Morphological Structured Model for Hairy Root Cultures

MORPHOLOGICAL STRUCTURED MODEL FOR HAIRY ROOT CULTURES I. BERZINl, D. MILLS2,

J.e. MERCHUK3

I. Department of Chemical Engineering, Ben-Gurion University of the Negev, Beer-Sheva, Israel. 2. Institutes for Applied Biology, Ben-Gurion University of the Negev, Beer-Sheva, Israel. 3. Unit of Biotechnology, Ben-Gurion University of the Negev, Beer-Sheva, Israel.

INTRODUCTION The possibility of using hairy root (HR) cultures for producing secondary metabolites on a large scale has recently received a great deal of attention (Flores et aI., 1987; Hamill et aI., 1987; Rhodes et aI., 1987; Scheidegger, 1990; Toivonen, 1993). However, in order to reliably design and scale-up HR culture systems. their growth kinetics must be understood and mathematically mode led (Flint-Wandel et al. 1993 ; Inomata et al.. 1993; Kim et aI., 1995; Taya et aI., 1989). The shape of the HR batch growth curve has been described using Monod's equation (Hilton et aI., 1988) or the logistic equation (Toivonen et aI., 1990), both of which predict the change of total root biomass with time. However, published results (Croes et aI., 1989; Yonemitsu et aI., 1990; F1ores, 1987; Aird et aI., 1988) suggest that different HR morphologies result in dissimilar levels of secondary metabolite production. Thus two HR cultures with a similar biomass but different root architectures could have completely different product yields. A morphological structured model would therefore be of great interest. 8ecause IIR cultures are highl) branched and are not connected to aerial plant parts, morphological structured models of natural root systems cannot adequately describe their architecture . A kinetic model of branching growth of plant HRs published by Taya et al. (1989) assumes linear root extension, binary division of the root-tip meristem and a linear relation between biomass and root length . Although this model provides a close correlation with the biomass data of some HR cultures, its description of HR morphology and branching patterns does not conform to the findings obtained in our experimental system (Duran, 1993). HR laterals are formed in the zone behind the tip meristem, resulting in delayed generation of successive branches, as in natural plant roots (Rose. 1983). Here

\\t:

present

a morphological structured model for HR cultures, that allows detailed description of root architecture and evaluation of root biomass at any desired moment of growth in a batch culture.

EXPERIMENT AL HR cultures of Symphyflll11 officinale were maintained by subculturing a single root tip in 250 m I Erlenmeyer flasks containing 30 ml of liquid MS (Murashige and Skoog, 1962) medium with 3% sucrose. The tissue was incubated at 25°C in the dark at 150 rpm on a gyratory shaker. Every 3-4 days the fre sh and dry weights of three root systems were measured. Their morphological characteristics (length and diameter of each lateral) were determ inated by image analysis using a desktop scanner (Pan et aI., 1991) and NIH Image program. Sugar concentrations in the medium were also determined using colorimetric and enzymatic methods (Chaplin et al.).

THE MODEL Definitions I. HR systems are described h ieran.:hically in terms ll[" 10\':" .; 0[" origin of the laleraJs (\jarley, 11)70 : Hackett et aI., 1972 ; Lungley, 1973). The inoculum tip is designated as "zero-order", laterals branching off from 173

inoculum as "first-order", laterals branching off from first-order laterals as "second-order", and so on . On Iy the first four orders (zero to third) are relevant to our HR system and will be considered here, but the model is capable of describing the growth of higher-order systems as well. 2. To distinguish chronologically between laterals ,,<:longing to the same order. each lateral is designated 0) a sequence of numerical indices indicating its chronological location; the first ("i-") index indicates order of branching among first-order laterals, the second ("j- ") index shows order of branching among second order laterals, and the third ("k-") index shows order of branching among third-order laterals. Obviously, the total number of non-zero indices of a lateral corresponds to its order (e.g., a lateral designated "000" is zero-order. i.e., it is the inoculum). For example, a lateral designated "ijk" (i,j,k =1= 0) must be a third-order lateral; it mllst have been the kth lateral to branch off from a second-order lateral, which was the /h lateral to branch off from a first-order lateral, itself the ith to branch off from the inoculum .

Nom-branching end 1.1.0

1.0.0

2.0.0

3.0.0

0.0.0 Figure 1. Components of the architecture in an idealized HR system. Each lateral is charact~rized b) an inde:-.. which specifies both its order and its chronologic:l1 h)c[ltioll . r"ch 1,,1\:1',,1 is hranching. rarts ( illll '> lrated hcre fllr the I.erll-llf<.ier lateral). 174

ClllllPllSCd

llfbranching and IlLln-

Assumptions Most of the following assumptions were tested by experiment and some are based on published data . I. The HR system can be treated as a set of cylinders of decreasing diameter. 2. The HR laterals grow only in one dimension by extension at the root meristem (Taya et al. 1989).

The diameter of a lateral of given order is considered constant . 3. Each HR lateral includes a non-branching part lapc in which cells divide and differentiate. and a

branching part leff which is called the effective part (Rose, 1983). 4. Along the effective part, branching occurs with a linear density qg, which is characteristic of each

order. 5. The ratio between HR biomass and volume (rv) is constant throughout the root system and remains

constant during entire culturing period . 6. The ratio between HR net water amount (wet weight minus dry weight) and biomass \vet weight (W d is constant throughout the root system and remains constant during entire culturing period . 7. The biomass yield Y xis is constant (Toivonen et al. 1990).

Morphological Structured Model for HR Growth The elongation rate of each lateral in the HR system can be described by the logistic equation : d(lijk) / d(l)

= kg lijk (1 - lijk / lijk -mJx)

(1)

where

I ijk-max = Y1/s-g

(2)

Sijk -O

This equation can be applied to each and every lateral of the HR system. It takes into account both the characteristics of the order and the changes in growth-medium composition . Thus it can describe the different elongation rates of two laterals of the same order that branched off at different times. and also the different elongation rates of two laterals of different order that branched off at the same time . After integration eq . I becomes: lijk

= [lg-o e(kg tijk)j / [1-

(Ig-0 / lijk-max) (I - e(kg tijk)lj

(~)

The overall length of each order of laterals can be calculated as follows : Lo

= tooo

(4 )

LI

= L liOO

(5)

The overall length of the HR system is therefore: L=Lo+LJ+L2+L3=rLg

(8)

Since the number of laterals of order (g+ I) is proportional to the effective length of the laterals of l)rder fonner can be calculated from :

(9) and the overall number of laterals is : ~

tU) 175

(g).

the

Using the typical diameter of each order. its volume can be calculated as follo\\ s:

=

1t D " '2 La / 4 ( I I) '" '" '" and the overall volume of the HR system is therefore:

V

0

(12)

The biomass can be calculated using the volumetric density: Xd

= pv V

( 13)

Xw

=Xd / (1- Wc)

(14 )

Changes in the sucrose concentration can be calculated using the yield factor (Y xis), which is the ratio of biomass fonned to substrate consumed .

RESULTS AND DISCUSSION Testing the model The first step was to check the reliabi Iity of the assumptions. Most of the latter were val idated by experiments. The above equations were used to write an iterative computer program for calculating changes in the llumber. length, volume and dry and wet weight of HR laterals of each order and of the overall HR system during the growth period . Changes in sugar concentration in the growth medium were also calculated. The predicted length and biomass are compared with the experimental data in fig . 2 and 3.

8e+3r------------------------------------------------,

E .... c

6e+3

~ :0:

I..

•

10

o

L1

•

L2

o

L3

A

L

.....:..I

-0::: ~

4e+3

::t: '0

.c .....

CL

c

,

:..I

2e+3

Time [d]

Figure 2. Lengths of each order and of overall HR system \'ersus time of cultivation. The dots represe nt experimental data and the curves show the results of the simulatioll. 176

10.------------------------------------------.

1

.1

.01

o

10

20

30

40

50

Time [d1 Figure 3. Biomass (dry weight) of the HR system versus time of cultivation . The dots represent experimental data and the curve shows the simulated results.

The values predicted by the model are in fair agreement with the experimental data. The model presented here leaves some questions unanswered. Due to the limited information given in the literature regarding the morphology of HR cultures, our model was confined to simulating HR culture in ,~Vll1phytllln

officillale and has yet to be tested with other HR cultures. As mentioned above, the cultures were

initiated with a single tip, which is not a realistic practice on a large scale. Therefore, the influence of the inoculum size (number of tips) should be considered. Although most of the parameters and constants used in this model, have a biological meaning which is quite easy to measure or estimate, finding expressions connecting these quantities would make the model easier to use. Finally, scaling-up HR cultures will have to a\\ ait elucidation of the correlations between HR morphology and secondary metabolite production.

CONCLUSIONS A morphological structured model of HR cultures has been proposed and found to satisfactorily simulate the growth characteristics and architecture of HR cultures of SYlllphvtll1ll officinale. Additional aspects should be considered in order to predict a closer fit to HR morphology and correlation with secondary metabolites production .

ACKNOWLEDGMENT We wish to express our especial gratitude to Mrs. Shi\ta Wenkart for sharing her experience and kno\\ ledge with us.

177

NOMENCLATURE D- diameter of lateral [mm]; k- parameter of the logistic equation [d- I ]; 1- length of lateral [mm], 10- initial length of lateral [mm] ; lape-length of non-branching area [mm] ; leff-length of branching area [mm]; Imax maximum length of the lateral [mm]; L- overall length of laterals [mm]; n- number of laterals of a given order

[-]; N- overall number of laterals [-]; q- branching frequency [mm-I] ; S- sucrose concentration [g/l); Sosucrose concentration at initiation [g/l]; t- time from inoculation [d]; V -volume of laterals [m 1], Wc water content of HR [-], Xd- dry biomass concentration [g/l]; X w - wet biomass concentration [g/l]; YI/s- length yie ld factor [-], Yx/s- biomass yield factor [-];

p v- density of HR . Subscript: g- index for order of HR

laterals

(g=O, I ,2,3); ijk- chronological index for HR laterals .

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