Fast Flow Studies of Biological Reactions with Ion-Selective Membrane Electrodes Bernard Fleet’ and Garry Rechnitz Department of Chemistry, State University of New York, Buffalo, N . Y . 14214
A rapid-mixing continuous-flow system, utilizing liquid membrane ion-selective electrodes as sensors, is constructed and evaluated. The system is capable of measuring reaction times as short as 10 msec under turbulent flow conditions. Using appropriate ionselective resins in conjunction with the flow system, the rates of complex formation of Ca2+,Mg2+,and Be2+ with biologically important ligands were measured. STUDYOF THE KINETICS of metal complex formation has long been used for the elucidation of reaction mechanisms, but in recent years it has assumed added interest owing to the possibility that certain metal chelates can act as models for the study of the role of metal ions in biological systems (1). Numerous thermodynamic investigations of the interaction of metal ions with organic ligands have been carried out (2), particularly in the study of metal ion activation of enzymatic reactions; however, these have not shed much light o n the nature of metal ion specificity. An alternative approach to the problem is to study the kinetics of the reactions involved, and during the last few years relaxation techniques (pressure jump, temperature jump, sound absorption) have been widely used for this purpose (3). Ion selective electrodes have been used as sensors in kinetic studies (4-6) and it seems that this technique might provide a new experimental tool for the study of fast reactions. Consequently, we have initiated a kinetic study of several ion combination reactions covering a wide range of rate constants to assess the capabilities of the technique. A systematic survey of the reactions of solvated metal cations with various ligands has been carried out by Eigen and others (7-13). They have shown that the process of complex formation often involves the formation of a n ion pair followed by the dissociation of a water molecule from the inner hydration sphere of the metal ion, e.g.
M(aq)
+ L(aq)
@
M(aq)L
(ion pair)
(1)
1 On leave from Imperial College of Science and Technology, London.
(1) R. J. P. Williams in “The Enzymes” P. 0. Boyer, H. Lardy, and K. Myrbach, Eds., Academic Press, New York, Vol. I, 2nd ed., 1959, p 391. (2) A. Ringbom, “Complexation in Analytical Chemistry,” Interscience Publishers, New York, 1963. (3) M. Eigen, Discuss. Faraday Soc., 17, 194 (1954). (4) G. A. Rechnitz and 2. F. Lin, ANAL.CHEM.,40, 696 (1968). (5) K. Srinivasan and G. A . Rechnitz, ibid., p 1818. (6) Ibid., p 1955. (7) M. Eigen,Z. Electrochem., 64, 115 (1960). (8) M. Eigen, in “Advances in the Chemistry of Coordination Compounds,” S . Kirschner, Ed., Macmillan, New York, 1961, p 371. (9) M. Eigen and K. Tamrn, Z . Electrochem., 66, 93 (1962). (10) Zbid.. p 107. (11) G. G. Hammes and J. I. Steinfeld, J . Amer. Chem. Soc., 84, 4639 (1962). (12) M. Eigen, Pure Appl. Chem., 6,97 (1963). (13) G. G. Hammes and S . A. Levison, Biochemistry, 3, 1504 (1964). 690
ANALYTICAL CHEMISTRY, VOL. 42, NO. 7, JUNE 1970
ko
M(aq)L
e ML(aq) + iiH20
(2)
k.0
Three different mechanisms have been proposed for the following rate determining processes: For reactions of alkali and most alkaline earth ions (Ca2+, S P , Ba2+) the rate constants for the loss of water are high (>lo7), but a small variation is observed between different ligands. This indicates that chelation is the rate determining step. Magnesium and several divalent transition metal cations exhibit rate constants that are less than lo7, but virtually independent of the nature of the ligand. This indicates that loss of water from the coordination shell of the metal ion is the rate limiting step. With a third group of cations [e.g. beryllium(II)] rate constants are relatively low and show a marked dependence on the nature of the ligand. It has been postulated that the hydrolysis of a water molecule in the coordination shell is the rate-determining step and that the rate constant is therefore dependent on the basicity of the anion, e.g. in the case of beryllium(I1)
+ ABe(OH)+ + H A
Be(Hz0)2+
--+
Be(OH)+
+
BeA+
+ HA
+ H20
(3) (4)
I n order to evaluate the utility of a liquid ion-exchange membrane electrode for continuous flow kinetics, a n example from each of the three classes discussed above was chosen for study. Consequently, the reactions of Ca2+, Mg2+,and Be2+ with several organic ligands of biological importance were investigated. EXPERIMENTAL
Chemicals. All chemicals used were of reagent grade. Solutions of the ligand anions were prepared by neutralizing the acids with tetramethylammonium (TMA) hydroxide (OSM). Stock solutions of CaC12, Mg(NO&, and BeS04 were standardized complexometrically. The ionic strength of the reaction media was adjusted with T M A chloride; p H adjustments were made with HCI. Apparatus. Ca reactions were monitored with a flowthrough calcium electrode obtained from Orion Research Inc., (type 98-20). The liquid ion exchange resin used in this electrode shows a high selectivity for calcium over most other divalent metal ions. Although this electrode shows a limited response to Mg2+ (Selectivity constant 1 X see Table I) the response is non-Nernstian and hence the electrode was not used to monitor reactions of magnesium. A divalent ion (water hardness) resin was used for this purpose (Orion, type 92-32). This electrode exhibits a n almost constant potentiometric response for a wide range of divalent cations. This electrode shows maximum stability, however, when the ion exchange resin is converted to the form of the cation under study. Consequently, for the Be2+ reactions, the resin was converted into the Be2+ form as recommended by the manufacturers. The internal reference solution consisted of 1 X 10-aM Be2+ in 1M KCl, in this case.
Table I. Dynamic Selectivity Ratios for Electrode Resins System Flow Rate 14.2 ml min-l SELECTIVITY RATIOS
Electrode resin Calcium (Orion 92-20) Divalent metal ion (Orion 92-32-02) Divalent converted to Be*+form
Ca2+
Mg2+
Li+
Na+
K+
Me4N+
EtaN+
PraN+
1
0.018
0.156
0.010
0.006
0.0067
0.0051
2.72
-5.7
X 103
0.091
1
0.124
0.025
0.018
0.016
0.156
7.40
-1.6
X lo4
0,091
.,
0.027
0.029
0.001 3
0.0005
0.0010
0.342
1 . 4 X IO2
0.009
1
... 0.063
PhMea- Be*+
0.0018
F o r some measurements, a flow through reference electrode (Orion model 98-20) was employed. Alternatively the effluent from the measuring electrode was allowed to flow into a 10-ml reservoir in contact with a saturated calomel electrode (Beckman type 39410 quartz fiber junction). A Beckman research model p H meter was used both for direct potentiometric measurements and also as a preamplifier in connection with a Beckman 10-inch potentiometric recorder for measuring E us. t rate curves. Two syringe pumps were used; a model 975 infusion pump (Harvard Apparatus, Inc.) was used in preliminary investigations and for the slower flow experiments (flow rates up to 25 ml min-l). For faster flow rates the syringes were located in a pushing block driven via a magnetic clutch by a 0.25horsepower motor (Model NSH-55, Bodine Electric Co.) (14). The use of the magnetic clutch was eventually discontinued as it induced noise in the measuring circuit. With this system and using a n electrode by-pass arrangement, pumping rates up to 250 ml min-l could be employed. Flow Assembly. A schematic diagram of the flow assembly is shown in Figure 1. Solutions of metal ion (syringe 1) and ligand reagent (syringe 2) are fed into at 4-inlet mixing chamber, each solution entering at diametrically opposed ports. The mixing chamber is constructed of Plexiglas and has a n annular mixing space of 4.8 X 1.3 mm. Mixing times below 10 msec are attainable a t flow rates >140 ml min-1. Inlet and outlet lines are made from 18-gauge syringe needle tubing with the inlet tubes entering tangentially to the mixing space while the exit tube is positioned vertically. The solution from the mixing chamber flows along the reaction tube ( u d ) to a T piece stream splitter; the bulk of the solution flows to waste while a small portion is led along the short flow path (u& through the measuring and reference electrodes. The volume of solution flowing through the electrode channel is controlled by a restrictor x . This consists of 4.0-cm piece of 0.034-cm. i.d. capillary tubing sealed inside the flow line. The measuring tubes uld1 and u.d, are 0.086-cm and 0.061-cm i.d. polyethylene tubing, respectively. Connecting lines to the mixing chamber are made from 0.14-cm polyethylene tubing. Wherever possible all connections are secured with epoxy resin and wire. The time of measurement is determined by the linear flow rate (u cm sec-I) and tube length (d cm) i.e., uldl u2d2. Measurement times as low as 10-15 msec can be attained. Procedure. A solution of metal ion (C,) in syringe 1 and solvent ( p = 0.02 with T M A chloride) in syringe 2 is pumped through the system and the electrode potential is balanced using the pH meter as a potentiometer. The recorder is connected so that the initial M *+ concentration will give the base line response. Next a solution of metal ion (C,)a t the lower end of the concentration range is introduced through syringe 1 and the amplifier gain adjusted to give full scale
+
(14) G. Dulz and N. Sutin, h o r g . Chem., 2, 917 (1963).
PhMe3N+
SYRINGE PUMP
WASTE IONREF. ELECTRODE ELECTRODE
Figure 1. Schematic diagram of flow assembly Flow Role ml.min-'
-
m
._ 0 -
?
-
4
-
I
W
I
."Il l
0
,
I
,
50 100 I50 Linear Flow R a t e Across M e m b r a n e , c m sec.-1
Figure 2. EKect of flow rate on electrode response i.
ii.
lo-*, iii,
(TMA chloride) pH
=
lo+, iv, 6.80
and v, 10-5M Ca2+.1.1 = 0.1
deflection. Typical values for C1 and Cyare 1 X and 5 X IO-jM, respectively. To carry out kinetic measurements, the solution of the ligand is introduced cia syringe 2 with metal ion (C,) in syringe 1. The steady state response of M2+ is measured a t several values of t. Variation of t is achieved by altering the length of the reaction tube by introducing a delay line between the flow restrictor and the electrode. RESULTS AND DISCUSSION Preliminary Investigation of Effect of Flow Rate on Electrode Response. Since the electrode is designed only for measurement at relatively low flow rates, it was first of all necessary t o measure the effect of flow rate on electrode response at various concentrations. The results obtained for the calcium electrode are shown in Figure 2 with the ionic strength of the solutions adjusted to 0.02M using TMA chloride. It is essential to maintain the ionic strength of the solution a t ANALYTICAL CHEMISTRY, VOL. 42, NO. 7, JUNE 1970
691
Table 11. Summary of Rate Data for Ca2+Reactions Ligand [L],, M [Cal,, M rmeas k M-lsec-l Lactate 1 x 10-3 1 x 10-4 0.013 > 2 . 0 x 105
x 1x 5 x 5 x 5
Gluconate Malate
x 5 x 2 x 2
Tartrate
L
I
!
I
10-3
I
I
10-2
10-1
Molarity Be SO,
Figure 3. Beryllium electrode response in flow stream Flow-through SCE, 14.4 ml min-l flow rate. Internal reference solution 1 X 10+M Be2S04in 1 X 10-lM KCI
10-2M o r greater to avoid the occurrence of streaming potentials. The slight increase in potential, 1-2 mV up to flow rates of about 35 cm sec-l, is regular and potential measurements can be made to a n accuracy of h0.2 to 0.4 mV. At concentrations below 10-4M, the electrode potential shows an initial jump of 3-4 mV as soon as the solution commences to flow. The response then levels off and actually starts to decrease at higher flow rates. The electrode response at flow rates >150 cm sec-1 becomes erratic and the initial increase rapidly falls off until the electrode reaches a potential below that at lower flow rates. This behavior is almost certainly due to the distortion of the membrane by the very high .pressures required to achieve these high flow rates. The limiting flow compatible with stable response was about 20 ml min-I (linear flow across the membrane of 80 cm sec-I). The response of the beryllium electrode under flow conditions is shown in Figure 3. Evaluation of Flow System. In the design of a continuous flow system, it is desirable that the time required for mixing the reactant streams be minimized (15, 16). Further, it is essential that the flow rate be sufficiently fast to create conditions of turbulence in the reaction tube. In order to match these requirements with the limiting flow rate at which a stable electrode response could be obtained, it was necessary to use a bypass arrangement. The solutions were pumped at flow rates of up to 200 ml min-I and immediately before the electrode a T piece stream splitter led most of the solution to waste while a small fraction was diverted through the measuring and reference electrode channels. The stream splitting ratio was adjusted by placing a capillary restrictor (4.0 cm of 0.034-cm i.d. syringe needle tubing) in the electrode arm; typical ratio values were of the order 1 :lo. It is essential that the splitting ratio should not alter as the time delay lines are introduced. No significant change in the ratio was observed over measuring times in the range 15-50 msec, but at longer measuring times it was necessary to make adjustments by increasing the length of the waste line from the T piece splitter. The efficiency of mixing was checked both by a visual and a potentiometric method. Solutions of 1 X 10-2M NaOH (15) H. Hartridge and F. J. W. Roughton, Proc. Royal SOC., Ser. A , 104, 376 (1923). (16) E. F. Caldin “Fast Reactions in Solution,” Blackwell, Oxford, 1964, p 29. 692
ANALYTICAL CHEMISTRY, VOL. 42, NO. 7, JUNE 1970
x 1x
10-5
0.010
10-4 10-5
0.010
10-4
5
10-3 10-4
5
10-4 10-4
1X 5 x 10-5
10-4 10-4
1 5
x
x x
10-4 10-6
0.013 0.013 0.010 0.013 0.010
> i . o x 106 > 2 . 0 x 105 > i . o x 106 > 2 . 0 X 106 > i . o x 106 > 2 . 0 x 105 > 1 . 0 x 106
Table 111. Measured Rate Data for Mg2+Reactions k M-lsec-1 Ligand [LI,, M [Mgl,, M tmeaa(sec) x 10-4 Lactate 1 x 10-3 1 x 10-4 0.013 8.80 i.0 . 4 Gluconate 1X 1X 0.013 9.80 rt 0 . 4 Malate s x 10-4 t x 10-4 0.013 9.40 + 0 . 4 Tartrate 5 x 10-4 I x 10-4 0.013 9.50 i 0 . 5
containing phenolphthalein were mixed with 5 x 10-2M HCI. No purple color could be observed in the reaction tube. The potentiometric method involved comparing the electrode response for mixed solutions of 2.0 x 10-2M Ca2+and water with two solutions 1 x 10-2M in Cas+. There was no difference in the measured potentiometric response. It is desirable, when measuring high rate constants, that the reactant concentrations be made as low as the measuring system permits. Thus, although all of the electrodes employed in this study respond to below 10-4M, at this level of concentration a serious interference can be caused by the cation of the supporting electrolyte. I n order to select the best medium for carrying out the reaction the selectivity constants for the alkali metal cations and several tetraalkylammonium ions were measured, using the method described by Eisenman (17). The results are shown in Table I. From the data of Table I, it was possible to select T M A chloride as the most suitable supporting electrolyte. The reactant solutions were adjusted to an ionic strength of 0.02M with TMA chloride. Although, as has already been mentioned, it is desirable to keep the concentration of reactants as low as possible, in view of the fairly low formation constants of most of the systems studied, it was necessary to employ a 10-fold excess of ligand to ensure reasonable completeness of the reaction. As a test of the apparatus, the rate constant for the exchange reaction, Ca2+
+ Mg - EDTA F? C a - EDTA + Mgz+
(5)
was measured. We have previously measured the rate of this reaction as 2.7 X 1O2M-l sec-l (18). Although the rate for this reaction is rather slow for measurement with the continuous flow apparatus, by working with fairly high concentrations of reactants, e.g. 10-2 to lO-’M, reaction half times in the region of 50-100 msec. were obtained. Under second order conditions, with concentrations of both reactants equal at 5 x 10-2M, a n average value for t l I 2of 75 msec. was obtained giving a rate constant for the reaction of 2.65 X 102M-lsec-1. (17) “Glass Electrodes for Hydrogen and Other Cations,” G. Eisenman, Ed., Marcel Dekker, New York. 1967. (18) G. A. Rechnitz and Z . F. Lin, ANAL. CHEM., 39, 1406 (1967).
c
10 9-
8-
c 0
x 7-
'I
I +
c
Y
7 8
6-
54-
0X 7
E-
;
8 4
3t*r
i
;
I 103
L.
'1
.*t
1
105
Figure 5. Dependence of rate constant on basicity of ligand
.9
I
104
A = l
I
8
I
l
I
~
~
~
gluconate-,A
=
lactate-, 0 = tartrate,2- 0 !
=
malate2-
~
~
0 IO 20 30 40 50 60 70 80 90 100 I10 I20 I 3 140 150 160 17C t sec
XIO
Figure 4. Rate plot for beryllium(I1) Be2+ = 1 X 10-4M, ligand 1 X 10-4M, p TMA chloride A, gluconate, pH 7.15 k = 4.45 X l o 4 A, lactate, pH 7.05 k = 6.15 X lo4 0, tartrate, pH 7.15 k = 5.50 X 10' 0 , malate, pH 7.15 k = 8.75 X lo4
=
0.04
Kinetic Measurements. The reaction of Ca2+ with the anions of lactic, malic, tartaric, and gluconic acid was first examined. Literature values for the rate constant for the reaction of Cat+ with various anions are in the range 10'108M-lsec-1 while the upper limit of measurement with the present apparatus is theoretically, 106-107M- sec-I. The results obtained are shown in Table 11. The initial Cat+ concentration was, in most cases, 1 x 10-4M, but, owing to the relatively low formation constants for these reactions (19,20) it was not possible to reduce the ligand concentration to below 5 X l W 4 M . This resulted in the maximum attainable value of the rate constant under the present conditions Several measurements were carbeing 2 X 10"-lsec-l. ried out with Ca2+ concentration of 5 x 10-5M, although the nonlinear response of the electrode in this region resulted in a considerable decrease in precision. Measured rate constants for the reaction of Mg2+ with various ligands has been shown by Eigen (12) to be of the order of 106M-lsec-l and independent of the nature of the ligand. The results obtained with the present system (Table HI),although slightly lower than 106, confirm the essential independence of the reaction on the nature of the ligand. Although rate constants of this order of magnitude should be readily measurable with our apparatus, a complicating factor arises, as with the C a system, from the low formation constant (19) G. A. Rechnitz and T. M. Hseu, ANAL. CHEM., 41, 111 (1969). (20) R. J. P. Williams, J . Chem. Soc., 1952, 3770.
of the reaction product which makes it necessary to keep the metal ion concentration around 1 X 10-4MM. The divalent ion resin used was noticeably less viscous than the CaZ+resin and a considerable amount of leakage occurs through the membrane. This results in a very slight drift in E"; nevertheless, the equilibrium potential is rapidly established and is stable. The measured rate constants for the reaction of Be2+ with ligands were found to be considerably higher than anticipated (Figure 4). In this case, however, where the rate of hydrolysis is the rate limiting step, the basicity of the ligand will markedly influence the rate. The dependence of the rate on ligand basicity is shown in Figure 5; in order to examine this effect more closely, it would be necessary to measure the rate constants for a much wider range of ligand basicities than has been possible here. The main limitation to the use of liquid membrane electrodes in flow-kinetics is the physical limitation imposed by the maximum rate of flow through the electrode. Under conditions of very fast now, the pressure on the membrane causes it to oscillate; this results in a response pattern similar to the limiting current region of a polarographic wave. As in polarography, these oscillations are very regular and by taking the midpoint of the oscillation, a precise measurement may be obtained. The use of a by-pass system, described above, serves to relieve pressure on the membrane. Despite this present design limitation, flow-through electrodes seem to be well suited for the measurement of many first and second order rate constants in the biological range and should prove especially useful since electrodes are available which respond to ions such as Ca2+,F-, NOo-, etc., (21) which are not readily measurable by other techniques. RECEIVED for review January 16, 1970. Accepted March 13, 1970. (21) G. Rechnitz, ANAL. CHEW, 41 (12), 109A (1969).
ANALYTICAL CHEMISTRY, VOL. 42, NO. 7,JUNE 1970
693
