν

-LRB-

-RRB-

aStoichiometric

coefficients

were

taken

from

Ref

-LSB-

-RSB-

Table

expression

of

the

fluxesFluxa

c

is

fixed

at

and

no

sucrose

synthesis

is

consideredaReaction

number

refers

to

pathways

of

SPMP

in

Fig.

and

of

TPMP

in

Fig.

shown

fluxes

are

related

to

exchange

between

the

cytoplasm

and

the

vacuole

and

were

not

included

in

this

modelcUse

of

NTP

NDP

NADH

NAD

NADPH

and

NADP

in

flux

kinetics

was

taken

from

Ref

-LSB-

-RSB-

d

-LSB-

-RSB-

e

-LSB-

-RSB-

f

-LSB-

-RSB-

Metabolic

regulation

Metabolic

regulation

of

two

kinds

is

integrated

into

the

model

that

associated

with

the

energetic

status

of

the

cells

and

that

related

to

the

nutritional

state

of

the

cells

variable

denoted

as

θi

below

Each

flux

-LRB-

ν

-RRB-

is

regulated

as

follows

according

to

a

multiplicative

kinetic

of

each

mechanism

involved

The

order

of

the

regulation

kinetics

can

also

be

adjusted

from

the

term

αi

to

account

for

multi-steps

mechanisms

Since

we

established

the

independent

pathways

for

the

SPMP

with

arbitrary

conditions

it

is

not

possible

to

compare

the

structure

of

the

resulting

kinetics

with

literature

However

the

identified

independent

pathways

have

been

selected

for

their

feasibility

and

their

combination

is

mathematically

equivalent

to

the

whole

metabolic

system

-LRB-

fluxes

-RRB-

given

that

the

pseudo-steady-state

hypothesis

is

acceptable

Furthermore

a

sigmoid

function

is

used

for

nutrients

acting

like

switches

to

avoid

large

discontinuities

when

solving

the

differential

equations

which

would

have

been

the

case

using

a

simple

on/off

switch

type

Continuous

functions

are

also

more

representative

of

biological

behaviour

-LSB-

-RSB-

The

sigmoid

function

is

also

used

for

imposing

maximum

accumulation

levels

-LRB-

see

Table

-RRB-

The

parameter

a

defines

the

steepness

of

the

function

Mi

is

the

concentration

of

the

nutrient

involved

in

the

regulation

of

a

flux

and

Mi

t

is

the

nutrient

concentration

threshold

The

role

of

energy

shuttles

in

the

regulatory

mechanisms

is

described

in

Table

NADH

NADPH

and

NTP

-LRB-

the

sum

of

ATP

GTP

CTP

and

UTP

-RRB-

as

well

as

their

reduced

forms

-LRB-

NAD

NADP

and

NDP

-RRB-

are

used

The

sum

in

energy

shuttles

per

g

DW

of

roots

in

both

oxidized

and

reduced

forms

-LRB-

NADH

NAD

NDP

NTP

NADPH

NADP

-RRB-

are

taken

constant

with

time

However

the

energetic

status

of

the

cells

-LSB-

NADH

-LRB-

NADH

NAD

-RRB-

NTP

-LRB-

NDP

NTP

-RRB-

NADPH

-LRB-

NADPH

NADP

-RRB-

-RSB-

was

not

assumed

constant

ATPase

proton

pumps

that

are

linked

to

H

nutrient

co-transport

and

involved

in

the

control

of

intracellular

pH

are

thus

included

ATP

consumption

for

transmembrane

transport

of

glucose

-LRB-

v

-LRB-

-RRB-

-RRB-

fructose

-LRB-

v

-LRB-

-RRB-

-RRB-

sucrose

-LRB-

v

-LRB-

-RRB-

-RRB-

nitrate

-LRB-

v

-LRB-

-RRB-

-RRB-

and

Pi

-LRB-

v

-LRB-

-RRB-

-RRB-

is

thus

included

A

unique

value

for

the

affinity

constant

for

NTP

-LRB-

KmNTP

-RRB-

is

used

The

same

strategy

of

using

unique

affinity

constants

for

NAD

NADH

NADP

and

NADPH

is

also

applied

Root

cells

nutritional

state

in

Pi

and

in

sugars

are

involved

in

metabolic

flux

regulation

Intracellular

Pi

is

involved

in

enzyme

activation/deactivation

processes

through

dephosphorylation/phosphorylation

in

the

biosynthesis

of

NTP

-LRB-

v

-LRB-

-RRB-

-RRB-

and

of

many

other

metabolites

as

described

below

Intracellular

is

involved

in

AA

biosynthesis

-LRB-

v

-LRB-

-RRB-

-RRB-

-LRB-

Fig.

Table

-RRB-

Michaelis

Menten

kinetics

with

and

Pi

are

at

power

two

since

a

second-order

mechanism

is

involved

has

first

to

be

transformed

into

radical

then

into

an

AA

which

is

finally

integrated

into

a

protein

structure

Management

of

carbon

source

is

crucial

for

plant

cells

since

glucose

fructose

sucrose

and

starch

can

be

used

However

since

the

model

is

based

only

on

glucose

biochemical

reactions

converting

other

sugars

into

glucose

are

described

-LRB-

Fig.

Table

-RRB-

Starch

biosynthesis

-LRB-

v

-LRB-

-RRB-

-RRB-

is

controlled

by

the

total

intracellular

available

sugar

concentration

and

the

sum

in

intracellular

GLC

FRU

and

SUC

has

to

be

above

mmol/g

DW

for

the

STA

biosynthesis

to

occur

A

maximal

STA

storage

capacity

of

mmol/g

DW

was

observed

experimentally

-LRB-

see

Sect.

-RRB-

Starch

is

degraded

-LRB-

v

-LRB-

-RRB-

-RRB-

when

the

GLC

concentration

is

below

mmol/g

DW

PPP

-LRB-

v

-LRB-

-RRB-

-RRB-

is

regulated

by

NADP

-LRB-

NADP+NAPH

-RRB-

ratio

which

has

to

be

above

for

the

pathway

to

be

active

Pyruvate

kinase

regulation

-LRB-

v

-LRB-

-RRB-

-RRB-

is

under

the

control

of

intracellular

Pi

concentration

with

a

flux

increase

at

mmol

Pi/g

DW

and

below

conversion

into

PEP

-LRB-

v

-LRB-

-RRB-

-RRB-

is

regulated

by

Pi

concentration

with

a

flux

increase

at

mmol

Pi/g

DW

and

below

TCA

cycle

-LRB-

v

-LRB-

-RRB-

-RRB-

is

regulated

by

the

NAD

-LRB-

NAD+NADH

-RRB-

ratio

and

a

ratio

that

is

above

will

induce

a

flux

increase

GLC

-LRB-

v

-LRB-

-RRB-

-RRB-

and

FRU

-LRB-

v

-LRB-

-RRB-

-RRB-

uptake

require

a

STA

concentration

that

is

below

and

mmol/g

DW

respectively

OP

synthesis

-LRB-

v

-LRB-

-RRB-

-RRB-

is

regulated

by

intracellular

Pi

concentration

with

a

flux

increase

at

above

mmol

Pi/g

DW

OP

degradation

-LRB-

v

-LRB-

-RRB-

-RRB-

is

controlled

by

intracellular

Pi

concentration

with

a

flux

increase

at

below

mmol

Pi/g

DW

LIP

-LRB-

v

-LRB-

-RRB-

-RRB-

and

ORA

-LRB-

v

-LRB-

-RRB-

-RRB-

degradation

into

A-CoA

is

controlled

by

NADH

concentration

with

fluxes

increase

at

below

mmol

NADH/g

DW

Phosphofructokinase

regulation

-LRB-

v

-LRB-

-RRB-

-RRB-

is

controlled

by

intracellular

Pi

with

a

flux

increase

below

mmol

Pi/g

DW

Respiration

rate

-LRB-

v

-LRB-

-RRB-

-RRB-

is

controlled

by

NDP

-LRB-

NTP+NDP

-RRB-

ratio

with

a

flux

increase

below

a

ratio

of

Finally

regulation

of

root

cells

growth

rate

-LRB-

v

-LRB-

-RRB-

is

controlled

by

the

intracellular

concentration

in

the

cell

building

blocks

such

as

OP

LIP

amino

acids

and

peptides

-LRB-

AA

-RRB-

ORA

and

STH

Monod

model

was

used

for

LIP

AA

and

ORA

A

hybrid

Moser

Monod

model

was

used

for

OP

and

STH

with

each

kinetic

term

at

power

and

respectively

-LRB-

Table

-RRB-

Since

OP

and

STH

are

crucial

to

cell

growth

the

steepness

of

the

affinity

for

both

cell

building

blocks

was

increased

Materials

and

methods

Culture

conditions

Liquid

cultures

of

hairy

roots

were

performed

in

Petri

dish

as

described

in

Jolicoeur

et

al.

-LSB-

-RSB-

The

major

problem

in

culturing

hairy

roots

is

the

difficulty

to

obtain

a

representative

sample

of

the

root

network

since

the

roots

develop

a

highly

dense

interlinked

bed

Petri

dish

culture

allowed

distributing

the

roots

inoculum

in

a

series

of

dishes

with

each

dish

taken

as

a

single

sample

Root

growth

was

also

limited

by

the

use

of

a

low

salt

medium

thus

preventing

the

occurrence

of

dense

root

network

Previous

results

in

Petri

dish

-LSB-

-RSB-

and

in

bioreactor

-LSB-

-RSB-

suggest

that

there

was

no

oxygen

limitation

in

the

cultures

of

this

work

Hairy

roots

of

C.

roseus

L.

G.

Don

were

established

as

described

by

Bhadra

et

al.

-LSB-

-RSB-

with

Agrobacterium

rhizogenes

strain

Hairy

roots

were

transferred

every

month

in

Petri

dishes

in

mL

of

minimum

medium

-LSB-

-RSB-

supplemented

with

-LRB-

w/v

-RRB-

sucrose

and

with

a

threefold

-LRB-

mM

-RRB-

In

the

batch

culture

experiments

approximately

g

fresh

weight

-LRB-

FW

-RRB-

of

hairy

roots

was

inoculated

in

each

Petri

dish

containing

mL

of

minimum

medium

In

the

medium

exchange

cultures

approximately

g

FW

of

hairy

roots

was

inoculated

in

Petri

dish

containing

mL

of

minimum

medium

The

medium

was

renewed

at

or

intervals

to

avoid

depletion

of

Pi

in

the

medium

Whole

Petri

dishes

were

harvested

in

triplicates

-LRB-

n

-RRB-

periodically

and

taken

as

distinct

samples

Liquid

from

each

dish

was

filtered

at

μm

-LRB-

Millipore

Billerica

Massachusetts

-RRB-

and

stored

at

°C

for

further

analysis

Roots

were

filtered

under

vacuum

on

a

glass

fiber

filter

-LRB-

mm

diameter

Glass

Microfiber

filters

GF/D

Whatman

-RRB-

and

rinsed

three

times

with

mL

of

de-ionized

water

The

filtered

roots

were

removed

from

the

filter

and

weighed

for

FW

in

a

disposable

aluminum

dish

-LRB-

Fisher

Scientific

-RRB-

on

a

precision

balance

-LRB-

Sartorius

-RRB-

Fresh

roots

were

immediately

frozen

into

liquid

and

stored

in

liquid

for

further

analysis

Root

samples

were

then

freeze

dried

-LRB-

Duratop

and

Duradry

FTS

Systems

Inc.

Stone

Ridge

NY

USA

-RRB-

weighted

for

DW

measurement

and

grinded

-LRB-

mortar

and

pestle

-RRB-

for

further

analysis

All

further

analyses

were

performed

using

freeze-dried

roots

Amino

acids

analysis

Approximately

mg

of

freeze-dried

roots

were

extracted

in

mL

of

w/v

acid

The

samples

were

sonicated

for

min

and

then

centrifuged

at

g

for

min

The

supernatant

was

analysed

for

AA

by

HPLC

using

a

modified

method

from

Gombert

et

al.

-LSB-

-RSB-

as

described

in

Benslimane

et

al.

-LSB-

-RSB-

The

column

is

a

high-efficiency

Nova-Pak

TM

-LRB-

μm

-RRB-

Precolumn

derivatization

of

the

AA

was

performed

using

AccQ.Fluor

-LRB-

carbamate

or

AQC

-RRB-

which

is

an

N-hydroxysuccinimide-activated

heterocyclic

carbamate

and

the

derivatized

AA

were

quantified

via

a

fluorescence

detector

α-Aminobutyric

acid

was

used

as

an

internal

standard

The

standard

error

of

measurement

using

this

method

was

routinely

below

AA

concentration

was

then

calculated

since

the

peak

for

each

individual

AA

accounted

for

the

combination

of

free

and

that

from

peptides

and

proteins

Extraction

of

sugars

Approximately

mg

of

freeze-dried

roots

was

washed

with

ethanol

and

then

centrifuged

at

g

for

min

This

wash

was

done

three

times

and

each

time

the

supernatant

was

kept

for

glucose

fructose

and

sucrose

analyses

After

the

third

wash

the

pellet

was

kept

for

starch

analysis

Analysis

of

sugars

Glucose

fructose

and

sucrose

analysis

was

performed

with

a

Beckman

Coulter

HPLC

-LRB-

Beckman

Coulter

Canada

Inc

Mississauga

Canada

Pump

model

automatic

injector

model

-RRB-

equipped

with

a

Gilson

model

refractive

index

detector

A

Prevail

Carbohydrate

ES

column

mm

mm

-LRB-

Alltech

Canada

Guelph

Ontario

Canada

-RRB-

coupled

with

a

Prevail

Carbohydrate

ES

All-Guard

mm

mm

guard

column

-LRB-

Alltech

Canada

Guelph

Ontario

Canada

-RRB-

was

used

at

a

column

temperature

of

°C

The

injection

volume

was

μL

The

mobile

phase

consisted

of

acetonitrile

and

water

-LRB-

v/v

-RRB-

at

mL/min

The

cell

pellet

obtained

from

the

soluble

sugars

extraction

was

re-suspended

in

mL

de-ionized

water

and

sterilized

at

°C

for

min

together

with

a

mL

g/L

starch

solution

in

de-ionized

water

Samples

were

allowed

to

reach

room

temperature

and

their

volume

was

readjusted

to

mL

with

de-ionized

water

if

necessary

Starch

calibration

standards

from

to

g/L

were

prepared

by

serial

dilutions

of

the

starch

solution

in

de-ionized

water

Calibration

standards

and

samples

were

diluted

with

an

amyloglucosidase

solution

-LRB-

Sigma

St.

Louis

Missouri

USA

Cat

-RRB-

and

incubated

for

min

in

an

ultrasound

bath

at

°C

Samples

and

standards

were

centrifuged

for

min

at

g

A

μL

aliquot

of

the

supernatant

was

directly

transferred

into

a

spectrometric

cuvette

with

μL

of

Glucose

Infinity

reagent

-LRB-

Sigma

Cat

-RRB-

After

incubation

-LRB-

min

-RRB-

at

room

temperature

μL

of

mM

buffer

pH

was

added

followed

by

spectrophotometric

reading

at

nm

Ions

extraction

Ions

were

extracted

from

approximately

mg

of

freeze-dried

roots

in

mL

of

-LRB-

w/v

-RRB-

trichloroacetic

acid

This

mixture

was

sonicated

at

°C

for

min

and

then

centrifuged

at

g

for

min

The

supernatant

was

filtered

at

μm

and

analysed

by

HPLC

Ions

analysis

Culture

medium

and

intracellular

contents

in

majors

ions

-LRB-

Cl

K

-RRB-

were

analysed

using

a

Dionex

HPLC

system

-LRB-

Dionex

Canada

Ltd.

Oakville

Canada

-RRB-

equipped

with

an

isocratic

pump

an

automated

sampler

and

a

pulsed

electrochemical

detector

in

the

conductivity

mode

controlled

by

the

Dionex

software

for

cations

and

the

Dionex

Peaknet

software

for

anions

Anions

were

separated

using

a

mm

IONPAC

analytical

column

an

guard

column

and

a

anion

self-regeneration

suppressor

to

improve

the

signal-to-noise

ratio

The

mobile

phase

consisted

of

an

aqueous

buffer

of

mM

mM

solution

flowing

at

a

rate

of

mL/min

Cations

were

separated

using

a

IONPAC

analytical

column

a

IONPAC

guard

column

and

a

cation

self-regenerating

suppressor

The

mobile

phase

was

an

aqueous

mM

methanesulphonic

acid

solution

flowing

at

a

rate

of

mL/min

Model

simulations

The

model

simulations

were

done

using

the

Matlab

software

-LRB-

The

MathWorks

Inc.

Natick

MA

USA

-RRB-

The

differential

equations

system

was

integrated

through

the

Ordinary

Differential

Equation

solver

The

model

error

minimization

was

performed

by

means

of

manual

and

algorithm-based

methods

The

former

was

done

to

find

good

initial

estimates

based

on

literature

-LRB-

when

available

-RRB-

The

latter

was

then

used

to

reduce

the

global

error

between

the

estimates

and

the

experimental

data

The

algorithm

used

was

the

lsqcurvefit.m

subroutine

-LRB-

Optimisation

toolbox

Matlab

-RRB-

based

on

the

Levenberg

Marquardt

algorithm

-LSB-

-RSB-

Results

and

discussion

Model

calibration

and

determination

of

the

kinetic

parameters

Model

calibration

was

performed

using

experimental

data

from

C.

roseus

hairy

root

batch

and

medium

exchange

cultures

Each

experiment

-LRB-

one

batch

and

one

medium

exchange

-RRB-

was

performed

in

triplicate

A

total

of

samples

were

taken

during

the

batch

experiment

and

during

the

medium

exchange

Parameter

values

were

obtained

from

experimental

data

-LRB-

maximum

uptake

rates

maximum

growth

rate

sucrose

maximum

hydrolysis

rate

and

some

of

the

maximal

accumulation

levels

-RRB-

and

from

literature

taking

values

from

other

plant

species

when

unavailable

for

C.

roseus

-LRB-

Tables

-RRB-

Adjustment

of

the

unknown

parameters

as

well

the

values

taken

from

literature

was

performed

manually

in

parallel

using

a

non-linear

least-square

algorithm

-LRB-

lsqcurvefit

-RRB-

from

Matlab

software

The

least-squares

criterion

was

applied

on

all

the

data

points

-LRB-

triplicates

taken

as

mean

in

-LRB-

Mi

-RRB-

exp

-RRB-

The

sum

of

squares

were

weighted

as

described

below

whereTable

constants

-LRB-

Km

-RRB-

Catharanthus

roseusmmol/g

DWModel

C.

roseusmmol/g

DWModel

C.

roseusmmol/g

DWModel

C.

roseusmmol/g

DWModel

C.

roseusmmol/g

DWModel

C.

roseusmmol/g

DWModel

C.

roseusmmol/g

DWModel

C.

roseusmmol/g

DWModel

C.

roseusmmol/g

DWModel

C.

roseusmmol/g

DWModel

C.

roseusmmol/g

DWModel

C.

roseusmmol/g

DWModel

C.

roseusmmol/g

DWModel

C.

roseusmmol/g

DWModel

C.

roseusmmol/g

DWModel

C.

roseusmmol/g

DWModel

C.

roseusmmol/g

DWModel

C.

roseusmmol/g

DWModel

Daucus

carotamM

-LSB-

-RSB-

D.

carotamM

-LSB-

-RSB-

Citrus

reticulatamM

-LSB-

-RSB-

Arabidopsis

thaliana

-LSB-

-RSB-

Zea

mays

-LSB-

-RSB-

A.

thalianamM

-LSB-

-RSB-

Z.

mays

-LSB-

-RSB-

D.

carota

-LSB-

-RSB-

C.

roseusmM

-LSB-

-RSB-

C.

roseus

-LSB-

-RSB-

C.

roseus

-LSB-

-RSB-

C.

roseus

-LSB-

-RSB-

Nicotinana

tabacum

-LSB-

-RSB-

Lemma

gibba

-LSB-

-RSB-

Z.

mays

-LSB-

-RSB-

Z.

mays

-LSB-

-RSB-

Chara

corallina

-LSB-

-RSB-

C.

corallina

-LSB-

-RSB-

Nitella

translucens

-LSB-

-RSB-

Neurospora

crassa

-LSB-

-RSB-

N.

crassa

-LSB-

-RSB-

D.

carota

-LSB-

-RSB-

C.

roseusmM

-LSB-

-RSB-

C.

roseus

-LSB-

-RSB-

Nicotinana

glutinosa

-LSB-

-RSB-

L.

gibba

-LSB-

-RSB-

C.

corallina

-LSB-

-RSB-

C.

corallina

-LSB-

-RSB-

N.

crassa

-LSB-

-RSB-

N.

crassa

-LSB-

-RSB-

D.

carota

-LSB-

-RSB-

C.

roseusmMModel

C.

roseusmmol/g

DWModel

calibrationTable

reaction

rates

-LRB-

Vmax

-RRB-

Reaction

in

TPMPCurrent

value

-LRB-

mmol/g

DW/d

-RRB-

Literature

-LRB-

mmol/g

DW/d

-RRB-

C.

roseusModel

roseusModel

C.

roseusModel

C.

roseusModel

roseusModel

roseusModel

C.

roseusModel

C.

roseusModel

C.

roseusModel

C.

roseusModel

C.

roseusModel

C.

roseusModel

C.

roseusModel

C.

roseusModel

roseusModel

C.

roseusModel

C.

roseusModel

C.

roseusModel

C.

roseusModel

C.

roseusModel

C.

roseusModel

C.

roseusModel

C.

roseusModel

C.

roseusModel

C.

reticulata

-LSB-

-RSB-

Z.

mays

-LSB-

-RSB-

Z.

mays

-LSB-

-RSB-

D.

carota

-LSB-

-RSB-

C.

roseusModel

roseusModel

C.

roseus

-LSB-

-RSB-

C.

roseus

-LSB-

-RSB-

C.

roseus

-LSB-

-RSB-

C.

roseus

-LSB-

-RSB-

N.

tabacum

-LSB-

-RSB-

N.

tabacum

-LSB-

-RSB-

L.

gibba

-LSB-

-RSB-

Z.

mays

-LSB-

-RSB-

C.

corallina

-LSB-

-RSB-

N.

translucens

-LSB-

-RSB-

N.

crassa

-LSB-

-RSB-

D.

carota

-LSB-

-RSB-

C.

roseus

-LSB-

-RSB-

C.

roseus

-LSB-

-RSB-

N.

glutinosa

-LSB-

-RSB-

L.

gibba

-LSB-

-RSB-

L.

gibba

-LSB-

-RSB-

C.

corallina

-LSB-

-RSB-

C.

corallina

-LSB-

-RSB-

N.

crassa

-LSB-

-RSB-

N.

crassa

-LSB-

-RSB-

D.

carota

-LSB-

-RSB-

C.

roseusModel

D.

carota

-LSB-

-RSB-

Table

variables

and

initial

values

-LRB-

t

-RRB-

used

for

model

mmol/g

DWC

roseusBatch/medium

mmol/g

DWC

roseusBatch/medium

mmol/g

DWC

roseusBatch/medium

mmol/g

DWC

roseusUnpublished

mmol/g

DWN

tabacum

suspension

cells

-LSB-

-RSB-

DWYoung

photosynthetic

tissue

-LSB-

-RSB-

DWYoung

photosynthetic

tissue

-LSB-

-RSB-

DWYoung

photosynthetic

tissue

-LSB-

-RSB-

DWYoung

photosynthetic

tissue

-LSB-

-RSB-

DWYoung

photosynthetic

tissue

-LSB-

-RSB-

mmol/g

DWC

roseusBatch/medium

DWYoung

photosynthetic

tissue

-LSB-

-RSB-

mmol/g

DWN

tabacum

suspension

cells

-LSB-

-RSB-

mmol/g

DWC

roseusBatch/medium

mmol/g

DWPotato

tubers

-LSB-

-RSB-

mmol/g

DWC

roseusBatch/medium

mmol/g

DWC

roseusBatch/medium

mmol/g

DWN

tabacum

suspension

cells

-LSB-

-RSB-

mmol/g

DWC

roseusUnpublished

mmol/g

DWC

roseusModel

mMC

roseusBatch/medium

mMC

roseusBatch/medium

roseusCulture

mMC

roseusBatch/medium

mMC

roseusBatch/medium

mMC

roseusBatch/medium

mmol/g

DWC

gDWC

roseusBatch/medium

exchange

Error

terms

were

weighted

using

the

maximum

-LRB-

max

-LRB-

Mi

-RRB-

exp

-RRB-

and

the

minimum

-LRB-

min

-LRB-

Mi

-RRB-

exp

-RRB-

experimental

values

-LRB-

exp

-RRB-

from

either

batch

or

medium

exchange

cultures

This

method

was

preferred

to

a

method

using

experimental

error

because

the

experimental

error

was

very

high

for

some

data

points

and

varied

with

experimental

data

-LRB-

Table

-RRB-

This

method

has

also

showed

previously

to

perform

adequately

to

calibrate

a

nutritional

model

on

hairy

root

data

-LSB-

-RSB-

All

the

experimental

data

points

from

batch

and

medium

exchange

culture

were

used

for

the

non-linear

least-square

regression

The

total

number

of

experimental

data

was

then

of

with

different

measurements

for

each

of

the

samples

plus

eight

measurements

for

intracellular

AA

Many

set

of

parameters

were

tested

as

initial

guesses

to

improve

the

fitting

A

combination

of

parameter

values

-LRB-

Tables

-RRB-

showed

to

minimize

the

global

error

for

combined

data

from

batch

and

from

medium

exchange

cultures

using

a

convergence

criterion

of

on

the

variation

of

the

global

error

From

the

calculation

of

values

-LRB-

Table

-RRB-

for

each

of

the

state

variables

that

were

fitted

-LRB-

state

variables

in

two

experiments

-RRB-

it

seems

that

the

best

fit

is

obtained

for

cells

growth

and

nutrient

transport

and

storage

-LRB-

Pi

-RRB-

However

the

sensitivity

analysis

also

suggests

that

some

parameters

can

still

be

optimized

-LRB-

Fig.

-RRB-

A

critical

problem

with

such

a

descriptive

model

is

a

high

number

of

parameters

The

model

has

maximum

reaction

rates

and

affinity

constants

and

the

least-square

regression

was

only

performed

on

only

of

the

state

variables

of

the

model

It

is

then

possible

that

the

identified

solution

corresponds

to

a

local

minimum

More

measurements

on

metabolite

concentration

are

thus

necessary

to

improve

the

performance

of

the

model

and

for

being

able

to

perform

an

adequate

identifiability

analysis

on

the

parameters

In

this

context

the

proposed

model

is

probably

over-parameterized

However

the

goal

of

this

work

was

not

to

establish

a

minimal

model

but

a

descriptive

model

that

can

be

used

as

a

tool

useful

at

improving

our

understanding

of

plant

cell

culture.Table

standard

deviations

on

measured

variables

and

correlation

coefficients

-LRB-

-RRB-

ComponentMean

SD

-LRB-

-RRB-

-LRB-

batch

-RRB-

Mean

SD

-LRB-

-RRB-

-LRB-

medium

exchange

-RRB-

-LRB-

batch

-RRB-

-LRB-

medium

exchange

-RRB-

Fig.

analysis

on

model

parameters

for

batch

-LRB-

solid

bar

-RRB-

and

medium

exchange

-LRB-

empty

bar

-RRB-

cultures

Relative

change

in

error

is

calculated

as

described

in

Sect.

Parameter

adjustment

of

-LRB-

a

-RRB-

Parameter

adjustment

of

-LRB-

b

-RRB-

Parameters

not

shown

have

absolute

relative

error

changes

that

are

below

Simulation

of

the

cells

physiological

state

Hairy

root

growth

The

model

allows

estimating

root

growth

from

flux

ν

-LRB-

-RRB-

as

well

as

from

the

total

estimated

mass

of

the

root

cells

constituents

per

dish

-LRB-

Σ

Mi

on

a

mass

basis

-RRB-

taking

average

molecular

weights

for

the

cell

building

blocks

-LRB-

Fig.

-RRB-

However

the

total

mass

calculated

at

initial

condition

-LRB-

t

-RRB-

was

lower

than

that

of

the

inoculum

with

g

DW

per

dish

as

compared

to

g

DW

per

dish

respectively

The

difference

of

g

DW

per

dish

can

be

explained

from

the

molecular

species

that

are

present

in

the

cells

but

which

are

not

included

in

the

model

Therefore

the

estimation

of

root

mass

with

time

obtained

from

ν

-LRB-

-RRB-

was

compared

with

that

calculated

from

total

cell

mass

but

adding

a

constant

correction

factor

of

Model

simulations

then

describe

hairy

root

growth

for

both

batch

and

medium

exchange

cultures

Both

root

mass

estimates

from

ν

-LRB-

-RRB-

and

ΣMi

are

superimposed

-LRB-

Fig.

-RRB-

However

the

sum

of

the

molecular

species

is

overestimating

measured

biomass

at

the

end

of

batch

culture

because

of

cell

accumulation

in

diverse

compounds

while

growth

slowed

down

Surprisingly

both

batch

and

medium

exchange

cultures

behaved

similarly

with

a

maximum

specific

growth

rate

of

d

and

a

growth

cessation

at

around

d.

Periodic

medium

renewal

has

avoided

nutrient

depletion

in

macronutrients

and

sugars

-LRB-

Fig.

-RRB-

However

the

plateau

observed

for

the

medium

exchange

culture

may

have

resulted

from

a

limitation

in

micronutrients

which

were

not

measured

Therefore

only

experimental

data

obtained

before

the

occurrence

of

the

plateau

for

the

medium

exchange

culture

were

used

for

model

calibration

and

other

analyses

The

strategy

of

describing

cell

growth

as

a

function

of

intracellular

content

in

building

blocks

thus

showed

to

perform

adequately

This

result

may

support

the

global

model

structure

as

well

as

the

hypothesis

of

pseudo-steady

state

for

the

SPMP

The

central

primary

metabolic

network

described

here

as

SPMP

was

observed

at

pseudo-steady

state

by

Rontein

et

al.

-LSB-

-RSB-

for

most

of

in

vitro

culture

duration

for

tomato

suspension

cells

-LSB-

-RSB-

However

this

hypothesis

has

to

be

further

investigated.Fig

simulation

for

Catharanthus

roseus

hairy

root

batch

-LRB-

filled

square

-RRB-

and

medium

exchange

-LRB-

triangle

-RRB-

liquid

cultures

in

Petri

dish

a

e.

Intracellular

concentration

in

cell

building

blocks

with

time

Batch

-LRB-

f

-RRB-

and

medium

exchange

-LRB-

g

-RRB-

cultures

The

specific

growth

rate

is

described

from

ν

-LRB-

-RRB-

as

a

function

of

intracellular

concentration

in

cell

building

blocks

Model

simulations

for

batch

-LRB-

solid

lines

-RRB-

and

medium

exchange

-LRB-

dashed

lines

-RRB-

cultures

and

total

mass

for

the

molecular

species

accounted

in

the

model

increased

of

g

DW

accounting

for

non-estimated

molecular

species

-LRB-

dashed

line

-RRB-

Root

mass

was

calculated

using

average

MW

for

STA

-LRB-

based

on

glucose

units

-RRB-

SEC

-LRB-

-RRB-

TRY

-LRB-

-RRB-

NAD/NADH

-LRB-

-RRB-

NADP/NADPH

-LRB-

-RRB-

NDP/NTP

-LRB-

-RRB-

ORA

-LRB-

-RRB-

STH

-LRB-

based

on

glucose

units

-RRB-

OP

-LRB-

average

of

from

nucleotides

-RRB-

LIP

-LRB-

based

on

that

of

A-CoA

-RRB-

IPP

-LRB-

-RRB-

and

AA

-LRB-

average

of

-RRB-

Fig.

concentration

in

nutrients

with

time

Experimental

data

for

C.

roseus

hairy

root

batch

-LRB-

filled

square

-RRB-

and

medium

exchange

-LRB-

triangle

-RRB-

liquid

cultures

Concentration

in

sugars

-LRB-

a

c

-RRB-

inorganic

phosphate

-LRB-

d

-RRB-

and

nitrate

-LRB-

e

-RRB-

in

the

culture

media

with

time

Model

simulations

for

batch

-LRB-

solid

lines

-RRB-

and

medium

exchange

-LRB-

dashed

lines

-RRB-

cultures

The

cells

building

blocks

The

measured

total

AA

concentration

decreased

with

time

for

the

batch

culture

and

reached

a

plateau

for

the

medium

exchange

culture

-LRB-

Fig.

-RRB-

Simulated

AA

concentrations

seem

to

follow

the

trend

for

experimental

data

but

were

overestimated

for

both

batch

and

medium

exchange

cultures

The

deviations

can

not

be

explained

however

by

exuded

AA

and

proteins

since

no

AA

were

detected

in

the

used

culture

media

Values

of

to

mmol

AA/g

DW

were

measured

for

the

batch

culture

which

corresponds

to

and

g

AA/g

DW

respectively

-LRB-

taking

an

average

amino

acid

MW

of

g/mol

-RRB-

Higher

values

were

measured

in

the

medium

exchange

culture

with

to

mmol

AA/g

DW

which

represents

and

g

AA/g

DW

respectively

Free

AA

content

of

mmol

AA/g

DW

-LRB-

estimated

at

g

AA/g

DW

-RRB-

is

reported

in

literature

for

tobacco

suspension

cells

using

medium

-LSB-

-RSB-

and

mmol

AA/g

DW

-LRB-

estimated

at

g

AA/g

DW

-RRB-

in

potato

tuber

-LSB-

-RSB-

In

tomato

cell

culture

the

total

protein

content

was

of

g

proteins/g

DW

-LSB-

-RSB-

The

total

AA

mass

per

root

dry

weight

that

have

been

measured

which

represents

the

sum

of

free

AA

and

that

of

peptides

and

proteins

is

thus

within

the

range

reported

in

literature

The

use

of

a

minimal

medium

may

explain

a

low

value

for

total

AA

The

other

cell

building

blocks

were

not

measured

but

the

model

estimations

were

close

to

literature

data

Total

ORA

concentration

was

estimated

at

mmol/g

DW

as

compared

to

mmol/g

DW

reported

by

Farré

et

al.

-LSB-

-RSB-

Total

STH

were

estimated

at

mmol/g

DW

as

compared

to

a

range

of

mmol/g

DW

-LRB-

on

the

basis

of

glucose

units

-RRB-

Maximal

simulated

rates

of

biosynthesis

were

compared

with

that

from

literature

The

rate

of

AA

biosynthesis

-LRB-

v

-LRB-

-RRB-

-RRB-

was

estimated

at

mmol/g

DW/d

which

was

within

the

range

of

mmol/g

DW/d

reported

by

Rontein

et

al.

-LSB-

-RSB-

for

tomato

suspension

cells

STH

biosynthesis

-LRB-

v

-LRB-

-RRB-

-RRB-

was

slow

with

mmol/g

DW/d

as

compared

to

mmol/g

DW/d

-LSB-

-RSB-

Maximal

net

rate

of

starch

-LRB-

STA

-RRB-

biosynthesis

-LRB-

v

-LRB-

-RRB-

-RRB-

was

mmol/g

DW/d

as

compared

to

mmol/g

DW/d

-LSB-

-RSB-

Differences

in

metabolic

fluxes

may

be

explained

from

the

differences

in

the

specific

growth

rate

Rontein

et

al.

-LSB-

-RSB-

have

reported

a

specific

growth

rate

of

d

for

tomato

suspension

cells

in

medium

as

compared

to

d

in

this

study

for

C.

roseus

using

a

minimal

medium

The

same

minimal

medium

has

been

reported

previously

to

induce

lower

growth

rate

as

compared

to

standard

media

for

carrot

hairy

root

-LSB-

-RSB-

The

cells

nutritional

state

Extracellular

sucrose

-LRB-

ESUC

-RRB-

concentration

profile

was

simulated

by

the

model

for

both

the

batch

and

the

medium

exchange

cultures

-LRB-

Fig.

-RRB-

thus

suggesting

that

the

sucrose

hydrolysis

modelling

strategy

was

adequate

In

the

case

of

glucose

-LRB-

EGLC

-RRB-

and

fructose

-LRB-

EFRU

-RRB-

simulations

for

the

batch

culture

followed

the

trend

of

experimental

data

but

before

growth

cessation

Then

estimated

glucose

and

fructose

levels

stayed

high

as

compared

to

experimental

data

This

may

suggest

that

the

model

is

underestimating

glucose

and

fructose

uptake

at

reduced

growth

However

simulated

concentrations

in

intracellular

sucrose

-LRB-

SUC

-RRB-

and

glucose

-LRB-

GLC

-RRB-

were

following

similar

trends

than

experimental

data

-LRB-

Fig.

-RRB-

However

model

simulated

constant

starch

-LRB-

STA

-RRB-

concentration

and

overestimated

fructose

-LRB-

FRU

-RRB-

concentration

In

the

case

of

the

medium

exchange

culture

the

model

simulated

adequately

experimental

data

on

extracellular

and

intracellular

sucrose

and

intracellular

glucose

Extracellular

glucose

and

fructose

concentrations

were

underestimated

and

starch

and

fructose

concentrations

were

overestimated

A

maximal

sucrose

rate

of

hydrolysis

-LRB-

v

-LRB-

-RRB-

-RRB-

of

mmol/g

DW/d

was

estimated

as

compared

to

mmol/g

DW/d

for

D.

carota

hairy

root

using

same

minimal

medium

-LSB-

-RSB-

Contents

of

mmol

SUC/g

DW

-LRB-

batch

-RRB-

and

mmol

SUC/g

DW

-LRB-

medium

exchange

-RRB-

were

obtained

as

compared

to

mmol

SUC/g

DW

-LSB-

-RSB-

mmol

SUC/g

DW

-LSB-

-RSB-

and

mmol

SUC/g

DW

-LSB-

-RSB-

For

free

glucose

cell

contents

of

mmol

GLC/g

DW

were

obtained

as

compared

to

mmol

GLC/g

DW

-LSB-

-RSB-

mmol

GLC/g

DW

-LSB-

-RSB-

and

mmol

GLC/g

DW

-LSB-

-RSB-

For

fructose

cell

contents

of

mmol

FRU/g

DW

were

observed

as

compared

to

mmol

FRU/g

DW

-LSB-

-RSB-

mmol

GLC/g

DW

-LSB-

-RSB-

and

mmol

GLC/g

DW

-LSB-

-RSB-

Starch

accumulation

reached

mmol

STA

-LRB-

based

on

glucose

-RRB-

g

DW

as

compared

to

-LSB-

-RSB-

and

mmol

STA

-LRB-

based

on

glucose

-RRB-

g

DW

-LSB-

-RSB-

Fig.

concentration

in

nutrients

and

metabolites

with

time

Experimental

data

for

C.

roseus

hairy

root

batch

-LRB-

filled

square

-RRB-

and

medium

exchange

-LRB-

triangle

-RRB-

liquid

cultures

Intracellular

concentration

in

sugars

-LRB-

a

d

-RRB-

inorganic

phosphate

-LRB-

e

-RRB-

nitrate

-LRB-

f

-RRB-

ammonium

-LRB-

g

-RRB-

and

in

secondary

metabolites

issued

from

tryptamin

-LRB-

h

-RRB-

and

secologanin

-LRB-

i

-RRB-

with

time

Model

simulations

for

batch

-LRB-

solid

lines

-RRB-

and

medium

exchange

-LRB-

dashed

lines

-RRB-

cultures

Model

simulations

of

extracellular

Pi

and

-LRB-

-RRB-

concentrations

followed

experimental

data

for

the

complete

duration

of

the

batch

and

the

medium

exchange

cultures

-LRB-

Fig.

-RRB-

Hairy

root

growth

-LRB-

simulated

and

experimental

-RRB-

has

ceased

concurrently

to

depletion

suggesting

this

ion

to

be

limiting

in

the

batch

culture

Intracellular

Pi

and

were

simulated

-LRB-

Fig.

-RRB-

It

is

interesting

to

note

that

the

final

intracellular

Pi

concentration

in

the

batch

culture

seemed

to

reach

a

plateau

at

mmol/g

DW

which

was

simulated

This

plateau

may

be

close

to

the

Pi

level

that

is

essential

to

maintain

the

endogeneous

metabolism

-LSB-

-RSB-

A

maximum

Pi

accumulation

plateau

was

also

observed

for

the

medium

exchange

culture

around

mmol/g

DW

This

value

is

close

to

the

maximum

value

of

mmol/g

DW

measured

for

carrot

hairy

root

-LSB-

and

references

therein

-RSB-

Maximum

intracellular

nitrate

of

mmol

DW

was

measured

for

both

cultures

Intracellular

nitrate

was

kept

constant

for

the

medium

exchange

and

decreased

to

its

initial

value

for

the

batch

Intracellular

ammonium

reached

a

value

of

mmol

DW

for

the

medium

exchange

culture

and

decreased

to

mmol

DW

after

d.

For

the

batch

culture

intracellular

ammonium

reached

a

maximum

value

-LRB-

mmol

DW

-RRB-

at

day

and

then

decreased

closely

to

its

value

at

inoculation

The

model

overestimated

intracellular

concentration

and

simulated

experimental

intracellular

concentrations

in

for

both

the

batch

and

medium

exchange

cultures

A

more

precise

description

of

the

secondary

metabolism

and

of

the

AA

biosynthesis

may

be

required

to

improve

model

simulation

of

nitrogenous

compounds

The

cells

energetic

state

Model

has

simulated

energy

rich

cells

with

high

levels

in

NTP

and

NADH

at

exponential

growth

-LRB-

Fig.

-RRB-

However

estimated

cell

content

in

NADPH

showed

an

opposite

trend

with

lower

values

at

exponential

growth

This

result

is

interesting

since

NADPH

is

produced

through

the

pentose-phosphate

pathway

which

is

mostly

active

at

secondary

metabolism

The

simulated

cell

energetic

level

decreased

after

d

at

the

initial

value

-LRB-

inoculation

-RRB-

in

batch

culture

and

was

constant

for

the

medium

exchange

culture

Since

the

medium

was

renewed

every

days

for

the

medium

exchange

experiment

a

pseudo-steady

state

was

expected

NTP

-LRB-

NTP+NDP

-RRB-

and

NADH

-LRB-

NAD+NADH

-RRB-

ratios

of

have

been

reported

for

tobacco

suspension

cells

-LSB-

-RSB-

Farré

et

al.

-LSB-

-RSB-

measured

ratios

of

for

NTP

-LRB-

NTP+NDP

-RRB-

in

potato

tubers

These

authors

have

measured

an

NTP

level

of

mmol/g

DW

as

compared

to

and

mmol/g

DW

that

was

obtained

from

simulations

at

exponential

growth

and

stationary

growth

respectively

We

have

recently

measured

by

in

vivo

NMR

ATP

levels

of

mmol/g

DW

at

day

and

and

of

mmol/g

DW

at

day

for

suspension

cells

of

E.

californica

cultured

using

medium

-LSB-

-RSB-

Energetic

levels

simulated

by

the

model

were

then

similar

to

that

found

in

literature

However

variation

of

energy

shuttles

concentration

has

to

be

further

investigated.Fig

level

of

the

cells

with

time

Intracellular

NTP

-LRB-

a

-RRB-

NADH

-LRB-

b

-RRB-

and

NADPH

-LRB-

c

-RRB-

relative

levels

with

time

Model

simulations

for

C.

roseus

hairy

root

batch

-LRB-

solid

lines

-RRB-

and

medium

exchange

-LRB-

dashed

lines

-RRB-

liquid

cultures

Conclusion

A

metabolic

model

capable

of

describing

hairy

root

growth

from

the

estimation

of

the

cells

physiological

state

was

developed

The

model

includes

the

central

metabolism

the

primary

metabolic

pathways

-LRB-

SPMP

-RRB-

assumed

at

steady

state

and

a

network

for

the

TPMP

At

this

point

the

model

is

simplified

and

intracellular

compartmentalization

processes

into

the

different

cell

compartments

and

organelles

are

not

included

Nevertheless

the

metabolic

model

showed

to

perform

efficiently

in

simulating

hairy

root

growth

and

nutrition

The

use

of

intracellular

concentrations

in

nutrients

and

co-substrates

as

well

as

the

cells

energetic

state

seems

an

efficient

strategy

in

describing

regulation

of

the

metabolic

fluxes

However

more

experimental

is

required

for

improving

the

model

structure

as

well

as

parameter

values

which

may

be

regulated

with

cell

physiological

state

Finally

the

model

will

be

applied

to

other

plant

species

as

well

as

cell

suspensions

and

it

will

be

studied

as

a

tool

to

describe

transient

processes

such

as

metabolic

regulation

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

metabolic model
plant cells
kinetic model
metabolic regulation