Kinetics of Template-Directed Pyrophosphate-Linked Dideoxyguanylate Synthesis as a Function of 2-MeImpdG and Poly(C) Concentration: Insights into the Mechanism

Article abstract of DOI:10.1021/jo990998k

Aqueous solutions of deoxyguanosine 5′-monophosphate 2-methylimidazolide, 2-MeImpdG, yield primarily deoxyguanosine 5′-monophosphate, 5′dGMP, and pyrophosphate-linked dideoxyguanylate, dG^5′ppdG, abbreviated G₂^p (see Chart 1). The initial rate of G₂^p formation, d[G₂^p]/dt in M h^-1, determined at 23°C, pH 7.8, 1.0 M NaCl and 0.2 M Mg²⁺ by timed high-performance liquid chromatography (HPLC) analysis, exhibits a second-order dependence on 2-MeImpdG concentration, [G]₀, indicating a bimolecular mechanism of dimerization in the range 0.02 M ≤ [G]₀ ≤ 0.09 M. In the presence of polycytidylate, poly(C), G₂^p synthesis is accelerated and oligodeoxyguanylate products are formed by incorporation of 2-MeImpdG molecules. The kinetics of G₂^p formation as a function of both monomer and polymer concentration, expressed in C equivalents, were also determined under the above conditions and exhibited a complex behavior. Specifically, at a constant [poly(C)], values of d[G₂^p]/dt typically increased with [G]₀ with a parabolic upward curvature. At a constant [G]₀, values of d[G₂^p]/dt increase with [poly(C)], but level off at the higher poly(C) concentrations. As [G]₀ increases this saturation occurs at a higher poly(C) concentration, a result opposite to expectation for a simple complexation of two reacting monomers with the catalyst prior to reaction. Nevertheless, these results are shown to be quantitatively consistent with a template-directed (TD) mechanism of dimerization where poly(C) acts as the template to bind 2-MeImpdG in a cooperative manner and lead, for the first time, to the formulation of principles that govern template-directed chemistry. Analysis of the kinetic data via a proposed TD cooperative model provides association constants for the affinity between polymer and monomer and the intrinsic reactivity of 2-MeImpdG toward pyrophosphate synthesis. To the best of our knowledge, poly(C)/2-MeImpdG is the first system that could serve as a textbook example of a TD reaction under conditions such that the template is fully saturated by monomers and under conditions that it is not.

Full text of DOI:10.1021/jo990998k

J . Org. Chem. 1999, 64, 7957-7964
7957
Kin etics of Tem p la te-Dir ected P yr op h osp h a te-Lin k ed
Did eoxygu a n yla te Syn th esis a s a F u n ction of 2-MeIm p d G a n d
P oly(C) Con cen tr a tion : In sigh ts in to th e Mech a n ism
Anastassia Kanavarioti* and Sumana Gangopadhyay1
Department of Chemistry and Biochemistry, University of California, Santa Cruz, California 95064
Received J une 22, 1999
Aqueous solutions of deoxyguanosine 5′-monophosphate 2-methylimidazolide, 2-MeImpdG, yield
primarily deoxyguanosine 5′-monophosphate, 5′dGMP, and pyrophosphate-linked dideoxyguanylate,
5
′
p
p
p
-1
dG ppdG, abbreviated G
2
(see Chart 1). The initial rate of G
2
2
formation, d[G ]/dt in M h ,
2
+
determined at 23 °C, pH 7.8, 1.0 M NaCl and 0.2 M Mg by timed high-performance liquid
chromatography (HPLC) analysis, exhibits a second-order dependence on 2-MeImpdG concentration,
[
G]
the presence of polycytidylate, poly(C), G
are formed by incorporation of 2-MeImpdG molecules. The kinetics of G
o
, indicating a bimolecular mechanism of dimerization in the range 0.02 M e [G]
o
e 0.09 M. In
p
2
synthesis is accelerated and oligodeoxyguanylate products
p
2
formation as a function
of both monomer and polymer concentration, expressed in C equivalents, were also determined
under the above conditions and exhibited a complex behavior. Specifically, at a constant [poly(C)],
p
values of d[G
G]
As [G]
2
]/dt typically increased with [G]
o
with a parabolic upward curvature. At a constant
]/dt increase with [poly(C)], but level off at the higher poly(C) concentrations.
increases this saturation occurs at a higher poly(C) concentration, a result opposite to
p
[
o 2
, values of d[G
o
expectation for a simple complexation of two reacting monomers with the catalyst prior to reaction.
Nevertheless, these results are shown to be quantitatively consistent with a template-directed (TD)
mechanism of dimerization where poly(C) acts as the template to bind 2-MeImpdG in a cooperative
manner and lead, for the first time, to the formulation of principles that govern template-directed
chemistry. Analysis of the kinetic data via a proposed TD cooperative model provides association
constants for the affinity between polymer and monomer and the intrinsic reactivity of 2-MeImpdG
toward pyrophosphate synthesis. To the best of our knowledge, poly(C)/2-MeImpdG is the first
system that could serve as a textbook example of a TD reaction under conditions such that the
template is fully saturated by monomers and under conditions that it is not.
In tr od u ction
2-MeImpG/poly(C) system the dimer (in this case the 3′-
′-linked one) does not accumulate because its formation
5
Template-directed (TD) synthesis with phosphoimid-
azolide-activated mononucleotides has frequently been
used as a model for the nonenzymatic construction of
4
a
is substantially slower than elongation. Dimer concen-
tration could only be determined indirectly from the
concentration of the oligomer products, thus making the
kinetic analysis less straightforward. For this reason we
were in search of a TD-oligomerizing system where the
dimer accumulates.
2
polynucleotides that carry information. However, the
principles which govern TD synthesis are not well
understood and the presently known TD chemical sys-
tems are far from being efficient. Dimerization represents
the formation of the primer that is necessary for further
polymerization, and the dimer yield is one of the param-
eters that critically determine polymerization efficiency.
Insights into the mechanism of dimerization would not
only contribute to our understanding of TD synthesis, but
also provide design principles toward more efficient
polynucleotide synthesizing systems.
The dimerization process was recently investigated in
the reaction between guanosine 5′-monophosphate mor-
5
pholinamide, mor-pG, and 2-MeImpdG. Based on the
observation that the yield of the 3′-5′-linked dimer
increased linearly with poly(C) concentration, the conclu-
sion was drawn that this dimerization is TD. It was
determined that the polymer catalyzes dimerization of
template-bound monomers by a factor of 4 to 5 over the
reaction in solution and that it reverses the regioselec-
tivity.5 However, this system was not amenable to a
determination of the kinetics as a function of monomer
concentration because of low yields and low solubility of
the guanosine derivatives.
Polycytidylate (poly(C)) facilitates oligoguanylate syn-
thesis with guanosine 5′-monophosphate 2-methylimid-
azolide, 2-MeImpG, as the activated monomer.3,4 In the
(
1) On leave of absence from the Department of Chemistry, Gurudas
College, Calcutta-54, India.
2) J oyce, G. F. Cold Spring Harbor Symp Quant Biol 1987, 52, 41-
1. Orgel, L. E. Nature 1992, 358, 203-209. J oyce, G. F.; Orgel, L. E.
In The RNA World; Gesteland, R. F., Atkins, J . F., Eds.; Cold Spring
Harbor Lab. Press: Cold Spring Harbor, 1993; pp 1-25. Kanavarioti,
A. Origins Life Evol. Biosph. 1994, 24, 479-495. Bag, B. G.; von
Kiedrowski, G. Pure Appl. Chem. 1996, 68, 2145-2152. Ferris, J . P.;
Hill, A. R.; Liu, R.; Orgel, L. E. Nature 1996, 381, 59-61. Luther, A.;
Brandsch, R.; von Kiedrowski, G. Nature 1998, 396, 245-248. Beier,
M.; Reck, F.; Wagner, T.; Krishnamurthy, R.; Eschenmoser, A. Science
(
5
(3) Inoue, T.; Orgel, L. E. J . Mol. Biol. 1982, 162, 201-218. Inoue,
T.; Orgel, L. E. Science 1983, 219, 859-862. Fakhrai, H.; Inoue, T.;
Orgel, L. E. Tetrahedron 1984, 40, 39-45.
(4) (a) Kanavarioti, A.; Bernasconi, C. F.; Alberas, D. J .; Baird, E.
E. J . Am. Chem. Soc. 1993, 115, 8537-8546. (b) Kanavarioti, A.; Baird,
E. E. J . Mol. Evol. 1995, 41, 169-173. (c) Kanavarioti, A.; Bernasconi,
C. F.; Baird, E. E. J . Am. Chem. Soc. 1998, 120, 8575-8581.
(5) Kanavarioti, A. J . Org. Chem. 1998, 63, 6830-6838.
1
999, 283, 699-703.
1
0.1021/jo990998k CCC: $18.00 © 1999 American Chemical Society
Published on Web 09/25/1999

7
958 J . Org. Chem., Vol. 64, No. 21, 1999
Kanavarioti and Gangopadhyay
Ch a r t 1
Recently, Orgel and co-workers reported the poly(C)-
directed oligomerization of the deoxy derivative, 2-Me-
6
ImpdG. They established that the products include
5
′
p
2
dG ppdG (G ) and a series of pyrophosphate-capped
5
′
oligomers, dG pp(dG)
n
with n e 8 (see Chart 1). Our own
observations of this oligomerization indicated that oli-
p
gomer formation lags behind G
2
synthesis, allowing the
conclusion to be drawn that oligomers longer than the
p
2
dimer are elongation products of G . It is known that
pyrophosphate synthesis is faster than internucleotide
7
bond formation and that TD elongation by incorporation
of monodeoxynucleotides is slower than elongation by
8
incorporation of ribonucleotides. On the basis of these
notions, we anticipated that the poly(C)/2-MeImpdG
system should exhibit an enhanced dimerization ac-
companied by a diminished elongation that would result
in the accumulation of higher dimer yields compared to
the poly(C)/2-MeImpG system. Indeed, this is the case.
p
Here we report the kinetics of G
2
formation as a function
of 2-MeImpdG as well as poly(C) concentration at 23 °C
in the presence of 1.0 M NaCl, 0.2 M MgCl and 0.5 M
HEPES (pH 7.80 ( 0.05). The kinetics of dimerization
in the absence of poly(C) were also determined.
2
F igu r e 1. Self-condensation of 0.092 M 2-MeImpdG in the
presence of 0.02 M poly(C) at 23 °C; y-axis, mAU stands for
milliabsorbance units, x-axis, time in min. (Top) 5 days of
incubation analyzed with C18 chromatography; (bottom) 19
days of incubation analyzed with HEMA chromatography.
Identification of peaks: 1, 5′dGMP, HEPES-pdG and 2-Me-
Exp er im en ta l Section
5
′
p
Materials, preparation of samples, pH measurements, and
ImpdG coelute; 2 stands for dG ppdG, abbreviated G in text,
2
3 stands for 3-mer, 4 stands for 4-mer, etc. (see Experimental
Section).
5
product identification follow already developed methods. The
sodium salt of 2-MeImpdG was 95.5% pure. Analysis by HPLC
shows one unidentified contaminant at 4% eluting ahead of
5
′dGMP which is only present at 0.5%. The contaminant stays
Figure 1, bottom). A HEMA-BIO 1000Q 10 µm analytical
column from TESSEK Ltd, Czechoslovakia, was purchased
from Melcor Technologies. Solvent A: 0.01 M NaOH, solvent
intact during incubation. HPLC analysis was performed with
a 1090 LC from Hewlett-Packard equipped with a diode array
detector. Samples were incubated at 23 °C in the thermostated
autosampler of the HPLC instrument, and the analysis was
run automatically. Absorbance was monitored at 254 nm. The
analysis of the samples containing only 2-MeImpdG was
4
B: 0.4 M NaClO in solvent A. Gradient: 0 to 60% B in 30
min, 3 min wash with 80% B and 12 min reequilibration with
solvent A. For the faster reactions, we used a somewhat
steeper gradient: 0 to 21% B in 7 min and 21% to 50% in 7
9
performed with a C18 Alltima (3.2 × 250 mm, 5 µm by
min; 80% B for 2 min elutes poly(C). The NaClO
9% ACS pure from Aldrich.
Product distribution was obtained directly from HPLC
4
used was
Alltech) solvent minimizer column run at 0.5 mL/min in
conjuction with C18 chromatography (see Figure 1, top):
9
solvent A: 0.02 M KH
2
PO
4
with 0.2% w/v trifluoroacetic acid
CN in water v/v with 0.2%
reports as the percent of the total HPLC area corresponding
(TFA) pH 2.5; solvent B: 30% CH
3
w/v TFA. 0 to 20% B in 10 min; isocratic at 20% B for 4 min
and then 20% to 45% B in 12 min. Analysis of samples
(9) C18 columns, including Alltima, retain poly(C) and oligoguan-
ylates longer than five nucleotides. We also noticed that in the presence
of poly(C), shorter oligoguanylates, including dimers, do not elute
quantitatively probably because they are complexed by poly(C). Thus
C18 chromatography, most likely, underestimates yields of oligogua-
nylates in samples containing poly(C). The advantage of C18 compared
to HEMA chromatography is that it allowed the determination of
substrate disappearance as well as the appearance of hydrolysis
products that are eluted quantitatively even in the presence of poly-
(C).
containing poly(C) was done by HEMA chromatography10 (see
(6) Kozlov, I. A.; Politis, P. K.; Van Aerschot, A.; Busson, R.;
Herdewijn, P.; Orgel, L. E. J . Am. Chem. Soc. 1999, 121, 2653-2656.
Kozlov, I. A.; Orgel, L. E. Origins Life Evol. Biosph., 1999, in press.
(
7) Dolinnaya, N. G.; Tsytovich, A. V.; Sergeev, V. N.; Oretskaya,
T. S.; Shabarova, Z. A. Nucl. Acids Res. 1991, 19, 3073-3080.
8) Lohrmann, R.; Orgel, L. E. J . Mol. Biol. 1977, 113, 193-198.
Wu, T.; Orgel, L. E. J . Am. Chem. Soc. 1992, 114, 317-322.
(
(10) Stribling, R. J . Chromatogr. 1991, 538, 474-477.

Template-Directed Dideoxyguanylate Synthesis
J . Org. Chem., Vol. 64, No. 21, 1999 7959
Ta ble 1. Deta iled Kin etic An a lysis of th e
Self-Con d en sa tion of 2-MeIm p d G a t 23 °C a n d p H 7.85 (
0
.05 in th e P r esen ce of 0.5 M HEP ES, 0.2 M MgCl2, a n d
1
.0 M Na Cl P er for m ed w ith C18 Ch r om a togr a p h y (see
Exp er im en ta l Section )
p
d
p
e
[
G]o,
M
d(% H)/dt,b -d(% G)/dt,c d(% G2 )/dt,
d[G2 ]/dt,
a
-1
-1
-1
-1
h
h
h
M h
-
-
-
-
-
-
-
6
5
5
5
5
5
5
0
0
0
0
0
0
0
0
.020
.040
.060
.080
.085
.090
.104
.092f
0.79
0.78
0.79
0.70
0.93
0.83
1.36
0.92
0.86
0.77
0.75
1.00
1.05
0.87
1.20
1.16
0.025
0.046
0.072
0.086
0.105
0.094
0.085
g
2.90 × 10
1.07 × 10
2.51 × 10
4.00 × 10
5.18 × 10
4.91 × 10
5.13 × 10
g
a
Initial 2-MeImpdG concentration. b Slope of a plot of percent
hydrolysis product, H, with time where H includes both 5′dGMP
c
and HEPES-pdG. Slope of a plot of percent 2-MeImpdG as a
function of time. d Slope of a plot of percent G2p formed as a
F igu r e 2. Percent yield of G p
during the reaction of 0.09 M 2-MeImpdG (open circles) and
the reaction of 0.08 M 2-MeImpdG with 0.005 M poly(C) (filled
squares). The percent yield is expressed in monomer equiva-
formed as a function of time
function of time; experimental error estimated at 15-20%. d[G2 ]/
dt calculated based on eq 1 with h ) 1.16. f Experiment run in
the presence of 0.02 M poly(C) and analyzed with C18 chroma-
tography. g Not determined.
e
p
2
lents and is not corrected for hypochromicity. The downward
p
p
curvature indicates that the rate of G
2
formation is slowed
G
2
is one of two possible dimers anticipated from the
p
-1
12a
at later times. Initial slope is equal to d(% G
2
)/dt in h
.
dimerization of 2-MeImpdG.
The other dimer is the
internucleotide-linked pdGpdG that was not detected. In
principle, the dimers are formed as phosphoimidazolide-
to the initial substrate. This could be done because all
5
′
guanosine monomers exhibit similar extinction coefficients.
activated derivatives, dG p(2-MeIm)pdG and 2-MeImp-
dGpdG, which slowly hydrolyze. Nevertheless, the ab-
sence of any other peak in the solutions that could be
p
Percent G
2
yields are reported in monomer equivalents and
p
are uncorrected for hypochromicity. G
calculated from [G
2
concentration was
] ) h[G] (% G )/200 where h is a hypo-
p
p
2
o 2
5
′
attributed to dG p(2-MeIm)pdG is interpreted to indicate
that this derivative hydrolyzes much faster than what
can be observed with our detection methods. Reaction of
5′dGMP with 2-MeImpdG provides an additional path-
chromicity correction factor with h ) 1.16 (acidic solutions,
C18 chromatography) and h ) 1.34 (basic solutions, HEMA
chromatography); the value of h was assumed to be the same
5
′
11
as the one determined for G ppG. The hypochromicity of
deoxyoligoguanylates longer than the dimer was assumed to
be the same as the one determined for the ribooligoguanylates
p
2
way for the formation of G , in analogy to the reaction
of the corresponding ribo-derivatives, 5′GMP with 2-Me-
4
a
h ) 1 (basic solutions).
5′
12a
ImpG leading to G ppG.
This reaction becomes in-
creasingly important for long incubation times as the
hydrolysis product accumulates and should result in an
Resu lts
p
p
increased G
2
formation. Enhanced G
2
formation at
Gen er a l F ea tu r es. Under our conditions and in the
absence of poly(C), there is still approximately 65% of
-MeImpdG left intact after 1 day and 20% to 30% left
after 5 days. Practically all substrate is consumed after
about 20 days of incubation after which a solution of 0.09
M 2-MeImpdG yields 58.5% of 5′dGMP, 17.2% of HEPES-
pdG (formed by reaction of the buffer), 16.2% of G
less than 1% of longer oligomers. In the presence of poly-
C), besides the above products, oligomers longer than
the dimer are formed. After 20 days of incubation, a
longer times was, apparently, counterbalanced by sub-
p
strate consumption, and this is why many plots of % G
2
2
vs time showed good linearity. Experiments (not listed)
indicate that the reaction between 5′dGMP and 2-Me-
p
ImpdG, to produce G
2
, is also catalyzed by poly(C). We
believe that it is this additional pathway that produces
p
2
, and
p
the substantial yields of G
2
that are observed both in
the absence and in the presence of the polymer after long
incubation times. To minimize this problem, samples
were analyzed immediately after mixing and initial rates
were determined from the first few hours of incubation.
Kin etics of 2-MeIm p d G Dim er iza tion in th e Ab-
sen ce of P oly(C). Experiments in the absence of poly-
(
mixture of 0.02 M poly(C) and 0.092 M 2-MeImpdG
and approximately 12% of longer
oligomers up to the 6-mer, i.e., substantially higher yields
p
produces 29% G
2
p
than the 16.2% G
2
and 1% oligomers observed in the
(
o
C) were run with 0.02 M e [G] e 0.104 M for about 15
absence of the polymer. These observations imply that
poly(C) has, at least, doubled dimerization and has
dramatically catalyzed the polymerization. A better way
p
to 20 h and produced 1-4% of G
and about 4% of HEPES-pdG. Plots of % G
tion of time were generally linear and provided slopes,
2
, up to 18% of 5′dGMP,
p
2
as a func-
to quantify the effect of poly(C) on the dimerization is to
p
2
d(% G )/dt, listed in Table 1. The experimental error of
p
monitor the percent yield of G
2
formed as a function of
these slopes is estimated at 15-20%. This table includes
also slopes of lines obtained by plotting the percent of
hydrolysis product H (H ) 5′dGMP + HEPES-pdG)
time, as shown in Figure 2 for two reactions, one with
.005 M poly(C) and the other without it. Plots such as
these were either linear or slightly curved mainly because
the reaction rate slows down as the substrate is being
consumed.
0
formed as well as the percent of substrate left unreacted,
p
d(% H)/dt and d(% G)/dt, respectively. Rates of G
2
p
2
formation, d[G ]/dt, were calculated via eq 1 and are
included in Table 1. In eq 1, h ) 1.16 is the hypochro-
(
11) Diguanylates exhibit hypochromicity correction factor of h )
.16 in neutral and acidic solutions (from T. Brian Hurley, Senior
Thesis for the Degree of B. S. in Chemistry, 1993, University of
1
(12) (a) Kanavarioti, A. Origins Life Evol. Biosph. 1997, 27, 357-
376. (b) Kanavarioti, A. J . Mol. Evol. 1998, 46, 622-632.
4
a
California at Santa Cruz) and h ) 1.34 in basic solutions.

7
960 J . Org. Chem., Vol. 64, No. 21, 1999
Kanavarioti and Gangopadhyay
Ta ble 2. Kin etics of G2p F or m a tion in th e
P oly(C)-Ca ta lyzed Self-Con d en sa tion of 2-MeIm p d G a t
3 °C a n d p H 7.85 ( 0.05 in th e P r esen ce of 0.5 M HEP ES,
.2 M MgCl2, a n d 1.0 M Na Cl a s a F u n ction of 2-MeIm p d G
a n d P oly(C) Con cen tr a tion
2
0
p
p
p
entry [G]o, poly(C), d(% G2 )/dt, d[G2 ]/dt (C), TD d[G2 ]/dt,
a
b
-1 c
-1
d
-1 e
no.
M
M
h
M h
M h
-
-
-
-
4
4
5
4
-4
-5
-5
-4
-4
-4
-4
-4
-4
-5
-4
-6
-4
-4
-5
-5
1
2
3
4
5
6
7
8
9
0
1
2
3
0.060 0.016
0.057 0.008
0.060 0.005
0.080 0.016
0.080 0.005
0.100 0.030
0.110 0.024
0.110 0.019
0.100 0.008
0.110 0.004
0.34
0.30
0.22
0.50
0.27f
0.96
0.81
0.61
0.31f
0.19
0.36
0.09
0.74
0.64
0.28
0.18
1.37 × 10
1.15 × 10
8.84 × 10
2.68 × 10
1.45 × 10
6.43 × 10
5.97 × 10
4.50 × 10
2.08 × 10
1.41 × 10
2.41 × 10
1.21 × 10
5.95 × 10
4.29 × 10
9.38 × 10
4.82 × 10
1.12 × 10
9.21 × 10
6.36 × 10
2.24 × 10
1.00 × 10
6.09 × 10
5.46 × 10
3.92 × 10
1.49 × 10
6.22 × 10
1.79 × 10
9.30 × 10
5.20 × 10
3.80 × 10
7.65 × 10
3.72 × 10
-4
-
-
-
4
4
4
-4
-
-
-
-
4
4
5
4
1
1
1
1
0.10
0.02
0.12
0.10
0.05
0.04
0.005
0.005
0.016
0.016
0.016
0.016
F igu r e 3. Rate of G p
formation, d[G
2
p]/dt in M h-1, in the
-4
2
14
15
16
-
5
absence of poly(C) as a function of the square of monomer
2
-5
concentration, (r[G]
o
) in the range 0.02 M e [G]
]/dt values from Table 1, [G] the initial monomer
concentration and r corrects for substrate purity (see Results).
The line is a linear fit of the data, excluding 0.104 M G , with
o
e 0.09 M.
p
d[G
2
o
a
Initial 2-MeImpdG concentration. b Poly(C) concentration ex-
pressed in C equivalents. c Slope of a plot of percent G2 formed
p
o
as a function of time; experimental error of the slopes estimated
-
1
-1
slope 0.0108 M
h
.
d
p
at 15-20%. d[G2 ]/dt (C) calculated based on eqs 1 and 2 with
h ) 1.34. e TD d[G2 ]/dt is the contribution to the rate by the TD
p
micity correction for the G p
last experiment listed in Table 1 was performed in the
presence of 0.02 M poly(C) and was analyzed with C18
under acidic conditions.11 The
process only; calculated from d[G2p]/dt (C) by subtracting the
2
contribution to the rate from the reaction of the monomer in
solution (see eq 3). f Average slope of duplicate experiments.
chromatography but for reasons explained in the Experi-
Kin etics of 2-MeIm p d G Dim er iza tion in th e P r es-
en ce of P oly(C). Experiments were conducted with 0.02
p
mental Section d(% G
2
)/dt was not determined from this
experiment.9
o
M e [G] e 0.12 M and 0.004 M e [poly(C)] e 0.03 M;
the upper range was dictated by solubility constraints,
p
h
p
p
the lower range by detectable G
2
yields. Samples were
d[G ]/dt )
[G] [d(% G )/dt]
(1)
2
o
2
2
× 100
incubated for up to 7 h and analyzed automatically by
HEMA chromatography (see Experimental Section). Lines
of % G2p as a function of time were either linear or
concave down (for a representative example see Figure
Table 1 indicates that the rate of G p
increases substantially with monomer concentration, but
levels off at [G] g 0.09 M. The effect of the enhanced
dimerization on the disappearance of the substrate, d(%
G)/dt, is negligible due to the fact that hydrolysis is by
formation
2
p
2
o
2); in the latter case the slope, d(% G )/dt, was deter-
mined as the zero time tangent by a second-order fit with
p
2
a polynomial function. Values of d(% G )/dt have an
far the most important reaction in this system. In
estimated experimental error of 15-20%. Due to the
p
contrast to d(% G
2
)/dt, d(% H)/dt values (excluding 0.104
relatively short reaction times, most experiments did not
p
2
M) in Table 1 indicate that hydrolysis is independent of
monomer concentration and allow the calculation of an
average d(% H)/dt ) 0.80. From d[H]/dt ) 0.01[d(% H)/
produce products longer than the G . However with high
concentrations of monomer and polymer, oligomerization
became evident and the corrected percent G2p (hypochro-
-
3
-1
p
2
dt] one calculates k
ment with the k value determined earlier. Moreover,
the constancy of d(% H)/dt adds confidence to the
H
) 8 ×10
h
, in excellent agree-
micity included, see Experimental Section), h(% G )cor,
5
p
H
was calculated from eq 2. h(% G ) was then used
2
cor
p
p
instead of h(% G ) in eq 1 in order to calculate d[G ]/dt
2
2
p
increases seen with d(% G
To correct for the fact that the substrate was only about
5% pure and that it was further consumed during
2
)/dt.
(C), where C indicates that these measurements were
done in the presence of poly(C).
9
incubation, we included a correction factor, r, with r )
.75. This value is approximately the average value of
the fraction of 2-MeImpdG observed at the beginning ([2-
MeImpG]/[G] ) 0.85) and at the end (([2-MeImpG]/
G] ) 0.65) of the analyses. Hence, the d[G
reported in Table 1 are plotted vs (r[G]
see Figure 3). Figure 3 shows that d[G
calculated via eq 1, exhibit a linear relationship with the
square of substrate concentration up to 0.09 M. The
linearity confirms the expected bimolecular mechanism
of dimerization, and the slope of the straight line in
p
p
5′
h(% G ) ) 1.34(% G ) + 2/3(% dG p(pdG) ) +
2
cor
2
2
0
5
′
2
/4(% dG p(pdG) ) + etc. (2)
3
o
p
[
o
2
]/dt values
We conducted experiments with 0.058 ( 0.002 M
(entries 1-3 in Table 2), 0.08 M (entries 4, 5), and
0.105 ( 0.005 M 2-MeImpdG (entries 6-11) at various
poly(C) concentrations and additional experiments with
0.005 M (entry 12) and 0.016 M poly(C) (entries 13-16)
2
2
o
) and not vs [G]
o
p
(
2
]/dt values,
at different monomer concentrations. The results sum-
p
marized in Table 2 include calculated values of d[G
2
]/dt
Figure 3 provides the rate constant for the formation of
(C), using eq 1 with h ) 1.34 (see Experimental Section).
p
p
the pyrophosphate bond, k
p
. Based on d[G
2
]/dt )
Table 2 also lists values TD d[G
2
]/dt that represent the
2
-2
-1 -1
k
p
o
(r[G] ) we find k
p
) 1.08 × 10
M
h . The plateau
contribution to the rate by the TD pathway only. TD
p
p
seen in Figure 3 will be dealt with in the Discussion.
2 2
d[G ]/dt were calculated from d[G ]/dt (C) by subtracting

Template-Directed Dideoxyguanylate Synthesis
J . Org. Chem., Vol. 64, No. 21, 1999 7961
out the rate contributed by the reaction in solution as
shown in eq 3.
p
p
2
TD d[G ]/dt ) d[G ]/dt (C) - k (r[G])
(3)
2
2
p
) 1.08 × 10 M-1 h-1 and r, discussed
-2
In eq 3 k
p
earlier, was estimated from the C18 analysis of a 0.092
M 2-MeImpdG/0.02 M poly(C) sample (see last entry in
Table 1). The value r ) 0.8 was used for all the
experiments done with poly(C). This value is somewhat
higher than r ) 0.75 used for the experiments in the
absence of poly(C), but was dictated by the shorter
incubation times used in the presence of the polymer.
Also in eq 3 we used [G] ) [G]
low template occupancy and [G] ) [G]
experiments that have high template occupancy (see
Discussion). Specifically, [G] ) [G] - [T] was used only
o
for experiments that have
o
- [T] for
o
o
o
with experiments done at 0.11 ( 0.01 M 2-MeImpG. This
approximation is an oversimplification, but it is justified
because the template concentration is much lower than
the monomer concentration and the contribution of the
template-bound monomer to the total amount minimal.
p]/
F igu r e 4. Rate of dimer formation on the template, TD d[G
2
-1
dt in M h , as a function of poly(C) at different initial
2-MeImpdG concentrations: circles, 0.105 ( 0.005 M; filled
squares, 0.08 M; and triangles, 0.058 ( 0.002 M 2-MeImpdG.
p
Poly(C) concentration expressed in C equivalents. TD d[G
2
]/
p
p
dt values from Table 2. The lines are linear for the data at
.105 M, and second-order fits for the lower concentrations.
It is seen that TD d[G
2
2
]/dt are 10-25% less than d[G ]/
0
dt (C); the above-mentioned approximations do not affect
the conclusions.
Figure 4 illustrates the effect of increasing poly(C)
p
concentration on the rates. In this figure TD d[G
2
]/dt
Discu ssion
are plotted vs [poly(C)] for three families of data
p
(0.058 ( 0.002 M, 0.08 M and 0.105 ( 0.005 M 2-Me-
Syn th esis of G
2
2
in Solu tion . Figure 3 indicates that
p
p
ImpdG). Values of TD d[G
2
]/dt increase both with
G
formation in solution is second-order in the range 0.02
M e [G] < 0.09 M and most likely proceeds by a
bimolecular mechanism. The slope of the straight line
in Figure 3 provides k
can be compared with k
monomer and polymer concentration. Qualitatively speak-
ing, the catalytic effect of the polymer is small at low [G]
and large at high [G] . The effect of the polymer at 0.06
o
o
,
-
2
-1 -1
o
p
) 1.08 × 10
M
M
h
. This value
determined
-2
-1 -1
M monomer is to catalyze the dimerization at most by a
factor of 4.5, whereas the effect of the polymer at 0.10 M
monomer becomes 12-fold at 0.03 M poly(C) compared
to the reaction in solution. There is a clear saturation
effect with the 0.058 and 0.08 M families and, perhaps,
a beginning saturation with the 0.105 M family. It is
worth noting that as monomer concentration decreases
the saturation occurs at lower poly(C) concentration. This
observation is inconsistent with the hypothesis that poly-
p
) 1.7 ×10
h
under otherwise identical conditions but in the presence
of 0.2 M Mn2 instead of Mg . The 60% lower k
+
2+ 5
p
value
observed with Mg2 compared to Mn2+ is consistent with
+
2
+
earlier observations indicating that Mn
is a better
catalyst for dimerization than Mg2
+ 12b
.
The low solubility of 2-MeImpdG precluded measure-
ments at [G] > 0.105 M. The plateau observed in the
range 0.09 M e [G] e 0.104 M supports the idea of a
o
o
(C) acts as a “simple” catalyst facilitating dimerization
switch from a second-order to a pseudo-first-order mech-
by a three-molecule complexation prior to reaction. If this
were the mechanism, then at low monomer concentration
complete complexation would require relatively high
polymer concentration (late plateau), and at high mono-
mer concentration complete complexation would occur
with lower poly(C) concentration (early plateau). Both
predictions are opposite to observation.
anism. The latter could be attributed to intermolecular
stacking interactions13 becoming important at [2-Me-
ImpdG]>0.09 M and, consequently, to a dimerization
occurring within a stack of monomers. On the basis of
this scenario, one calculates a pseudo-first-order rate
-
4
-1
constant, k
2
3
p
(stack) ) 4.9 ×10
h
(from 0.085 × 1.16/
-
1
00 where 0.085 h is the rate at the plateau in Figure
), for dimerization within a stack and in the absence of
Figure 5 illustrates the effect of increasing [G]
o
on the
]/dt are plotted vs
monomer concentration for the 0.016 and 0.005 M poly-
(C) families. The rates were plotted vs r[G] , instead of
[G] , to account for substrate purity (see Results). With
both families, the rate exhibits approximately a second-
order dependence on r[G] , but with the 0.016 M family
p
rates. In this figure values of TD d[G
2
a template.
p
Syn th esis of G
2
on th e Tem p la te. Values of slopes,
p
o
d(% G
2
)/dt, obtained in the presence of poly(C) are listed
p
o
in Table 2, together with calculated d[G
2
]/dt (C) values
(
G
see Results, eqs 1 and 2). From the latter the rate of
p
o
2
formation that occurs exclusively on the template,
p
the rates become increasingly faster with monomer
concentration compared to the 0.005 M family. How can
we understand these observations?
2
TD d[G ]/dt, was obtained by subtracting out a small
contribution coming from the dimerization that occurs
in solution (see eq 3, Results). These values, also listed
in Table 2, depend both on monomer and polymer
concentration, but in a complex way. For this reason, the
data were grouped in families and plotted accordingly.
Tem p la te-Dir ected Mech a n ism of Dim er iza tion .
Because of the known affinity of guanosine monomers
for poly(C),3 it is presumed that any catalysis observed
in di- or oligoguanylate synthesis is due to a TD mech-
anism. Such a mechanism was proposed for the first time
in the poly(C)-directed 3′-5′-linked dimer formation from
,13
(13) Saenger, W. Principles of nucleic acid structure; Springer-
Verlag: New York, 1984; p 134.

7
962 J . Org. Chem., Vol. 64, No. 21, 1999
Kanavarioti and Gangopadhyay
It is convenient to differentiate between systems that
are close to saturation, abbreviated “saturated” and
systems that are far from saturation, abbreviated “un-
saturated”. Assuming a one to one C:G binding, “satu-
rated” systems are such that [G]tem ) [T]
ated when [G]tem < [T] . Another useful parameter in TD
systems is the free monomer concentration at half
o
and unsatur-
o
1
5
occupancy, [G]0.5θ, where [G]0.5θ ≈ 1/Q.
Under saturated conditions (S) and at a constant poly-
C) concentration an increase in the monomer concentra-
(
tion should have no effect on template occupancy because
θ ) 1. Therefore any experimental parameter, such as
the rate of a TD process, that is proportional to [G]tem
should remain unchanged upon further increase in
monomer concentration. Similarly, an increase in tem-
plate concentration at constant monomer concentration
will have no effect on θ as long as saturation applies. On
the other hand, an experimental parameter that depends
on [G]tem will increase proportionally to template con-
centration.
F igu r e 5. Rate of dimer formation on the template, TD d[G
2
p]/
dt in M h , as a function of 2-MeImpdG concentration, r[G]
at a constant poly(C) concentration, expressed in C equiva-
-
1
o
,
p
lents; squares at 0.016 M and triangles at 0.005 M. TD d[G
2
]/
Under unsaturated conditions (U) and at constant
poly(C) concentration, an increase in monomer concen-
tration will increase occupancy. As a consequence of the
enhanced θ, the experimental parameter will increase.
At constant monomer concentration, an increase in
template concentration will result in a lower occupancy.
In this case the experimental parameter will be subject
to two effects. One is an increase because of the enhanced
dt values from Table 2. [G] is the initial monomer concentra-
tion and r corrects for substrate purity (see Results). The lines
o
are computer simulations of a cooperative association model
-
1
-1
with q ) 7 M , Q ) 9.5 M and an intrinsic rate of TD
-
1
dimerization k
p
* ) 0.06 h (line at 0.016 M) and k
p
* ) 0.07
-1
h
(line at 0.005 M, see Discussion).
2
-MeImpG which was investigated as a function of
4
a
monomer at a constant polymer concentration. This
model is summarized below. It presumes that G binds
cooperatively at C sites of the template (T). Binding of G
to an isolated site on the template occurs with an
association constant, q, and binding of G adjacent to an
occupied site occurs with an association Q with Q > q. Q
is assumed to be independent of the length of the stack.
o
[T] , the other a decrease because of the lower occupancy.
These two effects will counteract each other and, depend-
ing on the specific case, the experimental parameter will
either exhibit an increase or remain unchanged. If, e.g.,
the measured parameter exhibits an increase, this in-
crease will be less than the increase in template concen-
tration, i.e., parameter increase will not be proportional
to template concentration (see different scenario above
for a saturated system).
T‚G
m
is a template-bound stack of m monomers. T‚G
2
p
stands for a stack of two monomers in contrast to T‚G
2
5
′
that identifies a template-bound dG ppdG dimer stand-
The features that distinguish saturated from unsatur-
ated conditions are summarized in Table 3. They are
applicable to other TD reactions, not only dimerizations.
For example, TD oligoguanylate elongation was found to
exhibit a decreased rate with poly(C) concentration
increasing from 0.002 to 0.05 M at a constant 0.02 M
p
ing alone or within a stack of monomers, T‚G
2
‚Gm-2 (eq
4
). As long as the relative positioning of two molecules
is right for pyrophosphate bond formation, reaction can
occur between any two adjacent monomers within a stack
of monomers hydrogen-bonded to the template. For
p
simplicity it is assumed here that the rate of G
2
4
b
2
-MeImpG (see condition [T]
o
o
v w θ V, at constant [G] ).
formation is independent of the length of the stack, so
Moreover, these conditions or principles can be exploited
as diagnostic tools to identify whether a system is close
or far from saturation. Alternatively, if Q is known or
2
that k
p
) k
p p
*; k * is the intrinsic rate constant for TD
pyrophosphate synthesis from of 2-MeImpdG. For sta-
tistical reasons k
3
m
p
) 2k
p
* and k
p
p
) (m - 1)k *.
can be estimated, the relationship between [G]
o
, [G]0.5θ,
and [T] is useful in predicting whether a system is close
o
to saturation or not. Knowing if a system is close or far
from saturation is critical when the efficiency of poly-
nucleotide synthesizing systems is concerned. This is
because dimerization and elongation become kinetically
4
optimal processes in a saturated system. In this context,
comparison of oligomerization yields between two TD
systems, one being close to saturation and the other far,
could lead to erroneous conclusions regarding which one
is more efficient under optimal conditions.
Below we will show how the relationships in Table 3
rationalize the data in Figures 4 and 5. As the concentra-
tion of polymer increases and sites for binding become
available, catalysis is evident, as seen by the increased
Equations 5 and 6 describe the relationships between
total monomer concentration, [G] , and the concentration
of template-bound monomer, [G]tem (see later on how to
calculate [G]tem from the mass balance and mass law of
o
eq 4). [G]
in solution, [T]
expressed in C equivalents, and θ is the occupancy.
f
is the concentration of the monomer present
o
stands for the total poly(C) concentration,
[
G] ) [G] + [G]f
(5)
(6)
o
tem
(
14) Kanavarioti, A.; Hurley, T. B.; Baird, E. E. J . Mol. Evol. 1995,
4
1, 161-168.
θ ) [G]tem/[T]o
(15) For an explanation see ref 14 and references therein.

Template-Directed Dideoxyguanylate Synthesis
J . Org. Chem., Vol. 64, No. 21, 1999 7963
Ta ble 3. Rela tion sh ip s betw een Mon om er , P olym er , a n d Occu p a n cy in a Coop er a tive System u n d er “Sa tu r a ted ” a n d
“
Un sa tu r a ted ” Con d ition s
1
1
6
6
S
U
θ ) 1
0 < θ < 1
[G]o > [G]0.5θ + [T]o
[G]o e [G]0.5θ + [T]o
[G]o v w θ constant at constant [G]o
[G]o v w θ v at constant [T]o
[T]o v w θ constant at constant [T]o
[T]o v w θ V at constant [G]o
d[G p
reaction in solution (Figure 4). TD d[G
measured experimental parameter that in this system
is presumed to be directly proportional to the saturated
template/monomer complex. In the range 0 e [poly-
]/dt in the presence of the template compared to the
(for the 0.005 M) and k
Simulations were also performed for the rest of the
experimental conditions listed in Table 2 using q ) 7 M
* ) 0.06 h-1 (for the 0.016 M).
2
p
p
2
]/dt is the
-1
-
1
and Q ) 9.5 M . The k
p
* values derived from these
simulations and the experimentally determined TD
p
-1
-1
(
C)] e 0.004 M and with 0.08 and 0.105 M monomer the
d[G
average k
fit all the data in Table 2. Models presuming more
2
]/dt ranged from 0.035 h to 0.075 h . Thus an
p
-1
values of TD d[G
under these conditions, i.e., [T]
0
2
]/dt are the same, suggesting that
e 0.004 M and [G]
.08 M, the system is close to saturation (see [G] v w θ
). The fact that the two lines
p
* ) 0.055 ( 0.02 h is seen to satisfactorily
o
o
>
2
o
efficient dimerization in longer stacks, i.e., where k
p
)
3
m
2
3
const., at constant [T]
o
0, k
p
) k
p
p
*, k
p
) (m - 2)k
) (m - 3)k
p
*, or where k
p
) k
p
) 0,
4
m
digress at [T]
switches from saturated to unsaturated allowing an
o
> 0.004 M implies that the system
k
p
) k
fits.
The k
*, k
p
p
*, etc., did not result in better
* ) 0.055 h- for TD pyrophosphate bond
formation suggests a 110-fold catalysis by the template
when compared to the value of k
which assumes synthesis within a stack of monomers.
* ) 0.055 h compared to k
h , the TD rate constant for 3′-5′-internucleotide bond
1
estimate for [G]0.5θ ) 0.10 ( 0.01 M from [G]
T] and [T] , [G]
o
≈ [G]0.5θ
+
p
[
o
o
o
.
-
4
Furthermore, with the family of 0.105 M monomer an
increase in template concentration results in a propor-
p
(stack) ) 4.9 × 10
-1
h
p
-1
-3
tional increase in TD d[G
2
]/dt (see above discussion for
) up to about 0.024
The value k
p
d
* ) 4.1 × 10
-
1
[
T] v w θ constant, at constant [G]
o
o
5
M poly(C) where there is, perhaps, an indication for a
plateau. This plateau is clearly evident with the 0.08 and
formation between morpholine-pG and 2-MeImpdG,
indicates a 13-fold higher reactivity of the phosphate
anion compared to the ribose 3′-OH at pH 7.8 and in the
presence of Mg2 . These two systems, i.e., poly(C)/2-
MeImpdG and poly(C)/mor-pG/2-MeImpdG, are similar
in the sense that the reacting molecules act either as a
nucleophile or as an electrophile. This is in contrast to
the poly(C)/2-MeImpG, system, where each monomer has
dual reactivity. An even larger reactivity difference, 30-
fold, has been observed between pyrophosphate synthesis
and internucleotide bond formation with deoxyribose 3′-
0
.058 M families and occurs at about 0.013 and 0.008 M
+
poly(C), respectively. The curvarture seen with the 0.08
and 0.058 M families is a manifestation of the condition
[T]
o
o
v w θ V, at constant [G] , indicating unsaturated
conditions. The plateaus that occur earlier with lower
monomer concentration can be attributed to the fact that
it takes much less polymer before the system’s occupancy
is lowered.
Figure 5 depicts the effect of increasing monomer
concentration on the rate with two familes of data, one
with 0.005 M and the other with 0.016 M poly(C). Here
7
OH as the nucleophile and carbodiimide activation. Such
large reactivity differences, perhaps 30-fold or higher, can
explain why in the present study no internucleotide-
linked dimer was detected.
o
there is an approximately 3-fold increase in [T] between
the two families, but less than a 3-fold increase in the
rate in the range of measurements up to 0.1 M 2-Me-
p
Con clu sion s
ImpdG. For example, at 0.1 M 2-MeImpdG TD d[G
2
]/dt
-
4
-1
-4
measures 1.79 ×10 M h with 0.005 M and 3.8 ×10
M h with 0.016 M. This amounts to a 2.1-fold increase
in the rate for a 3.2-fold increase in [T] , suggesting that
one or both tested systems are unsaturated. Moreover,
the conclusion can be drawn that with decreasing [G]
In nonenzymatic TD polymerizations, dimerization is
slower than elongation so that the dimer does not
-
1
o
(17) Calculations were executed using Microsoft Excel on a Power
Mac computer. The following is based on the description given in ref
a. According to the proposed mechanism (eq 4), the rate of G
2
formation is given by eq 7 where r corrects for substrate purity and
o
p
4
these two systems are led farther from saturation. Thus,
Figure 5 can be seen as the experimental manifestation
F
D
is given by eq 8. [G]tem can be calculated from eq 9.
of the condition [T]
o
v w θ V, at constant [G]
o
.
p
TD d[G2 ]/dt ) k r FD
(7)
p
Com p u ter Sim u la tion of Mon om er Distr ibu tion
on th e Tem p la te. The lines shown in Figure 5 are the
result of a computer simulation. This simulation was
based on the mathematical equations derived from eq 4.
FD ) [T‚G ] + 2[T‚G ] + 3[T‚G ] + 4[T‚G ] +....+ (m - 1)[T‚G ]
2
3
4
5
m
(8)
[G]tem ) [T‚G] + 2[T‚G ] + 3[T‚G ] + 4[T‚G ] +
2
3
4
The concentration of the various T‚G
n
species in eq 4 was
5[T‚G ] +....+ m[T‚G ] (9)
5 m
calculated assuming a 100-unit long template and was
based on the mass balance equations.17 Optimization of
q and Q values to fit the experimental data in Figure 5
j
The concentration of T‚G species can be calculated from eqs 10 and
11 where [G] is the free monomer concentration in solution, [T] is
f
f
the free concentration of template sites that are free and whose next-
neighbor sites on both sides are unoccupied (eq 12). [T]
multiple iteration carried out with Microsoft Excel.
f
is found by
-
1
-1
provided values q ) 7 ( 0.5 M and Q ) 9.5 ( 0.5 M
the latter being in good agreement with [G]0.5θ ) 0.10 (
.01 M estimated from Figure 4. The relatively large
,
[
T‚G] ) q[T] [G]f
(10)
(11)
f
0
[T‚G ] ) q[T] [G] Qj-1[G]
j-1
value of q is a manifestation of the fact that the template
exhibits a catalytic effect even at low concentrations. The
best fit in Figure 5 was obtained with an intrinsic rate
j
f
f
f
j)m
[
T] ) [T] - [G] - 2
[T‚Gj]
(12)
f
o
tem
∑
-
1
constant for TD pyrophosphate formation k * ) 0.07 h
p
j)1
In practice, calculation was initiated by a chosen [G]
f
, iteration provided
(
16) These relationships are not mathematically exact, and they only
the correct [T]
f
and then [G]
]/dt was obtained as TD d[G
with r ) 1.
o
was obtained. To create the simulated
p
p
serve as a guide to deduce whether a system is close or far from
saturation or, alternatively, to estimate Q.
lines, TD d[G
2
2 p D
]/dt ) k F , and it was
plotted vs r[G]
o

7
964 J . Org. Chem., Vol. 64, No. 21, 1999
Kanavarioti and Gangopadhyay
stants, q ) 7 M- and Q ) 9.5 M-1, and one intrinsic
1
accumulate which makes it difficult to extract kinetic
information about the dimerization step. However, the
pyrophosphate-linked dimer, G
rapidly from two molecules of 2-MeImpdG and elongates
slowly, so that the kinetics of its formation could be
conveniently monitored by HPLC. Accumulation of G
-
1
p
rate constant k * ) 0.055 ( 0.020 h for TD pyrophos-
p
2
, is formed relatively
phate synthesis. Furthermore, it was concluded that
dimerization occurs efficiently within a stack of two or
more template-bound monomers.
p
2
made it possible, for the first time, to determine the
Ack n ow led gm en t. This research was supported by
the Exobiology Program of the National Aeronautics and
Space Administration (Grant No NCC 2-5309). We
thank Dr. L. E. Orgel from the Salk Institute for
constructive criticism. We also thank Dr. Mark Fonda
from the Planetary Biology Branch of NASA/Ames
Research Center and Prof. C. F. Bernasconi from the
Chemistry and Biochemistry Department of the Uni-
versity of California at Santa Cruz for providing the
facilities and Prof. Bernasconi for helping us with the
kinetic analysis.
kinetics of a TD dimerization as a function of both
p
monomer and polymer concentration. Rates of G
2
forma-
tion obtained in the range 0.02 M e [2-MeImpdG] e 0.12
and 0.004 M e [poly(C)] e 0.03 M varied by 65-fold from
the slowest to the fastest rate. This study allowed
conditions to be outlined that could diagnose whether a
TD reaction in general, not only a TD dimerization, is
close or far from saturation based on a limited set of
kinetic determinations. A TD cooperative model proposed
earlier for another TD dimerization ((poly(C)/2-MeImpG
3
′
that forms pG pG) was successful in fitting all the
experimental results using one set of association con-
J O990998K