/
operated between 200-250 “C,it seems safe to assume that the tube was at a temperature not much below this. The tube was sufficiently smooth on the 0.d. to form a vacuum seal and the wall of the open end of the tube was rounded to avoid arcing from high potential points. All that is necessary when changing from CI operation to E1 (or cice wrsa) is to simply replace the tube with the appropriate one. ACKNOWLEDGMENT
We would like to thank A. G . Grill for assistance in the design and for the fabrication of the ferrule and tube. Figure 1. Gas entry wsembly The gas pathway is shown from the coverplate to the hole in the ion source. The tube extending from within the coverplate to the ion source is shown for E1 operation. For CI operation, the tube would have a crimp as indicated by the dashed line
RECEIVEDfor review April 20, 1972. Accepted June 16, 1972. This work was made possible through financial assistance from the National Institutes of Health (GM 02055, G M 16216, NIH 69-2161) and the Robert A. Welch Foundation (Q 125).
Variable-Ratio Stopped-Flow Mixing Device Richard A. Harvey Department of Biochemistry, Rutgers Medical School, College of Medicine and Dentistry of New Jersey, New Brwzswick, N.J. 08903
Walter 0 . Borcherdt Science Products Corporation, Dover, N.J. 07801
STOPPED-FLOW PHOTOMETRY is one of several techniques which permit the measurement of the rates of reactions whose halftimes are less than approximately 5-10 seconds ( I ) . In this method two reactants are driven at high velocity through a mixing chamber into an observation tube. The flow of reactants is abruptly stopped and the extent of reaction is followed by measuring an optical property of the solution, e.g., changes in transmission or fluorescence emission. In the past, the scope of the stopped-flow method has been limited primarily by the usual performance parameters such as signal-to-noise ratio, instrument dead-time, and mixer efficiency ( I ) . However, as increasingly complex chemical reactions are investigated, the time consumed in the manipulative operations of the experiment becomes an important limitation. For example, the kinetic investigation of the enzyme catalyzed reaction Enzyme
A + B d C + D might typically involve rate measurements at 5 concentrations of reactant A, each measurement being repeated at 5 different concentrations of reactant B. With the usual fixed-ratio stopped-flow apparatus, this systematic investigation would typically require the introduction of 25 unique combinations of reactant solutions into the rapid mixing device in the stopped-flow system. Each change of solution is not only laborious, but also consumes considerable quantities of reactants in purging and re-equilibrating the fluids within the machine. The present paper describes a stopped-flow instrument in which the initial composition of the reactant solution can be varied by mixing different volumes of two reactants at any one of thirteen volume ratios. The apparatus significantly reduces manipulative operations (in the example above, only (1) F. J. W. Roughton and B. Chance, “Technique of Organic Chemistry,” S . L. Friess, S. E. Lewis, and A. Weissberger, Ed., Interscience, New York, N.Y., 1963, Vol. VIII, p 703. 1926
four manual dilutions are necessary to generate 25 different combinations of reactants) and facilitates extension of the stopped-flow method to complex chemical reactions. EXPERIMENTAL Apparatus. The stopped-flow apparatus consists of a fluid delivery system which ejects precisely controlled volumes of reactants, a mixer which forms a homogeneous solution from the two reactants, and a photometer which measures and records the time-dependent absorption of light by the reacting solution. The mixer and photometer have been described previously (2). The fluid drive system delivers two reactant solutions in any of thirteen volume ratios: 100:1, 50:1, 20:1, lO:l, 5:1, 2:1, 1:1, 1:2, 1:5, l : l O , 1:20, 1:50, and 1:lOO. This differential metering of reactants is achieved by mechanically varying the stroke of two equivalent drive syringes. The apparatus is, therefore, an extension of both the usual k e d ratio machine which delivers equal volumes of reactants ( I ) , and a more specialized instrument which delivers fixed but dissimilar volumes of reactants (3). The fluid drive system is most easily analyzed in terms of the linear and rotary motions of its basic components (Figure 1). Mixing is initiated by actuation of a solenoid valve (not shown) which creates a positive pressure in a pneumatic cylinder containing a piston. This causes a forward motion of the piston and its associated cam. Two opposed surfaces or facets of the cam are in contact with two push rods. Thus the forward motion of the cam is translated into differential motions in push rods A and B. A claw on each push rod translates this lateral movement into a small angular rotation of its bell crank, which in turn generates a linear forward motion of the plunger rod advance sleeves. The advance plunger rod ball grip within the sleeve contains spring-loaded balls which are forced into contact with a ring cone and the syringe plunger rod (Figure 2 4 . The balls, ring cone, and (2) R. A. Harvey, Anal. Biochem., 29,58 (1969). (3) B. Chance, Discuss. Faraday Soc., 17,123 (1954).
ANALYTICAL CHEMISTRY, VOL. 44, NO. 11, SEPTEMBER 1972
Table I.
Ratio setting 1OO:l 50:l 20:l 1O:l 5:l 2:l 1:1 a
Instrument Performance Parameters Instrument Reactant ratios dead time, Ratio of plunger (water plus dimsec rod displacement" chloroindophenol)n Erratic 114 & 20 103 f9 Erratic 57.7 Z!Z 8 47.3 i 3 21.4 i. 0.8 10.2 f 0.1 4.92 k 0.05 1.96 f 0.01 1 .oo 0.01
*
19.9 i 0 . 6 9.70 Z!L 0 . 2 4.70 f 0.03 1.93 Z!Z 0.01 1 .oo i 0.01
10 8 5 5 4
10 determinations at each ratio.
plunger rod are thus locked together, and the plunger rod advances with the sleeve. The plunger rod can move through the anti-return balls, because motion of the rod in this direction tends to reduce the force between rod, balls, and cone ring. When rod forward motion ceases, the anti-return balls are spring-loaded into the anti-return cone ring and against the plunger rod; thus the rod is locked against any tendency to move backward. When pneumatic pressure is released from the piston, a return spring (not shown) moves the piston rod, multi-faceted cam, etc. (Figure l), backward so that the push rods return to their original position on the cam and force on the bell cranks is relieved. This allows a return spring (not shown) to retract the plunger rod advance sleeve, cone ring, and advance balls backward to their original position. The sleeve retains contact with the clah of the bell crank and, through the bell crank, with the push rod; hence, all backlash is kept out of the system. Because the return spring of the plunger advance mechanism exerts a higher force than the advance ball loading spring, and because the return motion of this assembly is in a direction which relieves the ball-cone-rod force, the advance mechanism can return without causing any backward motion of the plunger rod. The ball grip release sleeve may be manually moved at any time by depressing the appropriate ball grip release lever (not shown). This action lifts both sets of rod grip balls out of their cone rings, reducing their grip on the syringe plunger rod sufficiently that the rod may be manually pulled back through the ball grips. This enables the syringe to be reWed. The plungers of the syringes containing the reactants are in contact with the plunger rod. Thus, the fluid delivered from each syringe can be varied according to the rise on the corresponding cam face. For example, if it is desired to mix five volumes of reactant A with one volume of reactant B, the cam angles would be as indicated (Figure 2B). Rotary positioning of the cam presents different pairs of cam facets to the push rods allowing different volume ratios of reactants to be delivered to the rapid mixer. In addition to providing the proper volume ratios, the cam angles are designed to keep the total volume of reactants (0.11 ml per measurement) constant at all ratios. This results in minimal consumption of reagents, an important consideration, particularly in experiments with scarce biological materials. Reagents. Diphosphopyridine nucleotide (DPN), lactic acid, and crystalline rabbit muscle lactate dehydrogenase were products of Sigma Chemical Co., St. Louis, Mo. RESULTS AND DISCUSSION Instrument Performance. The variable-ratio fluid delivery system has been analyzed by three methods. First, the relative linear displacement of the plunger rods was measured with micrometers using a specially constructed jig, The data, which are summarized in Table I, indicate that the motions of the plunger rods are in good agreement with the
SYRINGE RUNGER ROD
RATIO SELECT07
Figure 1. Schematic diagram of the variable-ratio fluid delivery system A SYRINGE " 9 " PLUNGER mD\
SYRINGE "A" /PLUNGER ROD
t TROKE CREMENT
ANTI - RETURN PLUNGERBX BAL
LL NK
ADVANCE PLUNGER ROD BALL GRIP
RETRKTED
POSITION
CAM
RETURN SPRING
ADVANCED
POSITION
BELL CRANK
B -
Figure 2. Details of ( A ) plunger rod advance mechanism and ( B ) cam and push rod assembly
design specifications for the ratios up to 20:1, however, at the extreme volume ratios (e.g., 50 :1 and 100 :l), the standard deviation in relative motion of the plunger rods increases. Similar data have been obtained for the reciprocal ratios, i.e., 1 :loo, 1 :50, etc. Second, the volumes delivered from the fluid delivery system to the stopped-flow observation cell were measured by placing water in one reactant syringe and a dye solution (5 X lOP4Mdichloroindophenol), which obey Beer's law over the concentration range studied, in the other syringe. Mixing these reactants at various volume ratios results in a solution whose composition can be determined by the absorption of light at 620 nm. From the spectrophotometrically determined composition, the relative volume of water and dye delivered to the stopped-flow mixer can be calculated (Table I). The accuracy and precision of the volume ratios are good for ratios up to 20:l. At 50:l and 100 :1, the reproducibility of the volumes is markedly decreased. Similar results were obtained with the reciprocal ratios. In the third method, the dead-time of the apparatus at different volume ratios was measured using the potassium ferricyanide-ascorbate reaction (2). The mixing time increased as the two reactant volumes become more dissimilar and at 50 :1 and 100 :1 the fluid velocity of the reactant delivered in low volume was too slow to ensure adequate mixing. Performance at these extreme volume ratios could be improved by using a mixer in which the cross-sectional area of the orifice for reactant A was one-tenth that of the orifice for reactant B. While this mixer was useful for mixing a small volume of reactant A with a large volume of B, it was predictably ineffective in the reverse volume ratio. Perhaps an adaptation of the four-jet-ball mixer described by Berger et af. (4) would result in improved mixing characteristics.
(4) R. L. Berger, B. Balko, and H. F. Chapman, Rev. Sci. Instrum., 39,493 (1968).
ANALYTICAL CHEMISTRY, VOL. 44, NO. 11, SEPTEMBER 1972
1927
,
”V 0
6.
21
1
\
51
0
II
X
0
0
Figure 3. A. Initial substrate concentrations at various volume ratios B. Substrate-velocity profiles at various volume ratios. Filled cirlces represent velocities (in arbitrary units) at [LDH] = 30 pg/ml Application. The variable-ratio technique is applicable to chemical systems where it is necessary to define the dependence of reaction velocity on the concentration of reactants. The method is particularly useful in the collection of the large sets of data frequently encountered in the study of enzyme-catalyzed reactions. For this reason the method is outlined in terms of the well-defined lactate dehydrogenase (LDH) reaction (5).
lactate
LDH + DPN+ e Pyruvate + DPNH + Hf
(2)
The effect of the concentration of DPN+ and lactate on the reaction velocity in the direction of pyruvate formation was studied at constant enzyme concentration. In a typical experiment, one drive syringe of the mixing apparatus contained lactate dehydrogenase, 30 pg/ml, and 60mM lactate, while the second drive syringe contained enzyme, 30 pglml, and 2mM DPN+. These solutions were mixed in five different volume ratios (1 :5, 1 :2, 1 :1, 2 :1, 5 :l), producing reaction mixtures containing lactate and DPN+ at five different concentrations. The concentration of the enzyme is identical in both syringes and is, therefore, invariant upon mixing, If the concentrations of lactate and DPN+ are represented on the X and Y axes, respectively, of Figure 3A, the initial compositions resulting from the various volume ratios can be (5) G. W. Schwert and A. D. Winer, “The Enzymes,” P. D. Boyer,
H. Lardy, and K. Myrback, Ed., Academic Press, New York, N.Y., Vol. 8, 1963.
1928
shown as points along the line connecting 60mM lactate and 2mM DPN+. The solution containing enzyme and 2mM DPN+ was removed from the apparatus and replaced by a solution containing LDH at the same concentration and 1mM DPN+. Reaction rates were measured at the initial substrate concentrations shown along the line connecting 60mM lactate and 1mM DPN+ and at three additional concentrations of DPN+ (two not shown in Figure 3 4 yielding a total of 25 rate measurements as a result of only four manual dilutions of reactants. If the X and Y axes are envisioned as being in the plane of the printed page, the initial reaction velocities can be plotted vertically on the mutually perpendicular Z axis generating the substrate-velocity profiles shown with horizontal hatching in Figure 3B. The smooth curves are computer calculated best fit to the rate equation proposed by Zewe and Fromm (6). Note that these planes define sets of rate measurements in which the concentration of neither substrate is held constant. This situation presents no problem if the data are to be fitted by computer directly to a suitable rate equation (7). The usual graphical analysis (8) is also possible if the rates examined are obtained at the same volume ratio, e.g., the vertically hatched substrate-velocity profile of Figure 3B corresponds to rates at constant (lactate) and varying (DPN+). Experiments similar to those described above were performed at enzyme concentrations ranging from 0.086 pg per ml to 300 pg per ml. Analysis of the data showed that the steady state kinetic properties of lactate dehydrogenase were virtually constant over a 4,500-fold range of enzyme concentration extending from the low levels typical of classical spectrophotometric assays to the high enzyme concentrations which occur within the cell (9, 10). These results strengthen extrapolations relating in oitro kinetic observations to intracellular function. The variable ratio fluid delivery system also facilitates concentration jump experiments in which a small volume of solution containing a chemical system at equilibrium is rapidly diluted into a large volume of water or buffer (11). The diluted concentration of components involved in bimolecular reactions will no longer be at equilibrium and, therefore, must adjust. The concentration jump technique has not been applied extensively because it usually requires a modification of the stopped-flow apparatus and it is applicable only if the chemical relaxation is slow relative to the time of mixing and observation. The variable ratio apparatus allows the exploration of a variety of perturbation conditions without troublesome instrument modification. ACKNOWLEDGMENT
We thank Mrs. Julie Heron for excellent technical assistance.
RECEIVED for review February 28, 1972. Accepted May 2 , 1972. This research was supported by NSF Grant GB 26081. (6) V. Zewe and H. Fromm, J. Biol. Chem., 237,1668 (1962). (7) W. W. Cleland, A d u a ~Bzzyrnol.,29, . l(1967). (8) K. Dalziel, Acta Chem. Scand., 11, 1706 (1957). (9) T. Wuntch, R. F. Chen, and E. S. Vesell, Scielzce, 167, 63 (1970). (10) P. A. Srere, ibid., 158,936(1967). (1 1) G. Czerlinski, “Chemical Relaxation,” Marcel Dekker, New York, N.Y., 1966, p 269.
ANALYTICAL CHEMISTRY, VOL. 44, NO. 11, SEPTEMBER 1972
