Analysis of strand slippage in DNA polymerase expansions of CAG/CTG triplet repeats associated with neurodegenerative disease.

Lengthy expansions of trinucleotide repeats are found in DNA of patients suffering severe neurodegenerative age-related diseases. Using a synthetic self-priming DNA, containing CAG and CTG repeats implicated in Huntington's disease and several other neurological disorders, we measure the equilibrium distribution of hairpin folding and generate triplet repeat expansions by polymerase-catalyzed extensions of the hairpin folds. Expansions occur by slippage in steps of two CAG triplets when the self-priming sequence (CTG)16(CAG)4 is extended with proofreading-defective Klenow fragment (KF exo-) from Escherichia coli DNA polymerase I. Slippage by two triplets is 20 times more frequent than by one triplet, in accordance with our finding that hairpin loops with even numbers of triplets are 1-2 kcal/mol more stable than their odd-numbered counterparts. By measuring triplet repeat expansions as they evolve over time, individual rate constants for expansion from 4 to 18 CAG repeats are obtained. An empirical expression is derived from the data, enabling the prediction of slippage rates from the ratio of hairpin CTG/CTG interactions to CAG/CTG interactions. Slippage is initiated internally in the hairpin folds in preference to melting inward from the 3' terminus. The same triplet expansions are obtained using proofreading-proficient KF exo+, provided 10-100-fold higher dNTP concentrations are present to counteract the effect of 3'-exonucleolytic proofreading.

The human genome has an abundance of simple sequence repetitions that are unstable and tend to expand in large numbers in some genetic loci. A prime example is the CAG/CTG class of triplet repeats whose large expansions occur in genes associated with Huntington's disease and six other neurological disorders (1). Such expansions represent a novel form of mutation whose cause is unknown. An attractive possibility under investigation is primer/template slippage during DNA replication or repair of tandemly repeated sequences (2)(3)(4)(5)(6)(7)(8).
Strand slippage can occur when there is local strand separation in DNA regions containing tandem repetitions (9). For example, in a region of CAG/CTG repeats, local separation creates single-strand loops of CAGs and CTGs whose repetitive character may allow the two strands to be displaced (i.e. slipped) by an integral number of triplets. Such slippage in the presence of DNA polymerases can result in the addition of integral numbers of triplets to give triplet repeat expansions (2)(3)(4)(5)(6)(7)(8). Large loops that form stable hairpin structures are ex-pected to increase the probability of slippage and expansion (8, 10 -14).
We (14) and others (10,12,13,15) have shown that single strands of CTG repeats form stable hairpin structures as a result of base pairing between antiparallel CTGs, yielding G⅐C and C⅐G base pairs alternating with T⅐T mispairs. Similar hairpins also form in strands of CAG repeats but are not as stable (14 -16), probably because A⅐A mispairs are bulkier and more destabilizing than T⅐T (17). Our thermal denaturation studies of strand folding (14) indicated that hairpin stability increases more slowly than expected with increasing numbers of repeats. A plausible explanation is that strands with more repeating triplets have more degrees of freedom and tend to form several shorter hairpin loops instead of one long one. For example, a strand with 10 triplet repeats may fold into a single hairpin structure, whereas a longer strand with 30 repeats may form a more complex structure with two or three hairpin folds of similar size (14).
Evidence of strand slippage in CAG/CTG repeat regions during DNA polymerization has been obtained using various gelbased primer extension assays (5)(6)(7)(8). Our assay differs from earlier ones mainly in the priming event. We engineered a DNA oligonucleotide of triplet repeats so that it is primed by intramolecular folding, rather than by intermolecular association. Being independent of concentration, the self-priming remains efficient at low DNA concentrations, unlike intermolecular priming that requires higher DNA concentrations. By using low concentrations, we avoid uncertainties arising from multimeric associations between DNA strands. Also, our starting primer 3Ј-end is fully complementary to template repeats, instead of partially complementary as in the only previous study of self-priming with triplet repeats (6).
In the present study we use a self-priming strand containing a large number of CTGs relative to CAGs, to measure the influence of CTG/CTG interactions on strand slippage in polymerase-catalyzed expansions of correctly paired (CAG/CTG) repetitions. This approach provides for the first time an opportunity to measure slippage and expansion rates as a function of the number of interacting triplets, for DNA polymerases with and without proofreading 3Ј-exonuclease activity.

Materials
DNA Polymerases-Escherichia coli DNA polymerase I Klenow fragment (KF) 1 mutant, exo Ϫ (D355A,E357A), devoid of proofreading 3Јexonuclease activity, was purified from overproducing strains (18). Normal proofreading-proficient KF polymerase (exo ϩ ) was obtained by 1 triplet (I 0 3 I 1 ), converting the even-numbered loop A 0 to the odd-numbered loop A 1 (Fig. 1). The assumption is that I 0 3 I 1 occurs with rate constant k 0 Ј, whereas I 1 3 I 3 occurs with rate constant k 1 for 2-triplet slippage. Then, applying the corresponding differential equation, dI 1 /dt ϭ k 0 ЈI 0 Ϫ k 1 I 1 , we find that k 0 Ј (for 1-triplet slippage) is an order of magnitude less than k 0 (for 2-triplet slippage), whereas k 1 for 2-triplet slippage of an odd-numbered loop is consistent with k 0 and k 2 for 2-triplet slippage of even-numbered loops.

RESULTS
The self-priming sequence, A ϭ (CTG) 16 (CAG) 4 , forms a series of hairpin loops (Fig. 1), to which integral numbers of CAG triplets can be added by polymerase-catalyzed reaction with appropriate dNTP substrates (N ϭ C, A, G). In Fig. 1, A 0 represents the most stable loop in the form of a blunt-ended hairpin; A 1 corresponds to slippage of A 0 by a single triplet; A 2 , slippage by two triplets; etc. Initially, there is an equilibrium distribution of loops reflecting their thermodynamic stability in the absence of polymerase. We verify that stable folds are formed by examining thermal denaturation profiles obtained by plotting UV absorbance (A 260 ) versus temperature (Fig. 2).
When DNA polymerase and dNTPs are added, the original loops are extended to blunt ends in a matter of seconds, so that the rates at which blunt-end hairpins rearrange by slippage and expand by triplet additions can be accurately measured over a period of minutes. To establish the equilibrium amounts of individual hairpins and their extension rates, we analyzed polymerase-catalyzed reaction products separated into discrete bands by electrophoresis on a denaturing, formamide-polyacrylamide gel. The products are first analyzed as a function of reaction time (t) at physiologically low (0.1 to 1 M) dNTP concentration, using a proofreading-deficient DNA polymerase, Klenow fragment exo Ϫ . The results shown (Fig. 3) 16 (CAG) 4 . The even-numbered loops (A 0 , A 2 , etc.) and less stable odd-numbered loops (A 1 , A 3 , etc.) are extendable by even and odd numbers of CAG triplets, respectively. The solid dots indicate correct base pairs; the asterisk indicates the 5Ј-end radiolabeled with 32 P. The most stable loop is blunt-ended A 0 , having the most correct base pairs, namely 23. The loops indicated as much less stable have less than 4 CAGs correctly paired with complementary antiparallel CTGs. Upon reaction with DNA polymerase and dNTPs (N ϭ C, A, G), the initial loops A n are rapidly extended (in seconds) to blunt-end products, A n ϩ (CAG) n , seen as band intensities I n (n ϭ 0, 1, 2, etc.) by denaturing gel electrophoresis. With increasing reaction time, the changes in I n indicate the rates of strand slippage in the blunt-ended hairpins and further expansion by addition of more CAG triplets. with 0.2 M each of the three dNTP substrates (N ϭ C, A, G). This concentration appears high enough to obtain near-maximum velocity of extension with a minimum of artifacts such as terminal transferase activity, seen at higher [dNTP] as an increase in background "pause" bands (data not shown).
Thermal Denaturation Profiles-Upon heat denaturation (Fig. 2), the 60-mer (CTG) 16 (CAG) 4 shows two sigmoidal transitions, with melting temperature T m ϭ 56 and 80°C at low ionic strength. By comparison, the 30-mer (CTG) 6 (CAG) 4 , having 10 fewer CTG repeats, shows only the higher transition with T m near 80°C. The biphasic melting curve of the 60-mer is consistent with the kind of hairpin folding shown in Fig. 1, in which the 4 CAG triplets are correctly base-paired with 4 CTG repeats to give the more stable component melting at 80°C, whereas the remaining 12 CTG triplets are more weakly paired to give the less stable component melting at 56°C. The latter T m value is close to that observed for hairpin folding of CTG triplets alone, e.g. (CTG) 10 and (CTG) 30 , each with T m ϭ 51°C (14). However, the melting curve is unable to resolve the kinds of hairpin folds present. The various possible folds ( Fig. 1) initially have the same strand length, but when extended with polymerase they acquire increasing lengths, which can be separated by electrophoresis on formamide-polyacrylamide gel.
Initial Hairpin Loops-As seen in Fig. 1, starting at the 5Ј-end marked by *, the 60-mer sequence A has a potential template of 16 CTG repeats followed by a primer of 4 CAG repeats. Upon hairpin folding, so that the CAGs align with CTGs in antiparallel fashion, the (CAG) 4 primer can be correctly base-paired with any 4 successive antiparallel CTGs, shown as (GTC) 4 in Fig. 1. The first loop, A 0 , is a blunt-ended structure with 3Ј-and 5Ј-ends juxtaposed. This is the most stable fold because it allows remaining CTGs to form the maximum number of base pairs with each other.
The even-numbered loops A 2 , A 4 , . . . , A 10 belong in the same group as A 0 , because they each have the same kind of 4-base hairpin bend and an even number of overhanging triplets. The odd-numbered loops A 1 , A 3 , . . . , A 11 belong in a separate group, because they each have a 3-base bend and an odd number of overhanging triplets. The even-numbered loops are expected to be somewhat more stable than the odd-numbered (10), because they each have one more base pair stabilizing the hairpin bend. For completeness, much less stable loops, A 12 to A 15 , having fewer than 4 correctly paired CAG/ CTG combinations, are also shown ( Fig. 1).
Being blunt-ended, A 0 is not suitable for extension by DNA polymerases until it rearranges by strand slippage into one of the other possible forms with an overhanging 5Ј-template, (GTC) n * (Fig. 1). These forms, A n (n ϭ 1, 2, etc.), are easily extended to blunt-end products, A n ϩ (CAG) n , by the addition of (CAG) n opposite (GTC) n *. The products are resolved as a series of bands on a denaturing gel, with band intensity I n proportional to the amount of product, (A n ϩ (CAG) n ). The 5Ј-end (*) is radiolabeled with 32 P to obtain quantitative band intensity measurements with a PhosphorImager.
Loop Resolution by Electrophoretic Analysis of Polymerasecatalyzed Extension Products-Using proofreading-deficient DNA polymerase KF exo Ϫ , we observed complete extension of initial loops within 0.5 min of reaction (Fig. 3). A 6-fold excess of polymerase is used to saturate all the self-primed loops originally present so that they can be completely extended to blunt ends in seconds, before appreciable primer/template slippage can occur. Also, we use a dNTP concentration low enough (0.2 M) to avoid the formation of anomalous pause bands arising by base misinsertion or by blunt end addition of a single nucleotide (19).
In Fig. 3 it is clear that the most intense bands correspond to additions of even numbers of CAG triplets. The bands formed by adding 0, 2, 4, etc. triplets are much more intense than those formed by adding 1, 3, etc. triplets. This striking result shows that even-numbered loops ( Fig. 1) are significantly more abundant, i.e. more stable, than odd-numbered, in agreement with earlier observations (10). The way the band intensities I n change with t, the time of reaction, indicates the rates at which the blunt-end loops, A n ϩ (CAG) n , rearrange by slippage and expand by the addition of more CAGs.
Measurement of Expansion Rates for Primer/Template Slippage in Polymerase KF exo Ϫ Reactions-By examining the band patterns in Fig. 3, we find that as the original 60-mer band (0 triplets added) decays with t, each subsequent even-numbered band, representing addition of 2, 4, etc. CAG triplets, intensifies to a maximum before decaying. This is better illustrated in Fig. 4, where the band intensity I n , expressed as percent of total intensity in each lane, is shown plotted versus t for the first three even-numbered bands, n ϭ 0, 2, and 4. Since oddnumbered bands (additions of 1, 3, etc. triplets) remain faint at all times, we see that slippage by two triplets is strongly favored over slippage by one triplet.
To describe how each band intensity I n changes because of slippage by 2 triplets and subsequent expansion by (CAG) 2 , we use the kinetic scheme in Fig. 5. The rate constants k n with n ϭ 0, 2, 4, etc. represent "macroscopic" rates for converting each even-numbered blunt-end loop (I n ) to the next (I nϩ2 ) by 2-triplet slippage and expansion. For n ϭ 0, the intensity I 0 decreases exponentially with t (Fig. 4), and the exponential curve fitted by least squares yields the slippage rate constant, k 0 ϭ 0.81 min Ϫ1 . By extrapolating to t ϭ 0, we find I 0 (t 3 0) ϭ 61% as the initial amount of hairpin A 0 (Table I). For n ϭ 2, band intensity I 2 rises rapidly until it reaches a maximum and then gradually declines (Fig. 4). By assuming k 0 is the rate constant for converting I 0 to I 2 by 2-triplet slippage, we obtain a good fit with the relationship, dI 2 /dt ϭ k 0 I 0 Ϫ k 2 I 2 , enabling us to determine k 2 relative to k 0 . Also, by extrapolating to t ϭ 0 we obtain I 2 (t 3 0), the initial amount of hairpin A 2 (Table I). Similarly, using dI n /dt ϭ k nϪ2 I nϪ2 Ϫ k n I n , we are able to evaluate k n relative to k nϪ2 and by extrapolation to estimate the initial amounts of the even-numbered hairpins with n ϭ 4 -14, i.e. A 4 to A 14 . In the case of A 14 , the initial amount (0.5%) is barely above the minimum level of detection, and the rate constant for slippage is not determined (ND, Table I).
Because odd-numbered loops give much less intense bands, comparable to faint pause bands in the background, we can only evaluate initial amounts for A 1 , A 3 , and A 5 (Table I). In the case of A 1 , there is sufficient intensity to estimate a rate constant k 1 for 2-triplet slippage (I 1 3 I 3 ), assuming A 0 contributes to A 1 (I 0 3 I 1 ) with rate constant k 0 Ј for 1-triplet slippage. In this case, dI 1 /dt ϭ k 0 ЈI 0 Ϫ k 1 I 1 , when applied to our data, yields k 0 Ј ϭ 0.04 Ϯ 0.02 min Ϫ1 and k 1 ϭ 0.7 Ϯ 0.1 min Ϫ1 (Table I, in brackets). Table I (last column) we see that the slippage rate constant k n decreases with increasing number, n, of added CAGs. The rate constant is highest (0.8 min Ϫ1 ) for n ϭ 0, the initial blunt-end hairpin A 0 (Fig. 1), which has the highest number of CTG/CTG interactions relative to CAG/CTG interactions. As Fig. 1 shows, A 0 has 4 strong CAG/CTG base pairing interactions and 5 weaker CTG/CTG interactions, so that (CTG/CTG)/(CAG/CTG) ϭ 5/4. The longer blunt-end hairpins, A n ϩ (CAG) n , formed by adding n CAG triplets complementary to the template (GTC) n * (Fig. 1), gain n more CAG/CTG interactions while losing n/2 CTG/CTG interactions. Thus, while (CAG/CTG) ϭ 4 ϩ n increases with n, both (CTG/CTG) ϭ 5 Ϫ (n/2) and the ratio, (CTG/CTG)/(CAG/CTG) ϭ (10 Ϫ n)/(8 ϩ 2n), decrease with n.

Relationship between Slippage Rate and Number of Interacting Triplets-In
The k n value (on a logarithmic scale) shows a positive correlation with (CTG/CTG) ϭ 5 Ϫ n/2 and a negative correlation with (CAG/CTG) ϭ 4 ϩ n (Fig. 6A). In each case, the correlation is nonlinear for even values of n from 0 to 8. However, when log k n is plotted against the ratio, (CTG/CTG)/(CAG/CTG) ϭ (10 Ϫ n)/(8 ϩ 2n), the points fall close to a straight line (Fig. 6B). Furthermore, k 1 obtained for 2-triplet slippage between oddnumbered loops (Table I, in brackets) also falls on this line, at the point corresponding to n ϭ 1 (Fig. 6B, open square).
The equation of the line fitted by least squares (Fig. 6B) is log 10 k n ϭ 0.38x Ϫ 0.56, where x ϭ (CTG/CTG)/(CAG/CTG). This equation can also be written as k n ϭ ␣e ␤x , where ␣ ϭ 0.28 min Ϫ1 and ␤ ϭ 0.87. We can interpret ␣ as the slippage rate constant for CAG/CTG interactions alone and e ␤x as the factor arising from the influence of (CTG/CTG) on the slippage of (CAG/CTG). This factor appears to hold as long as slippage by 2 triplets does not change the character of the hairpin bend made by CTGs.
The even-numbered loops A 0 to A 10 ( Fig. 1) have the same kind of 4-base bend made with two CTGs. However, in A 12 the bend acquires a CAG in place of a CTG at the expense of a CAG/CTG base-pairing interaction, making it more difficult for A 10 3 A 12 slippage to occur. As seen in Table I (last column), the slippage rate constant drops dramatically, from 0.28 min Ϫ1 for k 8 (I 8 3 I 10 ) to 0.08 min Ϫ1 for k 10 (I 10 3 I 12 ). This marked reduction in slippage rate is also evident in the accumulation of band intensity I 10 , corresponding to 10 CAG triplets added  (Fig. 1), and I 2 and I 4 indicate the amounts of the extension products, A 2 ϩ (CAG) 2 and A 4 ϩ (CAG) 4 , respectively. Each band intensity is expressed as percent of total integrated band intensities in the corresponding lane (Fig. 3), measured by PhosphorImager.

FIG. 5. Kinetic scheme used to evaluate rate constants for slippage and expansion by two triplets.
The rate constants k n (n ϭ 0, 2, 4, etc.) indicate the rate at which band intensity I n is converted to I n2 as a result of 2-triplet slippage and polymerase-catalyzed expansion by 2 CAG triplets. (Fig. 3). Subsequently, the slippage rate declines further to 0.06 min Ϫ1 for k 12 (I 12 3 I 14 ) and to an even lower value for k 14 , undetermined (ND) in Table I.
Effect of Proofreading Activity on Expansion Rate-When KF exo Ϫ is replaced by normal proofreading-proficient Klenow fragment, the 3Ј-exonuclease activity of proofreading markedly inhibits expansion at low dNTP concentrations (Fig. 7). At 0.2 M dTNP, band intensities similar to those found initially with KF exo Ϫ are observed in the 1st min of reaction, but expansion by slippage is greatly reduced because of 3Ј-end degradation with increasing time (Fig. 7). As dNTP concentration is increased to counteract the degradation, the band patterns for expansion by slippage are recovered for longer times. At 1.0 M dNTP, the same patterns of band intensities as in Fig. 3 are observed for the first 10 min, but some decreases in long expansions (notably I 14 and I 12 ) are evident at longer times. At 10 M, no significant decreases are evident for at least 60 min. Thus, to obtain the same degree of expansion in the presence of proofreading as in its absence, apparently 10 to 100 times as much dNTP is required.

DISCUSSION
Single DNA strands containing tandemly repeated CTG or CAG triplets form hairpin structures which, although not as stable as normal DNA duplexes, are nonetheless remarkably stable (10 -15, 20). To investigate the influence that such secondary structures have on strand slippage in polymerase-catalyzed repeat expansions, we have constructed a strand sequence, (CTG) 16 (CAG) 4 , forming a series of self-primed hairpins (Fig. 1) to which repeats of CAG triplets can be added by DNA polymerases. This sequence provides an opportunity to measure the influence of hairpin CTG/CTG interactions on primer/template slippage in repeating CAG/CTG regions. By using a DNA polymerase devoid of exonuclease activity (KF exo Ϫ ), we find that initial hairpin loops (formed at equilibrium) are fully extended to blunt-ended forms in a matter of seconds, so that the rates at which blunt-end loops rearrange by slippage and add more repeats can be measured over a period of minutes to about 1 h (Fig. 3). With this construct, we observe triplet repeat expansions in a series of discrete slippage steps for which rate constants can be evaluated.
Of the various hairpins formed initially (Fig. 1), those with an even number of bases in the bend appear most stable since they are found in the largest amounts (Table I). The series of even-numbered loops from A 0 to A 10 account for over 90% of all folded structures. As expected, the most stable loop is the  (8 ϩ 2n). The straight line is a least squares fit to k 0 , k 2 , . . . , k 10 (solid squares) found for 2-triplet slippage in even-numbered loops; the open square is the lone (k 1 ) value found for 2-triplet slippage in odd-numbered loops (Table I,  brackets).  16 (CAG) 4

and corresponding slippage rate constants for 2-triplet expansions
The rate constants for slippage and expansion by 2 CAG triplets are evaluated by analyzing gel band intensities versus reaction time with DNA polymerase KF exo Ϫ and 0.2 M dNTP (N ϭ C, A, G) at 37°C. Evaluations are made for each hairpin structure A n , starting with A 0 (Fig. 1), assuming rapid extension (in seconds) to a blunted-state, A n ϩ (CAG) n , and then slower expansion (in minutes) with rate constant k n , because of slippage by 2 triplets as illustrated in Fig. 5. The initial amount of A n is found by analyzing band intensity I n versus t and extrapolating to t ϭ 0. A good fit is obtained assuming slippage by 2 triplets, so that dI n /dt ϭ k nϪ2 I nϪ2 Ϫ k n I n . The results presented are average values (Ϯ S.D.) obtained from the experiment shown (Fig. 3) and a separate duplicate experiment not shown. In cases of faint bands or unclear expansions, rate constants were not determined (ND). Odd-numbered loops a Slippage rate constant k 1 for I 1 3 I 3 , found along with k 0 Ј ϭ 0.04 Ϯ 0.02 min Ϫ1 for I 0 3 I 1 (slippage of A 0 by 1 triplet), by analyzing the changes in I 1 versus t in accordance with dI 1 /dt ϭ k 0 ЈI 0 Ϫ k 1 I 1 .
blunt-ended structure A 0 , whose initial amount is 61% of total structures at 37°C. The next most stable loops are initially present in amounts of 5-7%, these being the five even-numbered loops, A 2 to A 10 . Surprisingly, each of the latter is as abundant or more abundant than all the odd-numbered loops collectively. The abundance of even-numbered loops does not decrease from A 2 to A 10 as might be expected but instead shows a minimum at A 4 (5%). Possibly the longer overhanging templates, shown simply as (GTC) n * in Fig. 1, form a second hairpin fold providing some additional stability.
The initial amounts of loops formed at equilibrium, in the absence of polymerase, can be used to calculate relative loop stabilities in terms of standard free energy, ⌬G o ϭ ϪRTlnK eq . From the ratio of equilibrium amounts, K eq ϭ 7/61, we find A 2 is less stable than A 0 by RTln(61/7) ϭ 1.3 kcal/mol at T ϭ 37°C or 310 K. Similarly, from K eq ϭ 2/61, A 1 is found to be 2.1 kcal/mol less stable than A 0 and thus 0.8 kcal/mol less stable than A 2 . Finding A 1 about 1 kcal/mol less stable than A 2 is consistent with our observation ( Table I, footnote) that slippage by 1 triplet, converting A 0 to A 1 , is an order of magnitude slower than the rate for 2-triplet slippage converting A 0 to A 2 .
As shown in Fig. 6B, the rate of slippage by 2 triplets may be simply related to the ratio of CTG/CTG interactions to CAG/ CTG interactions involved in slippage. The logarithm of the slippage rate constant, when plotted against the ratio (CTG/ CTG)/(CAG/CTG) in the blunt-ended hairpin undergoing slippage, shows a linear relationship with a positive slope. The slope indicates that slippage rate increases exponentially with the ratio. The implication is that hairpin CTG/CTG interactions promote slippage by 2 triplets and thereby provide a favorable way of propagating waves of expansion in CAG/CTG repeat regions.
In the expansion of the blunt-ended loops in our system, there are several reasons to think that slippage begins internally with CTG/CTG interactions rather than at the primer 3Ј terminus with CAG/CTG interactions. We observe (Fig. 2) that the CTG/CTG region has a melting temperature 24°C lower than the CAG/CTG region, so that local melting needed to initiate slippage is much more likely to occur in the CTG/CTG region. To initiate slippage by 2 triplets, three CAG/CTG interactions need to be disrupted at the primer 3Ј-end, but only one next to the CTG/CTG region where two weaker CTG/CTG interactions are more easily disrupted. Slippage by 2 triplets is favored over slippage by 1 triplet, in accordance with evennumbered loops of CTGs being more stable than odd-numbered ( Table I). The rate constant for 2-triplet slippage increases with CTG/CTG interactions but decreases with CAG/CTG interactions (Fig. 6A), so that the rate constant increases exponentially with the ratio of CTG/CTG to CAG/CTG interactions, as seen by the linear plot of log(rate constant) versus this ratio (Fig. 6B). Furthermore, in the presence of 3Ј-exonucleolytic proofreading (Fig. 7), as long as there are CTG/CTG interactions present (n ϭ 0 -8) and slippage rates are 0.28 min Ϫ1 or higher (Table I), less than 1.0 M dNTP concentrations are needed to restore normal slippage patterns, whereas 10 M concentrations are needed when CTG/CTG interactions are absent (n ϭ 12 and 14) and slippage rates fall to 0.08 min Ϫ1 or lower (Table I).
Since our system is single-stranded and relatively short, it is not certain how many of the points above may apply to long double-stranded DNA molecules in vivo. Nevertheless, with these points in mind, we can propose a simple model (Fig. 8) indicating how triplet repeat expansion may occur when there is local strand separation in a region of triplet repeats. Such separation could arise, for example, by negative supercoiling (21) of the kind needed to activate transcription or replication. Once separated in a region of triplet repeats, the strands may  (Fig. 3), at low (0.2 M) dNTP concentration, the self-priming sequence 32 P(CTG) 16 (CAG) 4 is extended to blunt-ended states in less than 1 min as before, but expansion by slippage is markedly reduced because of strand degradation by proofreading 3Ј-exonuclease activity. To counteract the degradation, much higher dNTP concentrations are needed. A 5-fold increase (1.0 M) restores the pattern of expansion by slippage seen in Fig. 3 for the first 10 min; another 10-fold increase (10 M) is needed to maintain the pattern for the full 60 min. fold on themselves to form hairpin loops that are initially opposite each other but because of repetition are able to migrate apart by strand slippage and remain separated for longer periods. While apart, if a nick (single-strand cleavage) occurs opposite one of the loops, that loop can stretch and become linear so that a DNA polymerase, perhaps a proofreadingdeficient polymerase involved in DNA repair, may fill in the gap to create an expansion on one strand. After the gap is filled and sealed by ligase, a nick opposite the other loop can lead to expansion on the other strand. According to this model, singlestrand loops that become separated and nicked in the presence of polymerase may behave like the simple hairpin system we have studied.
Our simple system enables one to evaluate the contributions that individual single-strand interactions make to strand slippage in duplex repeat regions. By using the sequence (CTG) 16 (CAG) 4 , we have made an evaluation of CTG/CTG interactions contributing to slippage and expansion of CAG/CTG repeats. Similarly, by using the sequence (CAG) 16 (CTG) 4 , a corresponding evaluation can be made for CAG/CAG interactions. Since CAG/CAG interactions are known to be weaker, forming less stable hairpin folds (14 -16, 20), it is of interest to see how much difference this makes in the slippage rate constants. Previously it has been generally considered (2,3,8,11,12,20) that the greater the stability of single-strand folding, the greater the probability of strand slippage and expansion in repeat regions. However, it is also possible that a difference in folding stability on opposite strands may be important in determining strand slippage and expansion rates. This may be a reason why repeats of triplets such as GAA/TTC, having only purines on one side and pyrimidines on the other, also expand to give diseases such as Friedrich's ataxia (22).