- Email: [email protected]
continuous-flow method for kinetic determinations
ANALYTICA
CHIMICA ACM ELSEVIER
Analytica Chimica Acta 309 (1995) 277-282
A stopped-flow/continuous-flow method for kinetic determinations Yun-Sheng Hsieh, S.R. Crouch Department
*
of Chemistry, Michigan State Unicersiiy, East Lansing, MI 48824, USA
Received 1 August 1994; revised 11 January 1995; accepted 13 January 1995
Abstract A simple stopped-flow/continuous flow method is introduced to acquire kinetics information and to make kinetic determinations. The technique uses a photometric detector placed within the sample loop of a stopped-flow/continuous flow system. Several different carrier streams (aqueous fluids, organic solvents and air bubbles) were investigated. The analytical performance of the system is illustrated with the enzymatic determination of glucose in wine and serum samples. Keywords:
Flow system; Kinetic methods
1. Introduction Kinetic methods of analysis have become increasingly popular in many areas of analytical and bioanalytical chemistry. This can be seen in several recent review articles [l-5] and books [6,7] on the subject. For studying the kinetics of slow reactions or for kinetic methods of analysis, many approaches have been proposed including several flow-based systems as indicated in our previous paper [8]. Of these techniques, stopped-flow measurements for extracting complete response curves and implementing kinetic determinations by flow injection (FI) [9,10] and air-segmented continuous flow (ASCF) systems [8] are quite promising for future development due to
* Corresponding
author
0003-2670/95/$09.50 0 1995 Elsevier Science B.V. All rights reserved SSDI 0003-2670(95)00069-O
the ease of automation of the instrument operation and data handling. In this work, we demonstrate a simple, rapid and inexpensive stopped-flow/continuous flow technique which uses an injection valve with the detector placed within the sample loop. With automated sample introduction and cleanup, the proposed system is capable of obtaining reaction progress curves for a given reaction mixture and performing kinetic determinations. The use of buffer solutions, organic solvents and air bubbles as carrier streams for the proposed stopped-flow/continuous flow system is reported. An analytical application of the system is illustrated with a kinetic method, based on enzymatic reactions, for glucose determinations in wine and serum samples. Results for wine samples were obtained using different carriers; results for standard serum samples are compared with manufacturer’s values.
278
K-S. Hsieh, S.R. Crouch /Analytica
Chimica Acta 309 (1995) 277-282
2.2. Procedures
Fig. 1. Schematic diagrams of the stopped-flow system. Samples and reagent are introduced directly (A) and indirectly (B) through the pump.
2. Experimental 2.1. Apparatus and reagents Schematic diagrams of the proposed stoppedflow/continuous flow system are shown in Fig. 1. The direct introduction method shown in Fig. 1A was employed throughout. Flow rates were controlled by appropriate choice of pump settings and flow-rated pump tubes (Technicon) as reported elsewhere [B]. The instrumentation for pumping, detection and data collection has been described previously [ 111. The glucose oxidase/Trinder reaction [B] was employed for the enzymatic determination of glucose. Absorbance measurements were made at 510 nm. The experiments were run at ambient temperature. All chemicals (reagent grade) were used without additional purification. The glucose standard solutions, composite enzyme solution, phosphate buffer and diluted wine and serum samples were prepared as reported elsewhere [B].
For stopped-flow experiments without chemical reaction, quinonimine dye samples (collected as the product of Trinder reaction [8,12]) were aspirated through the peristaltic pump into the sample loop of a six-port rotary injection valve. When the valve is in the “ load’ ’ position, the sample solutions are pumped through the sample loop and the flowcell of the detector to waste, and the carrier stream flows to waste. While in the “drain” position, the entire sample slug is propelled to waste by the carrier stream. The sample volume that fills the loop is a function of loop size and the length of the mixing tube between the tee and detector. Larger loop sizes, and longer tube lengths lead to more sample solution being consumed in determinations. For kinetic measurements, the sample stream was halted by turning off the pump for a period of time after the absorbance achieved a plateau while the valve was in the load position. After stopping the flow, the rate of change of absorbance for a trapped segment was observed. Reaction rates were obtained by measuring the slope of the absorbance vs. time plots after the flow was halted. After measurement, sample solution was washed out of the system with the carrier stream by switching the valve to the drain position. After washing, the absorbance signal returns to the baseline for the next measurement, the valve was switched back to the load position and the flow was halted after the detector signal reached the plateau. The wine and serum samples were diluted with phosphate buffer [B]. The diluted wine samples were tested here with buffer and air-carrier streams. A dye sample was employed to test the feasibility study of using the system with such carrier streams as phosphate buffer, organic solvents and air.
3. Results and discussion
3.1. Effect offzow rate The characteristics of the proposed stopped-flow system are analogous to those of the stoppedflow/air-segmented continuous flow (ASCF) system [B]. The influence of such important factors as delay time before stopping the flow, residence times on
Y-S. Hsieh, S.R. Crouch/Analytics
measurements and temperature and flow rate on peak height should be identical for both systems. In this work, the effect of flow rate on peak height was investigated with and without chemical reaction. To characterize this effect, sample and reagent were continuously aspirated into the sample loop at different flow rates, and the product was monitored. The effect of carryover is negligible for most measurements as indicated in Fig. 2A. The time required to reach the steady state absorbance is a function of flow rate. Higher flow rates yield smaller residence times, and the steady state absorbance plateau is
A.
279
Chimica Acta 309 (1995) 277-282
reached quickly. For a reacting solution, the steady state absorbance, as expected, is a function of the residence time (reaction time) which is determined by the flow rate and the tubing length as shown in Fig. 2B. Here, the reaction rates are dependent on the concentration of analyte, reagent and temperature. Replicate measurements made by switching the valve back and forth, yield response curves that are a function of valve positions at a constant flow rate as shown in Fig. 3A. Rate measurements were made by stopping the flow as each plateau was achieved as shown in Fig. 3B. As indicated in Fig. 3B, the
LOtId
rhm
I
0.25,
*
0.20 0.15 E 5 -E O.lOSI s 0.05 -
0.00
_I 7”
0
10
Ho
60
In0
Time (se-z)
B. 0.06
Load
lhl”
*
1 0.06 -
1
1
I
I
0
20
40
I
TirE kc) Fig. 2. Response curves at steady state for the proposed system: (A) without chemical (B) with glucose oxidase/Trinder reaction at different flow rates: (a) 0.98 ml/min; ml/min.
I
I
I
80
100
120
reaction (quinonimine dye samples were used) and (b) 0.56 ml/min; (c) 0.33 ml/min; and (d) 0.16
Y-S. Hsieh, S.R. Crouch /Analytica
280
throughput rate was over 60 samples/h. Because of low sample dispersion, this stopped-flow/continuous flow allows the simple extraction of kinetics information with little influence of dispersion-affected variables. The stopping time is unimportant as compared to stopped-flow/flow injection (FI) methods. 3.2. Effect of carrier streams There have been several previous attempts to use an immiscible fluid carrier and air to transport a
Chimica Acta 309 (1995) 277-282
liquid sample to a detector. Petersen and Dasgupta [13] adapted air as the carrier in a continuous flow analysis system with high throughput rates and low waste generation. Attiyat and Christian [14,1.5] used air and organic solvents as carrier streams to lower the sample dispersion and to enhance the sensitivity of determinations in an FI/atomic absorption spectrometry system. In this work, we used an air-carrier technique to limit dispersion between the sample and carrier phases and to minimize consumption of sample and reagent. The dispersion between the two phases is independent of flow rate. However, smaller
A. 0.23
Load
Drain
Time (se4
Ii
0.06
I
lmin
Time @EC) Fig. 3. Typical cycles of absorbance vs. time for enzymatic the flow and (B) with stopping the flow.
glucose determinations
using a buffer as the carrier stream: (A) without stopping
Y.-S. Hsieh, S.R. Crouch /Analytica D
A.
LDL
L
D I
I
Chimica Acta 309 (1995) 277-282 0
,
I Air
1
0.9 8
5i -i?
w 2
0.6
1
0
281
-
segments
Liquid segments
1
I
I
I
I
50
100
1M
200
2.w
Time bed B. 1.0
D
-
L
,
D,
L
I
I
D -1
P 9
Air segments
I
0.8
E %
L
-
0.6
0.4
0.2
r
0.0 Time
Table 1 Determination Wine sample
1 2 3 ’ Air-carrier
segmcnls
(set)
Fig. 4. Repetitive cycles of absorbance vs. time for enzymatic glucose determinations the flow and (B) with stopping the flow (D = drain and L = load).
flow rates yield longer residence times. A dramatic change in absorbance occurs when air segments enter the flow cell, because they reflect most of the source intensity, and the transmittance falls to near zero [16]. Organic solvents such as acetone, ethanol,
Liquid Cv
using air as the carrier stream: (A) without stopping
methanol and methyl isobutyl ketone (MIBK) were also tried as carrier streams. However, no noticeable improvements in terms of detector response were found. By switching valve positions back and forth for replicate kinetic determinations of glucose, re-
of glucose in wine samples ‘. Glucose (%o)
R.S.D. (%I
Air-carrier
Buffer-carrier
Air-carrier
Buffer-carrier
0.44 0.46 0.019
0.45 0.46 0.014
1.15 1.61 1.46
3.88 1.64 0.96
results for n = 4, buffer-carrier
for n = 3.
282
Y-S. Hsieh, S.R. Crouch/Analytics
sponse curves of the air-carrier system with and without stopping the flow are shown in Fig. 4. For kinetic measurements, the flow was stopped soon after each detector signal in the liquid segment reached the plateau. The reaction rate is measured as the slope of the absorbance-time curve after the flow is stopped. The R.S.D. was < 3% for glucose determinations.
Chimica Acta 309 (1995) 277-282
method, the glucose concentration in a standard serum sample was determined. The results show good agreement (< 8% error) with manufacturer’s reported mean values. The consumption of sample and reagent for each kinetic determination by the proposed method is small (a few ~1, associated with the size of the sample loop). The entire system is inexpensive and easy to operate and automate.
3.3. Glucose determinations
References One of the goals of this work was to apply the simple stopped-flow procedure in practical determinations. Therefore, kinetic determinations of glucose in wine samples were performed and compared with different carrier streams. Linear calibration curves with correlation coefficients r = 0.9992 (buffer carrier) and 0.9993 (air-carrier) were obtained over a concentration range of lo-80 ppm glucose. Results are presented in Table 1 for wine samples. Except for wine sample No. 3, which had a quite low glucose concentration, identical results were obtained by both the buffer and air carrier methods (Student’s t-test, 95% confidence level). Results for wine samples 1 and 2 were also identical at the 95% confidence level to results obtained by the hybrid air-segmented flow injection technique [17]. The precision of glucose determinations was also quite good with R.S.D.s less than 4% (Table 1). These findings support the hypothesis that the air carrier method can achieve similar results for kinetic determinations as the buffer carrier method. In order to test the accuracy of the proposed
[l] S.R. Crouch, Anal. Chim. Acta, 283 (1993) 453. [2] B. Quencer and S.R. Crouch, Crit. Rev. Anal. Chem., 24 (1993) 243. [3] H.L. Pardue, Anal. Chim. Acta, 216 (1989) 69. [4] D. Perez-Bendito, Analyst, 115 (1990) 689. [5] H.A. Mottola and D. Perez-Bendito, Anal. Chem., 64 (1992) 407R. [6] H.A. Mottola, Kinetic Aspects of Analytical Chemistry, Wiley, New York, 1988. [7] D. Perez-Bendito and M. Silva, Kinetic methods in Analytical Chemistry, Ellis Horwood, Chichester, 1988. [B] Y.S. Hsieh and S.R. Crouch, Anal. Chim. Acta, 284 (1993) 159. [9] J. Ruzicka and E.H. Hansen, Flow Injection Analysis, 2nd edn., Wiley, New York, 1988. [lo] J. Ruzicka and T. Gubeli, Anal. Chem., 63 (1991) 1680. [ll] C.L.M. Stults, A.P. Wade and S.R. Crouch, Anal. Chim. Acta, 192 (1987) 301. [12] D. Barham and P. Trinder, Analyst, 97 (1972) 142. [13] K. Petersen and P.K. Dasgupta, Talanta, 36 (1989) 49. [14] A.S. Attiyat and G.D. Christian, Anal. Chem., 56 (1984) 439. [15] A.S. Attiyat and G.D. Christian, Talanta, 31 (1984) 463. [16] C.J. Patton, M. Rabb and S.R. Crouch, Anal. Chem., 54 (1982) 1113. [17] Y.S. Hsieh and S.R. Crouch, Anal. Chim. Acta, in press.
CHIMICA ACM ELSEVIER
Analytica Chimica Acta 309 (1995) 277-282
A stopped-flow/continuous-flow method for kinetic determinations Yun-Sheng Hsieh, S.R. Crouch Department
*
of Chemistry, Michigan State Unicersiiy, East Lansing, MI 48824, USA
Received 1 August 1994; revised 11 January 1995; accepted 13 January 1995
Abstract A simple stopped-flow/continuous flow method is introduced to acquire kinetics information and to make kinetic determinations. The technique uses a photometric detector placed within the sample loop of a stopped-flow/continuous flow system. Several different carrier streams (aqueous fluids, organic solvents and air bubbles) were investigated. The analytical performance of the system is illustrated with the enzymatic determination of glucose in wine and serum samples. Keywords:
Flow system; Kinetic methods
1. Introduction Kinetic methods of analysis have become increasingly popular in many areas of analytical and bioanalytical chemistry. This can be seen in several recent review articles [l-5] and books [6,7] on the subject. For studying the kinetics of slow reactions or for kinetic methods of analysis, many approaches have been proposed including several flow-based systems as indicated in our previous paper [8]. Of these techniques, stopped-flow measurements for extracting complete response curves and implementing kinetic determinations by flow injection (FI) [9,10] and air-segmented continuous flow (ASCF) systems [8] are quite promising for future development due to
* Corresponding
author
0003-2670/95/$09.50 0 1995 Elsevier Science B.V. All rights reserved SSDI 0003-2670(95)00069-O
the ease of automation of the instrument operation and data handling. In this work, we demonstrate a simple, rapid and inexpensive stopped-flow/continuous flow technique which uses an injection valve with the detector placed within the sample loop. With automated sample introduction and cleanup, the proposed system is capable of obtaining reaction progress curves for a given reaction mixture and performing kinetic determinations. The use of buffer solutions, organic solvents and air bubbles as carrier streams for the proposed stopped-flow/continuous flow system is reported. An analytical application of the system is illustrated with a kinetic method, based on enzymatic reactions, for glucose determinations in wine and serum samples. Results for wine samples were obtained using different carriers; results for standard serum samples are compared with manufacturer’s values.
278
K-S. Hsieh, S.R. Crouch /Analytica
Chimica Acta 309 (1995) 277-282
2.2. Procedures
Fig. 1. Schematic diagrams of the stopped-flow system. Samples and reagent are introduced directly (A) and indirectly (B) through the pump.
2. Experimental 2.1. Apparatus and reagents Schematic diagrams of the proposed stoppedflow/continuous flow system are shown in Fig. 1. The direct introduction method shown in Fig. 1A was employed throughout. Flow rates were controlled by appropriate choice of pump settings and flow-rated pump tubes (Technicon) as reported elsewhere [B]. The instrumentation for pumping, detection and data collection has been described previously [ 111. The glucose oxidase/Trinder reaction [B] was employed for the enzymatic determination of glucose. Absorbance measurements were made at 510 nm. The experiments were run at ambient temperature. All chemicals (reagent grade) were used without additional purification. The glucose standard solutions, composite enzyme solution, phosphate buffer and diluted wine and serum samples were prepared as reported elsewhere [B].
For stopped-flow experiments without chemical reaction, quinonimine dye samples (collected as the product of Trinder reaction [8,12]) were aspirated through the peristaltic pump into the sample loop of a six-port rotary injection valve. When the valve is in the “ load’ ’ position, the sample solutions are pumped through the sample loop and the flowcell of the detector to waste, and the carrier stream flows to waste. While in the “drain” position, the entire sample slug is propelled to waste by the carrier stream. The sample volume that fills the loop is a function of loop size and the length of the mixing tube between the tee and detector. Larger loop sizes, and longer tube lengths lead to more sample solution being consumed in determinations. For kinetic measurements, the sample stream was halted by turning off the pump for a period of time after the absorbance achieved a plateau while the valve was in the load position. After stopping the flow, the rate of change of absorbance for a trapped segment was observed. Reaction rates were obtained by measuring the slope of the absorbance vs. time plots after the flow was halted. After measurement, sample solution was washed out of the system with the carrier stream by switching the valve to the drain position. After washing, the absorbance signal returns to the baseline for the next measurement, the valve was switched back to the load position and the flow was halted after the detector signal reached the plateau. The wine and serum samples were diluted with phosphate buffer [B]. The diluted wine samples were tested here with buffer and air-carrier streams. A dye sample was employed to test the feasibility study of using the system with such carrier streams as phosphate buffer, organic solvents and air.
3. Results and discussion
3.1. Effect offzow rate The characteristics of the proposed stopped-flow system are analogous to those of the stoppedflow/air-segmented continuous flow (ASCF) system [B]. The influence of such important factors as delay time before stopping the flow, residence times on
Y-S. Hsieh, S.R. Crouch/Analytics
measurements and temperature and flow rate on peak height should be identical for both systems. In this work, the effect of flow rate on peak height was investigated with and without chemical reaction. To characterize this effect, sample and reagent were continuously aspirated into the sample loop at different flow rates, and the product was monitored. The effect of carryover is negligible for most measurements as indicated in Fig. 2A. The time required to reach the steady state absorbance is a function of flow rate. Higher flow rates yield smaller residence times, and the steady state absorbance plateau is
A.
279
Chimica Acta 309 (1995) 277-282
reached quickly. For a reacting solution, the steady state absorbance, as expected, is a function of the residence time (reaction time) which is determined by the flow rate and the tubing length as shown in Fig. 2B. Here, the reaction rates are dependent on the concentration of analyte, reagent and temperature. Replicate measurements made by switching the valve back and forth, yield response curves that are a function of valve positions at a constant flow rate as shown in Fig. 3A. Rate measurements were made by stopping the flow as each plateau was achieved as shown in Fig. 3B. As indicated in Fig. 3B, the
LOtId
rhm
I
0.25,
*
0.20 0.15 E 5 -E O.lOSI s 0.05 -
0.00
_I 7”
0
10
Ho
60
In0
Time (se-z)
B. 0.06
Load
lhl”
*
1 0.06 -
1
1
I
I
0
20
40
I
TirE kc) Fig. 2. Response curves at steady state for the proposed system: (A) without chemical (B) with glucose oxidase/Trinder reaction at different flow rates: (a) 0.98 ml/min; ml/min.
I
I
I
80
100
120
reaction (quinonimine dye samples were used) and (b) 0.56 ml/min; (c) 0.33 ml/min; and (d) 0.16
Y-S. Hsieh, S.R. Crouch /Analytica
280
throughput rate was over 60 samples/h. Because of low sample dispersion, this stopped-flow/continuous flow allows the simple extraction of kinetics information with little influence of dispersion-affected variables. The stopping time is unimportant as compared to stopped-flow/flow injection (FI) methods. 3.2. Effect of carrier streams There have been several previous attempts to use an immiscible fluid carrier and air to transport a
Chimica Acta 309 (1995) 277-282
liquid sample to a detector. Petersen and Dasgupta [13] adapted air as the carrier in a continuous flow analysis system with high throughput rates and low waste generation. Attiyat and Christian [14,1.5] used air and organic solvents as carrier streams to lower the sample dispersion and to enhance the sensitivity of determinations in an FI/atomic absorption spectrometry system. In this work, we used an air-carrier technique to limit dispersion between the sample and carrier phases and to minimize consumption of sample and reagent. The dispersion between the two phases is independent of flow rate. However, smaller
A. 0.23
Load
Drain
Time (se4
Ii
0.06
I
lmin
Time @EC) Fig. 3. Typical cycles of absorbance vs. time for enzymatic the flow and (B) with stopping the flow.
glucose determinations
using a buffer as the carrier stream: (A) without stopping
Y.-S. Hsieh, S.R. Crouch /Analytica D
A.
LDL
L
D I
I
Chimica Acta 309 (1995) 277-282 0
,
I Air
1
0.9 8
5i -i?
w 2
0.6
1
0
281
-
segments
Liquid segments
1
I
I
I
I
50
100
1M
200
2.w
Time bed B. 1.0
D
-
L
,
D,
L
I
I
D -1
P 9
Air segments
I
0.8
E %
L
-
0.6
0.4
0.2
r
0.0 Time
Table 1 Determination Wine sample
1 2 3 ’ Air-carrier
segmcnls
(set)
Fig. 4. Repetitive cycles of absorbance vs. time for enzymatic glucose determinations the flow and (B) with stopping the flow (D = drain and L = load).
flow rates yield longer residence times. A dramatic change in absorbance occurs when air segments enter the flow cell, because they reflect most of the source intensity, and the transmittance falls to near zero [16]. Organic solvents such as acetone, ethanol,
Liquid Cv
using air as the carrier stream: (A) without stopping
methanol and methyl isobutyl ketone (MIBK) were also tried as carrier streams. However, no noticeable improvements in terms of detector response were found. By switching valve positions back and forth for replicate kinetic determinations of glucose, re-
of glucose in wine samples ‘. Glucose (%o)
R.S.D. (%I
Air-carrier
Buffer-carrier
Air-carrier
Buffer-carrier
0.44 0.46 0.019
0.45 0.46 0.014
1.15 1.61 1.46
3.88 1.64 0.96
results for n = 4, buffer-carrier
for n = 3.
282
Y-S. Hsieh, S.R. Crouch/Analytics
sponse curves of the air-carrier system with and without stopping the flow are shown in Fig. 4. For kinetic measurements, the flow was stopped soon after each detector signal in the liquid segment reached the plateau. The reaction rate is measured as the slope of the absorbance-time curve after the flow is stopped. The R.S.D. was < 3% for glucose determinations.
Chimica Acta 309 (1995) 277-282
method, the glucose concentration in a standard serum sample was determined. The results show good agreement (< 8% error) with manufacturer’s reported mean values. The consumption of sample and reagent for each kinetic determination by the proposed method is small (a few ~1, associated with the size of the sample loop). The entire system is inexpensive and easy to operate and automate.
3.3. Glucose determinations
References One of the goals of this work was to apply the simple stopped-flow procedure in practical determinations. Therefore, kinetic determinations of glucose in wine samples were performed and compared with different carrier streams. Linear calibration curves with correlation coefficients r = 0.9992 (buffer carrier) and 0.9993 (air-carrier) were obtained over a concentration range of lo-80 ppm glucose. Results are presented in Table 1 for wine samples. Except for wine sample No. 3, which had a quite low glucose concentration, identical results were obtained by both the buffer and air carrier methods (Student’s t-test, 95% confidence level). Results for wine samples 1 and 2 were also identical at the 95% confidence level to results obtained by the hybrid air-segmented flow injection technique [17]. The precision of glucose determinations was also quite good with R.S.D.s less than 4% (Table 1). These findings support the hypothesis that the air carrier method can achieve similar results for kinetic determinations as the buffer carrier method. In order to test the accuracy of the proposed
[l] S.R. Crouch, Anal. Chim. Acta, 283 (1993) 453. [2] B. Quencer and S.R. Crouch, Crit. Rev. Anal. Chem., 24 (1993) 243. [3] H.L. Pardue, Anal. Chim. Acta, 216 (1989) 69. [4] D. Perez-Bendito, Analyst, 115 (1990) 689. [5] H.A. Mottola and D. Perez-Bendito, Anal. Chem., 64 (1992) 407R. [6] H.A. Mottola, Kinetic Aspects of Analytical Chemistry, Wiley, New York, 1988. [7] D. Perez-Bendito and M. Silva, Kinetic methods in Analytical Chemistry, Ellis Horwood, Chichester, 1988. [B] Y.S. Hsieh and S.R. Crouch, Anal. Chim. Acta, 284 (1993) 159. [9] J. Ruzicka and E.H. Hansen, Flow Injection Analysis, 2nd edn., Wiley, New York, 1988. [lo] J. Ruzicka and T. Gubeli, Anal. Chem., 63 (1991) 1680. [ll] C.L.M. Stults, A.P. Wade and S.R. Crouch, Anal. Chim. Acta, 192 (1987) 301. [12] D. Barham and P. Trinder, Analyst, 97 (1972) 142. [13] K. Petersen and P.K. Dasgupta, Talanta, 36 (1989) 49. [14] A.S. Attiyat and G.D. Christian, Anal. Chem., 56 (1984) 439. [15] A.S. Attiyat and G.D. Christian, Talanta, 31 (1984) 463. [16] C.J. Patton, M. Rabb and S.R. Crouch, Anal. Chem., 54 (1982) 1113. [17] Y.S. Hsieh and S.R. Crouch, Anal. Chim. Acta, in press.