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SCIENCE SECTION

Westendorf 2

III. Procedure and Results

Procedures and Results appears in two Sections. Section B. Effect of Fluoride on the Permeability of Erythrocyte Membranes for Na+, K+,Ca2+, F-, HPO42-, and Glucose, begins on Page 7

Section A. Acetylcholinesterase Inhibition

1. General Information

The nomenclature for ACh hyrdrolases initially presented great difficulties because several enzymes that all catalyze the hydrolysis of ACh exist. Two enzymes exist that are substrate-specific and only hydrolyze ACh (abbr. AChE). In addition, there are 11 enzymes that can hydrolyze ACh as well as other esters. These enzymes have become known as pseudo-cholinesterases (abbr. PChE). The two substrate-specific enzymes, also known as "real cholinesterases", are found in the myelin sheath of nerves, at the motor endplate, in all cholinergic organs, and in erythrocytes. The two enzymes that are not categorized as iso-enzymes are differentiated only by their optimal pH (pH = 7.2 and pH = 8.6). W. PILZ (24) was able to separate them using starch gel electrophoresis. The same author was also able to separate the other 11 non-specific esterases, which are found in the serum. The characteristics of these PChE vary greatly, so a singular kinetic behavior is not to be expected upon investigating their inhibition. When using all of these enzymes together in the form of unpurified serum one must, in the worst case scenario (ie when the affinities of the individual components for the substrate or inhibitor are all different), deal with a function with 11 variables. We could, in fact, identify a non-homogeneous relationship in such an enzyme test.

Several models of the course of the hydrolysis of ACh have recently been developed. (25, 26) All of the models assume two binding sites, which are supposed to have a spacing of 7 Å, equivalent to the distance between the positive nitrogen and the carbonyl oxygen of the ester group in the ACh.

Figure 1.

According to this model, the ACh's quaternary nitrogen is bound to a negatively charged phosphate group by way of an ionic bond. Meanwhile, dipole-dipole reciprocal attraction occurs between the O atoms of the acetyl group and the OH group of a serine residue, as well as the N atom of an imidazole ring, which are components of the AChE's esterase binding subunit. The dipole-dipole interactions ultimately lead to the transfer of the acetyl residue onto the enzyme (ester-formation with the serine residue). The enzyme is afterwards regenerated by saponifying this ester bond.

2. Theoretical Treatment of the Enzymatic Kinetics

Enzymatically catalyzed reactions can often be represented by the following schema

If the reaction is exergonic (D H< 0), which is usually the case, k-2 can be ignored with respect to k+2. If one further assumes that the complex formation occurs far more quickly than the transformation that follows it, then the complex formation is subject to the Rules of Mass Action, which means that the complex formation leads to an equilibrium (equation 1).

Since the velocity of the reaction (v) is dependent on the concentration of ES, it is, by way of equation 1, also dependent on the substrate's concentration. At a given enzyme concentration, v = f[S] can be plotted as follows:

Figure 2. Enzyme Reaction Rate vs. Substrate Concentration

The reaction rate reaches a maximum (Vm). This saturation occurs when all of the enzyme is present as ES. The substrate concentration necessary for saturation can not be precisely read off the graph due to the asymptotic nature of the curve. Therefore, the half-maximal rate is used to characterize the enzyme. The substrate concentration at half-maximal rate is known as the Michaelis constant (KM). It is constant for a given enzyme/substrate pair held at constant reaction conditions. As can easily be shown from equation 1, the Michaelis constant is numerically equal to the dissociation constant KS.

For vm/2: [E] = [ES].


By substituting into equation 1, one gets


If v is limited by k+2, then (equation 2):


If one sets [E] = [Et] - [ES] and substitutes into equation 1, one gets:


k2[Et] corresponds to the maximum reaction rate, so that finally (equation 3):


This relationship is also known as the MICHAELIS-MENTEN equation. It represents the mathematical relationship of the plot in figure 2. If k+2 can not be ignored with respect to k-1 the following is not equivalent to KS:


The linear rearrangement of equation 3 according to LINEWEAVER and BURK. offers one possibility for the graphical representation of KM and Vm. Accordingly (equation 4):


If one depicts this equation graphically the plot of 1/v à 1/[s] runs as a straight line with y-intercept 1/vm and x-intercept -1/KM.

Figure 3. Generalized Lineweaver-Burk Plot

Enzymatic Inhibition

A reduction in the reaction rate can occur if there is an additional substance present in an enzyme-substrate system that reacts with the enzyme during complex formation. Such an "inhibition" develops when the inhibitor reacts with the reactive center of the enzyme and thereby displaces the substrate from the surface of the enzyme by way of a competitive reaction. Inhibitor binding at another location on the enzyme molecule can also lead to inhibition by causing a conformational change and/or shifting the charge distribution. The first case represents a competitive inhibition and the second a non-competitive inhibition. If both forms of inhibition arise at the same time it is known as a mixed-competitive inhibition.

The type of inhibition can be identified by analyzing the plot of the reaction in a Lineweaver-Burk diagram (figure 3). For a competitive inhibitor the magnitude of the maximum reaction rate is unchanged by addition of the inhibitor, since a constant increase in substrate concentration can eventually displace all of the inhibitor from the reactive center. The Michaelis constant, however, does change since the substrate concentration needed to reach half of the maximum reaction rate is higher. If one examines the course of the reaction rate as a function of substrate concentration, with and without inhibitor, a plot analogous to figure 3, with two straight lines of equal y-intercept but different x-intercepts, results. Such a case is diagrammed in figure 4.

Figure 4. L-B Plots Comparing Uninhibited And Competitive Inhibited Rates

In the case of 50% inhibition [ES] = [EI]. In this case the relation [S]/[I] is the same as the relationship between the two constants KS/KI. The quantitative expression of the inhibited reaction in figure 4 is (equation 5):

Legend:

[I] = Inhibitor concentration

KI = Dissociation constant for the enzyme/inhibitor complex

KM = Michaelis constant for the uninhibited reaction

K’M = Michaelis constant for the inhibited reaction


The inhibitor constant can be calculated from (equation 6):


The inhibitor constant is a measure of the affinity of the inhibitor for the enzyme and thereby of the effectiveness of a substance that acts as an enzymatic inhibitor. Enzymatic inhibition is described by the fraction:


Under conditions of substrate saturation equation 3 becomes v= vm = vo, which means that:


That is to say, KM can be disregarded with respect to [S]. By inserting the expression for the inhibition to rearrange equation 5 one gets:


When I approaches 0, the inhibition also approaches 0, since [S] / KM + [S] approaches 1, which is the case for the region of substrate saturation. Equation 7 describes the course of the inhibition as a function of inhibitor concentration when a competitively inhibitory substance is present. Once the values for KI and KM have been determined via a calculation based on figure 4, the inhibition can be calculated for any substrate and inhibitor concentration. However, outside the region of substrate saturation, v no longer approaches vo, even in the absence of an inhibitor.

Under conditions of a non-competitive inhibition the binding of substrate to enzyme is unaffected, that is to say KM is not a function of I. The reaction rate, on the other hand, is decreased. Similar to figure 4, the following results:

Figure 5. L-B Plots Comparing Uninhibited and Non-Competitive Inhibited Rates


The following equation holds for V'm:


The complete equation for the reaction rate is therefore (equation 8):


(Translator’s note: There is no text for nor any equation numbered “9”)

The second term = 1 when there is substrate saturation and the equation becomes (equation 10):


Equation 10 describes the dependence of the inhibition on the inhibitor concentration in the case of a non-competitive inhibition and substrate saturation. If there is no substrate saturation the second term must be multiplied by:


Mixed-competitive inhibition is a form of inhibition that results from the combination of competitive and non-competitive inhibition. Since this example was also represented among our measurements it will be discussed at this point. There are cases in which a reduction of both the maximum reaction rate and the Michaelis constant are observed. In such a case, the binding of substrate to the enzyme's reactive center as well as further reaction of the ES-complex with the enzyme and product are inhibited. The lines in a Lineweaver-Burk diagram intersect at a point where x is negative and y is positive.

Figure 6. L-B Plots Comparing Uninhibited and Mixed-Competitive Rates


In this case (equation 11):


Here K'M is the substrate concentration that yields half of the maximum reaction rate when there is an excess of inhibitor present. The y-intercept of the inhibited reaction (K'M'') obeys the following relationship (equation 12):


Substituting equation 11 and equation 12 into equation 3 yields the following expression for the reaction rate of the inhibited reaction (equation 13):


Equation 14 describes the complete course of the dependence of the inhibition on inhibitor concentration in the case of a mixed-competitive inhibition. If there is an excess of substrate KM can be disregarded with respect to S, as long as the inhibitor concentration is not too large. Equation 14 then becomes (equation 14):


If one solves equations 7, 10 and 15 for ((vo / v) - 1) one derives the following linear functions when viewing these values as a function of the inhibitor concentration (equation 15):


1. competitive inhibition (equation 16):


2. non-competitive inhibition (equation 17):


3. mixed-competitive inhibition (equation 18):


Independent of the type of inhibition, plotting the left side vs. [I] results in a straight line that intersects the origin, assuming that the conditions under which the equation was derived are maintained. This means that KM can be disregarded with respect to [S] and that there is excess substrate present, which further implies that no free enzyme is present. Furthermore, the enzyme must use the same number of binding sites with respect to the inhibitor as it does with respect to the substrate, since [I] would otherwise not take on a linear relationship. [I] would instead take on the form [I]n, where n can be either smaller or greater than 1 depending on whether the enzyme uses more or fewer binding sites with respect to the inhibitor than with respect to the substrate. If n1, but is constant within the observed concentration range, its value can be derived from a double-logarithmic plot.


1. competitive inhibition (equation 19):


2. non-competitive inhibition (equation 20):


3. mixed-competitive inhibition (equation 21):


If n changes within the observed concentration range the plot will follow a curved line, even with this method of representation.


3. Procedure

a. Description of the Tracer Method

ACh hydrolysis can be followed by either determining the decrease in ACh concentration or by measuring the increase in concentration of the reaction products, choline and acetic acid.

A procedure described by H.U. BERGMEYER(27) uses the first of these methods. Initial and final ACh concentrations are determined using the fact that hydroxylamine is converted to acetylhydroxamic acid, which forms a red complex with Fe3+ that can be photometrically followed. The large reaction volume (25ml) and the labor intensity are drawbacks of this technique.

The majority of experiments cited in the literature are carried out using the second approach. One can, for example, using a pressure gauge, determine the amount of C02 released from a bicarbonate buffer by the formation of acetic acid. Because certain conditions that must thereby be painstakingly maintained, this is also a rather laborious technique. Another possibility consists of measuring the pH changes caused by the acetic acid with the help of a glass electrode. The drawback of this method is that the enzymatic activity is affected by a pH change that occurs during the measurement. A detailed description of these procedures can also be found in H.U.Bergmeyer(27). To improve on the electrometric method one can immediately neutralize the released acetic acid with NaOH using an automatic titrator controlled by the EMK of the glass electrode. The amount of base used in titration then becomes a measure of the level of reaction. E. Heilbronn(18) uses this procedure as well. The advantage of this technique is that it is relatively easy to manage and can be carried out quickly. In addition, the hydrolysis can be read off directly at any time. The drawback is that the number of ions in solution changes over the course of the reaction, which can have an effect on the enzymatic activity. In addition, the finite response duration of the regulatory cycle limits the lower boundary of the reaction time. Measurement over small times does, however, become necessary when varying the substrate concentration to record a "Lineweaver-Burk" diagram, since the substrate concentration is not allowed to change noticeably over the course of the reaction.

To avoid the difficulties mentioned above, we developed a new procedure for measuring the rate of ACh hydrolysis. The procedure relies on the use of a radioactive tracer method. We used 1-C-14-ACh for this, which we obtained from the company Amersham-Buchler in Braunschweig.

Principle:

The labeled ACh decomposes into radioactive acetic acid and non active choline when hydrolysis occurs. After the reaction had run we precipitated the remaining ACh+choline by adding an excess of sodium tetraphenylborate (Kalignost), a substance that forms highly insoluble precipitates with many large monovalent cations. The solubilities of the salts are 3 x 10-5 g/ml for choline and 3 x 10-4 g/ml for ACh.(28)

After centrifugation we determined the radioactivity in the clear supernatant. The radioactivity stems from the 14C Acetic acid that has formed and is proportional to the amount of ACh that has been converted.

The great sensitivity of this method is one of its important advantages. The specific activity of the labeled ACh-specimen was 10 Ci/Mol. The unit 1 Curie (Ci) is equal to 3.7 x 1010 impulses/sec.

When using a fluid scintillator, 103 Imp./min (abbr. Ipm), which corresponds to 4.5x10-10 Ci or 4.5x10-11 Mol ACh (8.2x10-9 ACh-chloride), should be set as the lower boundary in order to achieve sufficient accuracy. When using such ACh concentrations one would fall short of the solubility product of the ACh-sodium tetraphenylborate compound. This difficulty can, however, be circumvented, after the reaction is complete, by adding an excess of non-radioactive ACh, which is precipitated out with an excess of Kalignost. Since the radioactivity is evenly distributed among all of the ACh, both in solution and in the precipitate, in the solution one basically only finds radioactive acetic acid that has not been precipitated out. A disruptive absorption of tiny amounts of acetic acid into the precipitate can also be inhibited by adding non-radioactive acetic acid. Upon measurement of different substrate concentrations, the influence of the latter on the accuracy of the measurement can be eliminated by using stock solutions with different concentrations but the same radioactivity. One therefore has a different specific activity for each concentration.

With other methods the measured concentration level is proportional to the acetic acid, which leads to very small concentrations yielding inaccurate values because the accuracy of the measurement is generally of an absolute value. In our case the measured value, that is to say the radioactivity, does not decrease with decreasing substrate concentration, but instead even increases because the growth in specific activity is greater than the decrease in the rate of the reaction resulting from the drop in substrate concentration.

b. Equipment

We used a LIQUID SCINTILLATION SPECTROMETER from the company PACKARD-INSTRUMENTS with the classification: Model 3320, for measuring radioactivity. The instrument had an automatic "sample changer" with 200 spaces to its disposal. The count occurs by way of three independent channels. The count-time can be varied between 1 sec. and 100 min. The background can be automatically subtracted as a fixed value. Fluctuations are thereby not taken into account. The numerical result is recorded through a printer. The counting yield can be optimized for different isotopes by changing the width of the window and the magnification. The measurements were done in 20ml disposable test tubes made of polypropylene, which is resistant to dioxane and toluene. As a scintillation liquid we used so called Bray's solution(29), which is composed of the following:

Naphthalene 60g

Diphenyloxazole (Abbr. PPO) 4g

1.4-Bis-(2-phenyl-oxazolyl)-benzene (Abbr. POPOP) 0.2g

Methanol 100 ml

Ethylene glycol 20 ml

1.4 - dioxane ad 1,000ml

PPO functions as primary scintillator (maximum fluorescence 3650 ), POPOP as secondary scintillator (maximum fluorescence 4180 . Up to 2 ml of aqueous test solution can be measured in 15 ml of this solution. The lowest measurable value for C-14 is about 90% in this case. Furthermore, we used a micro-liter system from the company EPPENDORF-GERÄTEBAU in Hamburg to carry out the experimental procedures.

The system consists of 12 bulb pipettes with exchangeable disposable tips for extracting volumes from 5 µl - 1ml, a thermal block for temperatures of 25o, 37o, 56o, and 95oC, as well as a micro-centrifuge with a centrifugal force constant of 12,000 G with only 1-2 sec of startup time. The thermal block and centrifuge were set up for disposable 1.5 ml polyethylene test tubes.


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