tresyl-mediated synthesis: kinetics of competing coupling and hydrolysis reactions as a function...

Tresyl-Mediated Synthesis: Kinetics of Competing Coupling andHydrolysis Reactions as a Function of pH, Temperature, and StericFactors

Jeffrey J. Sperinde, Benjamin D. Martens, and Linda G. Griffith*

Massachusetts Institute of Technology, Department of Chemical Engineering and Division of Bioengineering andEnvironmental Health, MIT 66-466, 25 Ames Street, Cambridge, Massachusetts 02139. Received June 19, 1998

Kinetic parameters have been measured for coupled nucleophilic and solvolytic reactions of 2,2,2-trifluoroethanesulfonyl (tresyl)-modified poly(ethylene glycol) based on a system of coupled differentialequations implied by recently proposed elementary reaction mechanisms. Fitted kinetic parameterswere found to be strong functions of pH, temperature, and steric factors. To maximize the total yieldof coupled amine as well as the fraction of secondary amine linkages, our model predicts that it isdesirable to run tresyl coupling reactions at low temperatures at pH ∼8.0, depending on the aminepKa for primary, unhindered amines. For branched primary amines, our data favor room temperatureat a slightly higher pH.

INTRODUCTION

Nearly two decades ago, 2,2,2-trifluoroethanesulfonylchloride (tresyl chloride) was introduced as a morereactive alternative to p-toluenesulfonyl chloride (tosylchloride) in activating hydroxyl groups to covalent modi-fication for the preparation of affinity chromatographysupports (Nilsson and Mosbach, 1981). Tresyl chloridehas found wide use in solid support activation as well asextensive use in poly(ethylene glycol) (PEG) activationfor PEG modification of small drugs and proteins forbiological stabilization and immuno-modulation (Harris,1992).

It had long been assumed that the reaction mechanismfor tresyl-mediated coupling was identical to that of tosylchloride and other sulfonyl chlorides where the substi-tuted sulfonyl acts as a leaving group. Recently, it hasbeen suggested that alternative mechanisms may prevail.Demiroglou et al. (1994) proposed a mechanism in whichthe sulfonyl sulfur is retained throughout the entirecoupling reaction. On the basis of experimental evidence,Gais and Ruppert (1995) as well as King and Gill (1995,1996) corrected this postulated mechanism to includenucleophile addition by an â-elimination/Michael-typeaddition reaction. The present understanding of tresylreactions in aqueous media includes three pathways(Scheme 1): hydrolysis, nucleophilic displacement, andâ-elimination/addition.

Experimental work regarding tresyl-chloride-mediatedcoupling has been focused on determining the molecularstructure of reaction products, yet for practical applica-tion of tresyl-mediated coupling, it is necessary to knowhow reaction conditions may affect the coupling yield.Here, we report effective rate constants for the recentlyelucidated reaction network for tresyl-mediated coupling,using PEG-Tr as a model. We further examine the effectsof temperature, pH, and steric factors that affect yieldsof the reaction products.

The central goal of this research was to define rateconstants useful in predicting coupling rates, product

distributions, and product yields for tresyl-mediatedcoupling based on fundamental parameters such as pH,temperature, steric effects, and nucleophilic amine pKa.It has recently been shown that pH can play a large rolein hydrolysis rates and coupling products (King and Gill,1996). Here, we sought to define the role of pH, temper-ature, and steric effects through the measurement ofapparent rate constants that might be representative ofthe elementary reaction mechanisms involved in tresyl-mediated coupling of amine nucleophiles to tresylatedPEG.

MATERIALS AND METHODS

Poly(ethylene glycol) (MW ) 6000) was purchased fromFluka. Tresyl chloride (2,2,2-trifluoroethanesulfonyl chlo-ride), L-phenylalanine (Phe), and N2-(carbobenzyloxy)-L-lysine (RCBZ-Lys) was from Aldrich. Glycyl-DL-phenyl-alanine (Gly-Phe) was from Sigma.

Synthesis of Tresylated PEG (1). The generalsynthesis procedure for PEG tresylation is detailedelsewhere (Sperinde and Griffith, 1997), employing amethod similar to that of Nilsson and Mosbach (1984).In the present study, dihydroxyl PEG (6000 MW) wasused as the starting material. Briefly, the tresylation wasperformed in a dried solution (over molecular sievesprevious to tresylation) of PEG-OH2 in methylenechloride (10 mL/g PEG) under argon with triethylamineas an acid acceptor. Purified PEG-Tr2 was obtained bysuccessive reprecipitations from acidified methanol, usingdecreasing concentrations of acid. Residual triethylaminewas found to be 0.02 wt % by 1H NMR. On the basis ofsulfur elemental analysis, tresylation was approximately100%, with 3.08 g/mmolTr [52.2% C, 8.54% H, 1.04% S].Each tresyl group ()[1], see Scheme 1) of PEG-Tr2 isassumed to react independently; therefore, designations“PEG-Tr” and “PEG-Tr2” are used interchangeably.

Isolated Hydrolysis Reaction. Progress of the hy-drolysis reaction was monitored by continuous titration.A weighed amount of PEG-Tr2 (about 50 mg) was addedto a measured volume (about 100 mL) of Milli-Q water.The solution was stirred continuously. Dilute potassium

* To whom correspondence should be addressed. Phone: (617)253-0013. Fax: (617) 258-5042. E-mail: [email protected].

213Bioconjugate Chem. 1999, 10, 213−220

10.1021/bc980070j CCC: $18.00 © 1999 American Chemical SocietyPublished on Web 02/24/1999

hydroxide (20 mM) was added as needed to maintain thepH within 0.05 units of desired pH as measured by astandard calomel electrode. The amount and time ofaddition of each acid aliquot was recorded. Continuoustitration experiments were run at 22 ( 1 °C with pH 6.0,7.0, 7.5, 8.0, 8.5, and 9.0 and at 4 ( 0.2 °C with pH 8.0,8.5, and 9.0. Each continuous titration reaction wasmonitored for 80 min. For slower reactions at 4 ( 0.2 °Cwith pH 5.0, 6.0, and 7.0, base was required much lessoften to maintain the desired pH. In these three condi-tions, the rate of acid evolution was measured by the rateof pH change, where the pH was always maintainedwithin (0.1 pH units of the desired level. These threeslower reactions were run at higher PEG-Tr2 concentra-tions (about 2 mg/mL) and were maintained over anumber of days, with frequent recalibration of the pHmeter.

The measurement of moles of base added to maintainconstant pH was used to calculate moles of tresyl groupsconsumed. By reaction stoichiometry, 4 mol of base isrequired to neutralize the acid evolved by the conversionof R-Tr to R-OSO2CH2COO-, and 1 mol of base isrequired to neutralize the hydrolysis of R-Tr to R-OH and-OSO2CH2CF3. The fractional conversion of tresyl groups(XTr) was calculated on the basis of the weight of PEG-Tr2 used in each experiment (measured to (0.1%), usingthe value of 3.08 g of PEG/mmol of Tr noted above,confirmed by total hydrolysis of PEG-Tr2.

Simultaneous Coupling/Hydrolysis Reaction. Ameasured amount of PEG-Tr to make a final concentra-tion of 40 mM in tresyl was added to a solution 100 mMin primary amine and 400 mM in potassium phosphateat the desired pH. The extent of the coupling reactionwas measured as a function of time by periodic samplingof the reaction solution by a HPLC Hitachi L-7200autosampler. The aliquot was immediately injected ontoone TSK G4000PW and one TSK G2000PW column inseries. The mobile phase was 0.50 M sodium chloridewith 10 mM potassium phosphate and 4% acetonitrile

at pH 4 delivered by a Hitachi L-7100 pump. Detectionwas by a Hitachi L-7420 UV-vis detector at 260 nmwhere PEG-Tr has an insignificant absorbance. For eachmeasurement, the fraction of amine bound to PEG wascalculated as the integral of absorbance at 260 nm forthe PEG peak (first to elute) divided by the total integral(PEG peak + free amine peak). Amines examined includeglycyl-phenylalanine, phenylalanine, and R-CBZ-lysine.All amines were examined at 4 and 22 °C.

Algorithm for Rate Constant Fitting. Whereasanalytical solutions to rate equations were unavailable,rate constants were fit using standard Fortran modelsextracted from Numerical Recipes (Press et al., 1986).The rate constants were fit by an iterative process. Afourth-order Runge-Kutta routine was used to generatedata for conversion as a function of time from a set ofguessed rate constants. This generated data was thencompared with measured data to calculate a new set ofmore accurate rate constants. A Levenberg-Marquardt(LM) ø-squared minimization routine generated this newguess. The same Runge-Kutta routine was used withinthe LM routine as well to calculate the necessary partialderivatives (∂ø/∂ki) for each rate constant, ki. This processwas repeated iteratively until ø was approximatelyminimized (øn+1/øn < 0.0001%).

The data were separated for rate constant analysis bynucleophile (n ) 3) and by temperature (n ) 2). For eachof these six data groups, rate constants were optimizedby the LM method for all pHs simultaneously.

RESULTS AND DISCUSSION

A number of reaction pathways for tresylated specieshave recently been elucidated, yet kinetic data whichcould be used to maximize desired products is somewhatlimited. The goal of this work is to measure apparent rateconstants for a reaction network that describes the setof possible reactions for the displacement of tresyl groupsby primary amines in an aqueous environment as a

Scheme 1

Scheme 2

214 Bioconjugate Chem., Vol. 10, No. 2, 1999 Sperinde et al.

function of pH temperature and steric factors. This hasbeen undertaken in two steps. First, in the absence ofan amine nucleophile, rate constants for hydrolysis andhydroxyl-mediated tresylate conversion were measured.Second, with knowledge of the solvent-mediated reac-tions, rate constants for coupling of various primaryamine species were measured by fitting to a kinetic modelconsistent with known reaction mechanisms.

Rate Constants for Hydrolytic Processes. Kingand Gill have shown that the ethyl trifluoroethane-sulfonate in the absence of a nucleophile will hydrolyzeto different species depending on the solution pH (Kingand Gill, 1996) as can be inferred from Scheme 2. Theyreported data at 25 °C supporting a traditional sulfonateester hydrolysis pathway (first-order rate constant ) kw)at low pH and reversible E1cB reaction at high pH(pseudo-first-order rate constant ) kOH[OH-]) in whichthe first step is rate limiting. Given the set of reactionsin Scheme 2, the disappearance of PEG-Tr (1) can bewritten as

where

The integrated form of this equation in terms ofconversion (≡XTr) is

where

This equation implies that a plot of -ln(1 - XTr) versustime would be linear, with the slope equal to (kw +kOH[OH-]). By varying the pH, unique values for kw andkOH can be computed. Data for hydrolysis reactions areplotted in Figure 1 at 4 °C for pH 8-9 and 22 °C for pH6-9.

Our data for the hydrolysis of tresylated PEG at 4 and22 °C supports the model given in Scheme 2. Linearityof the ln(1 - XTr) plot (Figure 1) confirms that the firsthydrolysis step is rate limiting under almost all condi-tions studied. The pH 9.0, 22 °C reaction deviatessomewhat from linearity, indicating that one or more ofthe multiple steps between 3 and 4 of Scheme 1 may belimiting in the high pH regime.

To derive rate constants kw and kOH, the apparenthydrolysis rate kh,app was fit by a least-squares methodto kh,app ) kw + kOH[OH-] separately for 4 and 22 °C asshown in Figure 2. Table 1 shows the rate constants fitto the data in Figure 2.

The hydrolysis rate constant kw was found to be astronger function of temperature than kOH, the apparentrate constant for the addition-elimination pathway. Thelow-temperature dependence of kOH may point to asignificant influence of kE1

rev, consistent with a reversibleE1cB mechanism. Because kw is of a similar order ofmagnitude as kOH[OH-] around room temperature andslightly basic pHs, this difference in temperature depen-dence might allow for the control of the distribution ofproducts by manipulating pH and temperature. This will

depend on the kinetics of SN2 nucleophilic displacementdiscussed below.

Development of a Tresyl-Mediated CouplingModel. It has been suggested that there are at least twopathways by which nucleophilic amines can couple totresylated species (Scheme 1) [Gais and Ruppert, 1995;King and Gill, 1995; ref 6 in King (1996)]. The firstpathway involves an SN2 nucleophilic displacement,similar to that which is observed for other sulfonateleaving groups. This SN2 pathway is thought to be minoror undetectable at very high pH (King and Gill, 1996).At high pH, the second pathway has been observed thatis thought to go through an addition-elimination inter-mediate (3) (King and Gill, 1995). This intermediate canundergo further modifications to an inactive product (4),or it can react with an amine to give a coupled product(6).

The apparent first-order rate dependence of the addi-tion-elimination pathway for hydrolysis suggests thatk′ . kOH[OH-]. This implies that as 3 is formed it israpidly converted to a mixture of 4 and 6, such that [3], [1]. We can describe the fraction of 3 that becomes 6as R, given by the following approximation:

-d[PEG - Tr]

dt) (kw + kOH[OH-])[PEG - Tr]

kOH )kE1

fwdkE1,2

kE1rev[H2O] + kE1,2

-ln(1 - XTr) ) (kw + kOH[OH])t ) kh,appt

XTr ) 1 -[PEG - Tr][PEG - Tr]0

Figure 1. Hydrolysis reaction at 22 °C (1a) at pH 6.0 (×), pH7.0 (+), pH 7.5 (0), pH 8.0 (]), pH 8.5 (4), pH 9.0 (O), and 4 °C(1b) at pH 8.0 (]), pH 8.5 (4), and pH 9.0 (O). All reactionswere followed by titration as detailed in the Materials andMethods. Conversion of tresyl groups (XTr ) 1 - [1]/[1]o) wascalculated on the basis of the initial concentration of tresylgroups for each experiment.

d[6]dt

≈ R(k1[OH-][1])

Tresyl-Mediated Coupling Kinetics Bioconjugate Chem., Vol. 10, No. 2, 1999 215

where

As suggested by the hydrolysis experiments, the aboveassumption should hold at least for pH j9.0. Becausereactions governed by k2 and k′ are downstream of therate-limiting step, (1 f 3), the absolute magnitudes ofk2 and k′ cannot be measured independently. Only theratio k2/k′ can be calculated.

The rate constants kw and kOH are known from theprevious section (Table 1). Here we will fit k1 and k2/k′for each amine species at each temperature, based onmeasured coupling data for a set of model amines. Onthe basis of Scheme 1 and the above approximation, wecan write the following differential equations that de-scribe the concentrations of the reaction components asa function of time:

The [OH-] concentration was calculated using themeasured pH and the ion product of water, Kw, at theappropriate temperature (see Table 2):

The concentration of unprotonated amine was calcu-lated from an algebraic variant of the Henderson-Hasselbach equation as

Both Kw and the pKa for each amine species vary withtemperature (Table 2). The pKas for the various aminespecies were adjusted for temperature based on the van’tHoff equation by

The temperature adjustments to the pKa are signifi-cant, yet small enough to allow for use of approximatevalues for ∆H°. For example, variations in ∆H° on theorder of 10 kJ/mol imply differences in pKa of only 0.1pH unit at 4 °C. The heat of ionization for the R-amineof phenylalanine was taken as 44 kJ/mol (Izatt et al.,1961). The heat of ionization for the R-amine of glycyl-phenylalanine was also approximated as 44 kJ/mol basedon the observation that chemical substituents removedfrom the R-amine have little effect on the ∆H°. Forexample, enthalpy literature values for similar moleculessuch as glycine (King, 1951), glycylglyine (Smith andSmith, 1942), and phenylalanine (above) were all givenas 44 kJ/mol. The heat of ionization for the R-amine ofR-CBZ-lysine was assumed to be similar to R-dimethyl-lysine (Marini et al., 1971) at 52 kJ/mol. Heat capacities,defined as the change in ∆H° with temperature, wereassumed to be insignificant based on typical literaturevalues. For example, the heat capacity for a prototypicalR-amine of glycine (King, 1951) predicts only a 0.2 kJ/mol difference in ∆H° between 4 and 22 °C.

To test the robustness of this tresyl reaction networkmodel, we chose to experimentally study three modelamine compounds (Figure 3)sa high pKa species, RCBZ-lysine; a low pKa species, glycyl-phenylalanine; and amore sterically hindered amine of intermediate pKa,phenylalaninesto probe for possible steric inhibition. Onthe basis of the results from the hydrolysis experiments,a pH range of 7.5-8.5 was chosen for study so thatkOH[OH-] is of the same order as kw for maximumresolution of the various pathways. Experiments at roomtemperature (22 °C) and in a 4 °C cold room wereconducted to measure the effects of temperature.

Figure 4 shows measured reaction time courses andcurves predicted by the model for the three model aminesat three pHs and two temperatures. The best-fit rate

Figure 2. Least-squares fit for hydrolysis reaction (kh,app ) kw+ kOH[OH-]) for 22 °C (b) and 4 °C (O). Values of kh,app are takenfrom the slopes of curves in Figure 1 for faster reactions (pointswhere log kh,app > -5) and from the rate of pH change (seeMaterials and Methods) for slower reactions (points where logkh,app < -5).

Table 1. Hydrolysis Rate Constants

temp (°C) kw (10-6 s-1) kOH (103 s-1 M-1)

4 0.22 6822 17.0 78.3

Table 2. Ionization Constants

temp (°C) pKwa pKa Gly-Phe pKa Phe pKa RCBZ-Lys

4 14.78 8.6 9.6 11.322 14.08 8.1 9.1 10.7

a pKw from Marshall and Franck (1981). The amine pKas at 4and 22 °C were calculated as explained in the text from literaturevalues at 25 °C for glycylphenylalanine (Biester and Ruoff, 1959)and phenylalanine (Nevenzel et al., 1949). The pKa of the RCBZ-Lys was assumed to be similar to lysine (Ellenbogen, 1952) and6-aminohexanoic acid (Smith and Smith, 1942), which have similarpKas.

[N:] ) [N]total10{pH-pKa(T)}

1 + 10{pH-pKa(T)}

pKa(T2) ) pKa(T1) - log{exp[-∆H°R ( 1

T1- 1

T2)]}

R )k2[N:]

k2[N:] + k′; [N:] ≡ unprotonated amine

d[1]dt

) (kw + kOH[OH-] + k1[N:])[1]

d[2]dt

) kw[1]

d[4]dt

) (1 - R)kOH[OH-][1]

d[5]dt

) k1[N:][1]

d[6]dt

) RkOH[OH-][1]

d[N]total

dt) -(k1[N:] + RkOH[OH-])[1]

[OH-] ) KW(T) × 10pH


constants from the ø-squared minimization fitting routineare given in Table 3. The model reaction network(Scheme 1) was able to fit the observed data quite wellconsidering that a single set of rate constants were fit toall pH values simultaneously. In all cases, the model wasable to capture the long time behavior trend as a functionof reaction pH, as well as the final conversion. Thetransient behavior was also fit acceptably well in allcases, with the exception of phenylalanine at 22 °C(Figure 4c). The transient portion of Figure 4c suggestsa weaker dependence on pH than predicted with [N:] asthe driving force, possibly due to an effect of the proximityof the carboxylate group to the nucleophilic amine.

Temperature Effects. The reaction temperature canhave a profound influence on the kinetics and product

distribution in tresyl-mediated reactions as illustratedin Figure 4. In general it can be said that room-temperature reactions lead to higher total coupling yields.Yet, our data suggest that the distribution of the coupledproducts, 5 and 6, can also be affected by temperature.

Our data suggest that at lower temperatures, a higherproportion of 5 is formed relative to 6. This is evidentfrom the temperature influence on the initial step of thereaction. Whereas kw and kOH appear to have significanttemperature dependencies, k1 appears to be only slightlyaffected by temperature. This suggests that lowering thetemperature serves to increase the relative yield of 5. Theratio of k2/k′ is also a function of temperature. Theapparent activation energy of k2 is higher than that ofthe hydrolysis rate constant, k′, as suggested by our data

Figure 3. Model primary amines used in coupling studies. Compounds were chosen to span a range of pKas (see Table 2). Glycine-phenylalanine, phenylalanine, and RCBZ-lysine were chosen as models for peptidyl N-termini, branched amines, and protein surface-presented lysines, respectively.

Figure 4. PEG(-Tr f -X-R) conversion data and model fit for the reaction PEG-Tr + H2N-R f PEG-X-R where X ) (NH) or[OSO2CH2C(O)NH]. Each panel (a-f) is fit by a single set of rate constants to the mechanism prescribed in Scheme 1. Data [symbols,(×) pH 7.5; (+) pH 8.0; (4) pH 8.5] and model predictions [lines, pH 7.5 (- - -); pH 8.0 (- -); pH 8.5 (s)] are given for Gly-Phe at 22°C (1a), Gly-Phe at 4 °C (1b), Phe at 22 °C (1c), Phe at 4 °C (1d), RCBZ-Lys at 22 °C (1e) and RCBZ-Lys at 4 °C (1f). Conversion data[)([5] + [6])/[1]o] was measured as the fraction of tresyl groups converted to PEG-N-R.

Table 3: Tresyl-Mediated Coupling Effective Rate Constants

Gly-Phe Phe RCBZ-Lys

rate constanta 4 °C 22 °C 4 °C 22 °C 4 °C 22 °C

k1 (10-2 s-1 M-1) 0.48(0.02) 0.69(0.05) 0.16(0.01) 3.1(0.2) 25(2) 29(2)k2/k′ (102 M-1) 13(6) b c 0.63(0.16) 12(6) 5.4(1.3)

a Rate constants are given as value (standard deviation). The large standard deviation in the case of k2/k′ for RCBZ-Lys at 4 °C reflectsa relative insensitivity of the fit to this parameter.


(Table 3). Thus, our data indicate that higher tempera-tures yield more 6 relative to 4. It should be noted thathigher temperatures also contribute to increased hy-drolysis through the (1 f 2) pathway.

Temperature also has a small, but significant effect onpKw and the pKas of the amines as shown in Table 2.

pH Effects. Increasing the pH of the reaction solutionincreases the rate of conversion of tresyl species, throughthe addition-elimination pathway as well as the amine-nucleophilic displacement pathway shown in Scheme 1.Increasing the hydroxyl concentration increases the fluxthrough the addition-elimination pathway (1f 3). In-creasing the pH also has the effect of creating a largerconcentration of unprotonated amines, increasing theamine-nucleophilic displacement as well as the conver-sion of 3 to 6.

The reaction pH has an especially strong influence onthe initial fate of 1. A detailed analysis and discussionof similarly competing pH-dependent reactions can befound in the literature (King et al., 1992, 1994). In thepresent case, the relative values of kw, kOH[OH-], and k1-[N:] must be considered to optimize the amount of 5formed relative to 2 and 3. This can be quantified as

where

The parameter Φ then expresses the relative rates as afunction of pH, regardless of the absolute concentrationof amine and the particular value of k1 and [N]total. InFigure 5 we show a plot of log(k1Φ) versus pH for thethree model amines at 4 and 22 °C. By solving for ∂Φ/∂pH ) 0, the pH that maximizes Φ is found to be

This defines the optimal pH for (1 f 5)-type coupling. Itcan be seen from Figure 5 that Φ(pH|maxΦ) increases withdecreasing pKa, predicting a lower required amine con-centration, but longer reaction times. Decreasing tem-perature has the effect of somewhat increasingΦ(pH|maxΦ) as well as pH|maxΦ.

On the basis of Scheme 1, the interplay of the pH effecton hydroxyl and unprotonated amine concentration canbe separated into three regimes: [OH-] , kw/kOH, [OH-]≈ kw/kOH, and [OH-] . kw/kOH. At low pHs, only hydroly-sis (1 f 2) and nucleophilic substitution (1 f 5) aresignificant, yet a large concentration of the amine specieswill be needed to favor addition over hydrolysis due tothe low fraction of unprotonated amines at low pH. Inthe intermediate regime, all three pathways can besignificant; however, the (1 f 5) pathway can be madedominant with a lower amine concentration than isneeded for the later low pH regime. In the high pHregime, hydrolysis is insignificant relative to the first stepin the addition-elimination pathway (1 f 3). This regimecan prove to be impractical because [OH-] increasesfaster than [N:] with increasing pH, requiring a largeexcess of amines.

In our model, we have attempted to represent allreactions in terms of possible elementary reactions.However, in the case of k1, in particular, our data suggeststhat there might be a dependence on the amine pKa thatwould not be consistent with the assertion that k1 is anelementary reaction. It can be seen from Table 3 that k1increases with pKa. This trend acts in the oppositedirection but with a smaller magnitude than the pKadependence imposed by using [N:] as the effective aminedependence. Attempts to fit the data with k1[N]total as thedriving force failed to yield a fit comparable to that ofk1[N:] as the driving force.

In an attempt to fit all the data for k1 to a single raterelation, an empirical model was developed for the SN2reaction as shown in Scheme 3. This empirical rateequation fits the data of all temperatures, reaction pHs,and amines except for the phenylalanine 4 °C reaction,possibly for steric reasons. The correlation of the empiri-cal rate equation with the measured values for k1 isillustrated in Figure 6. It is interesting to note that thek1 dependence on Ka

-0.63 is invariant with temperature,although only limited data is available at 4 °C. Theconsistency of this empirical relation across the varietyof amines may indicate a slightly different dependencethan the concentration of unprotonated amine, [N:].

Steric Effects. Phenylalanine was expected to be themost sterically inhibited. The effect was most noticeableat 4 °C (Figure 4d). This is best illustrated in Figure 6,where the phenylalanine 4 °C reaction is well removedfrom the trends established by all other rate constants.It is also possible that steric factors rather than the pKadependence supported above may account for the highervalues of k1 for RCBZ-Lys as compared to glycyl-phenyl-alanine 4 °C.

Control of Product Distribution. It could be arguedthat the relative amount of 5-type, 2° amine linkages and6-type, sulfonyl linkages may be more important thantotal yields, especially since 6-type linkages may besubject to slow hydrolytic cleavage. In general, it wouldbe desirable to maximize the number of 5-type, secondaryamine linkages. Our model predicts that reactions run

Figure 5. Plot of relative rates of reactions with PEG-Tr interms of k1Φ (see text). Curves at given at 4 °C (open symbols)and 4 °C (filled symbols) for Gly-Phe (O/b), Phe (∆/s) and RCBZ-Lys (0/9) The pH where k1Φ is a maximum is indicated(numeral) for each curve. Maximal k1Φ predicts an optimal pHfor (1 f 5)-type coupling.

rate1f5

rate1f2 + rate1f3)

k1[N:]

kw + kOH[OH-]) k1[N]totalΦ

Φ )

[N:][N]total

kw + kOH[OH-]

pH|maxΦ )pKw + pKa + log( kw

kOH)

2


at 4 °C would have more secondary amine bonds than at22 °C for a given amine concentration. In general, thefraction of secondary amine linkages increases withincreasing amine concentration by increasing the rate of1 f 5 relative to 1 f 2 + 3.

The distribution of 4 and 6 from 3 is best described byR. At any given time, R is the instantaneous fraction of3 that will become 6:

Because R is a function of [N:], its value changes as thereaction progresses. To compare values of k2 for the threemodel amines at both temperatures, it is instructive tocompare the initial value of R. R will tend to decreasesomewhat from its initial value as free amines areconsumed. Figure 7 shows R(t ) 0) for the 18 curvesexamined. The value of R was found to be consistentlylarger at 22 °C than at 4 °C. For any given amine, theinitial value of R is a increasing function of reaction pHthrough the dependence of [N:] on the solution pH. R wasfound to be a decreasing function of pKa, with a valueapproaching unity for 100 mM glycyl-phenylalanine at22 °C, suggesting that the driving force for this couplingpathway has a stronger dependence on solution pH thanis exerted through [N:].

CONCLUSIONS

With the judicious choice of reaction temperature andpH, tresyl-mediated couplings can be achieved with highyields. To maximize the total yield and the fraction ofsecondary amine linkages, our model predicts that it is

desirable to run tresyl coupling reactions at lower tem-peratures around pH 8, depending on the amine pKa asspecified by the above equation for pH|maxΦ and il-lustrated in Figure 5. Although total yields ([5] + [6])may be higher at elevated pH levels (Figure 4), 6-typeamide linkages may be unstable over prolonged periodsin aqueous environments. Where reactions must be runat higher temperatures due to solubility limitations,maximal secondary amine linkages are predicted atslightly higher pH levels to overcome the higher rate ofhydrolysis (kw).

Where the choice of nucleophilic amine is possible, itis advantageous to use an amine of low pKa to maximizethe concentration of the unprotonated species. This pointsto an advantage of coupling peptides via an N-terminalglycine rather than through an ε-amine group of a lysineresidue.

When coupling to tresylated species via a lysyl ε-amineis necessary, as may be the case with certain proteins,low temperature at pH ∼8.8 is indicated (Figure 5). Inthis case high concentrations of amine are necessary,even beyond the 100 mM amine used here, to achievehigh yields of secondary amine linkages. Beyond pH ∼8.8,additional tresyl conversion (Figure 4) is predicted to belargely through 6-type amide linkages.

In some applications, it may be the nucleophilic aminethat is limiting, rather than the tresyl-activated species.Such a case is encountered in attaching pendant PEGchains to proteins or small molecules. When the tresy-lated species is used in large excess, it can be seen fromScheme 1 that the 1 f 3 pathway (∼[Tr]) can quicklybecome dominant over the 1 f 5 pathway (∼[N:][Tr]).This raises the concern that the limited number ofamines might be consumed in a 3 f 6 reaction, disfavor-ing 1 f 5. To maximize secondary amine linkages in thiscase, it is advantageous to run under conditions whereR is small (Figure 7), i.e., at a somewhat lower pH thanprescribed by Figure 5.

ACKNOWLEDGMENT

The financial support of NSF BES9632714, the MITNIH Biotechnology Training Grant, NIH GM50047, andthe MIT Center for Biomedical Engineering Seed Grant

Scheme 3

b k′ was found to be negligible as compared to k2 under theconditions examined. c k2 was found to be negligible as comparedto k′ under the conditions examined.

Figure 6. Empirical correlation (see Scheme 3) for rateconstant k1 at 22 °C (b) and 4 °C (O) with the amine pKa (seeTable 2) fit to k1 ) kxKa

-γ where kx(22 °C) ) 6.4 × 10-8 M-1 s-1,kx(4 °C) ) 1.6 × 10-8 M-1 s-1, γ(22 °C) ) 0.62, and γ(4 °C) )0.63. Fit at 4 °C (- - -) is included to illustrate the similarity inγ to the fit at 22 °C (s) even though the data point at pKa ) 9.6is omitted due to suspicion of steric influences.

R )k2[N:]

k2[N:] + k′)

d[6]dt

d[4]dt

+d[6]dt

Figure 7. Plot of the initial distribution of products from ref3, given as R () rate3f6/rate3f4+6), based in Scheme 1 andmeasured rate constants, k2/k′. Because R is a function of theconcentration of the nucleophilic species [N:], R is expected tobe a function [N:], and will decrease with time proportional tothe depletion of [N:]. Error bars are 95% confidence intervals.


are gratefully acknowledged. The authors are also in-debted to Gizette V. Sperinde for assembling and opti-mizing the Fortran code used herein.

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