Modeling analysis of the L(�)-carnitine production

process by Escherichia coli

Daniel V. Guebel a,1, Nestor V. Torres b,c,*, Manuel Canovas d

aBiotechnology Counseling Services, Av San Martın 4927, (1417) Buenos Aires, ArgentinabGrupo de Tecnologıa Bioquımica, Dpto. Bioquımica y Biologıa Molecular, Facultad de Biologıa,

Universidad de La Laguna, (38206) La Laguna, Tenerife, Islas Canarias, Espanac Instituto Universitario de Bioorganica Antonio Gonzalez. Avda. Astfco. Fco. Sanchez, s/n 38206 La Laguna,

Tenerife, Islas Canarias, Espana, SpaindDepartamento de Bioquımica y Biologıa Molecular B, Facultad de Quımica, Universidad de Murcia, Espana

Received 17 May 2005; received in revised form 22 August 2005; accepted 23 August 2005

Abstract

The basis of a previous model for the crotonobetaine biotransformation into L(�)-carnitine by Escherichia coli strains [Canovas M, Maiquez

JR, Obon JM, Iborra JL. Modeling of the biotransformation of crotonobetaine into L(�)-carnitine by Escherichia coli strains. Biotechnol Bioeng

2002;77:764–75], are examined. The analysis focused on the multi-factorial nature of growth-limiting compounds and causes leading to rapid

decrease in L(�)-carnitine productivity. An explicit model for the maximum specific growth rate in anaerobic batch was formulated. Glycerol,

previously assumed to be the limiting substrate, actually exerts a negative, interactive, growth-effect on peptone. In contrast, peptone produces a

significant, positive, linear effect. Fumarate was also identified as a strong growth-promoting factor, while crotonobetaine interacts negatively with

this compound. Glycerol could be taken up through a regulated channel mechanism. Crotonobetaine and L(�)-carnitine could share a same type of

carrier transport, but their fluxes might be independent events of a reversible mechanism. Because of the reversibility of all the other participating

processes, the whole biotransforming network behaves as self-regulated. So, the decrease in L(�)-carnitine productivity can be explained by the

rapid network evolution toward a final equilibrium stage after its initial perturbation by the batch conditions applied. Thus, reported data have been

simulated by a simplified model based on these premises, which suggests that alternative transport mechanisms (e.g. concerted anti-port, ATP-

consuming transport) have little effect in the analyzed conditions. The proposed mechanism is consistent with the observed 1:1 ratio between

precursor input and product output, as well as with the bi-directionality constrains appearing due to the activities of CoA-ligase and

CoA-transferase enzymes. Some strategies for improving the process productivity are delineated.

# 2005 Elsevier Ltd. All rights reserved.

Keywords: L(�)-Carnitine; Biotransformation; Escherichia coli; Glycerol; Transport; Mathematical model

www.elsevier.com/locate/procbio

Process Biochemistry 41 (2006) 281–288

1. Introduction

Some Escherichia coli and Proteus strains transform

crotonobetaine and D(+)-carnitine into the specialty L(�)-

carnitine [1–4]. Crotonobetaine and carnitine are betaine-

related compounds, a series of aliphatic chemicals character-

ized by the presence of a cationic trimethylamino group. The

L(�)-carnitine enantiomer is increasingly in demand due to its

use in human medicine [5–7].

* Corresponding author. Tel.: +34 922 318334; fax: +34 922 318334.

E-mail addresses: dvguebel@hotmail.com (D.V. Guebel), ntorres@ull.es

(N.V. Torres), mcanovas@um.es (M. Canovas).1 Tel.: +54 11 4503 9355.

1359-5113/$ – see front matter # 2005 Elsevier Ltd. All rights reserved.

doi:10.1016/j.procbio.2005.08.013

The enzymes participating have been identified [8–10]

and have allowed for the construction of a recombinant strain

carrying plasmids with copies of the caiT, A, B, C, D, E

operon that governs the biotransformation [11,12]. These

efforts have been matched by others oriented toward the

technological application of the biotransforming strains.

Thus, several operation modes (batch, continuous recycling,

etc.), with growing or resting cells, cultured in minimal or in

complex media, under anoxic or aerobic conditions, have

been assayed [13–21]. Two mathematical, unstructured

models have recently been presented as corollary: one

of them describes the responses in the different operation

modes [18], while the other optimizes one of these reactor

configurations [22].

D.V. Guebel et al. / Process Biochemistry 41 (2006) 281–288282

Some critical questions still remain concerning the

physiology of these strains in spite of the great effort dedicated.

Hence, a quantitative study on the integrated physiology of the

producing strains would greatly contribute to optimizing

production processes [23,24].

Most of the reported process data are scattered through the

100 h batch-runs. However, a proper understanding of the

underlying physiology requires a more detailed analysis of the

exponential growth phase since L(�)-carnitine productivity

falls sharply soon after the beginning of the culture and because

the glycerol uptake rate may well be faster than is currently

assumed [25,26].

In previous studies, glycerol has been considered the sole

limiting source of carbon and energy, even when culture media

included peptides and/or free amino acids [18]. Previous

models regarded fumarate as a L(�)-carnitine yield enhancer

[16], but did not consider its effect on the anaerobic growth of

biomass.

Evidence about the plasmids impact on the harboring strain

is scarce [15,17]. Moreover, no plasmid-stability studies in

working conditions have been reported. Cellular death, cellular

lysis, and cellular maintenance have been treated as equivalents

in previous models, while the difference in the energy

consumption for cellular maintenance between the wild and

the recombinant strain was not considered.

A strong linkage between the primary metabolism and the

bacterial capacity to produce L(�)-carnitine, has been proposed

[21]. This hypothesis is in line with the fact that crotonobetaine

biotransformation does involve CoA-intermediaries [27,28].

However, verification of this hypothesis requires evaluation of

the energy metabolic efficiency and the energy requirements of

the crotonobetaine and L-carnitine transporters.

Unfortunately, there is no agreement about the role of the

different transporter systems involved in trimethylammonium

metabolism, namely the ProP and ProU [29,30], as well as the

CaiT system [2]. Moreover, comparison of the available

evidence for the ProP system with information contained in the

Fig. 1. Influence of culture media components upon the maximum specific grow

recombinant E. coli K38 PT7–5KE32; (*) experimental values; (~) predicted valu

being the number of experimental points. a[17]; b[21]; c[16]; d[18]; e[15].

E. coli data base (EcoCyc database. revision date: 10 January

2004. EcoCyc: encyclopedia of E. coli genes and metabolism

[online]. http://biocyc.org and http://ecocyc.pangeasystems.-

com/ecocyc/ecocyc), shows that the supporting driving force

(ATP, proton motive force, membrane potential) remains as an

open question. A similar situation occurs with the CaiT

transporter [2,31].

Quantitative studies in microbial physiology are usually

performed on the laboratory bench, using chemostats, under

steady conditions. In the present paper, however, we attempt to

make some inferences from an analysis of reported batch data.

This modus operandi was adopted because ‘‘limited-culture’’

physiology can be quite different from that observed in ‘‘excess

conditions’’ [32], as is the case with L(�)-carnitine production.

Moreover, we were convinced that reported data could still

contain some potentially useful physiological information that

should not be lost.

However, reported data coming from experiments that had

not been planned for the use herein intended. Recovery seemed

to be a laborious, but feasible work. So, we decide to focus on

the exponential growth phase, in which the metabolic processes

are in a quasi-steady state, while the L(�)-carnitine productivity

is maximized. Conceptually, analysis was made within the

main-frame of the macroscopic approach [33–35]. This strategy

finally resulted in the systematization of the available core

information and the possibility to test mathematically some of

the main assumptions currently accepted. In turn, the acquired

physiological background was used to delineate some feasible

optimization strategies.

2. Results and discussion

2.1. Factors influencing the growth rate

In Fig. 1 are shown the changes in the maximum specific

growth rate (mmax) according to the culture media composition

used. These rates were established from reported batch-runs in

th rate (mmax) in anaerobic batch-runs. WT: wild type E. coli O44 K74; R:

es from Eq. (1). When reported, the values are represented as mean � 3S.E; n

D.V. Guebel et al. / Process Biochemistry 41 (2006) 281–288 283

anaerobiosis with the wild and recombinant strain, by using

both ‘‘minimal’’ and ‘‘complex’’ culture media.

It is interesting to compare the wild and the recombinant

strain in relation to their growth capacity since their growth

difference (Dmmax) reflects the energy burden imposed by the

plasmids. However, a direct comparison is not feasible because

growth rates depend on the multiple culture conditions applied

and not only on the presence or absence of plasmids. To

overcome this problem and to better understand the substrates

effects, we established a simple model able to identify and

quantify the factors that influence mmax. This model is presented

by Eq. (1), which was established by multiple non-linear

regression with the available data (see Fig. 1).

As some mmax values are reported without their errors

(conditions D–H), but errors are available in others

(conditions A–C, I, J), and since ANOVA analysis requires

the occurrence of a common variance (homoscesdasticity

condition), and all data come from the same laboratory group,

we pooled the available variances to obtain an estimation of

the omitted errors. This was done by computing a weighted

average of the available variances according to their degrees

of freedom. Then, using a random number generator (Matlab

Software) we reconstructed the feasible mmax values by

simulating four replicates in each condition. This was done

following the specified errors according to a Gaussian

distribution centered on the reported mean values. Finally,

we performed a regression with ANOVA, which is

summarized in Eq. (1). Note that Eq. (1) only includes the

statistically significant terms ( p � 0.01) despite the data were

analyzed as a full factorial.

mmax ¼ 0:227 þ 0:119½peptone� þ 0:206½fumarate�

� 0:222½crotonobetaine� � 0:902½fumarate�

� ½crotonobetaine� � 0:159½peptone�½glycerol� (1)

In Eq. (1) is assumed that the growth effect produced by

0.5 g L�1 casamino acid (minimal medium) is equivalent to

that of the 0.5 g L�1 peptone (some complex media formula-

tions). Moreover, in terms of growth-promoting capacity,

culture media with 5–20 g L�1 of peptone have been

considered as equivalent to those containing 2.5 g L�1. In

fact, this latter value was the observed cut-off for the cellular

response to peptone [16].

As the independent variables in Eq. (1) have been centered

and normalized as [(X � Xaverage)/(Xmaximum � Xminimum)],

where X is the raw value of the considered variable, the

obtained regression coefficients give the effective contribution

of each variable to mmax, thus allowing the direct comparison of

their influences.

The type of microorganism (wild type or recombinant),

codified as binary variable (see table in Fig. 1), does not appear

in Eq. (1) because no difference was detected ( p = 0.433).

Although this result could seem somewhat unexpected, analysis

of some reported experiments [15,17] showed that plasmid-

mediated features were less important than might be expected

from a strong multi-copy system. Previously, values of

mmax = 0.603 h�1 were reported for the recombinant strain

and mmax = 0.650 h�1 for the wild type in anerobiosis, but the

experimental error was not indicated [18].

Neither was the linear term of glycerol effects significant

( p = 0.879). However, a negative, interactive effect between

glycerol and peptone was detected ( p < 0.01), being so

included in Eq. (1). Note that the omission of the linear glycerol

term in Eq. (1) has only little consequences on the descriptive

model capacity in the different analyzed conditions (see Fig. 1).

Fumarate is currently added to avoid the formation of the by-

product, g-butirobetaine [9,16]. Our analysis showed, however,

that fumarate also exerts a strong stimulant effect on biomass

growth ( p < 0.01). In fact, fumarate acts as electron acceptor,

improves NADH re-oxidation through the production of

succinate in the so-called anaerobic respiration [36,37]. In a

similar mechanism, fumarate prevents the above-mentioned

formation of g-butirobetaine.

Moreover, crotonobetaine neutralizes the positive growth

effect of fumarate since there was a negative interaction

between them ( p < 0.01). The basis of this effect was discussed

above in relation to the formation of g-butirobetaine, given that

crotonobetaine, as electron acceptor in anaerobiosis is a direct

competitor of fumarate. But, some other crotonobetaine effect

might also be produced: whilst the crotonobetaine linear effect

appears to be growth inhibitory ( p < 0.01), the linear effect

associated to fumarate appears to be growth stimulatory

( p < 0.01). Paradoxically, under saline hyperosmotic stress,

crotonobetaine exerts a protective growth-effect [17].

To illustrate the validity of Eq. (1), note that mmax in

condition C (poor growth condition) becomes very close to that

observed in condition B (good growth condition) when both are

compared after adjusting their fumarate and glycerol concen-

trations in Eq. (1) (see Fig. 1). As a whole, the above analysis

shows that the predictive quality of model Eq. (1) is good

(R2 = 0.922, average inaccuracy = 11.6%).

In conclusion, the achieved model was able to disaggregate

the growth effects of the different culture media components. In

contrast with previous assumptions, we not only concluded that

glycerol is not the sole source of carbon and energy that it is not

the main growth substrate for cells either. We showed that mmax

can be modulated either positively or negatively by several

factors. These factors were recognized and quantified their

influences. Both in the so-called ‘‘minimal medium’’ as well as

in ‘‘complex medium’’, it is apparent that the amino acids

(peptone or casamino) are the main growth substrates.

The latter is supported by the evidence that amino acids

contribute significantly to fulfilling the bacterial energy

demand in anaerobiosis [38], and that free proline availability

can limit bacterial growth due to its osmoprotectant role [39].

The role of amino acids in our system is also supported by the

fact that the recombinant strain maintained a constant biomass-

glycerol yield (Yx/glycerol = 0.0061 � 0.0007 g mmol�1) up to

67 h in batch experiments, while the exponential growth-phase

only lasted up to 36 h, such as can be verified on data from [18].

Since glycerol had a deleterious mmax effect, without any

apparent positive effect, it should be excluded. Since

crotonobetaine, being the L(�)-carnitine precursor, must be

D.V. Guebel et al. / Process Biochemistry 41 (2006) 281–288284

Table 1

Relationship between the initial concentration of glycerol in the culture medium ([glycerol]initial) and some parameters used to characterize the microbial growth

performance, such as the mean value of the specific glycerol consumption rate during the exponential phase (qglycerol exp. phase), the maximum specific growth rate

(mmax), and the presence or absence of lag-phases

[glycerol]initial (mmol L�1) qglycerol exp. phase (mmol g�1 h�1) Lag-phase (h) mmax (h�1)

20 3.88 � 0.43 (n = 3) 5.8 0.54 � 0.06 (n = 4)

40 2.29 � 0.05 (n = 2) 5.9 0.70 � 0.18 (n = 3)

75 2.82 � 0.43 (n = 4) 0 0.25 � 0.03 (n = 4)

150 3.11 � 1.24 (n = 5) 0 0.25 � 0.01 (n = 6)

Values determined from data in [18] with the recombinant strain in minimal medium, at pO2 = 30%, expressed as mean � S.E., n being the number of experimental

points used for parameter determination.

added despite its strong, inhibitory growth effect, its addition in

a fed-batch schedule is recommendable. In contrast, it could be

best to add the total required fumarate together with the peptone

from the very beginning, both for its growth stimulant effect

and because it prevents the formation of g-butirobetaine. Under

these new operating conditions, an increase by 140% in mmax

can be expected from Eq. (1). This would represent a significant

improvement since mmax in the working strains is a half of that

observed with other E. coli strains [29].

2.2. Glycerol uptake

The obtained results motivated us to explore whether the

negative growth-effect of glycerol is related with its cellular

transport. Detailed analyses of the reported data [18,21] led us

to conclude that working strains do not follow Monod’s model

for glycerol consumption. Instead, the linear trend observed is

consistent with the idea that glycerol may enter the cell through

a membrane channel (see Fig. 2).

Some lines of evidence could support the occurrence

of a channel transport: (i) it has been described a specific

bacterial membrane channel for glycerol, the so-called

glycerol facilitator protein (Glpf) [25,26]; (ii) the absence of

saturation despite the broad range analyzed is against a

carrier with Monod’s kinetic whilst the Glpf channel is not

saturated below 200 mmol L�1 glycerol [40]; (iii) the fact

that the low glycerol affinity constant (Km = 335 mmol L�1

glycerol) reported for the working strains [18] results

Fig. 2. Relationship between the specific rates of glycerol consumption (qgly-

cerol) and extra-cellular glycerol concentration. Data based on [18] for batch-

runs with recombinant strain in minimal medium at a fixed pO2 (30%). (*)

Glycerol: 20 mmol L�1; (*) glycerol: 150 mmol L�1.

inconsistent with the glycerol consumption rates associated

to the exponential growth phase (see Table 1); (iv) the fact

that glycerol consumption rates display a hysteresis

(memory) effect (see Fig. 2).

A system is associated with hysteresis when its dynamic

is strongly conditioned by its history rather than by its

instantaneous, present conditions. According to data in Fig. 2,

a same value of glycerol consumption rate is associated with two

very different extra-cellular glycerol concentrations, depending

on the initial glycerol concentration applied. So, glycerol

consumption at any time is not conditioned by the instantaneous,

extra-cellular glycerol concentration as is assumed in Monod’s

model, but it was by the previous consumption rates in the same

series, its ‘‘dynamical history’’, that ultimately depends on the

initial glycerol concentration. In fact, data appear grouped in two

different straight-lines and not in a unique overlapping curve that

would denote its independence on the initial conditions used.

Note that each straight-line actually trace a ‘‘dynamical

trajectory’’ since in decreasing order it gives the temporal

sequence of consumption rates occurred in despite that time is not

explicitly represented in Fig. 2.

The fact that the straight-line at high initial glycerol

concentration (150 mmol L�1) has a lower slope than the

straight-line at low initial glycerol (20 mmol L�1), raised the

question of whether the referred to glycerol channel could

actually ‘‘open’’ or ‘‘close’’ in response to extra-cellular

glycerol availability.

Althoughadefinitiveanswerto thisquestionhave tocomefrom

direct experimentation, we also explored for some indirect

evidence.Thus, fromthe available datawedetermined the specific

rate of glycerol consumption associated to the exponential growth

phase (qglycerol exp. phase),hereindefinedasavalue representativeof

the whole period in which the culture grows atmmax (see Table 1).

Operationally, this corresponds to performing a weighted average

of the several qglycerol values established within the exponential

growth phase, each value being weighted by the discrete time

elapsed between successive samples.

From results in Table 1, we concluded that qglycerol exp. phase

behaves as approximately constant for the different conditions

given that within the available error only little or moderate

variation was produced in spite of the great variations in the

extra-cellular glycerol concentration. But according to the

double relationship between qglycerol and glycerol concentration

showed in Fig. 2, the constancy of qglycerol exp. phase in Table 1

D.V. Guebel et al. / Process Biochemistry 41 (2006) 281–288 285

Fig. 3. (A) Time course of the specific L(�)-carnitine productivity during the batch-run. (B) Constant linear dependency of the cumulated L(�)-carnitine production

with the cumulated biomass production. Data based on [15].

can be explained only if the glycerol channel was able to be

regulated, probably opening or closing, whether the initial

extra-cellular glycerol available in each of the analyzed

conditions.

On the other hand, no causal relation between the lag-phases

and the initial concentration of glycerol was detected in Table 1.

So, the observed latencies might be attributed to technical-

operational reasons (i.e. low inoculum). However, from Table 1

is clear that in despite of the qglycerol exp. phase constancy, extra-

cellular glycerol concentrations higher than 75 mmol L�1

produced a significant mmax decrease.

Taken together, these facts suggest that glycerol growth-

inhibitory effect could be mediated by an extra-cellular

hyperosmotic stress. As this type of stress is associated with

plasmolysis and loss of the cellular water, but being the loss of

water a regulated process (by specific porin channels), this

could explain why not lag-phases have been observed with high

glycerol extra-cellular concentrations in despite that growth-

inhibitory effect was produced. In contrary, should be expected

Fig. 4. Diagram showing the self-regulated structure of the biotransforming netwo

crotonobetaine and the end-product L(�)-carnitine can either influx and/or efflux tr

transport constants; k�1 and k�5: reversal transport constants). The interplay betwee

CoA-transferase (k�2 and k4 represent its specific constant rates) buffering the net fl

hydratase, is a thermodynamically reversible reaction, being k3 and k�3 the forwa

the occurrence of increasing lag-phases by high extra-cellular

glycerol concentrations if cultured cells had have a massive,

sustained, no regulated glycerol influx, reinforcing thus the idea

that glycerol channel might be regulated.

2.3. L(�)-Carnitine production and excretion

Analysis of data from [15] showed that the specific rate of

carnitine excretion (qcarnitine) sharply decreases during the

exponential phase (see Fig. 3A). A similar trend can also be

verified in the data from [21], even when a longer exponential

phase occurs in this latter. This evidence suggests that the

decreasing qcarnitine pattern is not due to an energy shortage, as

was previously supposed [21].

Despite that qcarnitine decreases from the start of the culture,

Fig. 3B clearly shows that the carnitine-biomass yield remains

constant beyond the exponential phase (Yp/x = 27.51 � 2.29

mmol g�1, n = 5). The evidence obtained has two important

consequences: Firstly, decreasing productivity can not be

rk as consequence of the reversibility of the involved processes. The substrate

ough a same type of carrier by facilited diffusion mechanism (k1, k5: forward

n the enzymes CoA-ligase (k2 and k�4 represent its specific constant rates), and

ux in the network. The step process 3, catalyzed by the enzyme crotonobetaine

rd and reversal specific constant rates, respectively.

D.V. Guebel et al. / Process Biochemistry 41 (2006) 281–288286

Fig. 5. Testing the ‘‘overall equilibrium’’ hypothesis on the biotransformation

process. Predictions from a theoretical model (Eqs. (4) and (5)) are compared

with the experimental time course of crotonobetaine and L(�)-carnitine in batch

culture. (*) Carnitine experimental values; (*) crotonobetaine experimental

values. Solid lines give the predicted evolution of both metabolites. Experi-

mental values are taken from [21].

attributed to the decay of the transforming enzymes and/or

changes in the operating transporters because Yp/x remains

constant and cells in the exponential growth phase are in a quasi-

stationary metabolic state. Secondly, if productivity falls during

the exponential phase when m and Yp/x are constant, carnitine

productivity is not conditioned by its growth-associated com-

ponent (qcarnitine growth associated = Yp/x �m), but, perhaps, by its

non-growth associated component (qcarnitine non-growth associated =

qcarnitine total � qcarnitine growth-associated), which agrees with the

current knowledge since resting cells can also be used instead of

growing cells as biotransforming agents.

A further inspection of data in [21] led us to the hypothesis

that crotonobetaine biotransformation could be governed by an

overall equilibrium process as a consequence of all transport

and biotransformation processes steps are thermodynamically

or functionally reversible (see Fig. 4).

Fig. 4 summarize pictorially the available evidences. Thus,

steps 1 and 5 are only generic representations of the transport

processes since there is considerable uncertainty concerning the

incidence of the different operating carrier systems [2,17,29–31].

However, their reversibility is justified because of the cross

affinities between carnitine and crotonobetaine as regards some of

their common carriers [3,11], and because the CaiT transport

system has been described as an interchanger [2]. Note that step

processes 2 and 4 being both irreversible are catalyzed by

different enzymes in their forward and reverse directions (CoA-

ligase and CoA-transferase) [27,28]. Finally, step process 3 might

be associated with an equilibrium constant (K3 = k3/k�3) near to

unity because crotonobetainyl-CoA and carnityl-CoA have a very

similar reductance grade (5 and 5.14, respectively), the Gibbs’

energy being proportional to the reductance grade [33,34a].

The ‘‘overall equilibrium’’ hypothesis was mathematically

tested (see Fig. 5). To this aim, experimental data concerning the

evolution of crotonobetaine consumption and L(�)-carnitine

excretion during the batch culture were contrasted against a

theoretical model given by the differential Eqs. (2) and (3).

@CROT

@t¼ �kðCROT � CROTequilib:Þ (2)

@CARN

@t¼ k0ðCARN � CARNequilib:Þ (3)

Integration of the above equations permits to obtain Eqs. (4)

and (5), which give the predicted concentration of precursor

and product during the batch-run.

CROT ¼ CROTequilrib: þ ðCROT0 � CROTequilib:Þe�kt (4)

CARN ¼ CARNequilib:ð1 � e�k0tÞ (5)

In the above equations, the symbols CROT and CARN

represent the instantaneous concentration of crotonobetaine

and carnitine, respectively. The subscript 0 refers to the initial

concentration while the subscript equilib. indicates the final

concentration at the equilibrium; e is the natural logarithms

base; k and k0 are kinetic constants with time�1 units.

As can be see in Fig. 5, the proposed model based on the

equilibrium hypothesis was consistent with the experimental

data. However, in the case of L(�)-carnitine after a step of extra-

cellular accumulation up to 20 h, its concentration began to

decrease. As L(�)-carnitine is not degraded by E. coli, the

observed diminution implies that the net L(�)-carnitine efflux

turned into a net influx at 20 h culture. This phenomenon can be

explained by two concurrent causes: (i) the previous drop that

was operated in the specific productivity of L(�)-carnitine from

earlier times (see Fig. 3); (ii) the reciprocal competitive action

between L(�)-carnitine and crotonobetaine to be taken up by

their common carriers [3,11].

The biphasic feature of the L(�)-carnitine transport resulted

in a lower fitting quality because Eq. (5) did not consider neither

the extra-cellular nor the intra-celullar competition between

L(�)-carnitine and crotonobetaine for their common carriers.

However, when analysis of L(�)-carnitine kinetic was restricted

to the first 20 h (efflux step), the goodness of the fit was

appreciably improved, a determination coefficient as high as

R2 = 0.9824 being achieved. With crotonobetaine, for which

secondary transport was not apparent, the fitting achieved with

the whole data set was excellent (R2 = 0.988).

Importantly, we determined on data from [21] that

crotonobetaine consumption and carnitine excretion was in a

fixed 1:1 molar ratio throughout the batch. The model depicted

in Fig. 4 accomplish either with the restriction emerged from

this 1:1 ratio, as well as with the restrictions emerged from the

bi-directional fluxes due to the activities of the CoA-ligase

and CoA-transferase enzymes, as can be verified performing a

model dynamic simulation (data not shown). Our model,

however, did not consider the occurrence of an anti-port

transport mechanism for which an obligatory coupling between

the opposing fluxes of crotonobetaine and L(�)-carnitine must

exist [2]. In fact, this last restriction was incompatible with the

simultaneous accomplishment of the other constrains.

As the proposed model was able to reproduce the available

kinetic experimental data up to 20 h batch-culture, when

bacterial L(�)-carnitine productivity was just extinguished, we

D.V. Guebel et al. / Process Biochemistry 41 (2006) 281–288 287

concluded that at least during this step, the transport of

crotonobetaine and L(�)-carnitine could share the same

carriers, but their fluxes might occur as independent events

of a reversible mechanism, each one driven by its own diffusion

gradient (see Fig. 4).

Of note is the fact that the kinetic constants for crotonobetaine

uptake and for L(�) carnitine excretion that were determined

according to Eqs. (4) and (5), do not differ significantly

(k = 0.245 � 0.028 h�1 and k0 = 0.218 � 0.040 h�1). Regarding

this finding is worth mentioning that k and k0 not only

characterize the influx or efflux kinetics of the referred

metabolites when they are monitored from the extra-cellular

phase. According to the macroscopic theory principles, the

interchanges of matter and energy between cells and medium

must also reflect the operating intra-cellular processes [34b,35].

Thus, the inverses of k and k0 actually provide two redundant

estimations for the characteristic response time of the

biotransforming network.

From this new point of view, it can be considered that batch

operation really produces a flux perturbation in the biotrans-

forming network. As this network has a completely reversible

structure, it is self-regulated. Consequently, the network

responds to this perturbation by evolving as a whole toward

a final, well-defined, equilibrium stage and the productivity of

L(�)-carnitine evolves accordingly, as it does the biotransform-

ing network when goes to recover its thermodynamic stability

condition. So, interventions to improve L(�)-carnitine specific

productivity might to be aimed at breaking the self-regulatory

behavior of the biotransforming network.

3. Concluding remarks

The present study constitutes a new round in the laborious

process of model refinement which started with the first model

of L(�)-carnitine production presented by Canovas et al. [18],

followed by the model of Alvarez-Vasquez et al. [22]. However,

to attain a plausible model representation of a complex

biological system, progressive rounds of assumptions and

model predictions are required. Each theoretical round must be

followed by experimental checking.

Mathematical modeling, besides describing and optimizing,

can also contribute to data interpretation when based on

parameters with a clear physiological meaning. Thus,

mathematical modeling also offers the possibility to test in

silico conflicting hypotheses [41].

In the present work, we have examined some underlying

assumptions of the first presentation. As was shown in Section

2, some previous assumptions might be reconsidered. Thus,

from the developed mmax model, a new operating strategy to

increase the growth rate by about 140% was proposed. On the

other hand, from our new interpretation about the causes

leading to decreased L(�)-carnitine productivity, we concluded

that interventions to improve this parameter have to be aimed at

breaking the self-regulatory behavior of the biotransforming

network processes rather than at solving an energy limitation

problem.

These conclusions suggest new venues for basic and

technological research, since disruption of the self-regulatory

behavior of the network implies a first step in the search for

rational multi-objective policies for the optimal feeding of

substrates and precursors during bioreactor operation [42]. In a

second step, the construction of a new type of engineered

microorganism may be needed. However, in this case, the

rational design of an efficient recombinant strain would require

the role of the already characterized betaine-like carriers to be

clarified, whether for redefining their operating mechanism or

to determine if other alternative transport mechanisms are at

work.

Another question which remains to be explained is the basis

for the deviations (that can be verified on experimental data)

regarding high-density cell cultures in recycle reactors [18]

with respect to the 1:1 ratio herein quantified for the molar yield

between the crotonobetaine consumed and the L(�)-carnitine

excreted in batch operation.

Finally, for a precise evaluation of the mechanisms proposed

for L(�)-carnitine biosynthesis, further studies aimed at the

elucidation of the processes involved in the glycerol growth-

inhibitory effect, as well as at determining the energetic

efficiency of the wild and recombinant strains, are necessary.

This information would allow the energetic (ATP), reductive

(NADH, NADPH), and CoA dynamics to be accounted for.

However, since the catabolism of amino acids in anaerobiosis

leads to the formation of many end products common to those

associated with glycerol catabolism, previous studies [21]

might reconsider this topic.

In brief, we believe that the type of analysis carried-out in

this work constitutes a key feature in any model-building

project. It is expected that the observed discrepancies will

stimulate the next phase of model amendments and refine-

ments.

Acknowledgements

This work was funded by research grants from Spanish

MCyT, ref. no. BIO 2002-04157-C02-01 and BIO 2002-04157-

C02-02.

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