Analytical-Band Centrifugation of an Active Enzyme - Substrate Complex

Transcription

1 Eur. J. Biochem. 23 (1971) Analytical-Band Centrifugation of an Active Enzyme - Substrate Complex 1. Principle and Practice of the Centrifugation Renir COHEN and Michel MIRE t Institut de Biologie MolBculaire, Centre National de la Recherche Scientifique, Universith Paris VII (Received July 14, 1971) The analytical active-enzyme-centrifugation method permits the determination of the hydrodynamic properties of enzymes while they are fully active on their substrates ; the centrifugation can be performed at the very dilute concentrations used in kinetic studies (= 1 pg/ml) ; furthermore a purified enzyme preparation is not necessary and in many cases a crude extract is sufficient. This method is beginning to be used in several laboratories even though few of its experimental aspects have been published. This paper reports the details for carrying out an activeenzyme-centrifugation run, discusses the experimental conditions and deals with artifacts and ways, which are easy, to overcome them. A new method of analytical centrifugation, the active-enzyme-centrifugation method, has been developed during the last few years [l-51. In this procedure, a thin lamella of enzyme solution is layered onto a substrate solution in a rotating ultracentrifuge cell. Then the enzyme molecules sediment in a band through the substrate solution and catalyze the enzymic reaction. The sedimentation and diffusion coefficients of the enzyme. substrate complex are calculated from the optical observation of either the appearance of the product of the reaction or the disappearance of the substrate. This method has numerous advantages. Firstly, the hydrodynamic properties determined are those of the enzyme. substrate complex while it is fully active. Consequently differences of polymerization state, hydration or conformation between the free enzyme and the reacting enzyme can be directly determined. Then, the sedimentation of the enzyme can be observed at the very dilute concentrations generally used in kinetic studies (the concentration at band center is very often in the range 0.1 to 10 pg/ cm3). Therefore the determined hydrodynamic properties can be directly compared with the kinetic data. Also, since this method requires only a very small amount of enzyme for a run (very often less than 0.1 pg) it is preferable when only a small amount of enzyme is available. Moreover, this method does not require a purified preparation as only the active enzyme is observed. The enzymic reaction needs only to be specific for the studied enzyme. Therefore, in many cases, a crude extract is sufficient and it becomes possible to investigate enzymes associated in organized complexes (mitochondria, chloroplast, 18 t Deceased October 30, I<cir..I. I%iocliciii., Val. 23 membrane fragments, etc.) with a minimum of exposure to conditions favoring the dissociation of the complex. Even though few of its details have been published, the active-enzyme-centrifugation method is beginning to be used in several laboratories [S Therefore, the purpose of this paper is to report the details for carrying out an active-enzyme-centrifugation run and to discuss the experimental conditions which have to be fulfilled if the mathematical analysis of the data is to be valid. In particular, this method is subject to artifacts, not found in the more classical centrifugation methods and this paper deals in detail with these artifacts and the ways, which are easy, to overcome them. MATERIALS AND METHODS Enzymes Numerous enzymes can be studied using the active-enzyme-centrifugation method. The only condition is that the reaction can be followed by spectrophotometry either directly [l] or through coupling with a second enzyme system [3,4]. Several enzymes were used in the present work. /3-Galactosidase was a partially purified extract from Escherichia coli. L-Glutamate dehydrogenase, lactate dehydrogenase, pyruvate kinase and glucose- 6-phosphat,e dehydrogenase were obtained from Sigma Chemical Co, as crystalline suspensions in (NH,),SO,. These enzymes were used without further purification. Measurements of Enzymic Activities All assays were performed by following the change in absorbance at a convenient wavelength with a

2 268 Active-Enzyme-Centrifugation Method: Principle and Practice Eur. J. Biochem. Beckman model DB spectrophot,ometer equipped with a recorder. The temperature was thermostated at 20 C. Enzymic activities were determined in the same substrate solutions as those used for centrifugation experiments. CENTRIFUGATIONS Sedimentation experiments were performed in a Spinco model E analytical ultracentrifuge. Optical Systems The absorption optical track was used throughout this work, with ultraviolet or short-wavelength visible light (254, 334, or 436 nm); the monochromatic light was isolated with the appropriate filter (Br2, Cl,, Kodak Wratten, interference or glass filters) from the standard mercury light source. A similar result would be obtained by using the st,andard Spinco monochromator. For experiments at a wavelength of 667 nm, the standard mercury light source of the absorption optical track was replaced by an Osram 650 W visible light lamp, an MTO interference filter was used, and Kodak Tri-X film was substituted for the standard Kodak commercial product. It must be noted that the schlieren optical track can be converted to a visible absorption optical system [ll, 7,6]. However, the photographic images obtained from this system are not so sharp; furthermore the base line is badly defined. Ultracentrifuge Cells Generally, in band centrifugation of an active enzyme, pl of enzyme solution are layered onto approximately 500 pl of a substrate solution in the sector of a rotating ultracentrifuge cell. The earliest sedimentation experiments were carried out using a valve-type synthetic-boundary cell [ 11. Enzyme solution transfer normally occurred between and rev./min. However, this cell was not entirely satisfactory : the centerpiece made from dural does not avoid denaturation of the enzyme by metallic contact. Moreover, this cell was designated to layer a large volume of solution, approximately one-third to one-half of the volume of a sector; therefore, the transfer of only p1 solution was not always very reproducible. Band-forming centerpieces are now preferred to valve-type synthetic-boundary centerpieces in band centrifugation of active enzyme. These centerpieces are designed for the transfer of very small volumes (5 to 50 pl). Therefore, the enzyme solution transfers satisfactorily and reproducibly to the top of the substrate solution. Moreover, these centerpieces which are made from Kel-F or charcoal-filled Epon avoid enzyme denaturation by metallic contact. As in synthetic-boundary cells, the enzyme solution transfer can be observed in the schlieren viewer because of the formabion of a refractive-index gradient by the small molecules. However, this transfer occurs at a lower rotating velocity than in valve-type synthetic-boundary cells and generally between 500 and 2000 rev./min. Single sector 12 mm band-forming centerpieces are now extensively used in our laboratory. Type I single channel centerpiece is prefered to type I1 gap transfer. Indeed, in the former, the enzyme solution transfer occurs reliably and without mixing, even after extensive use of the centerpicee. Double sector 12 mm band-forming centerpieces are now available. These centerpieces have the advantage of providing a baseline. Type I centerpieces have been used in our laboratory. Close to the bottom of the sector, a thin V-shaped channel connecting the two substrate solutions was cut to permit exact equalization of the column lengths. Centrifugation Procedure Centrifugation runs were carried out at 20 C using either an AN-D rotor (up to 59780rev./min) or an An-H rotor (up to rev./min). In most experiments, 15 pl of enzyme solution were introduced into the well of the band-forming centerpiece and 500 pl of substrate solution into the sector space either with a pipet (as done with a sixchannel centerpiece) or, after tightening the cell assembly, with a syringe fitted with plastic tubing. With this procedure, no enzyme denaturation by metallic contact has been observed. The lamella when layered onto the substrate solution is about cm thick. Then, the band sediments and, due to diffusion, widens. Therefore, the concentration of enzyme at band center decreases with time. This concentration decreases after 40 min to about 37O/, of the initial concentration in the case of glutamate dehydrogenase and to about 27O/, in the case of glucose-6-phosphate dehydrogenase. Records Photographs were taken at appropriate time intervals. Because of the excessive refractive index gradient due to the diffusion of small molecules between the lamella and the substrate solution, the first photographs can show a light band and in this case were not taken into account for the mathematical analysis. Generally, this optical artifact becomes negligible before the rotor reaches maximal speed. Exposure times were chosen so that optical densities of the photographic images were always within the linear range of the emulsion sensitometric curve. Densitograph tracings of the photographs were recorded by a Joyce-Loebl double-beam microdensitometer.

3 Vo1.23, No.2,1971 R. COHEN and M. MIRE f 269 i c 8... " U =l e a A The approximate method assumes that the band of enzyme sediments, during the time At, without changing its shape and does not take into account the sedimentation-diffusion of the product once it is formed, during the time At. In summary, the difference distribution DE+ At (r) is considered to be due only to the synthesis of product by a fixed-shaped band of enzyme during a time interval At during which the product molecules do not move once they are produced. When every enzyme molecule of the band reacts on the substrate molecules with the same velocity, the maximum of this distribution coincides with the position of the band maximum at time t + At/2. Therefore, the sedimentation coefficient is calculated from the motion of this maximum according to the following equation : In ro = s co2 t + constant Fig. 1. Band-centrifugation of an active enzyme. substrate complex. (A) Distribution of product in the ultracentrifuge cell. (B) Difference distribution of product in the ultracentrifuge cell where co is the angular velocity and ro the position of the band maximum, by the method of least squares using a Wang Loci-2 desk computer. CALCULATIONS The enzyme band cannot be observed directly because of the very small concentration of enzyme used and of the wavelength generally chosen. Therefore, the sedimentation and diffusion coefficients of the enzyme were calculated from the only observable phenomenon i.e., the reaction catalyzed by the enzyme band. Two methods were used : the diffusion coefficient was always calculated using the rigorous method but the sedimentation coefficient was calculated using either the approximate method [a] or the rigorous one. Approximate Method The distribution of product in the ultracentrifuge cell Pt(r) (Fig. 1 A) was obtained from the densitograph tracings of the photographs. The difference distributions (r) were calculated at each point r (Fig.1B) according to the following relation : Df+dt(r) = Pt+nt(r) - Pt(r) where t and t + At are the times of two successive photographs and r is the distance from the axis of rotation. This difference corresponds to the variation of product concentration during the time interval At. Two reasons are responsible for this variation : (a) the sedimentation-diffusion during the time interval 4t of the product formed before the time t, and (b) the synthesis of product and its sedimentationdiffusion during 4t. 18' Rigorous Method This method has been extensively described in a previously published paper [5]. The sedimentation and diffusion coefficients were calculated according to the rigorous method using an IBM 7094 computer. No further details will be given here. RESULTS MEASUREMENTS OF SEDIMENTATION COEFFICIENT Photographs Fig. 2 shows photographs taken during a two sector (half wedged-half plane window) cell centrifugation of glucose-6-phosphate dehydrogenase (the base line is given by exposures 2, 4, 6,...). In exposures 1, 3, 5,... the dark region corresponds to the zone in the cell through which the band has migrated and therefore where NADH has been formed. This region increases in length as the band sediments toward the bottom of the cell. The light region at the bottom of the cell is the area in which no enzyme has yet migrated, and in which only NAD is present. Calculations llsing A pproxinaate Method The densitograph tracings of photographs taken during the sedimentation of glutamate dehydrogenase are shown in Fig.3. The difference distributions (Fig. 4) are calculated from the densitograph tracings, and the logarithmic plot of the position of the maxima versus time (Fig. 5) gives the sedimentation coefficient

4 270 Active-Enzyme-Centrifugation Method: Principle and Practice Eur. J. Biochem. Fig.2. Band-centrifugation of glucose-6-phosphate dehydrogenase. In one sector, 10 pl of a 10 pg/ml preparation containing about 1 glucose-6-phosphate dehydrogenase were layered onto 0.4ml of a substrate solution containing 0.08 M Tris-CI buffer ph 7.5, 1 mm NADP, 6 mg/ml glucose 6-phosphate. In the second sector, lop1 of buffer were layered onto 0.4 ml of substrate solution. Photographs were taken at 2 min intervals with the aid of a two-cell alternator, rev./min, 20 "C, 334 nm Fig.4. Difference distributions calculated, at each point r, from the densitograph tracings of Fig.3. For clarity, only five difference distribution curves are shown r Distance from axis of rotation Fig.3. Densitograph tracings of a series of photographs taken during a band-centrifugation of glutamate dehydrogenase. 15 p1 of a 3.3 pg/ml solution of enzyme were layered onto 0.6 ml of a substrate solution containing 0.15 M phosphate buffer ph 7.5, 50 mm glutamate, 2 mm NAD, 0.5 mm ADP. Photographs were taken at 2-min intervals, rev./min, 20 "C, 334 nm AMOUNT OF LAYERED ENZYME The amount of enzyme layered ont'o t,he substrate solution has to be chosen so that the reaction can be measured throughout the desired period of observation. Amounts of enzymes leading, after passage of Time (min) Fig. 5. Determination of the sedimentation coefficient of glutamate dehydrogenase using the approximate method. Plot of the logarithm of the position of the band maximum, calculated from Fig. 4, versus time the enzyme band, to an absorbance change of the ultracentrifuge cell between and are generally used. The choice of this amount must take into account the molecular activity of the enzyme and the absorption coefficient of the product (or substrate) at tjhe wavelength of observation. Fig.6 shows that this amount also depends on the rotation velocity of the rotor and on the sedimentation coefficient of the enzyme.

5 $01.23, Ho.2,1071 1E. COHEN and M. MIRE t 271 A 8 I 56) Fig.6. Amount of enzyme leading after passage of the band to zn absorbance change of about 1.0 in a double sector cell (Z ), :alculated for various rotation velocities (A) 68000, (B) 50000, (C) and (0) rev./min. One enzyme unit is defined as the amount which during an assay in the same substrate solution gives an absorbance change of 0.01 per minute (in a 3 ml solution with a 1 cm light path) 0 I Fig. 7. Conditions for convection- free band-sedimentation. (A) Densities in the cell: ~, total density; ----, density due to small molecules; -.-.-, density increment due to the band of enzyme. (B) Densities gradient in the cell: -, total density gradient; ----, stabilizing density gradient;, density gradient due to the band of enzyme Bccause of diffusion, the highest angular velocities ( and rev./min) are generally used when enzymic molecules are sedimented. However, when enzymes are associated into organized complexes (mitochondria, chloroplasts, membrane fragments, polyenzyme particles, etc.) available only in extracts of low specific activity, a lower rotation velocity may be prefered. Before each run the activity of the enzyme solutions must always be measured in the substrate solutions used for the centrifugation experiments ; it should be compared with the activity measured during the centrifugation. CONDITIONS FOR CONVECTION-FREE BAND SEDIMENTATION Density of the Enzyme Solution For successful layering, the enzyme solution must be less dense than the substrate solution. Otherwise, the system is unstable, the enzyme solution instantly sinks to the bottom of the cell. Stabilizing Density Gradient For convection-free sedimentation of the band, the total density gradient (apjar) in the direction of the centrifugal field must be positive. According to Svensson et al. 1121, this gradient can be stated in terms of the sum of two separate density gradients: where st and enz specify the stabilizing gradient and the density gradient associated with the enzyme distribution respectively. The enzyme gradient (a@/a,)en, is positive on the trailing part of the band, and negative on its leading part. The negative gradient must everywhere be compensated by the stabilizing gradient (Fig.7). This stabilizing gradient (ap/ar)st is generated in two ways: the diffusion of small molecules between the lamella and the substrate solution; the sedimentation of the small molecules in the substrate solution. The stabilizing density gradient increases with the concentration of small molecules in the bulk solution. Concentrated bulk solutions (for instance I M NaC1) are required when macromolecules are centrifuged as according to Vinograd and Bruner [13]. However, bccausc of thc vcry small cnzymc conccntrations uscd here, the band-centrifugation of active enzyme can be carried out in the very dilute solutions generally used in kinetic studies (for instance 0.1 M phosphate buffer). The stabilizing density gradient is minimal within the center part of the cell. Therefore, when very high amounts of enzyme are sedimented, the stabilizing gradient can be inadequate only within the center part of the cell. In which case, the band sediments convection-free in the top part of the cell and when the gradient becomes inadequated, the band sinks until its value becomes again adequate (Fig.8).

6 272 Active-Enzyme-Centrifugation Method : Principle and Practice Eur. J. Biochem I 1 Fig. 8. Partial "sinking" of a band of glutamate dehydrogenase. 15 pl of a 100 pg/ml solution of enzyme were layered onto 0.5 ml of a substrate solution containing 0.20 fir Tris-acetate buffer (ph 8.0), 5 mm 2-oxoglutarate, mm NADPH, 65 mm PU'H,CI. Photographs were taken at 2-min intervals, rev./min, 20 "C, 334 nm Initial [ S](K,) Fig. 9. Minimal ratio of the remaining-substrate concentration (behind the trailing part of the band) to the initial-substrate concentration for the enzymic activity in the trailing part not being smaller than: (A) 95O/,, (B) goo/,, (C) 80 /, of theactivity in the leading part of the enzyme band during the centrifugation. N. B. : Michaelian kinetics has been assumed to be valid I (A) b,and maximum (t,) CONDITIONS FOR THE VALIDITY OF THE MATHEMATICAL ANALYSIS Condition 1. The mathematical analysis assumes that every enzyme molecule in the band reacts on its substrate with the same velocity. Therefore, adequate conditions of enzyme reaction must be used during the whole centrifugation procedure. Irreversible Enzymic Reaction An easy way of fulfilling the above condition is to use an initial saturating substrate concentration (for instance 20 K,, where K, is the Michaelis constant) and an enzyme amount small enough for the substrate concentration to be still saturating (for instance 18 K,) behind the moving enzyme band. However, Fig. 9 shows that measurements at low substrate concentration can be made (for instance 1 K,), but the enzyme amount should be small enough for not reducing the initial concentration by more than a few percent j obviously bhe absorption coefficient of the observed molecule must be sufficiently high for the enzymic reaction to be still observable. Condition 1 is more difficult to fulfill when what is observed is the disappearance of an absorbing substrate and not the appearance of the product. In this case the maximum substrate concentration is limited leading part band maximum (t2) \ p l e a d / n g part / - ; ' Distance from axis of rotation Fig. 10. Artifact due to excessive enzyme amount. (A) Band at t, time; (B) band at t, time by the absorbance of the solution (for example to about 0.2 mm NADH when observing at 334 nm). However, it must be noted that more concentrated solutions can be used by choosing appropriate wavelengths. When condition 1 is not fulfilled, one enzyme molecule in the leading part of the band produces, between two photographs or scans, more product molecules than one enzyme molecule in the trailing part of the band. What follows then is mostly the enzymic reaction due to the leading part and since the band widens because of the diffusion during the centrifugation, a much higher and erroneous sedimentation value is obtained (Fig. 10).

7 Vol.23, No.?, 1071 R. COHEN and M. MIRE t '" 3 G I Tine (min) Fig. 11. Activity of 8-galactosidase measured using a spectrophotometer, in the substrate solution used for centrifugation. The substrate solution contained 0.33 M sodium-phosphate buffer ph 7.0, 0.66 mm MgSO,, mm MnSO,, 66.6 mm 2-mercaptoethanol, 2.22 mm orthoiiitrophenyl 8-galactoside. The absorbance of the cuvette, 1 cm light path, was followed at 436 nm and 20 "C. -, absorbance due to the formation of product; ~---, theoretical absorbance assuming a constant activity. For the centrifugation, the amount of layered enzyme was chosen so that the maximal absorbance in the cell was always less than 0.8 An easy way to be sure that condition 1 is fulfilled is by verifying that the enzymic activity is constant up to the maximum absorbance reached for centrifugation experiments (Fig. I I). Moreover, to determine if the artifact occurs, one performs a series of centrifugations wit,h varying amounts of enzymes. In the range where the conditions are adequate, the sedimentation value is constant, thus giving then the correct, value unaffected by the aforementioned artifact (Fig. 12). Whereas when the conditions are inadequate, the sedimentation value is too high (Fig. 13). Reversible Enzymic Reaction In the case of reversible enzymic reaction, the problem is more complicated because of the reverse reaction. Every molecule of the band does not react under identjical conditions. The enzyme molecules in the leading part react only in the presence of the substrate molecules, whereas the enzyme molecules in the trailing part react in the presence of the substrate plus the product molecules formed by the enzyme molecules of the leading part. Because of this fact, one enzyme molecule in the trailing part produces, between two photographs or scans, less product molecules than one enzyme molecule in the leading part. Fig. 12. Dependence on enzyme amount of the sedimentation coefficient value of 8-galactosidase. The substrate solution was identical to that of Fig.11. Each point is the average of at least five values 7.0 < 6' Enzyme (arbitrary units) Fig. 13. Dependence on enzyme amount of the sedimentation Coefficient value of glucose-6-phosphate dehydrogenase. The substrate solution contained 0.08 M Tris-CI buffer ph 7.5, 6 mg/ml glucose 6-phosphate, but only 80 pm NADP. The dashed line corresponds to the sedimentation coefficient of glucose-6-phosphate dehydrogenase as measured hy conventional methods. From kinetic studies, it was predicted that the artifact mentioned in the text would appear above 5 enzyme units Therefore, here as before, an artifact can arise, leading also to an excessive sedimentation value ; the correct, value can again be obtained from a series of centrifugations with varying amounts of enzyme and extrapolating to zero concentration. Obviously, this series of centrifugations must be carried out under conditions in which the direction of the observed reaction is as favored as possible. Attention should also be given to a possible inhibition of the activity by the product,

8 274 Active-Enzyme Centrifugation Method: Principle and Practice Eur. J. Biochrm. ~ Lactate dehydrogenase (pg/ml) Fig. 14. Dependence on lactate-dehydrogenase concentration of the sedimentution-coeificie?at aalue of pyruvute kinase. 15 pl of pyruvate kinase solution were layered onto 0.6 ml of a substrate solution containing 0.16 mm NADH, 0.3 mm ADP, 0.8 mm phosphoenol pyruvate, 8 mm MgSO,, 80 mm KC1, 0.1 M Tris-CI buffer ph 7.5 and lactate-dehydrogenase concentrations as indicated. Centrifugations were carried out at 67770rev./min and 20 C. The scale of lactate dehydrogenase concentration is logarithmic. The dashed line corresponds to the sedimentation coefficient of pyruvate kinase as measured by conventional methods. From kinetic studies it was predicted that the artifact mentioned in the text would appear for a lactate concentration smaller than 20 i*g/ml Enzymic Reaction Measured through Coupling with a Xecond Enzyme System A detailed paper dealing with the principle and the practice of this extension of the original method has already been published [4]. For the validity of the mathematical analysis, two new conditions dealing with the coupling enzyme E, must be added to condition 1 described above. (a) The sedimentation coefficient of the active unit E, must be lower than that of the studied enzyme El. (b) The concentration of E, must always be sufficient so that the intermediate product is transformed rapidly into the final product. When very low concentrations of E, are used, lower and erroneous sedimentation values are obtained. The correct value is determined from a series of centrifugations with varying concentrations of E,, and by extrapolating to an infinite concentration of E, (Fig. 14). In the case of a directly observable irreversible reaction it is often possible in the first run to get a very good sedimentation vahie, while many experiments could be needed for obtaining the same result in the case of coupled or reversible reactions. Condition 2. The mathematical analysis assumes that during the whole experiment, every enzyme molecule reacts on its substrate with a constant velocity. Therefore, no enzyme denaturation must occur Time (min) Fig.15. Amount of product formed in the ultracentrifuge cell during sedimentation of glutamate dehydrogenase. These amounts of NADH were calculated from the densitograph tracings of Fig. 3, taking into account the absorption coefficient of NADHand the densitometric curve of the photographic emulsion. The first exposure was taken 10.5 min after layering during the sedimentation procedure. This condition is fulfilled when, during the centrifugation procedure, the enzyme activity is constant i.e., when the total amount of product in the cell increases linearly with time (Fig. 15) and extrapolation to zero product leads to a time close to the time of layering. Moreover, the activity of the band of enzyme during the centrifugation must be equal to the activity of the layered volume of enzyme solution, which has been measured as previously mentioned, in the substrate solution used for the centrifugation experiments just before each run. Lesser activities are generally due to partial sinking of the enzyme, inhibition of the enzyme in the cell or, in the case of runs employing valve-type synthetic-boundary cells, to denaturation of the enzyme in the cup. DISCUSSION The active-enzyme-centrifugation method reported in the present paper allows one to obtain the hydrodynamic parameters s and D of the enzyme. substrate complex while it is fully active. Even in the case of one sector cell runs, the rigorous method of calculation gives the sedimentation coefficient value with good precision (about 1 O/,). However, because of the difficulties in accurate determination of the baseline, the rigorous method leads to a precision not better than about ioo/, for the diffusion coefficient value 151. Therefore, the molecular weight of the active unit cannot be obtained with a precision better than about 100/,. This precision is sufficient either to make a

9 Vol.23, No.2, 1971 K. COHEH and M. MIRE t 275 choice between various polymerization states of the enzyme or to show a change in the polymerization state under the influence of an effector of the enzyme. A system, involving two sector cell runs and an in-line connection of a scanning photomultiplier with a digital computer has just been completed in our laboratory. This system will avoid the tedious measurements on the densitograph tracings needed when using the rigorous method, and a better precision of s and D values is expected. The approximate method of calculation, which avoids the use of a computer, can be preferred when only 3--5O/, precision on the sedimentation coefficient s is required. All calculations can be made rapidly by hand. It is important to note that calculations using only the substrate-product boundary position on each tracing can only lead to erroneous sedimentation coefficient values. The active-enzyme-centrifugation method can be used to study the influence of the substrate or effectors on the polymerization state and on the conformat.ion of an enzyme molecule. As stated above the mathematical analysis assumes that everywhere in the solution and at any time during the centrifugation all the enzyme molecules have the same constant activity. As stated before non-observance of these conditions can lead to erroneous sedimentation values ; in particular, the observation of a variation of sedimentation value with substrate concentration should always be considered very carefully before drawing any conclusion. This work was supported in part by a research grant ( ) from the Comite' de biologie molkculaire de la dhle'gation ge'nch.de b la recherche scientifique. Thanks are due to Mrs A. Larousse for her continuous assistance. REFERENCES 1. Cohen, R., C.R. Acad. Sci. (Paris), 256 (1963) Cohen, R., and Hahn, C., C.R. Acad. Sci. (Paris), 260 (1965) Mire, M., Thhse 3e cycle, Orsay Mire, M., C.R. Acad. 8ci. (Paris), 264 (1967) Cohen, R., Giraud, B., and Messiah, A., Biopolymers, 5 (1967) Hathaway, G., and Criddle, R., Proc. Nut. Acad. Sci. U. S. A. 56 (1966) Criddle, R., Biochemistry of Chloroplasts, Academic Press, New York 1966, Vol. 1, p Arnaud, Y., J. Chim. Phys (1966) Arnaud, Y., J. Polymer Sci. Part C (Polymer Symposia), 16 (1968) Hoagland, V., and Teller, D., Biochemistry, 8 (1969) 594. Yoshida, A., and Hoagland, V., Biochem. Biophys. Res. Commun. 40 (1970) Schumaker, V., and Schachman, H., Biochim. Biophys. Acta, 23 (1957) Svensson, H., Hagdahl, L., and Lerner, K., Sci. Tools, 4 (1957) Vinograd, J., and Bruner, R., Biopolymers, 4 (1966) 157. R. Cohen Institut de Biologie Molkculaire, Universiti. Paris VII 2 Place Jussieu, F-75 Paris 5, France