For 13C-metabolic flux analysis, isotopically labeled substrates are introduced to the cell, and the labeled carbon atoms are distributed throughout its metabolic network. The final isotopic enrichment in the intracellular metabolite pools can then be measured (Matsuoka & Shimizu, 2010a) (Fig. 2). The amino acids in biomass hydrolysate are much more abundant than their precursors in the cell metabolism, and it has been often used to deduce the labeling patterns of the intracellular metabolites from that of the proteinogenic amino acids, based on precursor-amino acids relationships (Szyperski, 1995). Either NMR spectroscopy or GC-MS has been extensively used for the isotopic tracer experiments. NMR is used to measure the positional 13C enrichment (Szyperski, 1995; Marx et al., 1996). Although 13C NMR is powerful and attractive for metabolic flux analysis, it requires relatively large amount of sample. On the other hand, GC-MS can easily analyze metabolites with much less amount of sample. As a result, it may be suitable for flux analysis of the culture processes that have low concentrations of biomass (Fischer & Sauer, 2003; Wittmann, 2007). Currently, these tracer techniques, in combination with direct extracellular flux measurements, are considered to be a powerful method for obtaining intracellular metabolic flux distribution (MFD) using only a few modeling assumptions (Stephanopoulos, 1999; Marx et al., 1996;

In principle, metabolic flux analysis is based on mass conservation of key metabolites. The intracellular fluxes can be calculated from the measured specific rates by applying mass balances to these intracellular metabolites (Stephanopoulos et al., 1998) together with stoichiometric equations. The number of measureable extracellular fluxes is limited in practice, and the stoichiometric constraints often lead to an underdetermined algebraic system. Therefore, cofactor balances are sometimes required to be introduced into the stoichiometric model, or appropriate objective functions has to be introduced for optimization to determine the fluxes. The central metabolic pathway has both anabolic and catabolic functions, as it provides cofactors and building blocks for macromolecular system (anabolism) as well as energy (ATP) production (catabolism). The optimization may be made in terms of catabolism and anabolism, or both, under the constraints of the stoichiometric equations. Flux balance analysis (FBA) has been extensively used to predict the steady-state metabolic fluxes in order to maximize the cell growth rate (Edwards & Palsson, 2000; Schilling & Palsson, 1998; Price et al., 2003). However, the accuracy of the flux calculation depends on the validity of the cofactor assumptions and an appropriate choice of the objective function(s) employed (Schuetz et al., 2007). The presence of unknown reactions that generate or consume the cofactors may invalidate the assumption that their concentrations remain in balance, and the selected objective functions may not be appropriate, or their validity may be limited to certain states of the cell. Namely, this approach cannot essentially compute such fluxes as (1) recycled fluxes, (2) bidirectional fluxes, and (3) parallel fluxes due to the singularity of the stoichiometric matrix. Note, however, that the conventional FBA may be reasonably applied for the case without recycles such as anaerobic or micro-aerobic cultivation (Zhu & Shimizu, 2004, 2005). 13C-Metabolic flux analysis has been developed to overcome such problems as stated above and to estimate *in vivo* fluxes in more accurately. In this chapter, 13C-metabolic flux analysis (13C-MFA) is explained with some appications. The analytical approach for 13C-MFA is given to understand the feature of this method, and the basic principle of isotopomer dynamics is also explained. Finally, the metabolic regulation mechanism is also mentioned in view of

global regulators.

**2. 13C-Metabolic flux analysis (13C-MFA) and its application**

For 13C-metabolic flux analysis, isotopically labeled substrates are introduced to the cell, and the labeled carbon atoms are distributed throughout its metabolic network. The final isotopic enrichment in the intracellular metabolite pools can then be measured (Matsuoka & Shimizu, 2010a) (Fig. 2). The amino acids in biomass hydrolysate are much more abundant than their precursors in the cell metabolism, and it has been often used to deduce the labeling patterns of the intracellular metabolites from that of the proteinogenic amino acids, based on precursor-amino acids relationships (Szyperski, 1995). Either NMR spectroscopy or GC-MS has been extensively used for the isotopic tracer experiments. NMR is used to measure the positional 13C enrichment (Szyperski, 1995; Marx et al., 1996). Although 13C NMR is powerful and attractive for metabolic flux analysis, it requires relatively large amount of sample. On the other hand, GC-MS can easily analyze metabolites with much less amount of sample. As a result, it may be suitable for flux analysis of the culture processes that have low concentrations of biomass (Fischer & Sauer, 2003; Wittmann, 2007). Currently, these tracer techniques, in combination with direct extracellular flux measurements, are considered to be a powerful method for obtaining intracellular metabolic flux distribution (MFD) using only a few modeling assumptions (Stephanopoulos, 1999; Marx et al., 1996; Schmidt et al., 1999; Wiechert & Graaf, 1997; Sauer, 2004). Alternatively, flux ratio analysis can be used to constrain the fluxes at the important branch point (Szyperski et al., 1999; Fischer & Sauer, 2003; Sauer et al., 1999; Hua et al., 2003).

Fig. 2. 13C-Metabolic flux analysis by 13C-labeling experiment, the measurement of isotopomer distribution, and the flux determination.

13C-Metaolic flux analysis has been applied to such microorganisms as *Escherichia coli*, *Corynebacterium glutamicum*, *Saccharomyces cerevisiae* (Blank & Sauer, 2004; Raghevendran et al., 2004), *Bacillus subtilis* (Sauer et al., 1997), acetic acid bacterium *Gluconacetobacter oboediens* (Sarkar et al., 2010), and others (Fuhrer et al., 2005), and its application has been extended to other organisms such as Cyanobacteria (Yang et al., 2002a, b), plant cells (Schwender et al., 2004), and mammarian cells (Sherry et al., 2004; Kelleher, 2004; Hellerstein, 2004; Sidorenko et al., 2008), including mouse (McCabe & Previs, 2004), brain (Rothman et al., 2003), neural cells (Selivanov et al., 2006), and cancer cells (Selivanov et al., 2005) and so on.

Let us consider the several single-gene knockout mutants such as *zwf, gnd* and *pgi* gene knockout. Figure 3 shows how the NMR spectra patterns change for *pgi* gene knockout mutant as compared to wild type, where it shows the relative intensities of 13C-13C scalar coupling multiplet spectra patterns of amino acid measured by NMR, where the samples were taken from the labeling experiments using a mixture of [U-13C] and unlabeled [U-12C] glucose conducted under aerobic steady state condition (Hua et al., 2003). The differences between NMR spectra patterns of wild type and *pgi* gene knockout mutant result in different flux distribution. Based on NMR data such as shown in Fig. 3, Fig. 4 shows the result of 13Cmetabolic flux analysis for wild type and *pgi* gene knockout mutant cultivated in the continuous culture at the dilution rate of 0.1 h-1 (Hua et al., 2003). It can be seen that the knockout of *pgi* gene, which codes for the first enzyme of the EMP (Embden-Meyerhoff-Parnas) pathway after the branch point at G6P, resulted in exclusive use of the oxidative pentose phosphate (PP) pathway for glucose catabolism. The overproduced NADPH inhibits the activity of G6PDH thus reduces the glucose consumption rate, resulting in the low growth rate. The glyoxylate pathway was activated, and the Entner-Doudoroff (ED) pathway was activated in this mutant. The activation of ED pathway may be due to reducing NADPH production as compared to employing 6PGDH pathway. The activation of the glyoxylate pathway is considered to be due to the feedback regulation to compensate for the lowered

13C-Metabolic Flux Analysis and Metabolic Regulation 389

Let us consider next the *zwf* or *gnd* gene knockout mutants, where the 13C-metabolic flux distributions are given in Fig. 5 in the cases of using glucose (Fig. 5a) and pyruvate (Fig. 5b) (Zhao et al., 2004). Since the flux through oxidative PP pathway was significantly decreased or totally blocked in the mutants grown on glucose, the metabolic network has to give a higher flux through EMP or ED pathway to the TCA cycle. The opposite relations are seen in mutants grown on pyruvate, where the deletion of genes caused a reduction in the fluxes

(a) (b)

Fig. 5. Metabolic flux distributions in chemostat culture of (a) glucose-grown and (b) pyruvate-grown *E. coli* parent strain (*upper values*), *gnd* (*middle values*), and *zwf* (*lower values*) mutants at *D*=0.2 h–1.The exchange coefficients are shown in brackets for the reactions that were considered reversible. *Negative values* indicate the reversed pathway direction.

through the TCA cycle.

OAA concentration caused by the lowered flux of EMP pathway and the lowered anaplerotic flux through Ppc to supply OAA.

Fig. 3. 13C-13C scalar coupling multiplets observed for aspartate from glucose-limited chemostat cultures of *E. coli* W3110 (left) and the *pgi* mutant (right). The signals were extracted from the ω1(13C) cross sections in the [13C,1H]-COSY spectra. (A) Asp-α; (B) Asp-β. As indicated in panel A, the multiplets consist of a singlet (s), a doublet with a small coupling constant (da), a doublet split by a larger coupling constant (db), and a doublet of doublets (dd). Aspartate corresponds directly to its metabolic precursor, OAA.

Fig. 4. Metabolic flux distributions of (a) *E. coli* wild type and (b) its *pgi* gene knockout mutant under glucose-limited continuous cultivation at the dilution rate of 0.1 h-1.

OAA concentration caused by the lowered flux of EMP pathway and the lowered anaplerotic

Fig. 3. 13C-13C scalar coupling multiplets observed for aspartate from glucose-limited chemostat cultures of *E. coli* W3110 (left) and the *pgi* mutant (right). The signals were extracted from the ω1(13C) cross sections in the [13C,1H]-COSY spectra. (A) Asp-α; (B) Asp-β. As indicated in panel A, the multiplets consist of a singlet (s), a doublet with a small coupling constant (da), a doublet split by a larger coupling constant (db), and a doublet of

(a) (b)

Fig. 4. Metabolic flux distributions of (a) *E. coli* wild type and (b) its *pgi* gene knockout mutant under glucose-limited continuous cultivation at the dilution rate of 0.1 h-1.

doublets (dd). Aspartate corresponds directly to its metabolic precursor, OAA.

flux through Ppc to supply OAA.

Let us consider next the *zwf* or *gnd* gene knockout mutants, where the 13C-metabolic flux distributions are given in Fig. 5 in the cases of using glucose (Fig. 5a) and pyruvate (Fig. 5b) (Zhao et al., 2004). Since the flux through oxidative PP pathway was significantly decreased or totally blocked in the mutants grown on glucose, the metabolic network has to give a higher flux through EMP or ED pathway to the TCA cycle. The opposite relations are seen in mutants grown on pyruvate, where the deletion of genes caused a reduction in the fluxes through the TCA cycle.

Fig. 5. Metabolic flux distributions in chemostat culture of (a) glucose-grown and (b) pyruvate-grown *E. coli* parent strain (*upper values*), *gnd* (*middle values*), and *zwf* (*lower values*) mutants at *D*=0.2 h–1.The exchange coefficients are shown in brackets for the reactions that were considered reversible.  Note that the LHS of Eq. (3) is the formation rate of *O*1 , and the RHS is the consumption rate of *O*1 . In Eq. (3), *Ai* and *Pj* are the mole fractions of acetate and PYR isotopomers labeled at *i* -th and *j* -th carbons, respectively, and *Ck k* 0, 1 is the mole fraction of labeled CO2 through Ppc reaction. The similar equations can be derived for all the other isotopomers, and the set of equations can

where *AP* ( *R R* 16 16 ) is the coefficient matrix, and *AP b* ( *R*16 ) is the residual vector, where the detailed matrix and vector are given elsewhere (Matsuoka & Shimizu, 2010b). Eq.

if *AP* is nonsingular. In this case, Eq. (4) cannot be solved directly. Recall that the isotopomer

Let us consider the special case where 100 % [1-13C] pyruvate is used as a carbon source, and it is set *Mez v* 0 and *Pck v* 0 for simplicity. Then Eq. (5) gives the following equation

> *y O y O y O*

1 0

1 1

0 1 4

fractions must be summed up to 1, namely the following equation must be satisfied:

Therefore, Eq. (4) can be solved by replacing one of the equations using Eq. (6).

*i*

0 1 2 12 1 1 13 14 134 0

3 13 34 134 0 0 1 4 14 1

1 1

0 3 4 34 1

*z OOOOA*

holds, the following expression can be derived:

*v vvv Gly Glu Asp Mez* (2)

*AP OAA AP I b* (4)

*OAA AP AP I b* 1 (5)

*O* 1 (6)

(7)

(3)

Since *Ppc P ck v v* 1 1

> 1 1 2 12

be expressed as

(4) may be solved as

(Matsuoka & Shimizu, 2010b):

1 2 12

*z*

Then the isotopomer balance for *O*1 may be expressed as

2

1 0 1

*yP C z w y O*

1 2

*i*

#### **3. Analytical approach to 13C-metabolic flux analysis**

Let us consider how the fluxes are computed based on 13C-labeled metabolites. For this, consider how the isotopomer pattern changes with respect to fluxes. Let us cosider TCA cycle for the case of using pyruvate or acetate as a carbon source, where fate of carbons is shown in Fig. 6 (Matsuoka & Shimizu, 2010b).

Fig. 6. Metabolic network for the change in isotopomer distribution: pyruvate or acetate as a carbon source.

Referring to Fig. 6, let be the flux toward AcCoA from PYR, and let 1 be the other flux toward PEP. Moreover, let be the fraction toward gluconeogenic pathway from PEP, and let 1 be the other fraction toward anaplelotic pathway through Ppc to OAA. From the mass balance for OAA, the normalized molar formation rate of OAA is expressed as *OAA TCA Gly Mez Ppc v v vv v* 2 , and the molar consumption rate of OAA is expressed as *OAA TCA Gly Glu Asp Pck v v vvvv* . Since *OAA OAA v v* holds at steady state, the following expression can be derived:

$$
\upsilon \upsilon\_{\rmGly} + \upsilon\_{\rm ppc} = \upsilon\_{\rm Glu} + \upsilon\_{\rm Asp} + \upsilon\_{\rm Mez} + \upsilon\_{\rm Pck} \tag{1}
$$

Let us consider how the fluxes are computed based on 13C-labeled metabolites. For this, consider how the isotopomer pattern changes with respect to fluxes. Let us cosider TCA cycle for the case of using pyruvate or acetate as a carbon source, where fate of carbons is

1

1

1

*TCA v*

Fig. 6. Metabolic network for the change in isotopomer distribution: pyruvate or acetate as a

the mass balance for OAA, the normalized molar formation rate of OAA is expressed as *OAA TCA Gly Mez Ppc v v vv v* 2 , and the molar consumption rate of OAA is expressed as *OAA TCA Gly Glu Asp Pck v v vvvv* . Since *OAA OAA v v* holds at steady state, the following

be the flux toward AcCoA from PYR, and let 1

be the other fraction toward anaplelotic pathway through Ppc to OAA. From

be the fraction toward gluconeogenic pathway from PEP,

*Gly Ppc Glu Asp Mez Pck vvvvv v* (1)

*Gly v*

*Glu v*

be the other

**3. Analytical approach to 13C-metabolic flux analysis**

shown in Fig. 6 (Matsuoka & Shimizu, 2010b).

*Ppc v*

11

*Pck v*

*Asp v*

carbon source.

and let 1

Referring to Fig. 6, let

expression can be derived:

flux toward PEP. Moreover, let

*Mez v*

Since *Ppc P ck v v* 1 1 holds, the following expression can be derived:

$$\left( (1 - \eta)\alpha = 1 - \eta + \upsilon\_{\text{Gly}} - \left( \upsilon\_{\text{Glu}} + \upsilon\_{\text{Asp}} + \upsilon\_{\text{Mex}} \right) \tag{2}$$

Then the isotopomer balance for *O*1 may be expressed as

$$\begin{aligned} &\frac{1}{2}\Big(1-\frac{w}{1+2z}\Big)\Big[\left(O\_3+O\_{13}+O\_{34}+O\_{134}\right)A\_0+\left(O\_0+O\_1+O\_4+O\_{14}\right)A\_1\Big] \\ &+\frac{z}{2}\Big(1-\frac{w}{1+2z}\Big)\begin{bmatrix}2\left(O\_0+O\_1+O\_2+O\_{12}\right)A\_1+\left(O\_1+O\_{13}+O\_{14}+O\_{134}\right)A\_0+\\ \left(O\_0+O\_3+O\_4+O\_{34}\right)A\_1 \end{bmatrix} \\ &+yP\_1\mathbb{C}\_0-\left(1+2z-w+y\right)O\_1 \end{aligned} \tag{3}$$

where, *wv v Mez TCA* , *Ppc TCA y v v* , and *Gly TCA zv v* . Note that the LHS of Eq. (3) is the formation rate of *O*1 , and the RHS is the consumption rate of *O*1 . In Eq. (3), *Ai* and *Pj* are the mole fractions of acetate and PYR isotopomers labeled at *i* -th and *j* -th carbons, respectively, and *Ck k* 0, 1 is the mole fraction of labeled CO2 through Ppc reaction. The similar equations can be derived for all the other isotopomers, and the set of equations can be expressed as

$$
\Lambda\_{AP} I\_{OAA} = b\_{AP} \tag{4}
$$

where *AP* ( *R R* 16 16 ) is the coefficient matrix, and *AP b* ( *R*16 ) is the residual vector, where the detailed matrix and vector are given elsewhere (Matsuoka & Shimizu, 2010b). Eq. (4) may be solved as

$$I\_{OAA} = \Lambda\_{AP}^{-1} \mathfrak{b}\_{AP} \tag{5}$$

if *AP* is nonsingular. In this case, Eq. (4) cannot be solved directly. Recall that the isotopomer fractions must be summed up to 1, namely the following equation must be satisfied:

$$\sum\_{i} O\_{i} = 1\tag{6}$$

Therefore, Eq. (4) can be solved by replacing one of the equations using Eq. (6).

Let us consider the special case where 100 % [1-13C] pyruvate is used as a carbon source, and it is set *Mez v* 0 and *Pck v* 0 for simplicity. Then Eq. (5) gives the following equation (Matsuoka & Shimizu, 2010b):

$$
\begin{bmatrix} O\_0 \\ O\_1 \\ O\_4 \end{bmatrix} = \begin{bmatrix} 1 \\ \hline 1+y \\ \frac{y}{1+y} \\ 0 \\ \end{bmatrix} \tag{7}
$$

13C-Metabolic Flux Analysis and Metabolic Regulation 393

If [2-13C] acetate ( *A*2 ) and the unlabeled acetate are used as a carbon source, 12 isotopomers are present, and those reduce to 3 isotopomers when *A*2 1 as follows (Matsuoka &

*O z*

*O*

23

123

234

Figure 7 shows how the isotopomer distribution changes with respect to

that OAA isotopomers as well as mass isotopomers change with respect to

strange way, where Fig. 7c explains for the cases of

implies that the fraction of *O*3 becomes higher as

becomes maximum at certain value of

(right). In Fig. 7a, *O*3 increases as

Fig. 7c). The case where

highest at low values of

*O*24 become higher as

respect to

respect to

increases. When

0 (left), 0 1

is low, most of the [3-13C] pyruvate goes to OAA via Ppc and

, but the fractions of *O*13 and *O*24 become higher as TCA cycle flux

increases, and then the fractions of *O*123 and *O*234 become higher as

is high, where most flux goes through PDHc reaction, *A*2 ( *P*3 ) generates

becomes low. This is due to Ppc reaction (left figure in

*O z z*

using 100 % of [3-13C] pyruvate as a carbon source (Matsuoka & Shimizu, 2010a). It indicates

generates *O*3 . As proceeding TCA cycle, *O*3 and [2-13C] AcCoA (originated from [3-13C] PYR since the 1st carbon of PYR is lost as CO2 at PDHc reaction) generate *O*13 and *O*24 by the 1st turn of the TCA cycle, where *O*24 further generates *O*23 in the 2nd turn, and in turn *O*23 generates *O*123 and *O*234 at the 3rd turn of the TCA cycle (middle figure in Fig. 7c). Thus *O*3 , *O*13 , *O*24 , *O*23 , *O*123 , and *O*234 are eventually generated, where the amount of *O*3 is the

*O*2 and *O*3 at the 1st turn of TCA cycle, and in turn *O*2 and *A*2 generate *O*23 , while *O*3 and *A*2 generate *O*13 and *O*24 in the 2nd turn. Moreover, *O*23 and *A*2 generate *O*123 and *O*234 at the 3rd turn and so on. Namely, *O*123 and *O*234 become higher as cycling the TCA cycle, and thus those become higher at the steady state (right figure in Fig. 7c). The above observation

as seen in Fig. 7a. Figure 7b shows how the mass isotopomers change with

becomes further higher. This is the reason why *O*13 , *O*24 , and *O*23 give maximum with

and *O*23 as seen in Fig. 7a. These illustrate the complexity of the 13C-flux analysis in relation to TCA cycle. The transitions of the isotopomers with respect to turn of TCA cycle may be

Consider next the case of using glucose as a carbon source. Referring to Fig. 8 (Matsuoka & Shimizu, 2010a), let *v*1 be the normalized flux toward glycolysis at glucose 6-phosphate (G6P) and let *v*1 1 be the flux toward oxidative pentose phosphate (PP) pathway, where the input flux to the system is normalized to be 1 without loss of generality. Then the mass balance equations can be derived for each metabolite. Moreover, isotopomer balances may be considered for each metabolite. Since glucose has 6 carbons, the number of its isotopomers is 6 2 64 and let these be expressed as *GG G* 0 1 123456 , ,, , where *G*0 denotes unlabeled glucose, *G*1 denotes [1-13C] glucose, and *G*123456 denotes [U-13C] glucose and so on. The number of

. It indicates that *m*1 decreases while *m*3 increases as

expressed in more systematic way by introducing the transition matrix.

*z*

*z z* (11)

(middle), and

is low, whereas the fractions of *O*13 and

increases, whereas *m*2

. This is due to the changing patterns of *O O* 13 24

for the case of

in somewhat

1

Shimizu, 2010b):

In the case where 100 % [2-13C] pyruvate is used, the following equations can be derived (Matsuoka & Shimizu, 2010b):

$$O\_1 = O\_4 = \frac{1}{2\left(1+y\right)^2\left(1+2y\right)}\tag{8a}$$

$$O\_2 = \frac{y}{1+y} \tag{8b}$$

$$O\_{13} = O\_{24} = \frac{y}{(1+y)(1+2y)}\tag{8c}$$

$$CO\_{14} = \frac{y}{\left(1+y\right)^2 \left(1+2y\right)}\tag{8d}$$

In the case where 100 % [3-13C] pyruvate is used, the following expressions can be derived (Matsuoka & Shimizu, 2010b):

$$O\_2 = 0\tag{9a}$$

$$O\_3 = \frac{y}{1+y} \tag{9b}$$

$$O\_{13} = O\_{24} = \frac{y}{(1+y)(1+2y)}\tag{9c}$$

$$
\begin{bmatrix} O\_{23} \\ O\_{123} \\ O\_{234} \end{bmatrix} = \left| \frac{\frac{y}{\left(1+y\right)^2 \left(1+2y\right)}}{\frac{1}{2\left(1+y\right)^2 \left(1+2y\right)}} \right| \tag{9d}
$$

Let us consider the case of using acetate as a carbon source by letting *Ppc v* 0 in Fig. 6. If the mixture of [1-13C] acetate ( *A*1 ) and the unlabeled acetate is used, only 4 isotopomers ( *OOOO* 0 1 4 14 ,,, ) are present, and if *A*1 1 , those can be expressed as (Matsuoka & Shimizu, 2010b)

$$
\begin{bmatrix} O\_1 \\ O\_4 \\ O\_{14} \\ O\_{14} \end{bmatrix} = \begin{bmatrix} \frac{1+2z}{(1+z)(2+3z)} \\ \frac{1}{2+3z} \\ \frac{z}{1+z} \\ \frac{z}{1+z} \end{bmatrix} \tag{10}
$$

In the case where 100 % [2-13C] pyruvate is used, the following equations can be derived

21 1 2

1 4 2

*y O O*

*y O*

*O O*

*y O*

*y*

14 2 1 12

In the case where 100 % [3-13C] pyruvate is used, the following expressions can be derived

*y O*

13 24 1 12

*y y O*

*y y O*

Let us consider the case of using acetate as a carbon source by letting *Ppc v* 0 in Fig. 6. If the mixture of [1-13C] acetate ( *A*1 ) and the unlabeled acetate is used, only 4 isotopomers ( *OOOO* 0 1 4 14 ,,, ) are present, and if *A*1 1 , those can be expressed as (Matsuoka & Shimizu,

*z O*

*O z*

123 2

*O*

23

234

*O*

1

4

14

*y O O*

*y y*

*y*

2

*y*

2

1

*z z*

*z z*

*y y*

*y y*

*y y*

1

*y y*

(8a)

(8d)

(9c)

(9d)

(10)

2 1 (8b)

*O*2 0 (9a)

3 1 (9b)

13 24 1 12 (8c)

(Matsuoka & Shimizu, 2010b):

(Matsuoka & Shimizu, 2010b):

2010b)

If [2-13C] acetate ( *A*2 ) and the unlabeled acetate are used as a carbon source, 12 isotopomers are present, and those reduce to 3 isotopomers when *A*2 1 as follows (Matsuoka & Shimizu, 2010b):

$$\begin{bmatrix} O\_{23} \\ O\_{123} \\ O\_{123} \\ O\_{234} \end{bmatrix} = \begin{array}{c} z \\ \hline 1+z \\ 1 \\ \hline 2+3z \\ \hline 1+2z \\ \hline (1+z)(2+3z)} \end{array} \tag{11}$$

Figure 7 shows how the isotopomer distribution changes with respect to for the case of using 100 % of [3-13C] pyruvate as a carbon source (Matsuoka & Shimizu, 2010a). It indicates that OAA isotopomers as well as mass isotopomers change with respect to in somewhat strange way, where Fig. 7c explains for the cases of 0 (left), 0 1 (middle), and 1 (right). In Fig. 7a, *O*3 increases as becomes low. This is due to Ppc reaction (left figure in Fig. 7c). The case where is low, most of the [3-13C] pyruvate goes to OAA via Ppc and generates *O*3 . As proceeding TCA cycle, *O*3 and [2-13C] AcCoA (originated from [3-13C] PYR since the 1st carbon of PYR is lost as CO2 at PDHc reaction) generate *O*13 and *O*24 by the 1st turn of the TCA cycle, where *O*24 further generates *O*23 in the 2nd turn, and in turn *O*23 generates *O*123 and *O*234 at the 3rd turn of the TCA cycle (middle figure in Fig. 7c). Thus *O*3 , *O*13 , *O*24 , *O*23 , *O*123 , and *O*234 are eventually generated, where the amount of *O*3 is the highest at low values of , but the fractions of *O*13 and *O*24 become higher as TCA cycle flux increases. When is high, where most flux goes through PDHc reaction, *A*2 ( *P*3 ) generates *O*2 and *O*3 at the 1st turn of TCA cycle, and in turn *O*2 and *A*2 generate *O*23 , while *O*3 and *A*2 generate *O*13 and *O*24 in the 2nd turn. Moreover, *O*23 and *A*2 generate *O*123 and *O*234 at the 3rd turn and so on. Namely, *O*123 and *O*234 become higher as cycling the TCA cycle, and thus those become higher at the steady state (right figure in Fig. 7c). The above observation implies that the fraction of *O*3 becomes higher as is low, whereas the fractions of *O*13 and *O*24 become higher as increases, and then the fractions of *O*123 and *O*234 become higher as becomes further higher. This is the reason why *O*13 , *O*24 , and *O*23 give maximum with respect to as seen in Fig. 7a. Figure 7b shows how the mass isotopomers change with respect to . It indicates that *m*1 decreases while *m*3 increases as increases, whereas *m*2 becomes maximum at certain value of . This is due to the changing patterns of *O O* 13 24 and *O*23 as seen in Fig. 7a. These illustrate the complexity of the 13C-flux analysis in relation to TCA cycle. The transitions of the isotopomers with respect to turn of TCA cycle may be expressed in more systematic way by introducing the transition matrix.

Consider next the case of using glucose as a carbon source. Referring to Fig. 8 (Matsuoka & Shimizu, 2010a), let *v*1 be the normalized flux toward glycolysis at glucose 6-phosphate (G6P) and let *v*1 1 be the flux toward oxidative pentose phosphate (PP) pathway, where the input flux to the system is normalized to be 1 without loss of generality. Then the mass balance equations can be derived for each metabolite. Moreover, isotopomer balances may be considered for each metabolite. Since glucose has 6 carbons, the number of its isotopomers is 6 2 64 and let these be expressed as *GG G* 0 1 123456 , ,, , where *G*0 denotes unlabeled glucose, *G*1 denotes [1-13C] glucose, and *G*123456 denotes [U-13C] glucose and so on. The number of

13C-Metabolic Flux Analysis and Metabolic Regulation 395

4 *v*

*Gly v*

*Glu v*

be the rest of the fraction

3 *v*

1 2 *v*

1

1

1

1

*Ppc v*

1

*Pck v*

*Asp v*

*Mez v*

glucose.

1 *v* 1 1 *v*

5 *v*

6 *v*

*TCA v*

be the fraction from PEP to PYR through Pyk, and let 1

Fig. 8. Main metabolic pathways in the central metabolism together with the fate of [1-13C]

Consider next how the isotopomers of GAP affect those of TCA cycle. Referring to Fig. 8, Let

on the isotopomer distribution of OAA, and Fig. 9b shows its effect on the mass isotopomer distribution using 100 % of [1-13C] glucose for the case where *v*1 1 for simplicity

which flows from PEP to OAA by the anaplerotic pathway. Figure 9a shows the effect of

Fig. 7. Effect of on (a) isotopomer and (b) mass isotopomer distributions for the case of using 100 % [3-13C] pyruvate ( 0.4 ). (c) schematic illustration of how the specific isotopomers are generated.

isotopomer balance equations is 6 2 64 for G6P, 5 2 32 for P5P (Ru5P, X5P, R5P), 7 2 128 for S7P, 4 2 16 for E4P, 6 2 64 for F6P, and 3 2 8 for GAP. The same number of isotopomers is present, and therefore, the isotopomer distribution for each metabolite can be obtained uniquely as a function of the labeling patterns of glucose on condition that the fluxes are given. Consider the case of using 100 % of [1-13C] glucose as a carbon source for simplicity. It may be easily shown that *GAP*3 decreases, while *GAP*0 increases as *v*1 decreases, because the labeled 1st carbon is lost at 6PGDH reaction in the PP pathway, and thus the flux *v*1 may be identified by the mass isotopomer patterns of GAP (or Ser).

(a) (b)

(c)

isotopomer balance equations is 6 2 64 for G6P, 5 2 32 for P5P (Ru5P, X5P, R5P), 7 2 128 for S7P, 4 2 16 for E4P, 6 2 64 for F6P, and 3 2 8 for GAP. The same number of isotopomers is present, and therefore, the isotopomer distribution for each metabolite can be obtained uniquely as a function of the labeling patterns of glucose on condition that the fluxes are given. Consider the case of using 100 % of [1-13C] glucose as a carbon source for simplicity. It may be easily shown that *GAP*3 decreases, while *GAP*0 increases as *v*1 decreases, because the labeled 1st carbon is lost at 6PGDH reaction in the PP pathway, and thus the flux *v*1 may be

on (a) isotopomer and (b) mass isotopomer distributions for the case of

). (c) schematic illustration of how the specific

0.0

0.2

0.4

Mass isotopomer distribution

0.6

0.8

1.0

0.2 0.4 0.6 0.8 1.0

 m1 m2 m3

η

 O3 O13=O24 O23 O123=O234

0.2 0.4 0.6 0.8 1.0

η

0.0

Fig. 7. Effect of

isotopomers are generated.

using 100 % [3-13C] pyruvate ( 0.4

identified by the mass isotopomer patterns of GAP (or Ser).

0.2

0.4

Isotopomer distribution

0.6

0.8

1.0

Fig. 8. Main metabolic pathways in the central metabolism together with the fate of [1-13C] glucose.

Consider next how the isotopomers of GAP affect those of TCA cycle. Referring to Fig. 8, Let be the fraction from PEP to PYR through Pyk, and let 1 be the rest of the fraction which flows from PEP to OAA by the anaplerotic pathway. Figure 9a shows the effect of on the isotopomer distribution of OAA, and Fig. 9b shows its effect on the mass isotopomer distribution using 100 % of [1-13C] glucose for the case where *v*1 1 for simplicity

13C-Metabolic Flux Analysis and Metabolic Regulation 397

the viewpoint of the replacement of the broth by the labeled substrate. However, another dynamic behavior must be taken into account for the analysis of the TCA cycle, since the isotopomer distribution changes with respect to each turn of the TCA cycle. Although several analysis methods have been developed in the past for the special case of 100 % [2- 13C] acetate (Chance et al., 1983; Merle et al., 1996; Tran-Dinh et al., 1996a; Tran-Dinh et al.,

Let be the transition matrix which converts the isotopomer distribution at the *i* th turn to

special cases of *A*1=1, *A*2=1, *A*12=1, and *A*0=1, respectively, and superimposing the results into one matrix, the general expression for may be expressed as the matrix (Appendix A),

expression for may be useful in analyzing the transient behavior of the isotopomer distribution with respect to turn of the TCA cycle together with glyoxylate pathway. If we

*n n x x*

implies that the isotopomer distribution at the *n* th turn can be expressed once the initial state or at any known state was given, and this expression may be more useful than Eq. (13). Moreover, we can derive the same equations as Eq. (10) and (11) already derived in the steady state analysis if we set *n* (Appendix B). Thus, Eq. (14) can show not only steady state but also dynamic behavior of isotopomer. Appendix C shows the details of *n* .

As stated before, most of the flux analysis has been made based on the steady state assumption. However, this assumption must be carefully considered for the TCA cycle, since the 13C-labeled isotopomer distribution changes for each turn of the TCA cycle. Figure 10a shows how the isotopomer distribution changes with respect to turn of the TCA cycle, where 100 % [2-13C] acetate was used as a carbon source, and only TCA cycle was assumed to be active. Figure 10a indicates that *O*2 and *O*3 appear at the 1st turn, and *O*13 and *O*24 as well as *O*23 appear at the 2nd turn, but those reduced to zero as further cycling in the TCA cycle. On the other hand, *O*123 and *O*234 appear after the 3rd turn and converged to the steady state values. The converged values coincide with the values obtained by setting *z* 0 in the analytical expression (11). This result may be explained as follows: The *C*2 position of AcCoA becomes *C*4 position of CIT and αKG, and *C*3 position of SUC, while *C*5 position of CIT and αKG are never labeled if *C*1 position of AcCoA is not labeled (Fig. 6). Randomization of carbons in SUC is made by allowing 13C in the *C*3 of SUC to be distributed equally to either *C*2 or *C*3 position of MAL in the first turn of the cycle. Thus at the end of the first turn of the cycle, *O*2 and *O*3 are produced with equal portions (Fig. 10a), which in the 2nd turn of the cycle generate *C*34 and *C*24 of CIT, *C*34 and *C*24 of αKG, and *C*23 and *C*13 of SUC. *C*23 of SUC only produces *O*23 since *O*23 is equivalent to *O*32 , while *C*13 of SUC produces equal amount of *O*24 and *O*13 . Condensation of these with *C*2 of AcCoA ( *A*2 ) produces *C C* 234 134 , , and *C*246 of CIT,

0 is the isotopomer distribution vector before labeling experiment. This equation

*x* is the isotopomer vector at the *i* th turn of the TCA cycle. By considering the

*i i x x* 1 (13)

*T G* 2 . Note that *T G* 2 1 holds. This

0 (14)

1996b), here more general approach is considered.

that at the *i* 1 th turn in the TCA cycle such that

2 , and

repeat the operation of Eq. (13), the following equation is obtained:

letting *Tv Gv TCA Gly* , , *T G* 1

which eventually produce *O*123 and *O*234 .

where *i*

where *x*

(Matsuoka & Shimizu, 2010a). Note that *Oi* is the isotopomer of OAA labeled at *i* -th carbon(s) and *mj* is the mass isotopomer, where it is the linear combination of the isotopomers of OAA. For example, *m O* 0 0 , *i i m O* 4 1 1 , and so on. Unlike glycolysis and PP pathway, TCA cycle provides a variety of isotopomers as given in Fig. 9a, and Fig. 9b indicates that may be identified by MS measurement of *m m* 0 3 ~ . The reason why *m*1 is less sensitive with respect to as compared to the other mass isotopomers is that *O*2 increases while *O*3 decreases as increases. Note that *GAP*3 and *GAP*0 are generated at Fba reaction from [1-13C] glucose. Those bring *O*3 and *O*0 via Ppc reaction. Another isotopomers such as *O*2 and *O*23 appear as proceeding TCA cycle (Matsuoka & Shimizu,

2010a). Although [1-13C] glucose and/or [U-13C] glucose are exclusively used in practice, [1,

Fig. 9. Simulation result of (a) isotopomer and (b) mass isotopomer distributions of OAA with respect to for the case of using 100 % [1-13C] glucose ( *v*1 1.0 ).

So far, we considered how the isotopomer distribution is expressed with respect to the flux. In practice, the fluxes must be found from the measured signals for the isotopomer distribution. Let these signals be obtained by either NMR or MS, and let these be *s i i* 1,2, . Then the fluxes may be obtained by minimizing the following objective function:

$$J = \left(\hat{\mathbf{s}} - \mathbf{s}\right)^{T} \sum\_{S}^{-1} \left(\hat{\mathbf{s}} - \mathbf{s}\right) \tag{12}$$

where *s* represents the measured signal vector containing *is* , *s*ˆ is its estimated vector, and *S* is the variance-covariance matrix associated with the measured errors.

#### **4. Dynamic behavior of isotopomer distribution**

2-13C] glucose may be also used for the flux estimation.

The metabolic flux analysis with 13C-labeled substrate has been made based on the steady state condition. However, the sampling is usually made during instationary phase due to economical reason, and unsteady correction is made by assuming the 1st order washout behavior (van Winden et al., 2001). In many practical applications, this may be justified from

(Matsuoka & Shimizu, 2010a). Note that *Oi* is the isotopomer of OAA labeled at *i* -th carbon(s) and *mj* is the mass isotopomer, where it is the linear combination of the

PP pathway, TCA cycle provides a variety of isotopomers as given in Fig. 9a, and Fig. 9b

Fba reaction from [1-13C] glucose. Those bring *O*3 and *O*0 via Ppc reaction. Another isotopomers such as *O*2 and *O*23 appear as proceeding TCA cycle (Matsuoka & Shimizu, 2010a). Although [1-13C] glucose and/or [U-13C] glucose are exclusively used in practice, [1,

for the case of using 100 % [1-13C] glucose ( *v*1 1.0 ).

(a) (b) Fig. 9. Simulation result of (a) isotopomer and (b) mass isotopomer distributions of OAA

So far, we considered how the isotopomer distribution is expressed with respect to the flux. In practice, the fluxes must be found from the measured signals for the isotopomer distribution. Let these signals be obtained by either NMR or MS, and let these be *s i i* 1,2, . Then the

> 1 ˆ ˆ *T S J ss ss*

where *s* represents the measured signal vector containing *is* , *s*ˆ is its estimated vector, and

The metabolic flux analysis with 13C-labeled substrate has been made based on the steady state condition. However, the sampling is usually made during instationary phase due to economical reason, and unsteady correction is made by assuming the 1st order washout behavior (van Winden et al., 2001). In many practical applications, this may be justified from

Mass isotopomer distribution

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

*i m O* 4

may be identified by MS measurement of *m m* 0 3 ~ . The reason why *m*1 is

as compared to the other mass isotopomers is that *O*2

increases. Note that *GAP*3 and *GAP*0 are generated at

, and so on. Unlike glycolysis and

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

 m0 m1 m2 m3

φ

(12)

1 1

isotopomers of OAA. For example, *m O* 0 0 , *i*

2-13C] glucose may be also used for the flux estimation.

 O0 O1 =O4

O2

O23

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

φ

=O13=O24

fluxes may be obtained by minimizing the following objective function:

*S* is the variance-covariance matrix associated with the measured errors.

**4. Dynamic behavior of isotopomer distribution**

 O3 O12=O34=O123=O234

indicates that

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

with respect to

Isotopomer distribution

less sensitive with respect to

increases while *O*3 decreases as

the viewpoint of the replacement of the broth by the labeled substrate. However, another dynamic behavior must be taken into account for the analysis of the TCA cycle, since the isotopomer distribution changes with respect to each turn of the TCA cycle. Although several analysis methods have been developed in the past for the special case of 100 % [2- 13C] acetate (Chance et al., 1983; Merle et al., 1996; Tran-Dinh et al., 1996a; Tran-Dinh et al., 1996b), here more general approach is considered.

Let be the transition matrix which converts the isotopomer distribution at the *i* th turn to that at the *i* 1 th turn in the TCA cycle such that

$$\mathbf{x}^{(i+1)} = \boldsymbol{\Phi} \cdot \mathbf{x}^{(i)} \tag{13}$$

where *i x* is the isotopomer vector at the *i* th turn of the TCA cycle. By considering the special cases of *A*1=1, *A*2=1, *A*12=1, and *A*0=1, respectively, and superimposing the results into one matrix, the general expression for may be expressed as the matrix (Appendix A), letting *Tv Gv TCA Gly* , , *T G* 1 2 , and *T G* 2 . Note that *T G* 2 1 holds. This expression for may be useful in analyzing the transient behavior of the isotopomer distribution with respect to turn of the TCA cycle together with glyoxylate pathway. If we repeat the operation of Eq. (13), the following equation is obtained:

$$\mathfrak{x}^{(n)} = \mathfrak{O}^n \mathfrak{x}^{(0)} \tag{14}$$

where *x* 0 is the isotopomer distribution vector before labeling experiment. This equation implies that the isotopomer distribution at the *n* th turn can be expressed once the initial state or at any known state was given, and this expression may be more useful than Eq. (13). Moreover, we can derive the same equations as Eq. (10) and (11) already derived in the steady state analysis if we set *n* (Appendix B). Thus, Eq. (14) can show not only steady state but also dynamic behavior of isotopomer. Appendix C shows the details of *n* .

As stated before, most of the flux analysis has been made based on the steady state assumption. However, this assumption must be carefully considered for the TCA cycle, since the 13C-labeled isotopomer distribution changes for each turn of the TCA cycle. Figure 10a shows how the isotopomer distribution changes with respect to turn of the TCA cycle, where 100 % [2-13C] acetate was used as a carbon source, and only TCA cycle was assumed to be active. Figure 10a indicates that *O*2 and *O*3 appear at the 1st turn, and *O*13 and *O*24 as well as *O*23 appear at the 2nd turn, but those reduced to zero as further cycling in the TCA cycle. On the other hand, *O*123 and *O*234 appear after the 3rd turn and converged to the steady state values. The converged values coincide with the values obtained by setting *z* 0 in the analytical expression (11). This result may be explained as follows: The *C*2 position of AcCoA becomes *C*4 position of CIT and αKG, and *C*3 position of SUC, while *C*5 position of CIT and αKG are never labeled if *C*1 position of AcCoA is not labeled (Fig. 6). Randomization of carbons in SUC is made by allowing 13C in the *C*3 of SUC to be distributed equally to either *C*2 or *C*3 position of MAL in the first turn of the cycle. Thus at the end of the first turn of the cycle, *O*2 and *O*3 are produced with equal portions (Fig. 10a), which in the 2nd turn of the cycle generate *C*34 and *C*24 of CIT, *C*34 and *C*24 of αKG, and *C*23 and *C*13 of SUC. *C*23 of SUC only produces *O*23 since *O*23 is equivalent to *O*32 , while *C*13 of SUC produces equal amount of *O*24 and *O*13 . Condensation of these with *C*2 of AcCoA ( *A*2 ) produces *C C* 234 134 , , and *C*246 of CIT, which eventually produce *O*123 and *O*234 .

13C-Metabolic Flux Analysis and Metabolic Regulation 399

 : *aceBAK*, *acnA*, *cydB*, *fbp*, *icdA*, *pckA*, *pgk*, *ppsA*  : *acnB*, *adhE*, *eda*, *edd*, *pfkA*, *ptsHI*, *pykF*, *zwf*

: *acnAB*, *aceEF*, *acs*, *focA*, *fumA*, *fur*, *gltA*, *malT*, *manXYZ*, *mdh*, *mlc*,

: *aceBAK*, *aceEF*, *acnAB*, *cyoABCDE*, *fumAC*, *gltA*, *icdA*, *lpdA*, *mdh*,

*pckA*, *pdhR*, *pflB*, *pgk*, *ptsG*, *sdhCDAB*, *sucABCD*, *ugpABCEQ*

*nuoABCDEFGHIJKLMN*, *pdhR*, *sdhCDAB*, *sodA*, *sucABCD*

: *acnAB*, *cyoABCDE*, *cydAB*, *fnr*, *fumA*, *icdA*, *ndh*,

: *acnA*, *acs*, *adhE*, *fumC*, *gadAB*, *osmC*, *poxB*, *talA*, *tktB*

*nuoABCDEFGHIJKLMN*, *sdhCDAB*, *sucABCD*

**Global regulator Metabolic pathway gene**

: *cyaA*, *lpdA*, *rpoS*

: *cydAB*, *focA*, *pflB*

: *acs*, *focA*, *frdABCD*, *pflB*, *yfiD*

Table 1. Effect of global regulators on the metabolic pathway gene expressions.

Among the culture environment, carbon sources are by far important for the cell from the point of view of energy generation (catabolism) and biosynthesis (anabolism). Catabolite

Cra

Crp

ArcA/B

Fnr

RpoS

IclR : *aceBAK*, *acs*

SoxR/S : *acnA*, *fumC*, *fur*, *sodA*, *zwf*

: *ompF*

Fur : *entABCDE*, *sodA*

IclR : *aceBAK*, *acs*

PdhR : *aceEF*, *lpdA*

PhoB : *phoABERU*, *pstSCAB*

Mlc : *crr*, *manXYZ*, *malT*, *ptsG*, *ptsHI*

FadR : *iclR*

Figure 10b shows the case where the glyoxylate pathway is active as well as TCA cycle. It indicates that at the first turn, *O*2 and *O*3 are generated, while *O O* 23 123 , and *O*234 appear as each turn is repeated, resulting in the eventual convergence to the steady state, where *O*23 newly appears as compared with the case of only TCA cycle. The converged values are the same as those computed using Eq. (11).

Fig. 10. Isotopomer distribution with respect to turn of the TCA cycle with glyoxylate pathway: Case of using the 100 % [2-13C] acetate where (a) only TCA cycle is active, and (b) glyoxylate pathway as well as TCA cycle is active.

#### **5. Metabolic regulation by global regulators in response to culture environment**

The main goal of metabolic engineering is to improve the metabolic phenotype through genetic modifications (Bailey, 1991; Stephanopoulos & Vallino, 1991). Most of the past metabolic engineering approach has been considered to improve a particular biosynthetic capacity through engineering the target pathway. The resulting phenotypes are, however, often suboptimal and not satisfactory due to distant effects of genetic modifications or regulatory influences. It is, therefore, strongly desirable to take into account the metabolic regulation mechanism for metabolic engineering. Roughly speaking, metabolic regulation is made by recognition of culture environment (or cell's state) and the adjustment of the metabolism, where global regulators and/or sigma factors play important roles in regulating the metabolic pathway genes. Note that the high-throughput techniques for transcriptomics, proteomics, metabolomics, and fluxomics have the potential to disclose the metabolic regulation mechanism, but most of them provide a snapshot from one stage, and the methodology in interpreting different levels of information is not established yet (Vemuri & Aristidou, 2005). In order to put forward advanced fermentation toward biofuel production etc., it is quite important to understand the effect of culture environment on the metabolism based on gene level regulation, and modify the cell metabolism based on such information. In the followings, a brief explanation on the carbon catabolite regulation is given.

Figure 10b shows the case where the glyoxylate pathway is active as well as TCA cycle. It indicates that at the first turn, *O*2 and *O*3 are generated, while *O O* 23 123 , and *O*234 appear as each turn is repeated, resulting in the eventual convergence to the steady state, where *O*23 newly appears as compared with the case of only TCA cycle. The converged values are

Fig. 10. Isotopomer distribution with respect to turn of the TCA cycle with glyoxylate pathway: Case of using the 100 % [2-13C] acetate where (a) only TCA cycle is active, and (b)

**5. Metabolic regulation by global regulators in response to culture**

the followings, a brief explanation on the carbon catabolite regulation is given.

(a) (b)

The main goal of metabolic engineering is to improve the metabolic phenotype through genetic modifications (Bailey, 1991; Stephanopoulos & Vallino, 1991). Most of the past metabolic engineering approach has been considered to improve a particular biosynthetic capacity through engineering the target pathway. The resulting phenotypes are, however, often suboptimal and not satisfactory due to distant effects of genetic modifications or regulatory influences. It is, therefore, strongly desirable to take into account the metabolic regulation mechanism for metabolic engineering. Roughly speaking, metabolic regulation is made by recognition of culture environment (or cell's state) and the adjustment of the metabolism, where global regulators and/or sigma factors play important roles in regulating the metabolic pathway genes. Note that the high-throughput techniques for transcriptomics, proteomics, metabolomics, and fluxomics have the potential to disclose the metabolic regulation mechanism, but most of them provide a snapshot from one stage, and the methodology in interpreting different levels of information is not established yet (Vemuri & Aristidou, 2005). In order to put forward advanced fermentation toward biofuel production etc., it is quite important to understand the effect of culture environment on the metabolism based on gene level regulation, and modify the cell metabolism based on such information. In

0.0

0.2

0.4

Isotopomer distribution

0.6

0.8

1.0

0 2 4 6 810

O0

O3

O2

 O13 O23 O24 O123 O234

Turn number

the same as those computed using Eq. (11).

0 2 4 6 810

O0

O3

O2

 O13 O23 O24 O123 O234

Turn number

glyoxylate pathway as well as TCA cycle is active.

0.0

**environment**

0.2

0.4

Isotopomer distribution

0.6

0.8

1.0

Table 1. Effect of global regulators on the metabolic pathway gene expressions.

Among the culture environment, carbon sources are by far important for the cell from the point of view of energy generation (catabolism) and biosynthesis (anabolism). Catabolite

13C-Metabolic Flux Analysis and Metabolic Regulation 401

G6P PGL/6PG

NADP NADPH

G6PDH PGDH

(*zwf*) (*gnd*)

TKb

(*tktA*, *B*)

RU5P

Ru5P R5PI

(*rpe*) (*rpiA*, *B*)

X5P R5P

S7P

KDPG

(*tktA*, *B*)

CO2

E4P TKa TA

> (*eda*) Eda

NADP NADPH

Edd (*edd*)

(*talA*, *B*)

3PG/2PG

PEP

Pfl PDH

(*pflABCD*) (*lpdAaceEF*)

CO2

ETH AcAld AcCoA AcP ACE

ALDH

(*adhE*)

(*acs*) (*adhE*)

FUM

Frd

Fum

MAL

MDH

NADH

NAD

Fig. 11. Main metabolic pathways of *Escherichia coli*.

(*mdh*)

FOR

Pyk ATP ADP

ATP

ADH

(*pckA*)

Mez NADPH NADP

CO2

(*maeB*)

ATP Pck (ADP) CO2

PEP

EI

EI-P HPr

(*pfkA*, *B*)

(*gapA*)

PYR

NAD NADH

CO2 (ADP) Ppc

(*ppc*)

ATP ADP

(*ppsA*) (*pykA*, *F*)

NAD

GAPDH NADH

Pfk ADP ATP

(*fbaA*, *B*)

(*pgi*)

PTS GLC

EIIA-P

HPr-P EIIA

EI HPr EIIA (*ptsG*) (*ptsI*) (*ptsH*) (*crr*) EIICB

PGP

F6P

FDP

Fdp

(*fbp*)

GAP/DHAP

Ald

Pgi

Eno

Pps

NAD NADH ADP ATP

OAA ICT

CS (*gltA*)

Icl

(*aceA*)

SUC

SDH FAD

(*sdhCDAB*)

GOX

FADH2

(*fumA, B, C*)

(*frdABCD*)

MS

(*aceB*)

NAD

NADH

CIT

PYR LAC LDH

(*pta*)

(*pgk*, *pgm*)

(*eno*)

Pta Ack

NADH NAD

(*ldhA*)

(*ackA*)

Acs

ADP ATP

(*acnA*, *B*) Acn

αKG

ICDH

NADPH

(*icdA*)

NAD

NADH

NADP

SucCoA

ADP

αKGDH

(*lpdAsucAB*)

CO2

CO2

SCS

(*sucCD*)

ATP

Pgkm

regulation is made when different carbohydrates are present in a medium, where glucose is preferentially consumed, and the uptake of other carbon sources is repressed. The center of the regulatory network for catabolite repression in *Escherichia coli* is the phosphoenol pyruvate (PEP): carbohydrate phosphotransferase systems (PTSs). These systems are involved in both transport and phosphorylation of carbohydrates. The PTS in *E. coli* consists of two common cytoplasmic proteins, EI (enzyme I) encoded by *ptsI* and HPr (histidine-phosphorylatable protein) encoded by *ptsH*, as well as carbohydratespecific EII (enzyme II) complexes. The glucose-specific PTS in *E. coli* consists of the cytoplasmic protein EIIAGlc encoded by *crr* and the membrane-bound protein EIICBGlc encoded by *ptsG*, which transport and concomitantly phosphorylate glucose (Fig. 11). The phosphoryl groups are transferred from PEP via successive phosphorelay reactions in turn by EI, HPr, EIIAGlc and EIICBGlc to glucose. The cAMP-Crp complex and the repressor Mlc are involved in the regulation of *ptsG* gene and *pts* operon expressions. It has been demonstrated that unphosphorylated EIICBGlc can relieve the *ptsG* gene expression by sequestering Mlc from its binding sites through protein-protein interaction depending on the glucose concentration. In contrast to Mlc, which represses the expressions of *ptsG*, *ptsHI* and *crr* (Plumbridge, 1998), cAMP-Crp complex activates *ptsG* gene expression (De Reuse & Danchin, 1988). These two antagonistic regulatory mechanisms guarantee a precise adjustments of *ptsG* expression levels under various conditions (Bettenbrock et al., 2006). It should be noted that unphosphorylated EIIAGlc inhibits the uptake of other non-PTS carbohydrates by the so-called inducer exclusion (Aiba, 1995), while phosphorylated EIIAGlc (EIIAGlc-P) activates adenylate cyclase (Cya), which generates cAMP from ATP and leads to an increase in the intracellular cAMP level (Park et al., 2006). In the absence of glucose, Mlc binds to the upstream of *ptsG* gene and prevents its transcription. If glucose is present in the medium, the amount of unphosphorylated EIICBGlc increases due to the phosphate transfer to glucose. In this situation, Mlc binds to EIICBGlc, and thus it does not bind to the operator of *pts* genes (Bettenbrock et al., 2006; Tanaka et al., 2000; Lee et al., 2000). The overall catabolite regulation mechanism is briefly shown in Fig. 12 (Matsuoka & Shimizu, 2011). The catabolic regulation phenomenon has been modeled by several researchers (Bettenbrock et al., 2006; Kremling et al.; 2004; Kremling & Gilles, 2001).

In addition to cAMP-Crp, which acts depending on the level of glucose concentration, the catabolite repressor/activator protein (Cra) originally characterized as the fructose repressor (FruR) controls the carbon flow in *E. coli* (Moat et al., 2002; Saier, 1996; Saier & Ramseier, 1996). The carbon uptake and glycolysis genes such as *ptsHI*, *pfkA*, *pykF*, *zwf* and *edd-eda* are repressed, while gluconeogenic pathway genes such as *ppsA*, *fbp*, *pckA*, *icdA* and *aceA*, *B* are activated by Cra (Moat et al., 2002; Saier & Ramseier, 1996) (Table 1, Fig. 11). It has been known that the mutant defective in *cra* gene is unable to grow on gluconeogenic substrates such as pyruvate, acetate and lactate (Saier et al., 1996). Since gluconeogenic pathway genes are deactivated, and the glycolysis genes are activated by *cra* gene knockout, the glucose uptake rate may be enhanced, but it must be careful since *icdA*, *aceA*, *B*, and *cydB* genes are repressed, while *zwf* and *edd* gene expressions are activated and thus ED pathway is activated by *cra* gene knockout (Sarkar et al., 2008).

The effects of other culture environments than carbon source are given elsewhere (Matsuoka & Shimizu, 2011).

regulation is made when different carbohydrates are present in a medium, where glucose is preferentially consumed, and the uptake of other carbon sources is repressed. The center of the regulatory network for catabolite repression in *Escherichia coli* is the phosphoenol pyruvate (PEP): carbohydrate phosphotransferase systems (PTSs). These systems are involved in both transport and phosphorylation of carbohydrates. The PTS in *E. coli* consists of two common cytoplasmic proteins, EI (enzyme I) encoded by *ptsI* and HPr (histidine-phosphorylatable protein) encoded by *ptsH*, as well as carbohydratespecific EII (enzyme II) complexes. The glucose-specific PTS in *E. coli* consists of the cytoplasmic protein EIIAGlc encoded by *crr* and the membrane-bound protein EIICBGlc encoded by *ptsG*, which transport and concomitantly phosphorylate glucose (Fig. 11). The phosphoryl groups are transferred from PEP via successive phosphorelay reactions in turn by EI, HPr, EIIAGlc and EIICBGlc to glucose. The cAMP-Crp complex and the repressor Mlc are involved in the regulation of *ptsG* gene and *pts* operon expressions. It has been demonstrated that unphosphorylated EIICBGlc can relieve the *ptsG* gene expression by sequestering Mlc from its binding sites through protein-protein interaction depending on the glucose concentration. In contrast to Mlc, which represses the expressions of *ptsG*, *ptsHI* and *crr* (Plumbridge, 1998), cAMP-Crp complex activates *ptsG* gene expression (De Reuse & Danchin, 1988). These two antagonistic regulatory mechanisms guarantee a precise adjustments of *ptsG* expression levels under various conditions (Bettenbrock et al., 2006). It should be noted that unphosphorylated EIIAGlc inhibits the uptake of other non-PTS carbohydrates by the so-called inducer exclusion (Aiba, 1995), while phosphorylated EIIAGlc (EIIAGlc-P) activates adenylate cyclase (Cya), which generates cAMP from ATP and leads to an increase in the intracellular cAMP level (Park et al., 2006). In the absence of glucose, Mlc binds to the upstream of *ptsG* gene and prevents its transcription. If glucose is present in the medium, the amount of unphosphorylated EIICBGlc increases due to the phosphate transfer to glucose. In this situation, Mlc binds to EIICBGlc, and thus it does not bind to the operator of *pts* genes (Bettenbrock et al., 2006; Tanaka et al., 2000; Lee et al., 2000). The overall catabolite regulation mechanism is briefly shown in Fig. 12 (Matsuoka & Shimizu, 2011). The catabolic regulation phenomenon has been modeled by several researchers (Bettenbrock

et al., 2006; Kremling et al.; 2004; Kremling & Gilles, 2001).

activated by *cra* gene knockout (Sarkar et al., 2008).

& Shimizu, 2011).

In addition to cAMP-Crp, which acts depending on the level of glucose concentration, the catabolite repressor/activator protein (Cra) originally characterized as the fructose repressor (FruR) controls the carbon flow in *E. coli* (Moat et al., 2002; Saier, 1996; Saier & Ramseier, 1996). The carbon uptake and glycolysis genes such as *ptsHI*, *pfkA*, *pykF*, *zwf* and *edd-eda* are repressed, while gluconeogenic pathway genes such as *ppsA*, *fbp*, *pckA*, *icdA* and *aceA*, *B* are activated by Cra (Moat et al., 2002; Saier & Ramseier, 1996) (Table 1, Fig. 11). It has been known that the mutant defective in *cra* gene is unable to grow on gluconeogenic substrates such as pyruvate, acetate and lactate (Saier et al., 1996). Since gluconeogenic pathway genes are deactivated, and the glycolysis genes are activated by *cra* gene knockout, the glucose uptake rate may be enhanced, but it must be careful since *icdA*, *aceA*, *B*, and *cydB* genes are repressed, while *zwf* and *edd* gene expressions are activated and thus ED pathway is

The effects of other culture environments than carbon source are given elsewhere (Matsuoka

Fig. 11. Main metabolic pathways of *Escherichia coli*.

13C-Metabolic Flux Analysis and Metabolic Regulation 403

**8. Appendix B: Derivation of eq. (10) and (11) using** *n*  **as** *n*

By inspection, if we assume *n* to be large enough, *n* can be reduced to

2

diagonalized by multiplying the eigen matrix *P* and its inverse such that

*P P*

1

*n*

0.5 0.5 0.5 0.5 0.5 0.5

where only the terms associated with *O*23 , *O*123 and *O*234 were left. Note that can be

1

*i i* 1,2,3 are the distinct eigen values of . Since we have the relationship

2

0 0 0 0 0 0

3

*GG G T TG T T TG TG* *n*

*n n PP P P* 1 1 (B3)

(B1)

(B2)

1. The case where *A*2 1 :

where

**7. Appendix A: The general expression for .**

Fig. 12. Transcriptional regulation in response to carbon catabolite regulation.

#### **6. Conclusion**

13C-Metabolic flux analysis is quite useful to understand the cell metabolism. In this chapter, analytical approach for 13C-metabolic flux analysis is also explained to make the relationship between fluxes and isotopomer patterns to be transparent. Metabolic regulation occurs in response to culture environment. The global regulators sense such a change, and those regulate metabolic pathway genes. To predict cell metabolism in response to environmental change, the relationships between culture environment and global regulators and the relationships between global regulators and metabolic pathway genes have to be figured out. For this, it is desired to integrate different levels of information as well as 13C-metabolic flux distribution.

Fig. 12. Transcriptional regulation in response to carbon catabolite regulation.

information as well as 13C-metabolic flux distribution.

13C-Metabolic flux analysis is quite useful to understand the cell metabolism. In this chapter, analytical approach for 13C-metabolic flux analysis is also explained to make the relationship between fluxes and isotopomer patterns to be transparent. Metabolic regulation occurs in response to culture environment. The global regulators sense such a change, and those regulate metabolic pathway genes. To predict cell metabolism in response to environmental change, the relationships between culture environment and global regulators and the relationships between global regulators and metabolic pathway genes have to be figured out. For this, it is desired to integrate different levels of

**6. Conclusion**

#### **7. Appendix A: The general expression for .**

#### **8. Appendix B: Derivation of eq. (10) and (11) using** *n*  **as** *n*

1. The case where *A*2 1 :

By inspection, if we assume *n* to be large enough, *n* can be reduced to

$$\boldsymbol{\Phi}^{n} = \begin{bmatrix} 2\,\text{G} & \text{G} & \text{G} \\ 0.5T & 0.5(T+\text{G}) & 0.5T \\ 0.5T & 0.5(T+\text{G}) & 0.5T+\text{G} \end{bmatrix}^{n} \tag{B1}$$

where only the terms associated with *O*23 , *O*123 and *O*234 were left. Note that can be diagonalized by multiplying the eigen matrix *P* and its inverse such that

$$P^{-1} \Phi P = \begin{bmatrix} \lambda\_1 & 0 & 0 \\ 0 & \lambda\_2 & 0 \\ 0 & 0 & \lambda\_3 \end{bmatrix} \tag{B2}$$

where *i i* 1,2,3 are the distinct eigen values of . Since we have the relationship

$$\left(P^{-1}\Phi P\right)^{\prime\prime} = P^{-1}\Phi^{\prime\prime}P \tag{\text{B3}}$$

13C-Metabolic Flux Analysis and Metabolic Regulation 405

*O G T T O G T O T GT*

23 123 234

which is equivalent to Eq. (11) already derived previously for the steady state.

In the similar was as above, *n* is expressed for *n* to be large enough as follows:

2

14 4 1

*n*

  (B8)

(B9)

(B10)

  (C1)

*T T T G T T G T G*

1 1 1 1 11

3 2 2 3 2

*G TGT*

0.5 0.5 0.5 0.5 0.5 0.5

where only the terms associated with *O*14 , *O*4 and *O*1 are left. Then the steady state values

*O G T T O G T O T GT*

where this equation is equivalent to Eq. (10) as previously derived for the steady state.

**9. Appendix C: Isotopomer pattern of OAA at the** *n* **th turn of the TCA cycle**

Let us consider deriving the general case for *A*2 1 , where can be reduced from 16 16

0 00 0 0 0 0 0 20 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 2

*TG G G G T G G G*

*T T G*

1 1

1 1

0 0 0 0 0 2 2 0 2 0 2 2 0 0 0 0 0 0 0 0 2 22

*T G G T*

3 2 2 3 2

*G TGT*

*G*

*GG G T TG T T TG TG* *n*

*G*

Then, we can derive the following relationships:

2. The case where *A*1 1 :

could be obtained as follows:

**together with glyoxylate pathway**

to 8 8 due to the limited appearance of the isotopomer as

*TG G G G T G G*

2 0

1 1 1 1

*n* can be expressed as

$$\boldsymbol{\Psi}^{\rm n} = \boldsymbol{P} \left( \boldsymbol{P}^{-1} \boldsymbol{\Phi} \boldsymbol{P} \right)^{\rm n} \boldsymbol{P}^{-1} = \boldsymbol{P} \begin{bmatrix} \mathcal{A}\_{1} \ \prescript{\rm n}{}{\boldsymbol{\cal}} & \boldsymbol{0} & \boldsymbol{0} \\ \boldsymbol{0} & \mathcal{A}\_{2} \ \prescript{\rm n}{}{\boldsymbol{\cal}} & \boldsymbol{0} \\ \boldsymbol{0} & \boldsymbol{0} & \mathcal{A}\_{3} \ \prescript{\rm n}{}{\boldsymbol{\cal}} \end{bmatrix} \boldsymbol{P}^{-1} \tag{B4}$$

Here *i i* 1,2,3 and *P* are obtained for as follows:

$$
\begin{aligned}
\lambda\_1 &= G, \quad \lambda\_2 = 2G + T, \quad \lambda\_3 = \frac{G}{2} \\ \\
 P &= \begin{bmatrix} 1 \\ 1 \\ 0 \\ -1 \end{bmatrix} \frac{1}{T + G} \begin{bmatrix} 1 \\ \left(2G + T\right)^2 \\ G\left(3G + 2T\right) - T \\ -1 \end{bmatrix} \begin{array}{c} 0 \\ 1 \\ -1 \\ \end{array} \tag{B5} \\ &= \frac{T\left(2G + T\right)}{G\left(3G + 2T\right)} \end{aligned} \tag{B6}
$$

Then *n* could be calculated as

 *n n n n n n n n T GG G G T GT GT GT T GT GGGG G T T T GG G T GT GT GT T GT T T GT G G GT GT GT GT GG T* 2 2 0 1 2 0 2 32 2 3 2 2 3232 32 32 2 (B6) 22 2 3 22 2 3 2 2 3 2 3 22 3 2 2 2 2 2 2 3 2 3 2 3 22 *n nn nn n n n n nn n n n n n T G G G G GT G GT G GT GT GT G T G T T GT G T GT G G T G T G T G T GT GT G T T G T GT T GT G G T G G GT G TGT GT G TGT T G G T* 2 2 3 2 3 3 22 3 22 *n n n n n G T GT T G G T GT G TGT GT G T G G T G T*

Noting that *G* is less than 1 and 2 1 *G T* , we have for *n*

$$\begin{array}{c|cc} & \frac{G}{G+T} & \frac{G}{G+T} & \frac{G}{G+T} \\ & T & T & T \\ & \frac{T}{3G+2T} & \frac{3G+2T}{3G+2T} & \frac{T}{3G+2T} \\ & T(2G+T) & T(2G+T) & T(2G+T) \\ \hline \hline \text{(3G+2T)(G+T)} & \frac{T(2G+T)}{(3G+2T)(G+T)} & \frac{T(2G+T)}{(3G+2T)(G+T)} \end{array} \tag{B7}$$

Then, we can derive the following relationships:

$$
\begin{bmatrix} O\_{23} \\ O\_{123} \\ O\_{234} \end{bmatrix} = \begin{bmatrix} G \\ \overline{G+T} \\ T \\ \overline{3G+2T} \\ T\left(2G+T\right) \\ \hline \left(\overline{3G+2T}\right)\left(\overline{G+T}\right) \end{bmatrix} \tag{B8}
$$

which is equivalent to Eq. (11) already derived previously for the steady state.

2. The case where *A*1 1 :

404 Chemical Biology

*PP P P P P* 1 1 1 1

12 3 *G GT* , 2, 2

2

*n*

*T GT GGGG G T T T GG G T GT GT GT*

*T GT G G GT GT GT GT*

32 32 32 222 32 32 32

*GGG G T G T G T TTT GT GT GT T GT T GT T GT G TGT G TGT G TGT*

*n*

2 3232 32

*n n n nn n*

3 22 3 22

*GT G T G G T G T*

*n n*

22 2

*n nn nn n*

*T GT P T T GG G T T GT GG T*

*T GG G G T*

1 1 0 1 2 0 1 3 2 1 1 2 3 2

*n*

2

0 0 0 0 0 0

*n*

(B4)

(B5)

 2 2

3 2

*G T GT T G G T GT G TGT*

*n n n*

(B7)

(B6)

*GT GT GT*

*T GT T*

3

3

*G*

*i i* 1,2,3 and *P* are obtained for as follows:

1 2

*n n*

*n n*

Noting that *G* is less than 1 and 2 1 *G T* , we have for *n*

3

3 2 3 2

*n n n*

2 2

*T G T GT T GT G G T G G GT G TGT GT G TGT*

>

2 2 0

32 2

32 2

*T GT G T GT G G T G T G T*

3 22 2 3 2 2 3 2 3 22 3 2 2

*T G G G G GT G GT G GT*

2 2

*GT GT G T G T*

*G T GT GT G T*

*GG T*

2

*n n n*

*n* can be expressed as

Then *n* could be calculated as

*n n*

0 2

Here

3 22

*T G G T*

*n*

In the similar was as above, *n* is expressed for *n* to be large enough as follows:

$$\boldsymbol{\Phi}^{n} = \begin{bmatrix} 2\,\text{G} & \text{G} & \text{G} \\ 0.5T & 0.5(T+\text{G}) & 0.5T \\ 0.5T & 0.5(T+\text{G}) & 0.5T+\text{G} \end{bmatrix}^{n} \tag{B9}$$

where only the terms associated with *O*14 , *O*4 and *O*1 are left. Then the steady state values could be obtained as follows:

$$
\begin{bmatrix} O\_{14} \\ O\_4 \\ O\_1 \end{bmatrix} = \begin{bmatrix} \text{G} \\ \frac{\text{G} + T}{T} \\ \frac{T}{3\text{G} + 2T} \\ T(2\text{G} + T) \\ \boxed{(3\text{G} + 2T)(\text{G} + T)} \end{bmatrix} \tag{\text{B10}}
$$

where this equation is equivalent to Eq. (10) as previously derived for the steady state.

#### **9. Appendix C: Isotopomer pattern of OAA at the** *n* **th turn of the TCA cycle together with glyoxylate pathway**

Let us consider deriving the general case for *A*2 1 , where can be reduced from 16 16 to 8 8 due to the limited appearance of the isotopomer as

$$
\Phi = \begin{bmatrix}
0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
2^{-1}(T+G) + G & G & 2^{-1}G & 0 & 0 & 0 & 0 & 0 \\
2^{-1}(T+G) & 0 & 2^{-1}G & 0 & 0 & 0 & 0 & 0 \\
0 & 0 & 2^{-1}T & 2^{-1}(T+G) & 0 & 0 & 0 & 0 \\
0 & T + G & G & 2G & T + G & G & G \\
0 & 0 & 2^{-1}T & 2^{-1}(T+G) & 0 & G & 0 & 0 \\
0 & 0 & 0 & 0 & 2^{-1}T & 0 & 2^{-1}(T+G) & 2^{-1}T \\
0 & 0 & 0 & 0 & 2^{-1}T & 0 & 2^{-1}(T+G) & 2^{-1}T + G
\end{bmatrix}
\tag{C1}
$$

13C-Metabolic Flux Analysis and Metabolic Regulation 407

This research was supported in part by Strategic International Cooperative Program, Japan

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2578-2584

**11. References**

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*Eng.*, vol.6, pp. 85-100

138-150

vol.49, pp. 111-129

Let this matrix be subdivided into 4 submatrices as

$$\begin{array}{cc} \cline{2-5} \spadesuit & \cline{4-5} \begin{bmatrix} A \ (4 \times 4) & 0 \ (4 \times 4) \\ B \end{bmatrix} \end{array} \tag{C2}$$

Then it can be shown that the following equation holds

$$\mathbf{O}^{n^{n}} = \begin{bmatrix} A^{n} & \mathbf{0} \\ B^{n} = \sum\_{r=0}^{n-1} D^{r} B A^{n-r-1} & D^{n} \end{bmatrix} \tag{C3}$$

where *n A* and *n D* can be expressed as

$$A^{\
u} = \begin{bmatrix} 0 & 0 & 0 & 0 \\ -\frac{T+G}{G} 2^{-\imath} G^{\imath} + \frac{T+2G}{G} G^{\imath} & G^{\imath} & -2^{-\imath} G^{\imath} + G^{\imath} & 0 \\ & \frac{T+G}{G} 2^{-\imath} G^{\imath} & 0 & 2^{-\imath} G^{\imath} & 0 \\ -\frac{T+G}{G} 2^{-\imath} G^{\imath} + 2^{-\imath} \left(T+G\right)^{\imath} & 0 & -2^{-\imath} G^{\imath} + 2^{-\imath} \left(T+G\right)^{\imath} & 2^{-\imath} \left(T+G\right)^{\imath} \end{bmatrix} \quad \text{(C4a)}$$

 2 *n n T G T G G T G T G* 2 1 2 *n n n n T TG G G T G T nG G G T G T G n n G G T G G T G T G* 2 *n n G G T G G T G T G* 2 *n D* 0*n G* 0 0 (C4b) *n n n T G T G T T G T G* 2 2 3 2 2 3 *n n n n TG T TG G GT G T T G T G* 1 2 2 2 3 2 2 3 *n n n T G G T G T T G T G* 3 2 2 3 2 2 3 *n n n T G T G T T G T G* 2 2 3 2 2 3 *n n n n T G T G T G T G TT G T G TG T G* 2 2 3 2 2 2 3 2 1 2 2 2 3 2 2 2 3 *n n n n n n T TG GG T G TG T G T nG G TG TG T G GT G TT G T G TG T G n n n n G G T G T G G T G TT G T G TG T G* 3 2 2 3 2 2 2 3 *n n n n G G T G T G T G TT G T G TG T G* 2 2 3 2 2 2 3

#### **10. Acknowledgement**

This research was supported in part by Strategic International Cooperative Program, Japan Science and Technology Agency (JST).

#### **11. References**

406 Chemical Biology

 4 4 04 4 44 44

1

2

2

*n*

*n*

*T G*

2

*T G*

2

2 3

*TG T G*

*T G T G TT G*

2 2 3

*n n*

2 3

2 3

*n*

*G G T G*

*n n*

*T T G*

*n*

*n*

*G T G*

*T G T G*

2

*T T G*

2

*n n*

2

*n*

*n*

*T G*

2

*G G T G*

*T G*

*n*

*n*

*G T G*

*G G T G*

*T G*

*T G G T G*

3 2 2 3

*T G*

*n*

*T G G T G TT G*

3 2 2 3

*G G T G*

2

2 3

*TG T G*

*n n*

2 3

*nn n n n nn n n n*

2 02 0

(C3)

0 *n*

0 00 0

2 2 20

(C2)

(C4a)

*B D*

1

*n n n r nr n*

*B D BA D*

*A*

0

*n n n n nn n*

*TG T G G G G GG*

*A T G G G*

*G T G*

1

*T TG G G T G T nG G*

*n n*

2

*T G*

*n*

2

2

*T G*

*n*

*n n n*

*TG T TG G GT G*

2 3 2

*n*

*TG T G T nG G TG*

*n n*

*n n*

*G*

*T T G T G*

1 2

2 3

2

2

*T TG GG T G*

*GT G TT G*

*TG T*

1

2 2 3 2

2 3

*TG T G*

2

*n n n n*

*n*

*n*

*n D* 0*n G* 0 0 (C4b)

*T G G TG G TG TG*

2 2 02 2 2

*r*

*A*

Let this matrix be subdivided into 4 submatrices as

Then it can be shown that the following equation holds

*G G*

*G*

where *n A* and *n D* can be expressed as

*G*

2

2

*n*

*n*

*T G*

2

*n n*

*n*

*n*

*G T G*

*T G T G*

2

*T G*

*n*

2

2 3

2 2 3

*TG T G*

*n n*

2 3

2 3

*T G T G T G T G TT G*

*T T G*

*T G T G*

*T G*

*n*

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Sons

**1. Introduction**

**1.1 History of the quartz crystal microbalance**

essence of the small-load approximation.

**1.2 Biological applications of the QCM**

**19**

*Taiwan, R.O.C.*

**QCM as Cell-Based Biosensor**

*Institute of Bioengineering, Tatung University*

Tsong-Rong Yan, Chao-Fa Lee and Hung-Che Chou

Piezoelectricity is defined as electric polarization produced by mechanical strain in certain crystals, the polarization being proportional to the strain (Cady, 1946). The Curies first observed piezoelectricity in 1880 as a potential difference generated across two surfaces of a quartz crystal under strain. The converse piezoelectric effect, the deformation of a piezoelectric material by an applied electric field, was predicted by Lippmann (Lippmann, 1881). In 1959 Sauerbrey provided a description and experimental proof of the massfrequency relation for foreign layers deposited on thickness-shear mode crystals that are still widely used today for determination of mass-sensing format is commonly referred to as the QCM. The mass increases when a film is deposited onto the crystal surface and monolayer sensitivity is easily reached (Lu & Lewis, 1972). However, when the film thickness increases, viscoelastic effects come into play. In the late 80's, it was recognized that the QCM can also be operated in liquids (Konash & Bastiaans, 1980), if proper measures are taken to overcome the consequences of the large damping and viscoelastic effects contribute strongly to the resonance properties (Bruckenstein & Shay, 1985; Ward & Buttery, 1990). Today, microweighing is one of several uses of the QCM (Johannsmann, 2008). Measurements of viscosity and more general, viscoelastic properties, are of much importance as well. The "non-gravimetric" QCM is by no means an alternative to the conventional QCM. Many researchers, who use quartz resonators for purposes other than gravimetry, have continued to call the quartz crystal resonator "QCM". Actually, the term "balance" makes sense even for non-gravimetric applications if it is understood in the sense of a force balance. At resonance, the force exerted upon the crystal by the sample is balanced by a force originating from the shear gradient inside the crystal. This is the

The use of biological coatings, such as enzymes and antibodies, was a natural progression from the initial piezoelectric (Pz) sensor development. The first reported gas phase biosensor was in fact an enzyme-based Pz sensor (Guilbault, 1983). The first Pz immunosensor for microbial pathogens was developed by Muramatsu et al. in 1986 (Muramatsu et al., 1986). Their Pz crystals were coated with antibodies against *Candida albicans*. The antigen was detected from 1×106 to 5×108 cells mL–1. The sensor proved to be

### **QCM as Cell-Based Biosensor**

Tsong-Rong Yan, Chao-Fa Lee and Hung-Che Chou *Institute of Bioengineering, Tatung University*

*Taiwan, R.O.C.*

#### **1. Introduction**

410 Chemical Biology

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Zhao, J.; Baba, T.; Mori, H.; Shimizu, K. (2004). Global metabolic response of *Escherichia coli*

measurement of enzyme activities. *Appl. Microbiol. Biotech.*, vol.64, pp. 91-98 Zhu, J. & Shimizu, K. (2004). The effect of *pfl* genes knockout on the metabolism for optically

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*cerevisiae* by 13C-NMR spectroscopy. *Eur. J. Biochem.*, vol.242, pp. 770-778 Vemuri, G. N. & Aristidou, A. A. (2005). Metabolic engineering in the –omics era:

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metabolic fluxes through the citric acid and the glyoxylate cycles in *Saccharomyces*

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Modeling and simulation of carbon isotope labeling experiments. *Biotech. Bioeng.*,

analysis of 2D [13C, 1H] COSY NMR spectra for metabolic flux analysis purpose.

and metabolic fluxes for the analysis of the regulatory mechanisms in *Synechocystis*.

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*E. coli* for D-lactate production under microaerobic condition. *Metab. Eng.*, vol.7, pp.

#### **1.1 History of the quartz crystal microbalance**

Piezoelectricity is defined as electric polarization produced by mechanical strain in certain crystals, the polarization being proportional to the strain (Cady, 1946). The Curies first observed piezoelectricity in 1880 as a potential difference generated across two surfaces of a quartz crystal under strain. The converse piezoelectric effect, the deformation of a piezoelectric material by an applied electric field, was predicted by Lippmann (Lippmann, 1881). In 1959 Sauerbrey provided a description and experimental proof of the massfrequency relation for foreign layers deposited on thickness-shear mode crystals that are still widely used today for determination of mass-sensing format is commonly referred to as the QCM. The mass increases when a film is deposited onto the crystal surface and monolayer sensitivity is easily reached (Lu & Lewis, 1972). However, when the film thickness increases, viscoelastic effects come into play. In the late 80's, it was recognized that the QCM can also be operated in liquids (Konash & Bastiaans, 1980), if proper measures are taken to overcome the consequences of the large damping and viscoelastic effects contribute strongly to the resonance properties (Bruckenstein & Shay, 1985; Ward & Buttery, 1990). Today, microweighing is one of several uses of the QCM (Johannsmann, 2008). Measurements of viscosity and more general, viscoelastic properties, are of much importance as well. The "non-gravimetric" QCM is by no means an alternative to the conventional QCM. Many researchers, who use quartz resonators for purposes other than gravimetry, have continued to call the quartz crystal resonator "QCM". Actually, the term "balance" makes sense even for non-gravimetric applications if it is understood in the sense of a force balance. At resonance, the force exerted upon the crystal by the sample is balanced by a force originating from the shear gradient inside the crystal. This is the essence of the small-load approximation.

#### **1.2 Biological applications of the QCM**

The use of biological coatings, such as enzymes and antibodies, was a natural progression from the initial piezoelectric (Pz) sensor development. The first reported gas phase biosensor was in fact an enzyme-based Pz sensor (Guilbault, 1983). The first Pz immunosensor for microbial pathogens was developed by Muramatsu et al. in 1986 (Muramatsu et al., 1986). Their Pz crystals were coated with antibodies against *Candida albicans*. The antigen was detected from 1×106 to 5×108 cells mL–1. The sensor proved to be

QCM as Cell-Based Biosensor 413

information about the establishment of cell–substrate and cell–cell contacts. A computer-

Pioneering works using the QCM showed that viscoelastic properties of films deposited on the sensor surface can be examined using frequency changes (Kanazawa & Gordon, 1985; Okahata et al., 1989). However, measurement of alone is not easily and specifically related to structural or conformational changes occurring at the sensor surface, especially for cytoskeletal changes that imply cellular volume and mass redistribution over the adhesion surface.  Most real scenarios are actually in between these two limits. Rodahl et al. extended the QCM technique by performing the direct monitoring of energy dissipation (D) considered a useful indicator of the viscoelastic properties of the material deposited at the sensor surface (Rodahl et al., 1996a, 1996b). Among the different QCM-D investigations of cells, it was showed that the interaction between cells and a surface produced a unique and reproducible dissipation against

frequency plot, also referred to as a QCM-D signature (Fredriksson, 1998a, 1998b).

These new tools were called as the whole-cell QCM biosensor. Initial use of the QCM was for measuring chemicals in the gas phase binding the QCM surface and more recently as a

In the past decades the QCM has been used to create biosensors. Infrequently, whole cells have been studied at the QCM surface (Gryte et al., 1993; Muratsugu et al., 1997; Wegener et al., 1998). Marx suggests the potential of this cellular biosensor for the real-time identification or screening of all classes of biologically active drugs or biological macromolecules that affect cellular attachment and cellular spreading, regardless of their molecular mechanism of action (Marx et al., 2003, 2007). The interconnected cytoskeleton structural elements depicted provide targets for drugs or macromolecules that bind and alter their structures or dynamical properties. Biosensor output is proportional to a particular detected concentration of the drug

Applications for the QCM have been invested in our laboratory for a long-term. We combine some surface modify methods to immobilize the oligonucleotide probe on the gold electrode surface of QCM that could use to detect the PCR product of *Vibrio parahaemolyticus* and breast cancer. We study a modified antibody-coated QCM biosensor will be constructed for detecting food pathogenic bacteria *Vibrio parahaemolyticus* and to find the most suitable surface modification method. We have recently started to observe and research the cell growth process on QCM. Utilize a silver electrode QCM mass sensor to detect the physiology of cells by the plasma surface modification as a protection film (Chou et al., 2009). Develop a new method that utilizes the QCM technique to measure the tight junction of the Caco-2 cell (Chou & Yan, 2010). Using QCM to design a cell detection platform is an important application of QCM. In the process of system design and application, there still have some points, which are easily overlooked or are not understood by researchers. Most of the problems can be separated into three types. One is the cell culture environment conditions that affect the system signals, another is the

controlled relay allows switching between both modes.

tool in analytical electrochemistry.

or macromolecule effector.

**1.4 Scope of the present study**

specific with no detectable response observed with the other species tested. Conventional bacterial detection methods generally require laborious procedures and many hours or even days for complete analysis. The relatively large mass of bacterial cells, combined with the availability of antibodies to most species means that Pz immunosensor detection offers a very attractive alternative to microbiological methods. Generally giving results in minutes, with adequate sensitivity and selectivity. Su & Li design the automatic QCM immunosensor system was fabricated by immobilizing anti-Salmonella polyclonal antibodies on 8 MHz ATcut quartz crystal with Protein A method. The oscillation frequency of the QCM sensor was monitored in real time (Su & Li, 2004). The direct detection of nucleic acid interactions based on the use of acoustic wave devices was first provided by Fawcett et al. (Fawcett et al., 1988). They described a quartz crystal microbalance (QCM)-based biosensor for DNA detection by immobilizing single-stranded DNA onto quartz crystals and detecting the mass changes after hybridization. Since this early work, a number of articles have appeared employing similar procedures, resulting in microgravimetric measurements based on nucleic acids (Itamar et al., 2002). A QCM detection system consisted of a sensitive element (QCM wafer), an inlet subsystem, and a frequency acquisition unit. In Hao et al. work, a DNA probe functionalized quartz crystal microbalance (QCM) biosensor was developed to detect *B. anthracis* based on the recognition of its specific DNA sequences (Hao et al., 2011).

#### **1.3 The QCM in cell biological**

The QCM was already well-known and established as an analytical tool for studying adsorption phenomena at the solid-liquid interface (Martin et al., 1991; Buttry & Ward, 1992) when its potential for studying cell-substrate adhesion was recognized. It was then recognized that the adhesion of cells to the quartz surface also induced a shift in resonance frequency that was shown to be linearly correlated with the fractional surface coverage (Gryte et al., 1993; Redepenning et al., 1993). Time-resolved measurements of the resonance frequency were then used to follow the attachment and spreading of cells to the quartz surface, with extraordinary time resolution. Comparison with established cytological techniques has proven that the QCM readout reports reliably on the number of cells on the surface and the time course of adhesion (Wegener et al., 1998). Specifically, they have demonstrated that QCM is a convenient method for measuring in real time the attachment of African Green Monkey kidney cells as well as their detachment that accompanies cell death caused by either NaOH addition or virus infection. Additionally, the observed QCM responses are consistent with attached cell layers that behave as viscous films rather than rigid masses, illustrating that care must be exercised in the interpretation of QCM measurements involving cell adhesion or binding events.

Impedance analysis of cell-covered gold-film electrodes was first introduced by Giaever and Keese (Giaever & Keese, 1991, 1993), who showed that the frequency dependent electrical impedance for such a system is dependent on the impedance of the cell-free electrode, the resistance between adjacent cells, Rb, the capacitance of the cell membranes, Cm, and an additional impedance contribution that is associated with the current flow between the basal plasma membrane and the substrate. The resistance, Rb, is dependent on the width of the intercellular cleft between adjacent cells and the establishment of tight junctions, and is therefore a sensitive parameter for cell–cell contacts. Thus, impedance analysis of the shear displacement (from now on referred to as "quartz mode") and impedance analysis of the cell-covered surface electrode (referred to as "cell mode") may provide independent

specific with no detectable response observed with the other species tested. Conventional bacterial detection methods generally require laborious procedures and many hours or even days for complete analysis. The relatively large mass of bacterial cells, combined with the availability of antibodies to most species means that Pz immunosensor detection offers a very attractive alternative to microbiological methods. Generally giving results in minutes, with adequate sensitivity and selectivity. Su & Li design the automatic QCM immunosensor system was fabricated by immobilizing anti-Salmonella polyclonal antibodies on 8 MHz ATcut quartz crystal with Protein A method. The oscillation frequency of the QCM sensor was monitored in real time (Su & Li, 2004). The direct detection of nucleic acid interactions based on the use of acoustic wave devices was first provided by Fawcett et al. (Fawcett et al., 1988). They described a quartz crystal microbalance (QCM)-based biosensor for DNA detection by immobilizing single-stranded DNA onto quartz crystals and detecting the mass changes after hybridization. Since this early work, a number of articles have appeared employing similar procedures, resulting in microgravimetric measurements based on nucleic acids (Itamar et al., 2002). A QCM detection system consisted of a sensitive element (QCM wafer), an inlet subsystem, and a frequency acquisition unit. In Hao et al. work, a DNA probe functionalized quartz crystal microbalance (QCM) biosensor was developed to detect *B.*

*anthracis* based on the recognition of its specific DNA sequences (Hao et al., 2011).

The QCM was already well-known and established as an analytical tool for studying adsorption phenomena at the solid-liquid interface (Martin et al., 1991; Buttry & Ward, 1992) when its potential for studying cell-substrate adhesion was recognized. It was then recognized that the adhesion of cells to the quartz surface also induced a shift in resonance frequency that was shown to be linearly correlated with the fractional surface coverage (Gryte et al., 1993; Redepenning et al., 1993). Time-resolved measurements of the resonance frequency were then used to follow the attachment and spreading of cells to the quartz surface, with extraordinary time resolution. Comparison with established cytological techniques has proven that the QCM readout reports reliably on the number of cells on the surface and the time course of adhesion (Wegener et al., 1998). Specifically, they have demonstrated that QCM is a convenient method for measuring in real time the attachment of African Green Monkey kidney cells as well as their detachment that accompanies cell death caused by either NaOH addition or virus infection. Additionally, the observed QCM responses are consistent with attached cell layers that behave as viscous films rather than rigid masses, illustrating that care must be exercised in the interpretation of QCM

Impedance analysis of cell-covered gold-film electrodes was first introduced by Giaever and Keese (Giaever & Keese, 1991, 1993), who showed that the frequency dependent electrical impedance for such a system is dependent on the impedance of the cell-free electrode, the resistance between adjacent cells, Rb, the capacitance of the cell membranes, Cm, and an additional impedance contribution that is associated with the current flow between the basal plasma membrane and the substrate. The resistance, Rb, is dependent on the width of the intercellular cleft between adjacent cells and the establishment of tight junctions, and is therefore a sensitive parameter for cell–cell contacts. Thus, impedance analysis of the shear displacement (from now on referred to as "quartz mode") and impedance analysis of the cell-covered surface electrode (referred to as "cell mode") may provide independent

**1.3 The QCM in cell biological**

measurements involving cell adhesion or binding events.

information about the establishment of cell–substrate and cell–cell contacts. A computercontrolled relay allows switching between both modes.

Pioneering works using the QCM showed that viscoelastic properties of films deposited on the sensor surface can be examined using frequency changes (Kanazawa & Gordon, 1985; Okahata et al., 1989). However, measurement of alone is not easily and specifically related to structural or conformational changes occurring at the sensor surface, especially for cytoskeletal changes that imply cellular volume and mass redistribution over the adhesion surface.  Most real scenarios are actually in between these two limits. Rodahl et al. extended the QCM technique by performing the direct monitoring of energy dissipation (D) considered a useful indicator of the viscoelastic properties of the material deposited at the sensor surface (Rodahl et al., 1996a, 1996b). Among the different QCM-D investigations of cells, it was showed that the interaction between cells and a surface produced a unique and reproducible dissipation against frequency plot, also referred to as a QCM-D signature (Fredriksson, 1998a, 1998b).

These new tools were called as the whole-cell QCM biosensor. Initial use of the QCM was for measuring chemicals in the gas phase binding the QCM surface and more recently as a tool in analytical electrochemistry.

In the past decades the QCM has been used to create biosensors. Infrequently, whole cells have been studied at the QCM surface (Gryte et al., 1993; Muratsugu et al., 1997; Wegener et al., 1998). Marx suggests the potential of this cellular biosensor for the real-time identification or screening of all classes of biologically active drugs or biological macromolecules that affect cellular attachment and cellular spreading, regardless of their molecular mechanism of action (Marx et al., 2003, 2007). The interconnected cytoskeleton structural elements depicted provide targets for drugs or macromolecules that bind and alter their structures or dynamical properties. Biosensor output is proportional to a particular detected concentration of the drug or macromolecule effector.

#### **1.4 Scope of the present study**

Applications for the QCM have been invested in our laboratory for a long-term. We combine some surface modify methods to immobilize the oligonucleotide probe on the gold electrode surface of QCM that could use to detect the PCR product of *Vibrio parahaemolyticus* and breast cancer. We study a modified antibody-coated QCM biosensor will be constructed for detecting food pathogenic bacteria *Vibrio parahaemolyticus* and to find the most suitable surface modification method. We have recently started to observe and research the cell growth process on QCM. Utilize a silver electrode QCM mass sensor to detect the physiology of cells by the plasma surface modification as a protection film (Chou et al., 2009). Develop a new method that utilizes the QCM technique to measure the tight junction of the Caco-2 cell (Chou & Yan, 2010). Using QCM to design a cell detection platform is an important application of QCM. In the process of system design and application, there still have some points, which are easily overlooked or are not understood by researchers. Most of the problems can be separated into three types. One is the cell culture environment conditions that affect the system signals, another is the

QCM as Cell-Based Biosensor 415

However, these sealed apparatuses open up the surface functional analysis. A kind of variability situation involves in a liquid media, there are some and important significant phenomena due to liquid contact. For the quartz crystal in contact with liquid, the resonant

> 1 / 2 2 ΔR = (2 π2ρl

References are also made to other types of electrochemical detection techniques, such as impedance analysis that measures both resistance and reactance (Mirsky et al., 1997). The oscillation was damped and the Q factor was significantly reduced (Auge et al., 1994). Q

2

πρ

Impedance analysis of cell-covered gold-film electrodes and the frequency dependent electrical impedance for such a system is dependent on the impedance associated with the current flow between the basal plasma membrane and the substrate (Giaever & Keese, 1991, 1993). More information about changes in dissipation (D) can be obtained via either impedance spectroscopy by recording the oscillation decay or the freely oscillating crystal after rapid excitation at resonance (Rodahl et al., 1995), the f =f0-fr and D are obtained

*ft*

*t RC*

π

where 0*f* is the resonance frequency of the crystal, and *rf* is a constant reference frequency. Another variety of the reaction from electrochemical and quartz crystal microbalance measurement provides a powerful utility in studying solution phase transformations (Bard & Faulkner, 2001). When solution phase reactions are considered, there is also a capacitive component of the current that decays exponentially in time according to the following

> *c e R*

The above mentioned equation is useful for analysis on QCM sensor. In situ localizes a nonrigid coating, the damping behavior of the crystal is also required and can be evaluated by QCM-D (Edvardsson et al., 2006), electrical impedance (Wudy et al., 2008) and transepithelial resistance (TEER). To establish QCM cell-culture instrument, it is a useful method to monitor the interactions between the cells with the surface of a non-invasive type. The attitude about the entire cells investigated with the process of spreading, separation,

*D*

ωρ η

2

ω

*q q w w*

*v*

η) A/k (3)

≈ (4)

is the angular frequency.

1 = (5)

*E I t* / ( ) Δ − = (6)

resistance change was first derived by Muramatsu et al., as shown in Eq. (3).

factor formula can be described in liquid applications as shown in Eq. (4).

*Q*

where k is the electromechanical coupling factor.

where *q v* is the velocity of the liquid at the surface and

where R is resistance (ohms) and C is the capacitance (F).

movement or ingestion (Tan et al., 2008).

directly via the relation as shown in Eq. (5):

equation, as shown in Eq. (6).

system unification or lack of communication over regulations, and the other is the overanalysis of the experimental data (Chou et al., 2009). A QCM has been constructed and used for chemical sensing and biochemical detecting. Frequency shift has a relation with mass changed in the gaseous condition. However, the velocity, density, and viscosity also cause frequency changed in liquid solution. We develop a new method and system to investigate the variable value of amplitude and frequency from the oscillator of quartz (Lee et al., 2009). A biosensor consists of the immobilized biological recognition element (e.g. antibody, DNA, enzyme, receptor, microorganism, or cell) in intimate contact with a signal transducer (electrochemical, optical, thermal, or acoustic signal) that together permit analysis of chemical properties or quantities. We show that the QCM technique is a sensitive method not only to measure quasi-static cell adhesion processes but also dynamic changes of mechanical cell properties. A new cell-based QCM biosensor system which can real-time monitor the adhesion and growth of animal cells will be developed. A QCM chip sensor can measure the frequency, amplitude, trans-epithelial resistance, and A/C impedance. These materials were all fabricated under the cell unit to monitor cell growth conditions (Lee et al., 2010).

#### **2. Electronic behavior of quartz resonators**

QCM (Quartz crystal microbalance) refers to a sensor based on a piezo-electric. A QCM can be used in fixed and immobility area, and the mass can be found while changing the surface of the QCM with the relation between mass and frequency in Sauerbrey formula (Sauerbrey, 1959). The change of frequency ( Δ*f* ) is proportional to the added mass ( Δ*M* ) Eq. (1). The characteristic can merely be adapted to special application. QCM can be used as gas detectors when coated with various materials (King, 1964).

$$
\Delta f = \frac{2f\_0^2}{\sqrt{\mu\_q \rho\_q}} \frac{\Delta M}{A} \tag{1}
$$

0*f* , μ*q* , ρ*q* , and *A* denote the specific resonant frequency, density, shear modulus and the piezoelectrically active area of quartz, respectively.

The use of biological coatings, such as enzymes and antibodies, was a natural progression from the initial QCM development. Guilbault reported an enzyme-based QCM sensor in gas phase (Guilbault, 1983). A quartz immunosensor for microbial pathogens was developed by Muramatsu et al. (Muramatsu et al., 1986). Since then, liquid QCM began to be applied to cell biology, biotechnology, immunology and electrochemistry. Kanazawaand and Gordan prospected that Δ*f* as a linear function of a square root of ρq q ×η and ρw w ×η (density, ρ and viscosity, η ), as shown in Eq. (2) (Kanazawa & Gordon, 1985). It was discovered that changes in the physical-chemical property of the contacting materials/media will result in frequency changes of the quartz crystal resonator when used in liquid phase (Muramatsu et al., 1988; Shumacher, 1990).

$$
\Delta \! \! \_{w} \approx \sqrt{\mathbb{p}\_{\text{q}} \times \mathbb{q}\_{\text{q}}} - \sqrt{\mathbb{p}\_{\text{w}} \times \mathbb{q}\_{\text{w}}} \tag{2}
$$

ρw , ηw represent the change of dissolvent in liquid phase.

system unification or lack of communication over regulations, and the other is the overanalysis of the experimental data (Chou et al., 2009). A QCM has been constructed and used for chemical sensing and biochemical detecting. Frequency shift has a relation with mass changed in the gaseous condition. However, the velocity, density, and viscosity also cause frequency changed in liquid solution. We develop a new method and system to investigate the variable value of amplitude and frequency from the oscillator of quartz (Lee et al., 2009). A biosensor consists of the immobilized biological recognition element (e.g. antibody, DNA, enzyme, receptor, microorganism, or cell) in intimate contact with a signal transducer (electrochemical, optical, thermal, or acoustic signal) that together permit analysis of chemical properties or quantities. We show that the QCM technique is a sensitive method not only to measure quasi-static cell adhesion processes but also dynamic changes of mechanical cell properties. A new cell-based QCM biosensor system which can real-time monitor the adhesion and growth of animal cells will be developed. A QCM chip sensor can measure the frequency, amplitude, trans-epithelial resistance, and A/C impedance. These materials were all fabricated under the cell unit to monitor cell

QCM (Quartz crystal microbalance) refers to a sensor based on a piezo-electric. A QCM can be used in fixed and immobility area, and the mass can be found while changing the surface of the QCM with the relation between mass and frequency in Sauerbrey formula (Sauerbrey, 1959). The change of frequency ( Δ*f* ) is proportional to the added mass ( Δ*M* ) Eq. (1). The characteristic can merely be adapted to special application. QCM can be used as gas

> 2 0 2 *q q f M f* μ ρ*A*

The use of biological coatings, such as enzymes and antibodies, was a natural progression from the initial QCM development. Guilbault reported an enzyme-based QCM sensor in gas phase (Guilbault, 1983). A quartz immunosensor for microbial pathogens was developed by Muramatsu et al. (Muramatsu et al., 1986). Since then, liquid QCM began to be applied to cell biology, biotechnology, immunology and electrochemistry. Kanazawaand and Gordan prospected that Δ*f* as a linear function of a square root of ρq q ×η and ρw w ×η (density, ρ and viscosity, η ), as shown in Eq. (2) (Kanazawa & Gordon, 1985). It was discovered that changes in the physical-chemical property of the contacting materials/media will result in frequency changes of the quartz crystal resonator when used in liquid phase (Muramatsu et

and *A* denote the specific resonant frequency, density, shear modulus and the

Δ Δ = (1)

Δ∝ − *fw* ρqq ww ×η ρ ×η (2)

growth conditions (Lee et al., 2010).

0*f* , μ*q* , ρ*q* ,

**2. Electronic behavior of quartz resonators**

detectors when coated with various materials (King, 1964).

ρw , ηw represent the change of dissolvent in liquid phase.

piezoelectrically active area of quartz, respectively.

al., 1988; Shumacher, 1990).

However, these sealed apparatuses open up the surface functional analysis. A kind of variability situation involves in a liquid media, there are some and important significant phenomena due to liquid contact. For the quartz crystal in contact with liquid, the resonant resistance change was first derived by Muramatsu et al., as shown in Eq. (3).

$$
\Delta \mathbf{R} \equiv \left( 2 \,\pi \mathcal{Q} \rho \,\eta \right)^{1/2} \mathbf{A} \mathbf{\hat{x}}^{\top} \tag{3}
$$

where k is the electromechanical coupling factor.

References are also made to other types of electrochemical detection techniques, such as impedance analysis that measures both resistance and reactance (Mirsky et al., 1997). The oscillation was damped and the Q factor was significantly reduced (Auge et al., 1994). Q factor formula can be described in liquid applications as shown in Eq. (4).

$$Q = \frac{\pi \rho\_q v\_q^2}{\sqrt{2 \alpha \rho\_w \eta\_w}} \tag{4}$$

where *q v* is the velocity of the liquid at the surface andωis the angular frequency.

Impedance analysis of cell-covered gold-film electrodes and the frequency dependent electrical impedance for such a system is dependent on the impedance associated with the current flow between the basal plasma membrane and the substrate (Giaever & Keese, 1991, 1993). More information about changes in dissipation (D) can be obtained via either impedance spectroscopy by recording the oscillation decay or the freely oscillating crystal after rapid excitation at resonance (Rodahl et al., 1995), the f =f0-fr and D are obtained directly via the relation as shown in Eq. (5):

$$D = \frac{1}{\pi ft} \tag{5}$$

where 0*f* is the resonance frequency of the crystal, and *rf* is a constant reference frequency.

Another variety of the reaction from electrochemical and quartz crystal microbalance measurement provides a powerful utility in studying solution phase transformations (Bard & Faulkner, 2001). When solution phase reactions are considered, there is also a capacitive component of the current that decays exponentially in time according to the following equation, as shown in Eq. (6).

$$I\_{\varepsilon}(t) = \frac{\Delta E}{R} e^{-t/RC} \tag{6}$$

where R is resistance (ohms) and C is the capacitance (F).

The above mentioned equation is useful for analysis on QCM sensor. In situ localizes a nonrigid coating, the damping behavior of the crystal is also required and can be evaluated by QCM-D (Edvardsson et al., 2006), electrical impedance (Wudy et al., 2008) and transepithelial resistance (TEER). To establish QCM cell-culture instrument, it is a useful method to monitor the interactions between the cells with the surface of a non-invasive type. The attitude about the entire cells investigated with the process of spreading, separation, movement or ingestion (Tan et al., 2008).

QCM as Cell-Based Biosensor 417

Fig. 2B shows that the QCM is inlaid on the ceramic substrate so that the twist force does not directly contact the chip surface. This design stabilizes the chip effectively during oscillation when the chip is connected to the incubator chamber. The gold electrode connected to the chip is behind the ceramic substrate to avoid any biotoxicity caused by line materials in the connect circuit contacting the cell culture solution. By having the ceramic substrate on the double o ring, it not only prevents solution leakage from the cell incubator chamber, but also reduces the possibility of contamination. All chip materials that contact the cells have improved biocompatibility so they do not influence the growth of cells. A Glass tank used to culture the cell and has a detection portion in the underside. Glass tank is made of Pyrex® glass and chip material choice has a good biocompatibility.

Fig. 2. Schematic diagram of the proposed QCM cell detection system. (A) Schematic diagram of the measurement system hardware setup used the QCM; (B) Schematic diagram

A Pierce oscillator uses an inverting amplifier so that its phase of 180o must be shifted to 360o through the feedback network, in order to fulfill the phase condition (Pierce, 1923). In our system, self-resonant circuit was designed with a 50% duty cycle crystal oscillator, based

All materials do not affect cell growth.

of the QCM sensor chip.

**3.2 Circuit description**

**3.2.1 Self-resonant circuit and amplitude capture**

#### **3. A construction of QCM measurement**

#### **3.1 Overview of the system Integration**

A quartz crystal microbalance cell-culture incubator system includes environmental control system, QCM detecting system and data collection system. An environmental control system is divided into two major parts, incubator and cell-container. A QCM detecting system is a real-time measurement of the shift in resonance frequency and energy dissipation due to changes in mass and viscoelastic properties. A trans-epithelial resistance is also monitored in this system. This system was designed two channels of QCM to monitor the grow cell. Use 8-bits processor (Pic18F45J10, Microchip) and a complex programmable logic device (CPLD, LCMXO640, Lattice) to construct measurement and control circuit. All signal materials can make a hand-shaking, recording and controlled via computer synchronically (Fig. 1).

Fig. 1. Schematic diagram of the proposed QCM cell detection system.

Cells can be isolated from tissues for *ex vivo* culture in several ways. Mononuclear cells can be released from soft tissues by enzymatic digestion with enzymes such as collagenase, trypsin, or pronase, which break down the extracellular matrix. Alternatively, pieces of tissue can be placed in growth media, and the cells that grow out are available for culture. There are numerous well established cell lines representative of particular cell types. Fig. 2A shows the schematic system design of this study. The system includes three parts: the cell incubator chamber, the QCM sensor chip, and the circuit system. Signals are detected by a sensor chip, stored on a personal computer (PC), and are processed by custom made software. The cell incubator chamber is made of Pyrex1 glass, together with stainless steel tongs and other accessories to sterilize the autoclave directly. The QCM biosensor used in this study was purchased from a local source (Mercury Electronics Ind. Co., Ltd., Taiwan) and only the bare crystal was fixed on a ceramic base.

A quartz crystal microbalance cell-culture incubator system includes environmental control system, QCM detecting system and data collection system. An environmental control system is divided into two major parts, incubator and cell-container. A QCM detecting system is a real-time measurement of the shift in resonance frequency and energy dissipation due to changes in mass and viscoelastic properties. A trans-epithelial resistance is also monitored in this system. This system was designed two channels of QCM to monitor the grow cell. Use 8-bits processor (Pic18F45J10, Microchip) and a complex programmable logic device (CPLD, LCMXO640, Lattice) to construct measurement and control circuit. All signal materials can make a hand-shaking, recording and controlled via computer

Fig. 1. Schematic diagram of the proposed QCM cell detection system.

Cells can be isolated from tissues for *ex vivo* culture in several ways. Mononuclear cells can be released from soft tissues by enzymatic digestion with enzymes such as collagenase, trypsin, or pronase, which break down the extracellular matrix. Alternatively, pieces of tissue can be placed in growth media, and the cells that grow out are available for culture. There are numerous well established cell lines representative of particular cell types. Fig. 2A shows the schematic system design of this study. The system includes three parts: the cell incubator chamber, the QCM sensor chip, and the circuit system. Signals are detected by a sensor chip, stored on a personal computer (PC), and are processed by custom made software. The cell incubator chamber is made of Pyrex1 glass, together with stainless steel tongs and other accessories to sterilize the autoclave directly. The QCM biosensor used in this study was purchased from a local source (Mercury Electronics Ind. Co., Ltd., Taiwan) and only the bare crystal was fixed on a ceramic base.

**3. A construction of QCM measurement**

**3.1 Overview of the system Integration**

synchronically (Fig. 1).

Fig. 2B shows that the QCM is inlaid on the ceramic substrate so that the twist force does not directly contact the chip surface. This design stabilizes the chip effectively during oscillation when the chip is connected to the incubator chamber. The gold electrode connected to the chip is behind the ceramic substrate to avoid any biotoxicity caused by line materials in the connect circuit contacting the cell culture solution. By having the ceramic substrate on the double o ring, it not only prevents solution leakage from the cell incubator chamber, but also reduces the possibility of contamination. All chip materials that contact the cells have improved biocompatibility so they do not influence the growth of cells. A Glass tank used to culture the cell and has a detection portion in the underside. Glass tank is made of Pyrex® glass and chip material choice has a good biocompatibility. All materials do not affect cell growth.

Fig. 2. Schematic diagram of the proposed QCM cell detection system. (A) Schematic diagram of the measurement system hardware setup used the QCM; (B) Schematic diagram of the QCM sensor chip.

#### **3.2 Circuit description**

#### **3.2.1 Self-resonant circuit and amplitude capture**

A Pierce oscillator uses an inverting amplifier so that its phase of 180o must be shifted to 360o through the feedback network, in order to fulfill the phase condition (Pierce, 1923). In our system, self-resonant circuit was designed with a 50% duty cycle crystal oscillator, based

QCM as Cell-Based Biosensor 419

frequency detector. The circuit structure in this embodiment of this topic is further illustrated below in detail. Fig. 4 is a circuit diagram of a measurement system. The detailed circuits of the oscillation circuit (OC), the clock generation circuit (CGC), the enable circuit (EC), the bias circuit (BC), and the sample and hold circuit (SHC) can be obtained. The switch unit (SW) can be implemented as a two-to-one changeover switch or a multiplexer. When the SW switches to the frequency scanning signal (FSS), FSS output by the CGC is transmitted to the quartz (Q) and to be scanned through the SW, so as to scan the Q, followed by generating an output of the impedance sensing signal IMS at the other end of the Q. In addition, it should be noted that the clock output signal (COS) was a generated clock of QCM resonant by the OC and the amplitude output signal (AOS) was

Fig. 4. Dual mode measurement system with frequency and impedance Analysis

A cell measurement system, particularly a cell measurement system integrated with a QCM and a technique measuring TEER, is suitable to measure the changes of the frequency and the TEER. Currently, as the techniques are improved, QCMs are gradually used as a sensor in fields such as biological and medical science. Not only are the parameters of QCMs measured, the TEER can also be measured by ion flows between a QCM electrode and an external electrode in our system. A circuit diagram of the cell measurement system is shown in Fig. 5. The cell measurement includes: a power unit (PU), an oscillation module (OM), a frequency-monitoring module (FMM), a level-shift unit (LSU), a quartz crystal sensing module (QSM), a periodic wave-generation module (PWGM), a low-pass filtration module (LPFM), and a control module (CM).The PWGM includes a resistor R1 and a third electrode (E3), and the E3 contacts with a cell lines to be

an amplified signal of IMS by the SHC.

**3.2.3 Trans-epithelial resistance circuit**

tested as TEER.