4536
J . Phys. Chem. 1984,88,4536-4542
culated from the transfer function in the Laplace domain. The results for plate height are identical with those obtained by use of the ”near-equilibrium” assumption for reactions with relaxation times short with respect to residence time in the chromatograph so the plate height due to secondary equilibria is a linear function of the mobile phase velocity. However, if the relaxation and residence times are commensurate, the magnitude the plate height is determined by exponential terms in velocity, eq 24. Band spreading due to the slow kinetics of secondary equilibria increases to the limiting values with an increase in flow velocity until the characteristic time for the reaction and the mobile phase holdup time in the column, to, are commensurate. At this velocity, the character of the chromatographic profile changes from an extremely broad Gaussian peak to one composed of two spikes separated by an intermediate “reaction” region that does not fall to the baseline. The governing equation is written in terms of the dimensionless parameters Da, K,,, and t B / t A .The Damkohler number Da ex-
presses the relative rates of reaction to the rate of axial convective transport in the mobile phase. Thus for a given set of reaction rates, it determines the flow velocity for the onset of change in the peak character. The equilibrium constant K , and the retention time ratio of the two forms t B / t A ,as well as Da, determine the shape of the profile. It is possible to extract the rate constants for the reaction in both the mobile or stationary phase from analysis of the peak profile provided that the rates in the two phases are markedly different or that the rate constants in one phase are obtained from independent experiments. Acknowledgment. The authors gratefully acknowledge support of their research by Grants CA 21948 and GM 20993 from the National Cancer Institute and National Institute for General Medical Sciences, U.S. Public Health Service, Department of Health and Human Services, and by a dissertation fellowship from the American Association of University Women.
Kinetic Study on Cis-Trans Proline Isomerization by High-Performance Liquid Chromatography Jana Jacobson, Wayne Melander, Gintaras Vaisnys, and Csaba Horvlth* Department of Chemical Engineering, Yale University, New Haven, Connecticut 06520 (Received: May 11, 1983)
The retention time for cis-trans isomerization around peptide bonds containing the imide nitrogen of prolyl residues is on the time scale of separation of such proline-containing peptides by HPLC. As a result, when a secondary equilibrium distribution of the cis and trans isomers in the chromatographic column occurs in addition to the primary distribution of the species between mobile and stationary phases, additional band spreading and distortion of peak shape occurs. On the basis of previous theoretical work, the first and second moments of the elution profiles obtained with proline peptides were employed to evaluate the rate constants for cis-trans isomerization of L-alanyl-L-prolineand L-valyl-L-proline on the stationary phase surface by using the appropriate rate constants for isomerization in the eluent proper.
Introduction Denaturation of certain small proline-containing proteins is believed to proceed in two or three steps. The slowest step has been postulated as cis-trans isomerization around peptide bonds that contain the imide nitrogen of prolyl residues.’ This has been supported by studies comparing the denaturation of carp parvalbumins having one or no proline residues and very similar amino acid as well as studies on the mechanism of unfolding and refolding of ribonuclease A,@ The a-carbons across most peptide bonds are trans to one another under normal conditions unless the imino nitrogen of proline is a constituent of the bond, i.e., it is a “proline peptide”, which can exist in both the cis and trans configurations. Small peptides having the latter type of peptide bond have been used in extensive thermodynamic On the other hand, the (1) J. F. Brandts, H.R. Halvorson, and M. Brennan, Biochemistry, 14, 4953 (1975). (2)’J. F.’Brandts, M. Brennan, and L.-N. Lin, Proc. Natl. Acad. Sci. U.S.A.,74, 4178 (1977). (3) L.-N. Lin and J. F. Brandts, Biochemistry, 17, 4102 (1978). (4) L.-N. Lin and J. F. Brandts, Biochemistry, 22, 559 (1983). (5) L.-N. Lin and J. F. Brandts, Biochemistry, 22, 564 (1983). (6) L.-N. Lin and J. F. Brandts, Biochemistry, 22, 573 (1983). (7) S. L. Portnova, V. F. Bystrov, T. A. Balashova, V. T. Ivanov, and Yu. A. Ovchinnikov, Izo. Akad. Nauk., SSSR,Ser. Khim., 4, 825 (1970). (8) H. L. Maia, K. G. Orrell, and H. N. Rydon, Chem. Commun., 1209 (1971). (9) W. A. Thomas and M. K. Williams, J . Chem. SOC.,Chem. Commun., 994 (1972). (10) K. Wuthrich and C. Grathwohl, FEES Lett., 43, 337 (1974).
0022-3654/84/2088-4536$01.50/0
kinetics of isomerization of such peptides have been investigated to a lesser extent. Brandts et al.’ have studied the isomerization kinetics of the dipeptides glycyl-L-proline, L-alanyl-L-proline,and L-valyl-L-proline in aqueous solution by measuring their relaxation times subject to a pH jump. The rate constants were calculated from the relaxation times by using equilibrium data from the literature. The relaxation times of cis-trans isomerization for these proline peptides were on the order of minutes, so that they are commensurable to their retention times observed in high-performance liquid chromatography (HPLC) with hydrocarbonaceous bonded phases.16 Under such conditions the mobile phase is more polar than the stationary phase and the magnitude of retention increases with the “hydrophobic surface area” of the ~olute.’~J*As seen in the representation of the molecular structures of cis- and trans-Ala-Pro in Figure 1, the cis conformer has a larger hydrophobic surface area than the trans conformer and therefore (11) C. A. Evans and D. L. Rabenstein, J. Am. Chem. SOC.,96,7312 (1974). (12) C. Grathwohl and K. Wuthrich, Biopolymers, IS, 2025 (1976). (13) C. Grathwohl and K. Wuthrich, Biopolymers, 15, 2043 (1976). (14) D. F. DeTar and N. P. Luthra, J . Am. Chem. SOC.,99, 1232 (1976). (15) H. N. Cheng and F. A. Bovey, Biopolymers, 16, 1465 (1977). (16) W. R. Melander, J. Jacobson, and C. Horvlth, J . Chromatogr., 234, 269 (1982). (17) Cs. Horvlth, W. R. Melander, and I. Molnlr, J . Chromatogr., 125, 129 (1976). (18) Cs. Horv6th and W. R. Melander, Am. Lab. (Fairfield, Conn.), 10, 17 (1978).
0 1984 American Chemical Society
Kinetics of Cis-Trans Proline Isomerization
The Journal of Physical Chemistry, Vol. 88, No. 20, 1984 4537 TABLE I: Equilibrium Constants and the Mobile Phase Rate Constants for Isomerization of Proline-ContainingDipeptides %
Figure 1. Cis and trans forms of L-alanyl-L-proline.
binds more strongly to the hydrocarbonaceous ligands of the stationary phase. Consequently, they are readily separated by reversed-phase chromatography. In continuation of our experimental16 and theoreti~al’~ studies on the effect of such secondary equilibria in HPLC we have chosen L-alanyl-L-proline and Lvalyl-L-proline which have relaxation times similar to their retention times in HPLC for the kinetic investigation of such cistrans isomerization. Rate constants have been calculated from the experimentally measured moments of the proline peptide elution profiles by two different methods. First, experimental data were subjected to nonlinear least-squares analysis by using the appropriate analytic expression for the plate height contribution due to secondary equilibria, H , (ref 19, eq 24). Second, the governing differential equations (ref 19, eq 13) were solved numerically for a particular set of parameters and the solution was compared with the experimental results. The two methods yield similar results for the sum of the rate constants of such cis-trans isomerization in both the mobile and stationary phases. Experimental Section The chromatograph consisted of a Model lOOA Altex (Berkeley, CA) solvent metering pump, a Model 7010 Rheodyne (Berkeley, CA) sampling valve, a Model LC-75 Perkin-Elmer (Nonvalk, CT) variable wavelength spectrophotometer set at 210 nm, and a Model 123 Perkin-Elmer recorder. The precolumn heat exchanger, the precolumn, and the column were thermostated to 22.5 and 40 OC with a Model K-2/R Messgeraetewerke (Lauda, G.F.R.) circulating water bath. Absorbances at 210 nm were measured with a Model 240 Gilford (Oberlin, OH) spectrophotometer. All experiments were carried out on 5-hm Partisil ODS columns (250 X 4.6 mm id.). Phosphate buffers (0.05 M) were made from reagent grade phosphoric acid, monobasic sodium phosphate, and dibasic sodium phosphate and were obtained from Fisher Pittsburgh, PA) as was the sodium hydroxide. The dipeptides were purchased from Sigma (St. Louis, MO) and D-glucose from Aldrich (Milwaukee, WI). Glucose was used to determine the residence time of an unretained tracer in the column. A Barnstead distilling unit produced the distilled water. The digitized HPLC detector signal was collected via a Fortran IV programz0 on a PDP 11/10 computer (Digital Equipment Corp., Maynard, MA) and the first and second moments of the peak distribution were calculated. The differences between the second central moments of Ala-Pro and Pro-Ala, and between Val-Pro and Pro-Val, were used to estimate the contribution of the kinetics of secondary equilibria to band broadening for the N-terminal prolines at specified conditions. Rate constants were evaluated from the variance due to secondary equilibria at several flow rates by an analytic expression, eq 24 in ref 19, which was solved by using a nonlinear regression routine, NLIN, in the SAS statistics package.21 The governing differential equations were solved by the finite difference method and the resulting calculated elution profiles were plotted with the TELLAGRAF system.22 Molecular models were drawn on the PROPHET system.23 (19) W. R. Melander, H.-J. Lin, J. Jacobson, and C. Horvlth, J . Phys. Chem., preceding paper in this issue. (20) G . Vaisnys, unpublished. (21) J. T. Helwig and K. A. Council, Eds., “SAS User’s Guide”, SAS Institute Inc., Cary, NC, 1979. (22) ISSCO, “Tellagraf User’s Manual”, Integrated Scientific Systems Corp., San Diego, CA, 1981.
compd T, “C pH 7-l: SKI cis Ala-Pro 22.5 7.07 0.0034 35b Ala-Pro 40.0 7.07 0.022 35b Val-Pro 22.5 7.07 0.0025 41‘ Val-Pro 40.0 7.07 0.016 41‘ Val-Pro 22.5 3.00 0.0031 25d a Determined from Figure 2, ref 1 . ence 9. Determined from eq 1 in ref
Km
4 3 ,
s“
kw S-’
1.86 0.0022 0.0012 1.86 0.014 0.0077 1.44 0.0015 0.0010 1.44 0.0094 0.0066
3.00 0.0023 0.00077 Reference 11. Refer1.
In order to compare calculated mass profiles and experimental absorbance profiles at the chromatograph detector outlet, we determined the ratio of the molar absorptivities at 210 nm for the two conformers at pH 2.4 and 6.2 as follows: to solutions containing 20 r L of 0.033 M Ala-Pro or Val-Pro in 1.6 mL of 0.050 M phosphate buffer, pH 2.4, at 25 “C, was added 20 fiL of 6.0 M sodium hydroxide. The final pH was approximately 6.2. The ratio of the cis molar absorptivity to trans molar absorptivity was calculated from the absorbances of the equilibrated initial and final solutions, corrected for dilution, with use of published pK, values. Results and Discussion The present results are in agreement with the general conclusions of an earlier report16 on the peak shape of Ala-Pro as a function of temperature, pH, flow velocity, and the retention characteristics of the two isomers. For the peptides studied here, the trans isomer is retained to a lesser extent on the stationary phase than the cis conformer. This result is expected from qualitative consideration of the hydrophobic surface areas of the two conformers.16 This effect is seen in Figure 2 for results obtained with Val-Pro and Pro-Val under identical chromatographic conditions in accord with findings for the retentions of Ala-Pro and Pro-Ala. Each pair of eluites is expected to have similar retention factors and molecular diffusivities so the main contribution to differences in their peak shape would be secondary equilibria. The retention time of the leading spike in the chromatogram of Ala-Pro at 22.5 ‘C, pH 7.07, corresponds to the retention time of the Pro-Ala peak. Since as the latter peptide exists almost entirely in the trans conformation, the late elution of Ala-Pro must be due to the presence of the cis isomer. The effect of secondary equilibria on peak shape can be seen from the greater band spreading of the Ala-Pro and Val-Pro elution bands than the corresponding Pro-Ala and Pro-Val bands. At a higher temperature the rate of isomerization of the proline peptides increases and the expected decrease in peak width is seen by comparing the chromatograms obtained at 22.5 and 40 O C in Figure 2. Differences in peak shape can also be seen in Figure 2 between the results obtained at pH 3.00 and 7.07. At an eluent pH of 3.00 the Val-Pro bands are narrower than at pH 7.07 and the overall retention time as measured by the first moment of the distribution of all isomeric forms is reduced. This result can be understood in light of the relationship between relaxation time for secondary equilibria and band spreading as measured by the second central moment of the sample elution profile, or the related plate height, that is given in eq 24 of ref 19. As the relaxation time decreases, the magnitude of the moment decreases. Since the Val-Pro cis-trans equilibrium is shifted to favor the tram conformer at lower pH, the decrease in retention is expected. Since the isomerization rate is more rapid at low pH,’ the peak becomes more Gaussian and narrower by changing to a low pH eluent. For both Ala-Pro and Val-Pro, the peak shape changed with a change in the flow velocity. In general, the dependence of the peak shape on the mobile phase conditions and the flow velocity, in agreement with the previous qualitative study on Ala-Pro,16 is not described by commonly used relationships between the flow velocity and (23) W. P. Rindone and T. Kush, Eds., “Prophet Molecules”, National Institutes of Health, Washington, DC, 1980.
4538 The Journal of Physical Chemistry, Vol. 88, No. 20, 1984
Jacobson et al,
9,urK'
0
600
120 240 360 0
pH7.07
0
120240 3600
1200 1800
300 600 900
pH7.07
600
1200 le00
300 600 900
0
pH300
300600900
300600900
0
TIME (sec) Figure 2. Experimental elution profiles of proline-containing dipeptides. The chromatogramsat the top were obtained with L-alanyl-L-prolineand L-valyl-L-proline, both present in cis and trans forms. The chromatograms at the bottom were obtained with L-prolyl-alanine and L-prolyl-L-valine that are present only in the trans form. Comparison to the two sets of elution profiles shows the band spreading and band distribution caused by cis-trans isomerization superimposed on the chromatographicprocess. All experiments were carried out on 5-pm Partisil ODS (250 X 4.6 mm i.d.) as the stationary phase and 0.050 M phosphate buffers as the mobile phase. The flow rate was 1.5 mL/min. the second moment of the peaklg and suggests a significant additional influence of the kinetics of secondary equilibria on band spreading.24 Val-Pro was found to elute as a single unimodal peak under most of the conditions studied. Insofar as the influence of conformational change on peak shape is governed by the rate of isomerization with respect to the time scale of HPLC elution, higher isomerization rates and relatively long retention times would most likely result in a single peak. Inspection of Table I shows that the relaxation time of Val-Pro is about 35% greater than that of Ala-Pro; thus Val-Pro will show greater band spreading if the relaxation time in the chromatographic system is determined by the relaxation time in the mobile phase. This effect is offset in part by the fivefold greater residence time of Val-Pro in the system. The net result of these two opposing effects is that the chromatograms of Val-Pro show less band spreading due to secondary equilibria than Ala-Pro under comparable conditions. The aims of this investigation were to test the predictions of the theory for band spreading due to secondary e q ~ i l i b r i aand '~ to obtain rate constants for cis-trans isomerization of peptides in the systems under study. The analytic expressions obtained in the previous paper treat the detector response from all isomeric forms as one peak and use its first and second moments to determine rate constants. Therefore, statistical moments of the dipeptide bands were measured. The first moment of the concentration distribution, M I ,is defined as the retention time of the collective center of mass of the two dipeptide isomers, Le., M1is determined from the overall concentration profile and not from the isomers individually. The second central moment, a2, is a measure of variance of the entire dipeptide distribution. The first and second moments are related to the intrinsic kinetic parameters of the conformational changes giving rise to band spreading due to secondary equilibria. Determination of Rate Constants from M I and a2. The first method used in this study for extraction of kinetic information ChromatographyAdvances and Perspectives", Vol. 2, Cs. Horvlth, Ed., Academic Press, New (24) G. Guiochon in "High Performance Liquid
York, 1980.
(2)
cis
1
-
(3) trans
23 k32
mobile phase
_-_-stationary phase
cis
trans
Figure 3. Schematicrepresentation of the interconversion of the cis and trans isomers in the mobile and stationary phases and the pertinent rate constants. from chromatographic data employs analytic expressions that relate the first and second moments to the rate constants. In these expressions, the Damkohler number, Da, is introduced as a dimensionless rate constant. In the practice of chemical engineering, Da is the ratio of the residence time in the reactor to the characteristic reaction time. The analogous Damkohler number for secondary equilibria in the chromatographic system can be defined as the residence time of the compound in the mobile phase divided by the sum of the forward and reverse reaction times. For the simple scheme depicted in Figure 3 it is given by Da = Lk2(l + 1/Km)/u0 = L(k2
+ k3)/uo
(1)
where L is the column length, K,,, is the equilibrium constant for the reaction in the mobile phase, uo is the mobile phase velocity, and k2 and k3 are the overall forward and reverse rate constants, respectively, that are related to the simple forward and reverse rate constants for reaction, i.e., cis-trans isomerization, in the mobile phase, kzs and k32,and the corresponding rate constants in the stationary phase, kI4 and kdl. as k2
=
k14kA
+ k23
(2)
k3
=
k41 kB
+ k32
(3)
where kA and kB are the retention factors of the cis and trans isomers.1g
Kinetics of Cis-Trans Proline Isomerization
The Journal of Physical Chemistry, Vol. 88, No. 20, 1984 4539
TABLE 11: Rate Constants for Cis-Trans Isomerization on the Stationary Phase As Determined by (A) Curve Fitting of the Analytic Expression, Eq 4, and (B) Simulation of Elution Bands meth- Da/M,, compd T, "C pH od s-' k,,, s-l k,,, s-I K, Ala-Pro 22.5 7.07 A 0.0061 0.0038 0.0061 0.61 B 0.0075 0.0051 0.0082 0.61 Ala-Pro 40.0 7.07 A 0.10 0.069 0.13 0.54 Val-Pro
22.5
7.07
Val-Pro 40.0
7.07
Val-Pro
3.00
22.5
B A B A B A B
0.018 0.017
0.0054 0.0050
0.062 0.056
0.095
0.030
0.21
0.088 0.089 0.14
0.23
0.075
0.15
0.50
10000
tK
0000 .
N
V
I
1
6000 -
asymtotic compd
T, "C
Ala-Pro Ala-Pro Val-Pro Val-Pro Val-Pro
22.5 7.07 40.0 7.07 22.5 7.07 40.0 7.07 22.5 3.00
pH
Da/M,, standard s-, error 0.0061
b
0.10
0.018 0.095 0.23
lower
i
/
4000 -
/
/
L / /:: , A/
2000- /
/
200
400
600
800
1000
1200
(set')
Figure 4. Calculation of H,, for L-alanyl-L-proline. The difference in u2 between L-alanyl-L-prolineand the L-prolyl-L-alaninecurve at a particular retention time is used to calculate H,,(= u2L/tR2).The data were obtained with 5-pm Partisil ODS (250 X 4.6 mm i.d.) as the stationary phase and 0.050 M phosphate buffer, pH 7.07, 22.5 " C , as the mobile
upper 0.0076 0.14 0.022
phase with variation of flow rates from 0.2 to 2.0 mL/min. TABLE IV: Ratios of the Extinction Coefficients of Cis and Trans Forms, ec/eT, of the Dipeptides L-Alanyl-L-Proline and L-Valyl-L-Proline
0.10
0.27
The plate height due to secondary equilibrium, H,,, is related to Da and other parameters as (ref 19, eq 24) (4) where
H, and M1data were used in a nonlinear least-squares regression routine for eq 4 to determine Da/MI. Both Da and M I (see eq 19 of ref 19) are proportional to the flow rate, so for convenience the velocity-independent parameter Da/M1 was used in numerical evaluation of the rate constants rather than Da because Da/Ml is a constant characteristic for kinetics of secondary equilibria in a given system. It is given as
Insofar as Brandts et a1.l have reported rate constants for isomerization in the mobile phase, kZ3and k32,for the present systems, the rate constants for reactions on the stationary phase, k I 4and k41, can be measured if the retention times of the two isomers are known. The plate height due to secondary equilibria was evaluated with use of plate heights of molecules expected to have diffusivities similar to the eluite under study. The bandwidth is a nearly linear function of the retention factor, or retention time, at high reduced velocities normally encountered in HPLC,2s unless kinetic phenomena are also present.19 Therefore, the differences between the observed peak variance and that estimated from the linear behavior of the nonreactive probe is the variance due to secondary equilibria from which the plate height due to secondary equilibria can be evaluated as H,, (= uZL/tR2).The final stage of this calculation for the Ala-Pro and Pro-Ala pair is illustrated in Figure 4. The solid Pro-Ala line was calculated from a linear regression in the u-tR plane on the Pro-Ala data points. Da/Ml values were determined for both proline peptides and three experimental conditions by nonlinear regression of eq 4 and use of the observed peak dispersion and retention time. Da/Ml, the stationary phase rate constants, and the equilibrium constant for reaction on the (25) Cs. HorvPth and H.-J. Lin, J . Chromatogr., 149, 43 (1978).
/
a Pro-Ala
/
tR2 x
asymtotic 95% confidence
0.00069 0.0046 0.067 0.016 0.016 0.0011 0.0032 0.088 0.013 0.20
/
1
N
OO
TABLE 111: Statistical Measures for Da/M, Values Calculated by Using the Analytic Expression for H S E
A Ala-Pro
/
compd Ala-Pro Val-Pro
EdfT
1.75 1.41
stationary phase, K,,are given in Table 11. Statistical measures of Da/M1 thus obtained are given in Table 111. The confidence intervals obtained from moment analysis are somewhat broad. Since the chromatographic detector response changes with a change in the flow velocity, chromatograms were simulated at various values of Da/M1 and appropriate values of the first moment as an alternative method to evaluate Da/M,. The peak pattern is expected to be a sensitive function of Da/Ml so that Da/M1 could be estimated by comparison of elution profile patterns calculated at several mobile phase velocities to the experimentally determined shape. The calculated pattern that most closely matched the experimental result yielded the best estimate of the parameter Da/MI for the simulated elution band method. Elution band shapes were calculated for Ala-Pro and Val-Pro via numerical analysis of the governing differential equations written in terms of dimensionless quantities (ref 19, eq 13) with parameters chosen to mimic the experimental conditions used in this study. The absorbance of the cis conformer was corrected by multiplying the outlet concentration of cis by the appropriate cis-trans molar absorptivity ratio (vide Table IV). The mobile phase equilibrium constants, K,, in Table I were used in the simulation plots and the parameters tA and tB were assigned values corresponding to the retention times of the experimentally observed first (trans) and second (cis) spikes of the chromatogram. If spikes corresponding to the concentration bands of the cis or trans isomers were not observed so that tA or tBcould not be directly assigned from the Ala-Pro or Val-Pro chromatogram, tB was estimated as the retention time of the corresponding Pro-Ala or Pro-Val peak and tA was calculated from the first moment (ref 19, eq 19). The value of the system parameter Da/MI was varied until the calculated band shape matched the experimentally measured shape of the chromatogram. The results of the calculated elution bands for Ala-Pro at 22.5 OC and pH 7.07 are shown in the lower strip of Figure 5 . The calculated chromatograms compare well to the experimental chromatograms shown in the upper strip and suggest that the calculated elution band technique may be useful for determination of Da/Ml in certain cases. The simulation mimics the locations and amplitude of the elution band and isomer spikes as well as the overall distribution shape. Exact replication of the experimental chromatogram is not expected in the calculated distribution
4540
The Journal of Physical Chemistry, Vol. 88, No. 20, 1984
Jacobson et al.
-1
I I 0.4m1/min
0
300
1
I
I
0
300
600
900
V
600
900
2.0 ml/min
1
0
I
I
300 600 TIME (sec)
900
1.5 ml/min
a 01 +a
0
300
600
900
I Oml/min
c-
u m 0
3 I
z
no W F u
1
I
1
1
I
I
1
I
1
I
I
I
Do/M, = 0.017sec-l
Do/M, = 0 O I ~ S C C - ~ Da = 15.2
Da/Ml = 0.017r e d Do. 11.1
I
Do = 23.9
ZSd
-JFk
=z0
y w a aUp oz
s
,
I
I
I
since the number of theoretical plates in the model “column” is far less than that in the actual column, Le., N = 1500 for the model “column” whereas N = 10000 for the true column for eluites with less anomalous peak shapes. The effects of secondary equilibria are evident in these chromatograms and therefore one would expect Damkohler numbers near one.lg The calculated values of Da are in this region. In a similar fashion, the value of Da/M1 was determined for Val-Pro at 22.5 “C and pH 7.07. The calculated experimental elution profiles are shown in Figure 6. The peculiar features, Le., the position of the trans spike at 2.0 mL/min, the mass distribution, and the position of the peak maxima at each flow velocity, are replicated in the model. Broadened single peaks were observed for both Ala-Pro and Val-Pro at 40 “Cand pH 7.07 as seen in the left block of Figure 7. It is difficult to reproduce these chromatograms by employing the elution band model since no isomer spikes are present. Three potential simulations for each experimental chromatogram and their associated Da/M1 values are given in the right-hand block of Figure 7. Inspection of the figure shows no major differences
I
I
I
1
1
in the features of the patterns of the simulated elution bands which differ only in their peak widths. This is a poor measure for determining Da/Ml since the efficiency of the numerical “column” is far less than that of the true column and nonkinetic contributions due to band spreading are not included in the model. Therefore, one would not expect this model to produce peaks that accurately represent the unimodal experimental peaks. The simulated elution band method cannot be used to determine Da/Ml for these two systems unless the efficiency of the model “column” more nearly approaches that of the actual column and other contributions due to band spreading are accurately included in the model. The peak maximum of the chromatogram of Val-Pro at 22.5 O C and pH 3.00 appears to be a trans spike (viz. Figure 8). Closer examination reveals that this node does not have the same retention time as the Pro-Val peak (vide Figure 2), and thus is not a trans spike. The calculated elution band for Da = 10.7 in the right block of Figure 8 further illustrates this point. The trans spike and overall concentration profile do not replicate the experimental result at all. However, the two calculated concentration bands at higher Da/Ml values do not reproduce the chromatogram.
Kinetics of Cis-Trans Proline Isomerization
The Journal of Physical Chemistry, Vol. 88, No. 20, 1984 4541
EXPERIMENTAL RESULTS
CALCULATED CONCENTRATION BANDS DO/MI = 0.20
ALA-PRO
DO/MI = 0.03
1 p H 7.07
W J
-
LL
0
A
a z (3
120 240 360
v)
K
a a z 0 c a a Iz W
0
o
I-
o
VAL-PRO 40% p H 7.07
W
I-
w
0
z
sn
Do+ = 0 . 2 0 ~ ~ Do+ ~ ~ = O.IOsrc-~ D o * 156.4 Do 78.2
W
k-A A
I-
a A
3
o
-
a o
300 600 900 I )O TIME (sec)
Do/M, ~ 0 . 0 5 s e c - ~ Do = 39.1
I
I
7, n
I
1
300600900
I' I
I
1
I
1
1
'\,
03006009001 00
0300600900
TIME (sec)
Figure 7. Determination of Da/M, for broadened single peaks is unfeasible with the present model simulation. A range of Da/M, values from the
calculated elution bands of L-alanyl-L-prolineand L-valyl-L-proline,right block, describe the experimental chromatograms, left block. Experimental conditions are 40 OC,pH 7.07, and 1.5 mL/min. The column and curve descriptions are as given in Figure 5.
EXPERIMENTAL RESULTS
1 VAL- PRO 22.5% pH 3.00
J
a z
CALCULATED CONCENTRATION BANDS Do/MI = 0. IOsec-' Do = 71.0
D O / M ~ = O . O ~ O ~ ~ CDOIM, -~ =O.OI~KC-~ Do = 10.7 Do = 49.7
-
0 v)
a
0 I-
o W
IW
n I ~
0
300 600 900 1200
I
I
0 300 600 900
TIME (sec)
1
1
I
1
I
0 300 600 900
0 300 600900 1200
TIME (sec)
Figure 8. Calculated elution bands of L-valyl-L-prolineat pH 3.00 do not mimic the experimental chromatogram. The experiments were carried out at 22.5 OC,pH 3.00, and 1.5 mL/min. The column and curve descriptions are the same as those given in Figure 5.
Consequently, Da/M, cannot be accurately determined for Val-Pro at 22.5 OC and pH 3.00 by the trial-and-error calculated elution band approach. Implications of the Kinetic Analysis. As shown in Table 11, the equilibrium constant for isomerization on the stationary phase, K,, is smaller by a factor of 3 to 16 than the appropriate equilibrium constant in the mobile phase, K , in all cases investigated. Thus, the stationary phase appears to stabilize the cis isomer. Comparison of the rate constants in Tables I and I1 demonstrates that the rate of conformational change occurring on the stationary phase surface in many cases is of the same order of magnitude as that in solution, but the rate constants for isomerization at the surface, kI4and k4,,are in all cases significantly larger than those
for isomerization in solution, kz3and k32. This observation suggests that the hydrocarbonaceous surface of the stationary phase catalyzes the cis-trans isomerization. The surface of octadecylsilica used as the stationary phase resembles biological membranes and retention data measured in reversed-phase chromatography have already been used to quantify hydrophobic propertieszGz8that are believed to have an important effect on transport through lipophilic membranes in living systems. The results of the present study suggest that chromatographic measurements may facilitate the (26) E. Tomlinson, J . Chromatogr., 113, 1 (1975). (27) A. Nahum and Cs. Horvlth, J . Chromatogr., 192, 315 (1980). (28) E. Tomlinson, Int. J. Pharm., 13, 115 (1983).
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J . Phys. Chem. 1984, 88, 4542-4541
study of kinetic effects that occur with biological reactions in the lipophilic layer of the stationary phase that mimics biological membranes. The low dielectric environment and the essentially two-dimensional nature of the surface layer provide reaction conditions which are not attainable in solutions. As our knowledge with regard to the surface properties and design of such stationary phases is on the increase it is likely that the high precision, speed, and convenience of HPLC will be exploited to obtain not only thermodynamic but also kinetic information of biological significance from properly designed chromatographic experiments. Conclusions The results presented above show that reversible reactions that are first order in eluite concentration cause the elution band to spread. If the relaxation time for the reaction is commensurate with the time for chromatographic retention, the relaxation time can be extracted from the dependence on the chromatographic velocity of the first and second moments of the chromatographic mass distribution of all forms of the eluate at the outlet of the column. The analysis is complicated by the presence of other velocity-dependent terms that contribute to band broadening. Their magnitude can be estimated from nonlinear regression of the complete expression for dependence on flow velocity of the chromatographic plate height, that is simply related to the second central moment. They can also be estimated from the band
spreading of eluites with chromatographic characteristics similar to the eluite of interest. On the other hand, numerical solution of the equations for mass conservation in the chromatograph can be used to determine rate constants. Since the change in peak shape is a dramatic function of flow velocity in the domain when the Damkohler number is near one, the relaxation time may be estimated simply by comparing the predicted and experimental profiles. The results in such a comparison of experimental and predicted results for the cis-trans isomerization of proline in Ala-Pro and Val-Pro showed good agreement. If the relaxation time and equilibrium composition in the mobile phase are known from independent experiments, or if the reaction in the mobile phase is shown to require long times in comparison to the chromatographic elution time, the rate constants for the surface reaction can be determined. This may prove to be a superb tool for study of reactions on surfaces in contact with liquids. Acknowledgment. This work was supported by Grants CA 21948 and G M 20993 from the National Cancer Institute and National Institute of General Medical Sciences, U S . Department of Health and Human Resources, and by a dissertation fellowship from the American Association of University Women. Registry No. L-Alanyl-L-proline, 13485-59-1; L-valyl-L-proline, 20488-27-1.
Boron Atom Reactions with the Epoxides: Vibrational Distributions in the Product BO(A*II) State Marion K. Bullitt,t Rao R. Paladugu, James DeHaven,t and Paul Davidovits* Department of Chemistry, Boston College, Chestnut Hill, Massachusetts 02167 (Received: July 13, 1983)
The results of chemiluminescence studies are reported for the reactions of boron atoms with ethylene oxide, propylene oxide, butylene oxide, diepoxybutane, cyclopentene oxide, cyclohexene oxide, 3-vinylcyclohexeneoxide, and styrene oxide. The experiments were done under single-collision conditions in a beam-gas apparatus. The nascent vibrational distributions in the electronically excited product BO(A211) were determined. These distributions are well fitted by a statistical model which assumes that only those modes of the polyatomic product are excited which correspond to the conformation change in the transition from the reacting epoxide to the alkene product. Absolute cross sections for the production of the A'II state of BO are also reported.
Introduction The boron-epoxide reactions studied here are a continuation of work reported earlier.'P2 These reactions yield BO and the corresponding alkene. The BO is produced either in the XzZ or in the A211 state. The ground-state channel to B0(2Z) is predominant.2 The reactions of boron atoms are the simplest of the atom-molecule reactions involving ground-state p orbitals. The large total cross sections for the reaction of boron with the epoxides2 indicate that there is no barrier to these reactions. These results are in accord with recent M I N D 0 computer ~ t u d i e s . In ~ this aspect the reactions of boron with the epoxides are similar to that of the carbon atom with ethylene The latter studies suggest that it is carbon ('S) which reacts, and the orbital symmetry of ground-state boron (2P) resembles that of carbon ('S) rather than ground-state carbon (3P) in having one occupied and two unoccupied p orbitals. The epoxides in the present study are listed in Table I. They cover a broad range of complexity, from the simplest, ethylene oxide, to the 21-atom polyatomic 3-vinylcyclohexene oxide. The +Presentaddress: Air Force Geophysics Laboratory, OPR-1, Hanscom Air Force Base, MA 01731. 'Present address: Department of Chemistry, Stanford University, Stanford, CA 94305.
range of complexity offers a possibility to test theories which attempt to explain energy disposal in the reactions of p~lyatomics.~ Experimental Section Details of the experimental technique used have been previously described.l~lO~'The reactions were studied under single-collision conditions in a beam-gas apparatus. The system used in the present work is an enlarged and improved version of the earlier one with a significantly improved signal-to-noise ratio. The beam (1) S. M. Hosseini, J. DeHaven, and P. Davidovits, Chem. Phys. Letf.,86, 495 (1982). ( 2 ) R. D. Estes, M. B. Tabacco, T. G. DiGiuseppe, and P. Davidovits, Chem. Phys. Lett., 86, 491 (1982). (3) M. B. Tabacco and P. Davidovits, to be submitted for publication. (4) J. H. Plonka and P. S. Skell, J . Chem. Soc. D, 1108 (1970). (5) P. B. Shevlin, J . A m . Chem. SOC.,94, 1379 (1972). (6) C. MacKay and R. Wolfgang, Radiochim. Acta, 1, 42 (1962). (7) R. H. Parker and P. B. Shevlin, Tetrahedron Lett., 26, 2167 (1975). (8) Juan M. Fiauera, Philip B. Shevlin, and S. D. Worley, J . Am. Chem. SOC., 98, 3820 (1976). (9) (a) Donald G. Truhlar and David A. Dixon in 'Atom-Molecule Collision Theory", R. B. Bernstein, Ed.,Plenum, New York, 1979, p 595. (b) John C. Light, ibid., p 647; (c) R. D. Levine and J. L. Kinsey, ibid., p 693. (10) James DeHaven, Michael T. O'Connor, and Paul Davidovits, J . Chem. Phys., 75, 1746 (1981). (11) A . Brzychy, J. DeHaven, A. T. Prengel, and P. Davidovits, Chem. Phys. Lett., 60, 102 (1978).
0022-365418412088-4542$0 1.5010 0 1984 American Chemical Society
