Tools and Applications of Biochemical Engineering Science

46 C. Wittmann

2.3

Experimental Design of Tracer Experiments

The aim of experimental design is to obtain maximal information on metabolic flux distributions with requested accuracy and minimal costs for labeled substrates. Admittedly, the metabolic networks are usually complex. The complexity is increased by various experimental parameters that have to be chosen. These can be grouped into tracer substrate and measurement design. Tracer substrate design includes position and labeling degree in the tracer substrate which can be singly or multiply labeled or a mixture of differently labeled compounds. The right choice of label in the tracer substrate is very critical for the quality of the obtained information on intracellular flux distributions [23, 26]. In the measurement design those labels are selected which are most informative to determine the flux parameter of interest. This can significantly reduce the experimental effort in tracer experiments [27]. 13C tracer experimental design is illustrated for the flux partitioning ratio between PPP and glycolysis (FPPP). This flux parameter is of central interest in different biotechnological processes with industrial relevance. The PPP is the major source for NADPH formation, which is required in substantial amounts in lysine or penicilline production. In other cases the product itself, e.g. riboflavine, or an important precursor of the product, e.g. in phenylalanine production, is synthesized via the PPP. For simplicity reasons, the reactions in the PPP and the reaction of glucose 6-phosphate isomerase are assumed to be irreversible, and natural isotopes are

neglected in the example. The key for the determination of FPPP is the specificity of 6-phosphogluconate dehydrogenase, which exclusively releases the C1

from its substrate 6-phosphogluconate, equal to the C1 of the applied glucose, as CO2 . With 1-13C glucose as tracer substrate the 13C label from position C1 is thus quantitatively removed in the initial PPP reactions, whereas it is conserved in the glycolysis (Fig. 2).

The labeling of pyruvate can be used to visualize FPPP . 100% flux through the glycolysis results in the formation of equimolar amounts of non-labeled and single labeled pyruvate, whereas for 100% flux through the PPP an exclusive formation of non-labeled pyruvate occurs. Flux partitioning ratios between these two extremes cause a defined ratio between non-labeled and single labeled pyruvate. With the simplifications and assumptions chosen, the relative flux into the PPP can be obtained from the pyruvate labeling Im +1/m by a rather simple equation (Eq. 4).

Φ		=		1 -	Im+ 1/m, Pyruvate	(4)
	PPP		1+ 2		3 I m+ 1/m, Pyruvate

The calculation of corresponding analytical equations for realistic conditions, considering bidirectional fluxes, natural isotopes, or other tracer substrates such as multiply labeled compounds is much more complex or even impossible, with respect to the non-linearity of such systems. The same holds for alternative metabolites applied for the labeling measurement, such as glutamate or lysine, which are located in the network at a far distance to the flux node of inte-

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1-13C glucose

CO2

Fig. 2. Experimental design of a 13C tracer experiment for the determination of the flux partitioning ratio between pentose phosphate pathway and glycolysis (FPPP): 13C label distribution from 1-13C glucose through the network with 13C atoms (black) and 12C atoms (white)

rest and of which the carbon skeleton is subjected to substantial alterations in the metabolic reactions in between. Computer based tools for efficient experimental design of 13C tracer experiments have been recently developed. They are implemented in general modeling frameworks of metabolic networks and allow the optimal design of tracer experiments [23, 26]. As a great advantage, the design can be carried out under realistic flux situations including all isotopomer balances of the network and bidirectional fluxes. With such tools, a large number of different experimental approaches can be compared in short time. As an example, the dependence of Im+1/m of pyruvate on FPPP under realistic flux conditions, including bidirectional fluxes in the network, 99% 1-13C glucose and natural isotopes can be easily calculated (Fig. 3).

Obviously, the behavior of the network under realistic conditions is significantly different from the one, predicted in the simplified example in Eq. (4). Calculation of FPPP from the pyruvate labeling via the simplified approach thus leads to errors in the result.

An important task of experimental design studies is the characterization and visualization of the identified optimal experimental approach. For this purpose, quantitative parameters were suggested as output from such simulation studies, that directly provide quantitative information on the suitability of a certain experimental design and easily allow the identification of the optimal one among a large number [23, 26]. Wiechert and coworkers have developed a statistical tool for the design of tracer experiments. Considering measurement errors of the labeling data and parameter covariance matrices, different experimental approaches can be compared by statistical quality measures and approaches of choice can be computed [23]. Wittmann and Heinzle [26] suggested flux sensi-

48	C. Wittmann

Fig. 3. Change of the intensity ratio Im+1/m of pyruvate with variation of the flux partitioning ratio between pentose phosphate pathway and glycolysis (FPPP). The curves were calculated from the analytical expression (Eq. 4) of a simplified model and from computer based modeling considering a realistic flux situation with partitioning ratios and bidirectional fluxes and natural isotopes (Wittmann and Heinzle, 2001b)

tivities S for the quantitative evaluation of a experimental design. The flux sensitivity S for the quantification of a flux parameter F via an intensity ratio I can be expressed via the corresponding partial derivative for a certain flux situation (Eq. 5).

S I		=	∂ I			(5)
Φ	i		∂ Φ	i		Φ 1 ,Φ 2 ...Φ i

Using this approach, general guidelines for experimental design of 13C-tracer studies with MS could be shown for the central metabolism of Corynebacterium glutamicum comprising various flux scenarios and tracer substrates [26].

To summarize, among the benefits of general experimental design approaches are (i) the comparison of various different experimental approaches, (ii) the identification of an optimal approach by quantitative means,(iii) the possible consideration of the influence of MS measurement errors on the predicted precision of flux analysis, and (iv) the possible extension of the design to various flux scenarios of the regarded network and (v) the applicability to different networks. Unfortunately, the chosen modeling approaches in the literature are often rather specific and based on analytical equations. With such frameworks only a limited experimental design of tracer experiments can be carried out. The identification of a suitable experimental approach is then restricted to qualitative criteria. The quantitative evaluation and comparison of various different experimental conditions and the identification of an optimal experimental design is usually not possible.

Besides 13C, also other stable isotopes, such as 18O, 2H, or 15N have been applied. An example for the use of 18O is the quantification of the flux partitioning

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Fig. 4. Experimental design of an 18O tracer experiment for the determination of the flux partitioning ratio between pentose phosphate pathway and glycolysis (FPPP): 18O label distribution from 1-18O glucose through the network

ratio FPPP with 1-18O glucose. The estimation of FPPP is based on the measurement of mass isotopomer pools of CO2 [32]. As shown in Fig. (4), the 18O label is exclusively released as C16O18O in the initial reactions of the PPP, whereas it ends up in H218O in the glycolytic enolase reaction from 2-phosphoglycerate to phosphoenolpyruvate. Information on the relative flux of carbon through the PPP can be obtained from the intensity ratio between C16O18O and C16O2.

15N labeled tracers are frequent substrates for in vivo studies on amino acid metabolism and protein synthesis [33–36]. Deuterium labeled compounds are comparably cheap, but care has to be taken concerning exchange reactions with hydrogen atoms from the surrounding solvents [37]. 6,6-2H2 and 2-2H labeled glucose [38] and 1-2H-galactose [39] were used as substrates for in vivo tracer experiments on the hepatic glucose metabolism in humans. Deuterium labeled water (D2O) was applied for in vivo studies of fatty acid and cholesterol synthesis [40]. D2O incorporation studies can also serve for flux analysis of gluconeogenesis [41].

2.4

Parameter Estimation

The flux parameters are usually estimated from the 13C tracer studies data by minimization of the deviations between experimental and modeled labeling data corresponding to the optimized set of fluxes. In general, the isotopomer balance equations are non-linear and numerical routines are used for their so-

50	C. Wittmann

Fig. 5. Estimation of the flux partitioning ratio between pentose phosphate pathway and glycolysis (FPPP) from the lysine intensity ratio Im+1/m = 1.11 using the optimization function fmincon implemented in Matlab. The numbered data points indicate the results obtained through the different iterations. Starting from FPPP = 0.1, the optimal fit of experimental and calculated labeling was obtained after 14 iterations

lution. In the used iterative algorithms the flux parameters of interest, such as flux partitioning ratios or reversibilities of bidirectional fluxes, are varied by the optimization function starting from initial values until an acceptable agreement between measured and calculated labeling pattern is achieved. Usually, the optimization problem with several parameters estimated simultaneously from different labelings is multidimensional. The procedure of parameter estimation is illustrated by a simple example with only one parameter to be determined, which can be easily displayed in graphical form, the estimation of the flux partitioning ratio FPPP from the experimental lysine intensity ratio Im+1/m = 1.11, taken from [27], using the optimization function fmincon implemented in MATLAB via minimization of the relative deviation (s) between experimental and modeled labeling. All other flux parameters are held constant in this example. Starting with an initial guess (data point no. 1 with FPPP = 0.1) the optimization function calculates the corresponding labeling data, which is

Im+1/m, Lysine = 2.19 and compares it to the experimental value (Fig. 5).

The result of FPPP = 0.744 corresponding to the best fit of experimental to calculated lysine labeling is obtained within 14 iterations. Using MS, the labeling data are mainly molar enrichments [17] or intensity ratios of mass isotopomers [26, 27]. Different optimization functions such as gradient or adaptive random search functions are available. To increase the probability of the identification of a global optimum for the solution, the convergence is usually tested for different initial guesses. If several intensity ratios are fitted simultaneously, the sum of the squares of the relative deviations (s) between experimental (Iexp) and modeled (Imod) intensity ratios of mass isotopomers corresponding to the optimized set of fluxes is minimized (Eq. 6).

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	I		exp	− I		2
s = ∑					mod		(6)
				I mod

In case, the network is overdetermined a least square approach is possible. The information obtained by MS from 13C tracer studies can be combined with metabolite balancing for the estimation of flux parameters [25, 27]. Measurement errors can be included to predict uncertainties for the obtained flux parameters [23].

3

Mass Spectrometry Methods

Mass spectrometry (MS) has changed its appearance in the scientific world considerably during recent years. At the beginning of the 20th century first applications in physics were described. Gradually MS methods entered more and more into the fields of biology, biochemistry and biomedicine and became a major tool in life sciences. Mass spectrometers consist of a sequence of functional units for sample introduction, ion formation, mass separation, and detection. The data handling is carried out by computers. Currently, a variety of different mass spectrometric techniques are used for the analysis of biomolecules (Fig. 6).

To illustrate and evaluate the different methods available, the following chapter gives a short overview on the most important methods for sample introduction, ion formation, and mass separation with respect to metabolic flux analysis. For a more detailed insight into modern MS methods the reader is addressed to recent overviews [e.g. 42–44].

3.1

Sample Introduction and Ion Formation

The dominating method of ion formation in metabolic flux analysis is electron impact. It might be supplemented in the future by novel methods, such as matrix assisted laser desorption and electrospray. Additional techniques such as chemical ionization, fast atom bombardment or inductively coupled plasma ionization are only of minor importance and not further discussed in this context.

Fig. 6. Overview on different mass spectrometry methods

52 C. Wittmann

3.1.1

Electron Impact

Electron impact (EI) is probably the most widely used technique for ionization in MS. It is characterized by a high sensitivity, reproducibility and stability. The ionization is based on thermally produced electrons, which orthogonally cross the analyte stream and create mainly positive ions by extracting electrons from the analyte molecules (Fig. 7).

The resulting spectra from EI usually contain a number of fragments, providing extensive structural information about the analyte. A disadvantage of the observed fragmentation is eventually occurring isobaric overlay from different compounds in the analysis of sample mixtures, which often requires a separation step prior to the MS analysis. For this purpose the coupling of a GC with the ion source of the mass spectrometer via capillary inlet is a well established technique. Volatiles can be selectively introduced into EI mass spectrometers via pervaporation membranes. The principle and application of this technique, called membrane introduction (MI) MS was recently reviewed [45]. The accuracy of intensity ratio measurements by EI MS is about 0.1–0.5% [4, 8].

A specific variant of EI MS is isotope ratio (IR) MS [46]. It is based on electron impact ionization with maximized ionization probability. IR MS is limited to the analysis of gases of high volatility and low reactivity such as CO2 , N2 or SO2 . The analytes of interest thus have to be transformed into one of these gases before introduction into the IR MS. Information on the position of 13C labelings in the analyte can be only obtained, if all carbons are isolated position specific and subsequently combusted. In this context Corso and Brenna [47] showed position specific 13C analysis by IR MS for methylpalmitate through pyrolytic fragmentation. IR MS exhibits an extremely high precision of

±0.00001% for the isotope ratio measurement and is optimal to quantify low label enrichments [48]. This is especially important for in vivo studies with ani-

Fig. 7. Schematic view of electron impact ionization

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mals or humans. IR MS is often applied in combination with gas chromatography combustion. Recently LC coupling has been also realized [49].

3.1.2

Laser Desorption Ionization

A breakthrough in laser desorption techniques was reached by the observation, that compounds, that were not ionized in pure form, could be ionized in a mixture with a compound of high absorption capacity for the laser energy. This enhancement of ionization efficiency by selected, so called matrix compounds, initiated the development of matrix assisted laser desorption ionization (MALDI) [50, 51], which is nowadays broadly applied for the analysis of biomolecules [52]. For sample preparation, usually 0.1 to 1 µl droplets of sample and matrix solution are mixed and pipetted on selected positions of a plate, normally made of stainless steal, gold or glass, and subsequently dried. The plates with the crystallized sample spots are then introduced into the vacuum chamber of the instrument. The procedure of sample preparation can be automated. The crystals are irradiated by a pulsed laser. As a result a plasma is formed, causing vaporization and ionization of the analyte molecules. The ions are then accelerated by a strong electric field. The ionization procedure is soft and fragmentation does usually not occur. MALDI MS can be operated alternatively in positive or in negative mode by appropriate setting of the voltages of the accelerating electric field. The operation mode of choice depends on the target analyte. Compounds with electronegative or negatively charged functional groups, such as hydroxyl or carboxyl groups, respectively, are better ionized in the negative mode, whereas the positive mode is more suitable for basic compounds. MALDI MS is nowadays almost exclusively applied for the analysis of biopolymers. However, it has also been successfully used for low molecular weight compounds [18, 53, 54]. MALDI MS is a rapid, convenient and robust method. Automatization techniques for sample preparation and data accumulation are available. Due to the pulsed laser, it is mainly combined with time-of-flight analyzers. MALDI is not as easily compatible with liquid chromatography, as ESI. However, LC coupling has been established [55]. The accuracy of MALDI MS with standard deviations of about 1–5% for intensity ratio measurements is currently lower compared for example to EI MS, but will be surely increased during further improvements of this novel approach.

3.1.3

Electrospray Ionization

Different types of instrumentation have been developed to introduce liquid samples into the MS. Since Fenn has shown that molecular ions can be formed from liquids sprayed at atmospheric pressure in high electric fields, electrospray ionization (ESI) MS has gained increasing popularity for the analysis of biological samples [56]. In an electrospray inlet, the liquid sample is usually emitted as a spray from a capillary at a high potential compared to the mass analyzer into the electric field in front of the mass analyzer (Fig. 8).

54

C. Wittmann

Fig. 8. Schematic view of electrospray ionization

The optimization of the process in recent years, led to defined ion formation with solvent evaporation and complete desolvatation of analyte ions, which are then accelerated towards the mass separator. Analyte molecules often form multiply charged ions. ESI can be carried out both in positive and in negative mode. The sample introduction can be performed with microscale tips mainly made of fused silica capillaries, which are inexpensive and available in various sizes and geometric forms. Recently, nanospray technologies as microvariants of ESI with increased sensitivity were developed, which allowed the analysis of extremely small sample amounts [57].

Alternatively, the mobile phase of a high pressure liquid chromatography or a capillary electrophoresis system can be directly sprayed into the MS [58, 59]. An advantage of ESI MS is its compatibility with tandem MS techniques. ESI is most suitable for charged analytes, whereby uncharged and unpolar compounds may be difficult to be analyzed. ESI MS is limited by its high sensitivity to contaminants such as alkali metals or basic compounds. Non-volatile buffers frequently applied in liquid chromatography and detergents can cause efficiency problems in the subsequent ionization and require frequent cleaning.

3.2

Mass Separation

The most commonly used mass separators are quadrupoles, ions traps and time-of-flight analyzers, for which the principle of mass separation is discussed below. Additionally, other types such as magnetic sector field or Fourier-trans- form cyclotron-resonance instruments are available.

3.2.1

Quadrupole

Quadrupoles are the most commonly used type of mass separator in MS. The operation of quadrupoles is based on the motion of ions in oscillating electric fields. A quadrupole consists of four parallel rods of about 25 cm length each,

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whereby opposite rods are electrically connected. At a certain voltage between the rods, only analyte molecules of a distinct mass to charge ratio can pass, whereas ions of different mass to charge ratios are subjected to oscillations, which cause their collision with the rods. Variation of the voltage between the rods creates an oscillating radio-frequency field. The quadrupole thus works as a mass filter. It allows a fast scan over the whole mass range of the instrument within a few seconds. The short time needed for a full scan is especially important, when the MS is coupled to a GC eluting narrow peaks, that have to be scanned several times each. The sensitivity of a quadrupole detector can be significantly enhanced by selected ion monitoring (SIM), whereby only selected masses are sequentially measured with frequencies of 0.1 to 2 seconds each. The number of collected ions for the selected masses is increased by a factor of 102–103 in comparison to the scan mode. MS/MS can be performed by operating three quadrupoles in series, named triple stage quadrupole (TSQ) MS. In a TSQ isolation, collision and mass analysis of ions are taking place in different parts of the instrument (tandem in space). The first and the third quadrupole operate with a combination of direct current voltages and radio frequency, whereas the second stage quadrupole is only operated in the RF mode, mainly serving as collision cell. Parent ions selected by the first stage quadrupole are subjected to collision induced dissociation (CID) by collision with inert gas molecules (such as argon or helium) in the second stage. From the daughter ions formed through unimolecular fragmentation selected ones can be monitored.

3.2.2

Ion Trap

Ion traps are quadrupoles with a specific operation mode, by which ions can be trapped inside the high frequency field for a short time [60]. The field is usually formed via a ring shaped electrode. By varying the amplitude of the frequency, ions can be extracted from the field and directed towards a detector. The amplitude corresponds to the mass of the ions that loose their stability in the field. Limitations of ion traps are the limited dynamic range, the dependence of the quality of the mass spectrum on many operational parameters and possible artifacts in the mass spectra. Ion traps can be applied in combination with MALDI or ESI techniques. Manipulating the ions by using current voltage and radiofrequency electric fields in a series of carefully timed events provides some unique capabilities, such as extended MS/MS experiments, high resolution, and high sensitivity. In MS/MS analysis with ion traps a series of different steps are performed sequentially in the same space (tandem in time). Ions entering the trap e.g. from an ESI source, are trapped and allowed to “cool” by collision with the bath gas of the trap, followed by additional manipulation steps for collisional activation and isolation. MSn techniques with multiple stages of isolation and fragmentation can be applied.