Resolution of D-Serine Dehydratase by Cysteine AN ANALYTICAL TREATMENT*

A general method is presented for analysis of the resolution of pyridoxal-P-requiring enzymes by carbonyl reagents. The method is useful for accurately determining the very small equilibrium constants (I&) which characterize the dissociation of cofactor from many pyridoxal-P-requiring enzymes. The analysis also establishes the minimum number and relative stabilities of distinct enzymic species involved in the resolution process. Analysis of the resolution of D-serine dehydratase by L- and D-cysteine resulted in the establishment of an enzyme bound thiazolidine derivative as an intermediate in the pathway for resolution. The over-all equilibrium constant (KR) for the reaction, D-serine

The overall equilibrium constant (KR) for the reaction, D-serine KR dehydratase + cysteine -_ -thiazolidine derivative + Dserine apodehydratase was determined. At pH 7.80, F/2 0.33, 25", KE = 1.08 x 10e3. A value of 7.0 nM for the equilibrium constant for the dissociation of D-serine dehydratase to apoenzyme and free pyridoxal-P was determined from the ratio KRIKT, where K, is the equilibrium constant for the formation of a thiazolidine derivative from free pyridoxal-P and cysteine. An estimate of 14 no for KP was also obtained from partial resolution of D-serine dehydratase by high dilution.
The difficulties associated with this direct determination of KP from the dependence on the enzyme concentration of the activity of very dilute solutions of enzyme are discussed.
The driving force behind resolution with these aminothiols is cyclization of the transient Schiff base, formed between the reagent and pyridoxal-P. The existence of this Schiff base intermediate in the formation of the cyclic thiazolidine from cystcinc and pyridoxal-P was demonstrated in the preceding paper (18). Although aminothiols have been used to prepare apoenzymes (12-17), little quantitative information regarding the strength and nature of the interaction between protein and co-factor has been obtained from studies of the effect of aminothiols.
This work presents a general method of analysis of the resolution of pyridoxal-I' enzymes. This analysis yields an indirect method for accurately determining the very small equilibrium constants (Kp) which characterize the dissociation of many pyridoxal-I-' enzymes to apoenzyme and free pyridoxal-I'.
The analysis also establishes the minimum number and relative stabilities of distinct enzyme species involved in the resolution process. The application of this analysis to the resolution of D-serine dehydratasc by the aminothiol cysteine is also presented in this work.

Materials
Compounds used and the sources from which they were purchased are: EDTA (acid form) and n-penicillamine from Aldrich Chemical Co.; DEAF,-cellulose (Cellex D) from Bio-Itad Laboratories; n-cysteine hydrochloride, L-cysteine hydrochloride hydrate, D-, L-and nL-serine, sodium pyruvate, dithiothreitol, protamine sulfate ( which describe possible equilibrium states iI1 the resolution of pyridoxal-I-' enzymes by a carbonyl reagent, in this case cysteine, is given in Table I. Scheme 1 is the pathway proposed by Dowhan and Snell (14) for resolution of n-serine dehydratase in which the apoenzyme-thiazolidine complex does not dissociate. Scheme 2 is the simple alternative in which the apoenzyme-thiazolidine complex does not exist. The third scheme is the logical combination of Schemes 1 and 2 in which reaction of holoenzymc with cysteine results in an apoenzyme-thiazolidine complex which subsequently dissociates. Schemes 4 to 6 represent variations of Scheme 3 in which cysteine associates with holoenzyme prior to formation of thiazolidine.
The holoenzyme-cysteine complex can either be inactive (Scheme 4) or active (Scheme 5). Scheme 6 shows a pathway in which both active and inactive holoenzymecysteine complexes exist. Finally, Scheme 7 illustrates formation of an apoenzyme-cysteine complex. Clearly there are many possible pathways other than those listed in Table I. However, the schemes presented are representative of the major possible variations for the resolution of pyridoxal-P-requiring enzymes. Algebraic expression of each of these schemes in terms of the experimentally determinable parameters of free cysteine concentration at equilibrium, total enzyme concentration, the fraction of total enzyme which remains catalytically active at equilibrium, f a, and the fraction of total enzyme which contains a Schiff base linkage at equilibrium, f'a, results in the linear relationships of Equations 1 and 2.  these plots appear in Table II Table II the  Table II. The large error in the intercept makes it difficult to probability that, the real value of the intercept b' is non-zero and analyze the cysteine dependence of the intercept. The observation positive is greater than 99.7%; i.e. the experimental values are that m' was independent of the cysteine concentration, and the more than 3 standard deviations greater than zero (29). Re-non-zero value of t.he intercept establishes Scheme 3 as the  pathway for resolution. It should be pointed out, however, that Schemes 4 to 7 have not been excluded. These pathways may be operative and give rise to no observable dependence of m' on [Cys] if the terms containing [Cys] in the expressions for m' are small compared to unity. Whatever the pathway, the ratio (m')2/b' yields Ka, the dissociation constant for the thiazolidine from the enzyme, when the Cys terms are small compared to unity (Scheme 7). Values for this ratio are also listed in Table II. No significant differences could be detected for the value of KS with L-or n-cysteine. This result is consistent with the idea that the cysteine portion of the thiazolidine does not interact appreciably with n-serine dehydratase. Free cysteine does not appear to interact with the substrate binding site on the enzyme (14). Nei.ther D-nor L-cysteine compete with n-serine  (14). If the cysteine portion of the thiazolidine does not interact with the enzyme, the value of KS would be an estimate of the noncovalent interactions between the cofactor and the enzyme. The uncertainty associated with the measured value of b' and therefore KS (Table II), caused us to devise an independent method for checking this estimate of the noncovalent interactions between pyridoxal-P and the enzyme (30). Activity assays were also used to analyze the resolution of Dserine dehydratase by cysteine. However, this method was not as satisfactory as the spectral analysis. One problem associated with activity assays is that the substrate n-serine in the assay solution perturbs the resolution equilibrium. Table III presents data which show that fa calculated from the final lactate dchydrogenase assay slope is much larger than fa calculated from the initial slope. This effect diminishes but does not disappear as the n-serine concentration decreases. The fact that at the two low n-serine concentrations (1 mM and 5 mM) the values of fa calculated from initial slopes are the same suggests that the activity method of analyzing resolution is valid provided, (a) n-serine is less than 5 mM in the assay solution, and (b) the initial slope is used.
A major limitation of the activity method was the difficulty in determining the small values of the intercept b. The way to ensure a precise value of b is to get experimental points as close to the ordinate as possible, a task which requires high enzyme concentrations.
However, the activity assay cannot handle active enzyme concentrations greater than 20 nM. This fact puts a lower limit on the value of z which can be obtained at a given cysteine concentration.
Dilution of an enzyme-cysteine solution into the assay system in an attempt to overcome this problem is not satisfactory because dilution perturbs the very equilibrium the assay seeks to measure. This perturbation becomes more pronounced as the enzyme concentration increases. As total enzyme increases, the fraction of total enzyme existing as the AT complex increases. Dilution causes dissociat.ion of AT to both active holoenzyme and inactive apoenzyme (Scheme 3).
In spite of its disadvantages, the activity assay is a much more sensitive method, capable of analyzing enzyme concentrations 100 times lower than the spectral method. Therefore, the activity method was used to show that Scheme 3 describes resolution of n-serine dehydratase over a very large enzyme concentration range (Fig. 3). A slope (m) of 0.0435 (Fig. 3) for resolution at I'/2 0.39 correlates reasonably well with a value of 0.037 for m' determined at I'/2 0.40 using the spectral method.
To ensure that apoenzyme species AT and A had not been denatured during the resolution reaction (thereby invalidating the results), enzyme in final equilibrium mixtures (E, Cys, AT and A) was regenerated by treatment with pyridoxal-P.
In all x (fir')  Table I are small compared to unity, the value of (vL')~ is equivalent to the equilibrium constant for the over-all resolution reaction (Equation 4) regardless of the resolution pathway. Since dissociation of cofactor from enzyme (Equation 3) is simply the difference between the resolution reaction (Equation 4) and the reaction "r Pyridoxal-P + Cys e T , Kp = KR/KT. Values for KT have been presented in the preced-. ing paper (18). Applying this analysis to n-serine dehydratase, we obtain a value of 7.0 IIM for Kp (at I'/2 0.33, 25", pH 7.80) using a value of 1.56 X 10" 111-l for KT and an average value of 3.30 X 10m2 for m'. Since little uncertainty is associated with the values of K, and m' the value of Kp obtained from this analysis should be accurate. The relationship Kn = KpKT suggests that the ability of an aminothiol to resolve pyridoxal-l-'-requiring enzymes to apoenzyme and thiazolidine depends on the stability of the thiazolidine formed between pyridoxal-1' and the aminothiol. The thiazolidine formed from penicillamine and pyridosal-I' is 10 times more stable than the corresponding thiazolidine formed from cysteine (18). As expected penicillamine was found to be more effective than cysteine in resolving n-serine dehydratase. It should be pointed out, however, that the rates of resolution appear to be independent of the stability of the thiazolidine. Although an analysis of the kinetics of resolution was not undertaken, u-penicillamine was found to resolve n-scrine dehydratase at a rate comparable to D-cyst&e which in turn resolves the enzyme at a rate roughly 20 times slower than L-cysteine. For the squares at 115 and 162 hours, 76 and 417, of the initial enzymic activity was recovered after addition of excess pyridoxal-P.
For all other points, 100 f 10% of the enzymic activity present prior to resolution was recovered after addition of excess pyridoxal-P, pH 7.80, I'/2 0.33, 25".
In theory, it is of course possible to determine the equilibrium constant Kp directly by analyzing the dependence of the fraction of enzyme existing as holoenzymc on the total concentration of enzyme. However, this dilution analysis becomes difficult for enzymes such as n-serine dchydratase which bind cofactor very tightly. The high dilutiorts which must be used to observe significant concentrations of apoenzyme and pyridoxal-P make determination of holoenzyme from the absorption measurements at 415 rim, the absorption maximum for the Schiff base linkage, impractical.
Accurate determination of the equilibrium concentration of holoenzyme, using a sensitive activity assay, requires that the equilibrium not be perturbed during the assay. Another limitation of the dilution method for determining Kp is the unreasonably long time often required to reach equilibrium. Instability of holoenzyme or apoenzyme over the time period necessary to reach equilibrium would lead to erroneous values for Kp as determined by the dilution method.
In order to compare the two methods for determining Kp, the dilution method was used to determine the dissociation constant of pyridosal-P from u-serine dehydratasc. The activity assay used did not appear to perturb the equilibrium between holoerizyme and apoenzyme. A 20.fold reduction in the concentration of o-serine in all the assay mixtures did not alter the values obtained for the concentrations of holoenzyme from the activity assay. No significant change in the equilibrium constant was detected when the amount of enzyme in the assay mixture was altered by a factor of two. Equation 6 was used to calculate the value of K'p when 100 =t 10% of the enzymic activity was recoverable by addition of excess pyridoxal-1'.
cysteine over n-cysteine has been previously reported by Dowhan and Snell (14).
5 The complicated nature of the resolution pathway makes it difficult to assign accurate values to the relative rates of resolution by aminothiols without a detailed kinetic analysis.
where f" a is the ratio of activity at a given time after dilution to the activity after regeneration.
When less than 907, of the enzymic activity was recoverable by addition of excess pyridoxal-P, Equation 7 was used to calculate K',. Equation 7 rests on the assumption that enzyme which cannot be regenerated does not bind pyridoxal-I'. f$= (1 -f; fr) (1 -f;) [Et] f" (7) a where fV is the fraction of original activity recovered after regeneration, and it is obtained from the ratio of the activity after regeneration to the activity prior to resolution. The time dependence of the right-hand side of Equation 6 (circles) and 7 (squares) is illustrated in Fig. 4. A value of 14 nhr was estimated for the equilibrium constant KP from the limiting value of Klp in Fig. 4.
This value for Kp is significantly higher than the value of 7.0 nM determined by resolution with cysteine. Perhaps partial denaturation of apoenzyme to a functional protein which has a reduced affinity for pyridoxal-P occurs during the long incubation time in the dilution experiment. Such a situation would cause the dilution method for determining K, to yield an overestimate of the true value of Kp. The value of 35 IBM for Kp previously determined under similar conditions by Dowhan and Snell (14), from the activity of dilute solutions of previously isolated apoenzyme and cofactor, is also larger than the value of Kp determined here by resolution with cysteine. Although further work is required to resolve this discrepancy, the problems associated with making equilibrium measurements in dilute solutions of cofactor and apoenzyme may be at least partly responsible for the difference between the values of KP determined by dilution and resolution by cysteine. Because equilibrium is reached in minutes or hours when the enzyme is resolved with an aminothiol, instead of days when the enzyme is resolved by high dilution, resolution with an aminothiol is the method of choice for determination of the dissociation constant for n-serine dehydratase, and very likely for other pyridoxal-P-requiring enzymes which release cofactor slowly. APPENDIX Derivation of Equations 1 and 2 for Scheme 4 of Table I