The principle of the PCR nucleic acid amplification technique is described in US Patent US 4, 683, 195 (Cetus Corporation/Roche). The polymerase chain reaction (PCR) enables replication of nucleic acid in vits o througl1 the repeated action of a thermally stable DNA polymerase. Such a polymerase is most commonly one isolated from T/lerms Aqleaticlls and referred to as Taq DNA polymerase or simply"Taq". [1,2]. Apparatus for carrying out the PCR reaction have been described in, for example, European Patent application EP 0 236 069 (Cetus Corporation/Roche/PE). Such apparatus are commonly referred to as'thermocyclers".

Instruments capable of quantitative detection of amplification in real time (qPCR) enable sensitive analysis of gene expression and accurate determination of copy number, enhancing the utility of PCR as a diagnostics tool. [3, 4] Real time PCR techniques monitor the accumulation of amplification product during the reaction over a number of cycles. A single measurement of product quantity is typically made at the end of each extension phase of a PCR thermal cycling program in order to monitor the accumulation of product over a number of cycles. The quantity of product present after a particular number of cycles is typically used to draw a conclusion regarding the starting material sample.

Despite the routine use of PCR in molecular biology, enzymatic and kinetic studies have been limited. Early characterisation studies detailed the efficiency with which Taq DNA polymerase differentiates between matched and mismatched 3'nucleotides. [5-15] Those analyses used end point methods that considered the action of Taq in isolation of PCR dynamics.

The rapid cycling of contemporary qPCR instruments has been shown to strongly disfavour mismatch extension suggesting that abrupt transitions in temperature have effects that have not been previously considered. [16] A number of theoretical descriptions of PCR have been put forward that apply different mathematical approaches to simulate various physical parameters of the system. These include statistical estimations of amplification rate [17], probability of DNA replication [18], probability of DNA binding rates [19], and derivation of expressions for amplification efficiency [20-23].

Each model has yet to be evaluated using real PCR data.

It has now been found that measurements of kinetic parameters can be used as the basis for analysis of PCR reactions. The effects giving rise to the observable kinetic behavior strongly

influence reaction fidelity and efficiency and they are not readily apparent in conventional single quantity measurement analyses.

The invention provides a method of carrying out a nucleic acid amplification reaction, said reaction being carried out under a reaction regime comprising a multiplicity of cycles each cycle comprising at least an extension phase, wherein the nucleic acid extension reaction rate is measured in at least one extension phase.

The method of the invention is particularly suitable for use in a polymerase chain reaction. It also finds application, however, in other nucleic acid amplification techniques, for example isothermal amplification. Preferably, the reaction regime comprises a multiplicity of thermal cycles, each thermal cycle comprising (a) a denaturation phase (b) an annealing phase, and (c) an extension phase.

Suitable temperatures for the denaturation, annealing and extension phases are known to those skilled in the art or are derivable by use of conventional algorithms or standard optimisation techniques. In some implementations of the polymerase chain reaction, the DNA annealing and extension may be carried out at the same temperature and accordingly the annealing phase and the extension phase do not form discrete phases.

The invention provides, for the first time, a kinetic method of analysis of nucleic acid amplification reactions that may be used as an alternative to currently available methods based predominantly on the assessment of product quantity. A theoretical justification of this approach is given below and it is a result of novel kinetic analysis of the PCR reaction.

The reaction rate of an extension phase is generally obtained by making measurements at at least two time points during the extension phase. The rate of the extension reaction during a particular extension phase approximately follows a usual enzyme kinetics curve with a maximal rate initially followed by a tailing off of the rate as the substrate becomes depleted. The measurement of the nucleic acid extension rate is preferably carried out at a time in the extension phase when the reaction rate is maximal. If more than two measurements are taken during a given extension phase, a more accurate measure of the rate is obtained. It is preferable for all measurements to be taken during the initial portion of the extension phase. Initially the nucleic acid extension reaction rate is essentially constant and the quantity of product increases in an approximately linear fashion. Measurements obtained after the end of the linear portion are preferably not recorded.

Preferably, the nucleic acid extension reaction rate is measured in a plurality of extension phases. In practice, it may be simplest to arrange a machine to measure the reaction rate in every cycle. Useful diagnostic information can, however, be obtained from rate measurements from only a small number of cycles, or even from a single cycle.

It is found that, in a typical PCR reaction, the rate of product synthesis initially increases from one cycle to the next as the quantity of template DNA increases. After a certain number of cycles, however, the rate of product synthesis decreases from one cycle to the next, suggesting that some form of substrate inhibition occurs. The cycle number in which the rate of product synthesis is maximal is a diagnostic feature of a reaction.

The method of the invention may be applied to any nucleic acid that may be subjected to a polymerase chain reaction. At the time of writing DNA is the most commonly analysed nucleic acid. If analysis of RNA, for example mRNA, is required then the nucleic acid starting material is RNA and the amplification reaction is preferably preceded by the reverse transcription of the RNA. Reverse transcription may be carried out according to widely know methods. The method of the invention is then carried out on the cDNA so produced.

The method of the invention may be carried out using a known real-time PCR machine (i. e. a thermal cycler with a facility for analyzing a sample during the course of the reaction) adapted so that it is capable of taking more than one reading during the extension phase of each thermal cycle. For example, the measurements of product quantity at various time points may be based on measurements of fluorescence. For example, the LightCycler PCR instrument (Roche Applied Science) may be used.

The method may be carried out using existing real time PCR reagent technology based on, for example, SYBR-Green or 5'-exonuclease assays that have been adapted to obtain data at multiple time points during the extension phase.

The method of the invention finds application in the field of diagnostic PCR measurement. Such measurement may be quantitative or qualitative. The invention provides a method of measuring the quantity of a nucleic acid in a sample comprising a) carrying out a nucleic acid amplification reaction in accordance with the invention with the sample as the starting material, and b) comparing the nucleic acid extension reaction rate measured in a) with at least one nucleic acid extension rate measured for a nucleic acid extension reaction carried out with a known quantity of the nucleic acid as the starting material.

Conveniently, the at least one nucleic acid amplification reaction in accordance with the invention with a known quantity of the nucleic acid as the starting material may be carried out

separately from the nucleic acid amplification reaction in accordance with the invention with the sample as the starting material. The method may make use of a standard curve. Alternatively, the step of carrying out at least one nucleic acid amplification reaction in accordance with the invention and with a known quantity of the nucleic acid as the starting material may also form part of the method.

Preferably, a multiplicity of amplification reactions with a known quantity of the nucleic acid as the starting material are carried out.

In a preferred implementation of the method of measurement in accordance with the invention, the cycle number is determined in which the nucleic acid extension reaction rate of the nucleic acid amplification reaction with the sample as the starting material is closest to the nucleic acid extension reaction rate in a given cycle number of the at least one nucleic acid amplification reaction with a known quantity of the nucleic acid as the starting material. One way in which such a determination may be carried out is by plotting reaction rate against cycle number for the two or more reactions and calculating the number of cycles difference between the two curves for a given observed rate of reaction. For a more accurate analysis, a standard curve may be generated indicating the cycle number at which a particular reaction rate is achieved for a variety of given known quantities of starting material. An exemplary set of such standard curves are shown in Figure 1. By comparing the cycle number in which a PCR reaction carried out under the same conditions reaches a particular rate with the information in the standard curve, the relative or absolute quantity of starting material template in the sample of interest may be assessed. Alternatively, the cycle number in which the rate of the extension reaction is at its greatest may be deduced and that number may be used to generate a standard curve showing cycle number in which the rate is maximal against starting template concentration. Such a curve is shown in Figure 2. Such uses are illustrated in Examples 1 to 4 and they are based on the comparison of reaction rates between samples containing known amounts of target template and samples containing unknown amounts of target template.

An analogous method of measurement may be carried out to assess the relative or absolute efficiency of a PCR reaction. Rather than assessing the quantity of starting material template, the efficiency of a nucleic acid amplification reaction with a particular set of primers with a particular nucleic acid as the starting material may be measured. Accordingly, the invention provides a method of measuring the efficiency of a nucleic acid amplification reaction of interest comprising a) carrying out a nucleic acid amplification reaction in accordance with the invention with a set of primers of interest and a nucleic acid of interest as the starting material, and

b) comparing the nucleic acid extension reaction rate measured in a) with at least one nucleic acid extension rate measured for a nucleic acid extension reaction carried out with particular set of primers and a particular nucleic acid as the starting material.

The method may make use of information in a standard curve obtained using various different primers. Alternatively, the step of carrying out at least one nucleic acid amplification reaction in accordance with the invention and with a known quantity of the nucleic acid as the starting material may also form part of the method.

Preferably a multiplicity of amplification reactions with particular sets of primers and particular nucleic acids as the starting materials are carried out. Preferably, the cycle number is determined in which the nucleic acid extension reaction rate of the nucleic acid amplification reaction with the set of primers of interest and the nucleic acid of interest as the starting material is closest to the nucleic acid extension reaction rate in a given cycle number of the at least one nucleic acid amplification reaction with particular set of primers and a particular nucleic acid as the starting material.

The efficiency of a nucleic acid reaction may be used to infer the presence or absence of a primer to template mismatch. It may also be used to genotype the sample. Such genotyping may be with respect to a single nucleotide polymorphism (SNP).

PCR methods and data collection Amplifications in the methods of the invention are carried out in a convention manner. For example, a suitable regime may comprise a 10-min Taq DNA polymerase activation step at 95°C, 50 PCR cycles of denaturation at 95°C for 1 s, primer annealing at 65°C for 5 s, and primer extension for 5 s at 72°C. Temperature transition rates may be approximately 20°C/s and the reaction may be completed in approximately 40 min. The exact conditions for a particular PCR reaction are ascertainable by the person skilled in the art according to standard procedures.

In each cycle of the PCR in which a kinetic measurement is to be made, at least two data points are generally obtained during the extension phase each representing the quantity product at a given time. The greater the number of data points obtained during the period of linear kinetics, the more accurate the resulting calculated reaction rate will be. Each PCR cycle may, for example, be monitored by continuous fluorescence acquisition. In the LightCycier device, fluorescence gains (used to set sensitivity of detection) may, for example, be set at FI-I throughout. Continuous monitoring data may be recorded using suitable software (For example Microsoft Excel 2000) for further analysis.

After the PCR has been completed, reaction specificity may be confirmed by executing a melt curve analysis in the same closed capillary tube. Suitably, an initial denaturation at a denaturation temperature (suitably approximately 95°C) is followed by a cooling step to around 70°C (approximately 5°C above primer annealing) during which the product anneals, and a slow denaturation phase to 95°C at a rate of0. t°C. sec'', with continuous measurement of double stranded nucleic acid, for example continuous fluorescence acquisition. Product denaturation is observed as a rapid loss of fluorescence near the melting temperature (Tm) and converted to a melt peak by plotting the first negative derivative of fluorescence loss, Fl, with respect to temperature, T (-d (Fl) ldTvs T). A single peak at the predicted T, n confirms the optimal nature of the reaction conditions and the absence of contamination in control samples. The presence of a broad peak at a significantly lower T,, than PCR product indicates the presence of primer dimer amplification [29] Collection of'per cycle'rate data In the case of fluorescence measurements, the reaction rate v may be determined from the maximal (generally initial) increase in fluorescence signal FI with respect to time, t, at 72°C according to the linear equation, Fl=vt+c, (5) where c is the FI reading at time zero within a particular cycle. The slope v of fluorescence signal increase is assumed to be proportional to the rate of nucleotide incorporation by Taq DNA polymerase since this will be concomitant with the interchelation of SYBR Green I molecules into the newly-synthesised double-stranded DNA.

Kinetic data Figure 6A shows a typical plot of fluorescence A Fl during a PCR reaction over a number of cycles of melting, annealing and extension in which a double stranded nucleic acid intercalating fluorescence dye, for example SYBR-Green, is used to indicate product. As the sample is heated, fluorescence is high until denaturation occurs (apparent as a sharp drop in fluorescence). As the sample cools from denaturation to annealing temperature, fluorescence increases rapidly, reflecting product-to-product annealing and interchelation of dye into newly double stranded nucleic acid (Figure 6B).

Fluorescence also increases during extension wlZilst the tempera. ture is held within t : he optimeal limits for Taq DNA polymerase (Figure 6C). It is the increase in fluorescence during the extension phase that is measured in the method of the present invention. That increase is directly atl : ributable to polymel-isation and the accumulation of double stranded DNA. During ea. y and late cycles fluorescence changes over this period are generally negligible. This is in contrast to ini : ermediate cycles where significant increases in fluorescence were observed from the real time data during the extension phase of each cycle Previous methods of real time PCR have only recorded a single fluorescence measurement from each cycle (typically at the end of each extension phase). The method of the invention measures the rate of accumulation of the product during each phase. This allows al'1 analysis of the kinetics of product accumulation during the extension of each phase cycle. A new ma. thema. tical model of enzyme kinetics For the a. nalysis of product accumulation during the extension phase has been developed and that is described below.

Theoretical considerations Michaetis-Menten kinetics have been used to describe the variation of the rates of many enzyme- cata. lysed reactions as the substrate or effector concentration is varied.

In a. steady state, and for enzyme concentrations negligible to those of the substrate, the formation and breakdown of an enzyme-substrate complex is described by the rotation, where (E), (S), (ES) and (P) represent the concentra. tions of free enzyme, free substrate, enzyme- substrate complex and product, respectively. The rate of product formation or initial velocity is then given by the MichaeHs-Menten equation : The Michaelis-enten rate constant, KM, is given by: KM=# (3)

Fluorescence a) so increases during extension whitst the temperature is held within the optimal limits for Taq DNA polymerase (Figure 6C). It is the increase in fluorescence during the extension phase that is measured in the method of the present invention. That increase is directly attributable t. o polymerisation and the accumulation of double stranded DNA. During ea. rly and late cycles fluorescence change over this period are generally negligible. This is in contrast to intermediate cyctes where significant increases in fluorescence were observed from the real time data during the extension phase of each cycle. Previous methods of real time PCR have only recorded a single fluorescence measurement from each cycle (typically at the end of each extension phase). The method of the invention measures the rate of accumulation of the product during each phase. This shows an analysis of the kinetics of product accumulation during the extension oFeach phase cycle_ A new ma. thematical model ofenzyme kinetics For the analysis of product accumulation during the extension phase has been develped and that is described below.

Theoreticat considerations Micha. elis-Menteii I<inetics have been used to describe the variation of the rates of many enzyme- catalysed reactions as the substrate or effector concentration is varied.

In a steady state, and for enzyme concentrations negligible to those of the substrate, the formation and breakdown of an enzyme-substrate comptex is described by the relation, where (E), (S), (ES) and (P) represent the concentra. tions of free enzyme, free substrate, enzyme- substrate complex and product, respectively. The rate of product fromation or initial velocity is then given by the Michaelis-Menten equation : The Michaelis-Menten rate constant, KM, is given by: KM=# (3)

and the maximum velocity by Vmax=k2[Et] (4) where (Et) represents the total enzyme concentration [24]. In this simple description of Vmax, k2 is identical to the catalytic constant, kcat, a fundamental quantity defining the number of substrate conversions the enzyme can catalyse in unit time [25].

The method of the invention for the kinetic characterisation of PCR may be analysed on the basis of a mathematical model based on the Michaelis-Menten framework. Using that model an alternative parameter is provided for monitoring product production in order to quantify starting material. Parameters may also provided that aid the analysis of rapid cycle a. liele-specific PCR (AS-PCR) that may he used to discritninate between alleles of a gene based on single base pair differences. As discussed abovc AS-PCR relies on the ability of Taq DNA polymerase to extend efficiently a primer on ! y when its 3'end is perfectly complementary to the template.

A new model has now been formulated founded on the fact that PCR closely follows the general Icinetic equa. tion for reactions showing high substra. te inhibition [27]. In the model each cycle ! e of PCR is treated as a defined enzymatic reaction. The concentration of substrate (i. e. template DNA or DNA synthesized during earlier cycles of the reaction) increases with each cycle of the reaction. A simple sigmoidal function may be used to represent changing substrate concentration over the course of the reaction.

Mathematical mode ! The rate of reaction during the extension phase of each cycle may be calculated from the slope of a graph of linear F1 against time (for example region 1 of Figure 6C). Figures 7A to 7D show dai : a fiom example 5 for four different PCR reactions. It can be seen that following a. lag in respect of the first few cyc) es attributabie to fluorescence signa. ls being below the detection limits of instrument optics, the rate of product accumulation increases exponentially from one cycle to the next, peaks and then fans away. The number of cycles required before a peak is reached gives an indication of the reaction efficiency or template concentration.

The concentration of substrate (i. e. initial template and reaction product template generated during the reaction) increases as a. PCR reaction progresses. The dependency of reaction rate on substrate concentration illustrated in Figure 7 shows a strong departure from the hyperbolic relationship predicted by the Michaelis Menten equation. This is characteristic of high substrate inhibition in which the formation of abortive complexes inhibits the enzyme at high substrate concentrations. The reaction rates generated from real time data closely follow the general curve predicted for high substrate inhibition,

where Vll, ;"a, is the theoretical maximum velocity, K, the Michaelis-Menten constant, and Ki the inhibition constant. At low substrate concentration S, (S/Ks) is insignificant compared to and equation 6 becomes identical to the classic Michaelis-Menten equation 2. It follows that as S increases, the value of (S/Ki) increases to become the significant term in the denominator and, as observed in our experiments, the value of v decreases [27].

Since the equation is here used with data generated from PCR, a non-classical enzyme system, S must be represented appropriately. In PCR the product formed in cycle n-l S the substrate that is available for cycle n. Under non-limiting conditions this results in an exponential increase in substrate concetration over successive cycles described by the equation, Sn=2nS0, (7) where So is the initial template (substrate) concentration, and Sn is the substrate concentration after n successive cycles. It is well understood however that this model only holds for early cycles [20]. A simplified sigmoidal function was applied to describe the accumulation of substrate during PCR, <BR> <BR> <BR> <BR> <BR> 1<BR> <BR> <BR> <BR> <BR> <BR> <BR> <BR> <BR> <BR> (1+a*exp(-f*n)) (8) where a and are descriptive parameters of the sigmoid function at cycle n [30]. This simple function arises in many dynamical systems, describing simple exponential growth dynamics with a linear limiting control. Such systems are often called logistic growth. A similar sigmoidal function was recently reported as providing a good fit for the whole kinetic process of real time PCR [-j I].

The model was further refined by the inclusion of a compensation factor C. Equation 6 demands that at zero substrate concentration the rate of the reaction is zero. Since a PCR contains an initial substrate (template) concentration at cycle number n = 1, this compensation factor allows the criteria of the equation to be satisfied, such that an artificial cycle 0 is included. The overall equation becomes,

where S is represented by the sigmoidal function of equation 8.

Equation (9) and the theory that supports it may be used, preferably when incorporated into software of a PCR machine in order to provide an alternative parameter that may be used to give an indication of the relative or absolute quantities of starting material in a sample. This application is illustrated in Examples) to 4.

Alternatively the equation (9) and the theory that supports it may be used to develop an allele specific PCR assay of greater accuracy than known assays. This application is illustrated in Example 5.

In the model, substrate inhibition is assumed and a high degree of correlation is observed between PCR data and predictions based on the model. This suggests that PCR is sensitive to substrate during the plateau phase of the amplification.

Allele discrimination The kinetic analyses of the invention have particular application in the design of genotyping tests in particular the kinetic analyses may be applied to novel methods of detection of single or multi nucleotide polymorphisms. The detection of nucleic acid polymorphisms including the detection of single nucleotide polymorphisms is an important task of clinical laboratory services. Both diagnostic and pharmacogenomic applications require a method of detection of nucleic acid polymorphisms (including allelic discrimination) which is relatively rapid, low cost, accurate, and suitable for routine use and/or automation. A convenient method of nucleic acid polymorphism detection is also desirable in biological research. A number of methods of detecting nucleic acid polymorphisms based on the polymerase chain reaction (PCR) currently exist. They are not without their drawbacks.

One method currently in use for the detection of nucleic acid is described by Bottema et al. [34]. In essence that method which can be called"conventional allele specific PCR (AS- PCR)"allows discrimination between two polymorphisms, and is based on the principle that Taq DNA polymerase under appropriate PCR conditions is unable to extend efficiently a mismatch at

the 3'end of an oligonucleotide primer. Specificity is maintained by the lack of 3'to 5' proofreading activity of Taq. Two allele-specific primers are designed which differ by a single nucleotide at the 3'-end. One allele-specific primer is complementary to the wildtyp sequence and is referred to as the WT-ASP primer. The 3'-end of the other primer matches the known mutant sequence, and is referred to as the MUT-ASP primer. Each allele specific (AS) assay requires two separate PCR reactions, each containing a primer that is able to anneal to both alleles, and an allele-specific primer to provide the necessary information about the genotype under investigation. The first reaction comprises a pair of primers consisting of a wildtyp allele- specific primer (WT-ASP) and a non-allele specific primer (WT-OP). The second reaction comprises a pair of primers consisting of a mutant allele-specific primer (MUT-ASP) and a non- altele specific primer (MUT-OP). A homozygous wildtyp genotype will generate products in the first reaction only. A heterozygous genotype will amplify in both reactions, and a homozygous mutant genotype will be refractory to amplification in the first reaction, and produce amplification product in the second reaction only.

It is possible to use a"single-tube"adaptation of the above-described AS-PCR method by utilising a bi-directional amplification format. This adapted method utilises the complementary base-pairing phenomenon (Watson-Crick pairing) occurring within double stranded nucleic acid molecules, which ensures that any nucleic acid polymorphism will confer a base variation of both strands. Two primer pairs are designed, preferably using suitable software, with similar annealing characteristics allowing generic cycling conditions for the amplification. Each set consists of a primer that anneals to either allele and a primer that is allele-specific. The bi- directional amplification format is achieved by designing one allele-specific primer to anneal to a first strand of the target nucleic acid, and another allele-specific primer to anneal to the complimentary target nucleic acid strand. The 3'end of the allele specific primer of each set is designed to align with the position of the mutation. A mismatch at the 3'terminal oligonucleotide primer will be refractory to efficient extension, whereas a successful base pairing at the 3'terminal of the oligonucleotide primer will allow the primer to be extended, generating allele specific products in each successive PCR reaction. The allele of the target DNA can be inferred by the presence or absence of significant amounts of amplicon [25].

Such a comparison may be used to infer the presence or absence of a primer to template mismatch. Such an approach is illustrated in Example 5 and is based on the fact that the Taq polymerase extends an oligonucleotide with much greater efficiency when there is a match between the nucleic acid strand to be extended and the template nucleic acid strand. By choice of a PCR reaction primer that will anneal to the target strand and result in either a match or

mismatch at the 3'end depending on the genotype of target strand, efficiency of 3'primer extension will give an indication of the genotype of the same. Such a method may be especially suited to genotyping a sample with respect to a single nucleotide polymorphism (SNP).

The invention provides a method of detecting a single or multiple nucleotide polymorphism which includes the step of carrying out carrying out a nucleic acid amplification reaction, said reaction being carried out under a reaction regime comprising a multiplicity of cycles each cycle comprising at least an extension phase, wherein the nucleic acid extension reaction rate is measured in at least one extension phase. The invention also provides a method of detecting a single or multiple nucleotide polymorphism which includes the step of measuring the efficiency of a nucleic acid amplification reaction of interest comprising a) carrying out a nucleic acid amplification reaction in accordance with the invention with a set of primers of interest and a nucleic acid of interest as the starting material, and b) comparing the nucleic acid extension reaction rate measured in a) with at least one nucleic acid extension rate measured for a nucleic acid extension reaction carried out with particular set of primers and a particular nucleic acid as the starting material.

The method of the invention may be one wherein the cycle number corresponding to a similar reaction rate is compared between a multiplicity of amplification reactions so as to provide an estimate the relative or absolute efficiency of amplification reaction.

The invention provides a method of detecting the presence of a primer-to-template mismatch which includes the step of carrying out a nucleic acid amplification reaction in accordance with the invention. The invention also provides a method of genotyping a sample which includes the step of carrying out a nucleic acid amplification reaction in accordance with the invention. The method may be used to genotype the sample, for example to genotype the sample with respect to a single nucleotide polymorphism (SNP).

Determination of Kinetic constants in allele-specific PCR The method of the present invention enables differences in PCR extension efficiency between primers of different sequences or between target nucleotides of different sequences to be analysed not only with regard to total quantity of product generated but also with regard to kinetic parameters. The use of forward oligonucleotide primers that differ only at the 3'-terminal base, in various combinations of templates with a variant nucleotide at a defined position, provides a system to evaluate the effects of mismatches on PCR. Non-linear regression (NL-REG Version 5. 4; Phillip H. Sherrad) may be used to estimate informative kinetic parameters for each

combination of template and primer base configurations using equation 9. For each pair of base configurations, Vn1ax and KAI may becalculated.

The invention further provides a method of assessing the suitability of a primer for a polymorphism detection assay comprising carrying out a nucleic acid amplification reaction in accordance with the invention or comprising measuring the efficiency of a nucleic acid amplification reaction in accordance with the invention.

The invention further provides a method of designing a primer for use in a polymorphism detection assay comprising carrying out a nucleic acid amplification reaction in accordance with the invention or comprising measuring the efficiency of a nucleic acid amplification reaction in accordance with the invention. Preferably, the method comprises carrying out two or more nucleic acid amplification reactions with different primers and/or different target sequence DNA wherein (a) the reaction rate of the first nucleic acid amplification reaction is measured for a multiplicity of the extension phases; (b) the reaction rate of at least a second nucleic acid amplification is measured for a multiplicity of the extension phases; (c) the kinetic parameters Vmax and KM for each reaction are calculated from the reaction rate data, and the value of Vmax/KM is evaluated.

The value of Vmax/KM is indicative of the specificity of the reaction in question.

The invention also provides a method of preparing a primer for use in a polymorphism detection assay comprising the carrying out the inventive method of designing the primers and then synthesising primers to the sequence.

The ability of Taq DNA polymerase to bind and extend terminal mismatches is found to be dependent upon the identity of the mispair as illustrated in Example 5 and the results in Table 9.

It is assumed that Vmax represents the maximal rate of incorporation of SYBR into an extending DNA complex under non-limiting conditions. This provides an arbitrary measure of maximal polymerisation or catalytic activity. Although Vmax is not a fundamental property of an enzyme as it is dependent on enzyme concentration [25], reactions may be compared using this parameter if the same total enzyme concentration is used in each PCR test.

The nature of PCR means that a single copy of matched template can be amplified to plateau levels in just a few cycles. This causes failure in many prior art end-point genotyping tests by impairing discrimination. Therefore, Vmax alone is, in many cases, insufficient to ascertain the true effects of a mispair in PCR. A potentially more useful parameter for characterising enzymatic discrimination demonstrated to be the Michaelis constant K,,,, defined as the substrate concentration at which the reaction rate is half its maximal velocity [13]. The K,,, is an intrinsic property of an enzyme reflecting the binding constant for forming the enzyme substrate complex, as well as the catalytic constant. In PCR, this embodies template affinity and the thermodynamic environment of the reaction [20].

By considering the kinetic characterisation of Taq in a true rapid cycle PCR environment the kinetic model of the present invention overcomes the limitations of previous PCR genotyping methods.

The kinetic parameters calculated for given primer-template pairs may be used to define a value for the fundamental'specificity'constant, kCa IKM X where kGal is the catalytic constant or turnover number. This specificity constant determines the ratio of reaction rates for an enzyme acting on two competing substrates, when they are mixed together at equimolar concentrations.

Given that it is the ratio of specificity constants that determines the ratio of rates of the competing reactions a and b, Vmax/KM may be evaluated. If [Et] is identical throughout the tests [25] then the ratio between two specificity constants is: The comparison of these values between matched-and mismatch-primed PCR expresses the enzyme's ability to discriminate in favour of a particular base configuration in the presence of others [25], and consequently the relative extension efficiencies [5]. In agreement with work by Kwok et al. [6] it was found that a match provided the more specific substrate for Taq polymerase than a mismatch.

The model also provides estimate values for the inhibition constant K,, which provides a quantitative measure of inhibitor potency [27]. Values for K, are usually derived from an inhibition study of the effects of a substance on kinetics or binding of a substrate or effectors.

Such studies are usually performed in the presence of the true substrate (for kinetics) or ligand

(for binding) AND the inhibitor. Therefore the K, value in this model represents a substrate inhibition constant since the substrate only is present. This could be interpreted as the ability of the mismatched primer to form a dead-end complex by binding to the active site of the enzyme without efficient extension. In addition, it may represent the ability of the primers to bind dystopically to a particular template, such that replication rate is depressed. In both cases, one might expect Kj"for a mismatched primer to be higher than that of the true primer. This is supported by data in which the three transversion mispairs, G: A, A: A, and T: T, exhibited a significantly higher K, value than all other mispairs. Consistently, K, was lower for a match. By considering the other parameter values associated with each configuration, we propose that these particular mispairs bind to the enzyme with low affinity and extend with low efficiency, forming a stable dead-end complex that inhibits progression of the reaction.

The invention further provides apparatus for carrying out a nucleic acid amplification reaction comprising equipment for subjecting a sample to a reaction regime comprising a multiplicity of cycles, each cycle comprising at least an extension phase and equipment for measuring the nucleic acid extension rate in at least one extension phase. The apparatus is so arranged to calculate the reaction rate of at least one extension phase from data obtained by monitoring the progress of the reaction at multiple time points during the extension phase.

The apparatus of the invention may be made by a simple modification of known PCR apparatus. Essentially the controlling software settings of the apparatus must be changed so that multiple measurements of product accumulation are made during the extension phase of a PCR cycle. The detection means of the apparatus may be any detection means that works with known real time detection methodology, typically the detection means is a fluorescence detection means but it will be appreciated that the apparatus and method of the invention is generally application be to any real time PCR detection means and method that allows multiple measurements of product accumulation to be made during the extension phase of a PCR cycle.

The invention also provides apparatus for measuring the quantity of a nucleic acid in a sample comprising equipment for subjecting a sample to a reaction regime comprising a multiplicity of cycles, each cycle comprising at least an extension phase, equipment for measuring the nucleic acid extension rate in at least one extension phase and equipment for comparing the nucleic acid extension reaction rate measured with at least one nucleic acid extension rate measured for a nucleic acid extension reaction carried out with a known quantity of nucleic acid as the starting material. A similar apparatus may be provided for carrying out a method of measuring the efficiency of a nucleic acid amplification reaction.

The invention further provides a computer program product that, when executed causes a computer to direct a nucleic acid amplification apparatus to carry out a nucleic acid amplification reaction wherein the nucleic acid extension rate is measured in at least one extension phase. The invention further provides a computer program product that, when executed causes a computer to direct a nucleic acid amplification apparatus to carry out a nucleic acid amplification reaction in accordance with a method of the invention.

The computer program product may be supplied incorporated as part of a PCR machine incorporating hard ware for thermal cycling of the reaction vessels. The product may alternatively be supplied separately from a PCR machine. Such a separately supplied computer program product may be used to upgrade an existing PCR machine to apparatus of invention or to allow off-line analysis of data collected on known PCR machines. The invention provides a computer program product that, when executed causes a computer to direct a nucleic acid amplification apparatus to carry out a nucleic acid amplification reaction in accordance with the invention. The invention also provides a computer program product that, when executed, causes a computer to carry out the comparing step of a method of measuring the quantity of a nucleic acid in a sample or the efficiency of a nucleic acid amplification reaction of interest in accordance with the invention.

The computer program product may be supplied as part of a PCR machine installed on a hard drive of that machine or incorporated onto an EPROM or other programmable integrated circuit. Alternatively the computer program product may be supplied on a separate data carrier, for example as a magnetic floppy disk, data cartridge or CD-ROM. Alternatively the computer program product may be supplied as a download from the internet or other communications network.

The computer program product may provide a variety of outputs to the user. It may give an indication of reaction efficiency, an indication of genotyope or an indication of the amount target of nucleic acid in a sample. At the very least the computer program product should indicate to the user a statistic (for example cycle number at which a peak reaction rate took place) that allows the user to compare samples to arrive at useful information about the sample. It is an optional feature of the invention for means to be provided that do final stage calculations and present the user with indication s such as yes/no answers to the presence of a particular allele.

The computer program product may optionally include means for the control of the PCR machine's thermal cycling program.

Brief description of the figures Figure) is a graph showing measurements of the reaction rate of the extension step of a plurality of PCR reactions carried out with different quantities of starting material template DNA Figures 2 to 5 are graphs showing the number of the cycle in which the reaction rate of the extension step of a plurality of PCR reactions carried out with different quantities of starting material template DNA plotted against log (starting concentration of DNA).

Figure 6 shows the variation of fluorescence with time during thermal cycling in a typical PCR reaction.

Figure 7 shows the variation of the reaction rate of the extension step of a PCR reaction for a variety of template : primer base pairings.

Figure 8 shows a comparison between the accumulation of PCR product observed and the accumulation of PCR product predicted by a model for a variety of template : primer base pairings.

Figure 9 shows the difference between the accumulation of PCR product observed and the accumulation of PCR product predicted by a model for the variety of template : primer base pairings shown in Figure 8.

Examples Examples 1-5 Quantification of PCR starting materials 1. Amplification of the p-globin gene A PCR amplification was carried out several times with different quantities of template DNA under the same reaction conditions, that is to say the same cycling conditions, the same reagents and the same primers.

The starting materials for the reaction were standard p-globin primers that give rise to a 11 Obp product with a melting temperature of 87°C. The cycling conditions were as shown in Table 1 : Table 1 Fast-Start Activation Step: 1 cycle Temperature °C Time, Min : sec Trans rate (°C/s) Acquisition Acquisition Cont Non Cont 95 10 : 0020NONE NONE PCR Step : 60 cycles 95 0 20 CONT NON E 55 5 20 CONT NONE 72 10 20 CONT SINGLE Melt Curve Analysis: I cycle 95 0 20 CONT NONE 60 15 20 CONT NONE 95 0 0. I CONT CONT Corousel Cool : 1 cycle 40 30 20 NONE NONE

A Roche LightCycler device (Roche Applied Science) was used. The PCR reaction was carried out five times, once each with 30ng, 3ng, 300pg, 30pg and 3pg of starting material human template DNA. The rate of the double stranded DNA synthesis reaction was calculated during the extension phase for each cycle of the reaction using measurements of fluorescence of the sample. The results of the experiments are shown in Figure I. The curves for the four different concentrations of starting template are of a similar shape, but they have maxima at higher cycle numbers the smaller the amount of starting material was.

From the data in the graph in Figure I, it is possible to generate a standard curve with which information from further PCR reactions, carried out with an unknown amount of starting material template DNA, can be compared. A particularly diagnostic piece of information is k. k is the value of the abscissa at the turning point of the rate vs. cycle number plot (i. e. the cycle number at which the rate is greatest). The data from Figure 1 are shown in Table 2. The value given under" !"" is the cycle number at which the point of inflection occurs in a conventional plot of product quantity at a single time point at the end of an extension phase against cycle number.

Table 2 template DNA concentration/ngLog cone.) kst 30 1. 47712125 30. 14 26. 9 3 47712125 33.59 30. 75 0.3-0. 5228787 36. 91 33. 4 0. 03 -1.5228787 40.1 36.44 0. 003-2. 5228787 45. 31 40. 18

The values of k and"l S'plotted against Logjo (cone.) are shown in Figure 2. Linear behaviour is observed.

A sample containing an unknown quantity of p-globin nucleic acid can be subjected to the amplification reaction and the k value calculated. By reading from the graph, the concentration of p-globin present that is represented by the observed value of k may be obtained.

2. Amplification of the Sickle cell gene target region gene A PCR amplification was carried out several times with different quantities of template DNA under the same reaction conditions, that is to say the same cycling conditions, the same reagents and the same primers.

The starting materials for the reaction were standard PCR reagents and primers SC-WT OP 86 (AGG GCC TCA CCA CCA ACT TC) and SC-MUT OP 112 (AGG GCA GAG CCA TCT ATT GC) that give rise to a 158bp product with a melting temperature of 87. 5°C. The cycling conditions were as shown in Table 3 : Table 3 Fast-StartActivation Step : 1 cycle Temperature °C Time, Min:sec Trans rate (°C/s) Acquistion Cont Acquisition Non Cont 95 10 : 00 20 NONE NONE PCR Step : 60 cycles 95 1 20 CONT NONE 63 5 20 CONT NONE 72 7 20 CONT SINGLE Melt Curve Analysis: 1 cycle 95 0 20 CONT NONE 68 15 20 CONT NONE 95 0 0. 1 CONT CONT Carousel Cool : 1 cycle 40 30 20"'NONE JNONE A Roche LightCycler device (Roche Applied Science) was used. The PCR reaction was carried out five times, once each with 30ng, 3ng, 300pg, 30pg and 3pg of starting material human template DNA. The rate of the double stranded DNA synthesis reaction was calculated during the extension phase for each cycle of the reaction using measurements of fluorescence of the sample. The results of the experiments are used to generate a standard curve with which further PCR reactions, carried out with an unknown amount of starting material template DNA, can be compared. The standard curve is shown in Figure 3 and the data for the curve are shown in Table 4.

Table 4

Template DNA concentration/ng Log (conc.) k 1 st 1. 47712125 30.52 27. 33 3 0,47712125 33.81 30. 76 0. 3-0. 5228787 36.76 33. 69 0.03-1. 5228787 41. 02 38. 06 0. 003-47. 11 41.79 The values of k and I st plotted against Log, o (conc.) are shown in Figure 3. Linear behaviour is observed.

A sample containing an unknown quantity of sickle cell nucleic acid can be subjected to the amplification reaction and the k value calculated. By reading from the graph, the concentration of sickle cell nucleic acid that is represented by the observed value of k may be obtained.

3. Amplification of pGEM-T Easy Vector plasmid A PCR amplification was carried out several times with different quantities of template DNA under the same reaction conditions, that is to say the same cycling conditions, the same reagents and the same primers.

The starting materials for the reaction were standard PCR reagents and ICF (TGG CAG CAC TGC ATA ATT CTC) and ICR (AGC GGT AAG ATC CTT GAG AGT) primers that give rise to a 223bp product with a melting temperature of 85°C. The cycling conditions were as shown in Table 5: Table 5 Fast-Start Activation Step: I cycle Time, Minaec Trans rate (°C/s) Acquisition Cont Acquisition Non Cont 95 10 : 00 20 NONE NONE PCR Step : 50 cycles 95 1 20 CONT NONE 63 5 20 CONT NONE 72 6 20 CONT SINGLE Melt Curve Analysis : 1 cycle 95 0 20 CONT NONE 68 15 20 CONT NONE 95 0 0. 1 CONT CONT Carousel Cool : I cycle 40 30 20 NONE NONE

A Roche LightCycler device (Roche Applied Science) was used. The PCR reaction was carried out four times, once each with 20ng, 2ng, 200pg, 20pg and 2pg of starting material template plasmid DNA. The rate of the double stranded DNA synthesis reaction was calculated during the extension phase for each cycle of the reaction using measurements of fluorescence of the sample.

The results of the experiments are used to generate a standard curve with which further PCR reactions, carried out with an unknown amount of starting material template DNA, can be compared. The standard curve is shown in Figure 4 and the data for the curve are shown in Table 6.

Table 6 Template DNA concentration/ng Log (conc.) k Ist 20 1. 30103 14. 11 11. 38 2 0. 30103 16. 29 13. 69 0.2-0. 69897 21 17.92 0. 02-1. 69897 23. 92 21. 16 0. 002 -2. 69897 27. 72 24. 81

The values of k and 1st plotted against Log10 (conc.) are shown in Figure 4. Linear behaviour is observed.

A sample containing an unknown quantity of pGEM-T Easy Vector plasmid nucleic acid can be subjected to the amplification reaction and the k value calculated. By reading from the

graph, the concentration of pGEM-T Easy Vector plasmid nucleic acid that is represented by the observed value of 1 may be obtained.

4. Amplification of gene surrounding C282Y mutation from HFE gene in human genomic DNA A PCR amplification was carried out several times with different quantities of template DNA under the same reaction conditions, that is to say the same cycling conditions, the same reagents and the same primers.

The starting materials for the reaction were standard PCR reagents with primers C282Y OP76 (GGG CTC CCA GAT CAC AAT GA) and C282Y MUT OP 72 (GGC TGG ATA ACC TTG GCT GTA) that give rise to a 103bp product with a melting temperature of 87. 5°C. The cycling conditions were as shown in Table 7: Table 7 Fast-Start Activation Step : 1 cycle Temperature °C Time, Min : sec Trans rate (°C/s) Acquisition Acquisition Cont Non Cont 95 10 : 00 20 NONE NONE PCR Step: 50 cycles 95 1 20 CONT NONE 62 5 20 CONT NONE 72 7 20 CONT SINGLE Melt CurveAnalysis : 1 cycle 95 0 20 CONT NONE 67 15 20 CONT NONE 95 0 0. 1 CONT CONT Carousel Cool. I cycle 40 30 20 NONE NONE A Roche LightCycler device (Roche Applied Science) was used. The PCR reaction was carried out four times, once each with 30ng, 3ng, 300pg and 30pg of starting material human template DNA. The rate of the double stranded DNA synthesis reaction was calculated during the extension phase for each cycle of the reaction using measurements of fluorescence of the sample.

The results of the experiments are used to generate a standard curve with which further PCR reactions, carried out with an unknown amount of starting material template DNA, can be compared. The standard curve is shown in Figure 5 and the data for the curve are shown in Table 8.

Table 8

Template DNA concentration/ng Log (conc.) k I st 30 1. 47712125 32. 35 29.45 3 0. 47712125 36. 12 32. 73 0. 3-0. 5228787 36. 14 0. 03-1. 5228787 41. 4 38. 77 0. 003-2. 5228787 The values of k and 1"plotted against Logl0 (conc.) are shown in Figure 5. Linear behaviour is observed.

A sample containing an unknown quantity of pGEM-T Easy Vector plasmid nucleic acid can be subjected to the amplification reaction and the k value calculated. By reading from the graph, the concentration of pGEM-T Easy Vector plasmid nucleic acid that is represented by the observed value of k may be obtained.

Example 5-Allele specific PCR This example demonstrates the application of the methods of the invention to the detection of PCR primer to target mistakes as a demonstration of how the invention may easily be used in assays for specific alleles. Plasmids with each possible allelic variant at a particular location in a sequence were generated and then used as template DNA for a PCR using primers with each possible allelic variant at the location complementary to the variable location in the template.

Plasmid DNA Model System All oligonucleotides used in this example were designed using PrimerCalct software (Q-Biogene; Carlsbad, USA) and synthesised by Sigma-Genosys (Cambridgeshire, UK) with a reverse-phase cartridge purification step. A 374 bp insert from the ß-actin gene was amplified from human genomic DNA (Sigma-Aldrich ; Dorset, UK) directed by primers BF (5'-TTC CGT AGG ACT CTC TTC TCT GA-3') and BR2 (5'-GGG GTG TTG AAG GTC TCA AAC AT-3'). The resulting amplicon was purified using Wizard* PCR Purification Kit (Promega ; Madison, W 1).

Mutagenic primers, BFR (5'-CGG GAT CC TTC CGT AGG ACT CTC TTC TCT GA-3') and BR2X (5'-CGG GAT CC XGA GGG GTG TTG AAG GTC TCA AAC AT-3'where X is G, C, A or T respectively in each of the four different reactions) were used to re-amplify the purified PCR product introducing a 5'tail containing a variant nucleotide. Each re-amplified product was

ligated into plasmid DNA using a pGEM-T Easy Vector System I Kit (Promega), following manufacturer's protocol. Competent Escherichia coli cells (Q-Biogene) were transformed with the ligation mixes and resulting clones were screened colorimetrically to confirm transformation.

Plasmid Minipreps (Qiagen ; Sussex, UK) were used to purify the plasmid DNA following manufacturer's protocol. Plasmid preparations were sequenced to confirm presence and position of the variant nucleotide. Preparations were quantified by measuring absorbance at 260 nm using a Cary-100 UV-Visible Spectrophotometer (Varian; Surrey, UK). By this method a polymorphic allele was simulated in that four different plasmid populations were produced with G, C, T or A respectively at the X position. Those plasmids were used as target/templates in subsequent reactions.

Allele-specific PCR Amplifications Reverse primer PMOP98 (5'-GCTGTCCCCAGTGGCTT-3') and forward primers PMASX (5'- GAATTCGATTCGGGATCCX-3'where X is G, C, A or T in PMASG, PMASC, PMASA and PMAST respectively) directed amplification of a 98 bp allele specific amplicon from the plasmid DNA template. The 3'-terminus (position X) of primer PMASX was designed to anneal to the single polymorphic base within the plasmid sequence. Product melting temperatures were predicted as 85. 0 °C using PrimerCalc software, which employs nearest neighbour thermodynamic algorithms for T calculations [28].

Reactions were performed in a total volume of 20 Ill containing 2 p. l LightCyclerT DNA FastStart SYBR Green I mixture (Taq DNA polymerase, reaction buffer, dNTPs, and SYBR Green I dye; Roche Applied Science, Lewes, UK), a final concentration of 3 mM MgCI, and PCR-grade water. Forward and reverse primers were present at 0.5 pM each with 100 pg plasmid template. Each of the four forward primers (PMASX) was used separately with reverse primer PMOP98 to direct amplification from the four different plasmid templates (containing G, C, A or T variant target nucleotide). All sixteen possible combinations of template and primer variants were tested. Reactions were performed in triplicate with a single control sample void of template.

PCR Monitoring and Melt Curve Analysis PCR cycling and melt analysis protocols were performed using the LightCyclerTM PCR instrument and disposables (Roche Applied Science). Amplifications were completed in approximately 40 min, including a 10-min Taq DNA polymerase activation step at 95°C, 50 PCR cycles of denaturation at 95°C for I s, primer annealing at 65°C for 5 s, and primer extension for 5 s at 72°C. All temperature transition rates were set to 20°C/s and each PCR cycle was monitored

by continual fluorescence acquisition. Fluorescence gains (used to set sensitivity of detection) for the LightCycler were Ft-1 throughout. These continuous monitoring data were exported into Microsoft Excel 2000 for further analysis.

Reaction specificity was confirmed by executing a melt curve analysis immediately after amplification in the same closed capillary tube. An initial denaturation at 95°C was followed by a cooling step to 70°C (5°C above primer annealing) and a slow denaturation phase to 95°C at a rate of0. 1°C. sec , with continual fluorescence acquisition. Product denaturation was observed as a rapid loss of fluorescence near the calculated T, n, and converted to a melt peak by plotting the first negative derivative of fluorescence loss, Fl, with respect to temperature, T (-d (FI)/d T vs Z).

A single peak at the predicted Tm confirmed the optimal nature of the reaction conditions and the absence of contamination in control samples. A broad peak at a significantly lower T", than PCR product identifies primer dimer background amplification [29].

Collection of rate data Reaction rates were determined from the maximal increase in fluorescence signal at each time point measured FI with respect to time, t, at multiple time points at 72°C (i. e. during the extension phase) according to the linear equation, Fl=vt+ (,, where c is the Fl reading at time zero. The slope v of fluorescence signal increase is assumed to be proportional to the rate of nucleotide incorporation by Taq DNA polymerase since this will be concomitant with the interchelation of SYBR Green I molecules into the newly-synthesised double-stranded DNA.

Determination of kinetic constants in allele-specific PCR The use of forward oligonucleotide primers that differ only at the 3'-terminal base, in various combinations of templates with a variant nucleotide at a defined position, provided a system to evaluate the effects of mismatches on PCR. Non-linear regression (NL-REG Version 5.4 ; Phillip H. Sherrad) was used to estimate informative kinetic parameters for each base configuration using equation 9. The resulting data are shown in Table 9. The ability of Taq DNA polymerase to bind and extend terminal mismatches was dependent upon the identity of the mispair. In the table, the ratios of specificity constants are shown compared to a matched combination. Matched combinations are highlighted in bold type. Constants are displayed in arbitrary units.

Table 9 Predicted kinetic parameters (shown to 3 s. f.) for each base configuration

Template Primer 3' Vmax KM K1 Vmax/KM 1Ratio of Ase terminus C 530 1300 0.002 0.408 1.000 G G 448 43100 0. 083 0. 010 0.025 A 88. 1 479000 29.2 0.000 0.004 T 302 23600 0. 111 0. 013 0. 031 C 290 14700 0.046 0.020 0.106 C G 335 1800 0.006 0.186 1. 000 A 378 26100 0. 093 0. 015 0.078 T 271 25400 0. 128 0. 011 0. 058 C 906 49900 0. 037 0.018 0.089 A G 402 32500 0.082 0. 012 0. 061 A 45 1720000 369 0.000 0.000 T 377 1840 0. 007 0.204 1. 000 C 475 17700 0. 031 0.027 0. 120 T G 669 16700 0. 015 0.040 0. 180 A 245 1090 0.013 0. 224 1. 000 T t60 116000 2.63 0. 001 0. 006 It was assumed that Vmax represents the maximal rate of incorporation of SYBR into an extending DNA complex under non-limiting conditions. This provides an arbitrary measure of maximal polymerisation or catalytic activity. Although V is not a fundamental property of

an enzyme as it is dependent on enzyme concentration [25], it is possible to compare reactions using this parameter since the same total enzyme concentration was used in each PCR test.

For amplifications from template with a variant nucleotide G, vmax was highest in the presence of a matched primer 3'terminus. For all other templates at least one of the mismatched primers na value than the match. In PCR tests involving the transversion mispairs (template : primer) G: A, A: A and T: T, Vmax was lower than that found for a match. The transition mispairs C: A, A: C, T: G and transversion mispairs A: G and T: C exhibited equal or higher Vmax than a matched combination.

The latter observation is not surprising when one considers the consequence of mismatched primer extension in PCR. Certain nucleotide configurations vary in their affinity to bind to the enzyme and extend. However, once extension from a mismatched primer occurs, the resultant product and the complement synthesised in subsequent cycles are fully matched with both primers [6]. The nature of PCR means that a single copy of matched template can be amplified to plateau levels in just a few cycles. This causes failure in many prior art end-point genotyping tests by impairing discrimination. Therefore, vmax alone is insufficient to ascertain the true effects of a mispair in PCR.

The more useful parameter for characterising enzymatic discrimination demonstrated to be the Michaelis constant , defined as the substrate concentration at which the reaction rate is half its maximal velocity [13]. The K, w is an intrinsic property of an enzyme reflecting the binding constant for forming the enzyme substrate complex, as well as the catalytic constant. In PCR, this embodies template affinity and the thermodynamic environment of the reaction [20].

The transversion mispairs G: A, A: A, and T: T exhibited a Value between 100-to 1000-fold higher than a corresponding match. In all other cases, K, \,, for a mismatch was 8-to 33-fold higher than the equivalent match. These data suggest that a matched conformation binds with higher affinity than a mismatch to the active site of the enzyme.

This is discordant with the view of Huang et al. [5] who found that Taq polymerase binds with equal affinities to all base configurations. This is likely due to the reaction conditions employed where a single species of dNTP was used as the variable substrate for each template.

Single-turnover kinetics is unable to reflect a PCR test in which all dNTPs are present at equimolar concentration and in large excess. In the absence of competition, similar binding

affinities might be expected. Some groups were similarly conflicting [10, 14], whilst others were in agreement [7, 9, 13, 15]. The diversity of reaction conditions employed, enzyme source and DNA sequences may have caused this disparity. By considering the kinetic characterisation of Taq in a true rapid cycle PCR environment the kinetic model of the present invention overcomes the limitations of previous PCR genotyping methods.

The kinetic parameters displayed in Table 9 were used to define a value for the fundamental 'specificity' constant, kcat/KM, where kcat is the catalytic constant or turnover number. The specificity constant is also shown in Table 9. The specificity constant determines the ratio of reaction rates for an enzyme acting on two competing substrates, when they are mixed together at equimolar concentrations. Given that it is the ratio of specificity constants that determines the ratio of rates of the competing reactions a and b, we evaluated Vmax IKp, since [Et] was identical throughout our tests [25] : The comparison of these values between matched-and mismatch-primed PCR expresses the enzyme's ability to discriminate in favour of a particular base configuration in the presence of others [25], and consequently the relative extension efficiencies [5]. In agreement with work by Kwok et al. [6] it was found that a match provided the more specific substrate for Taq polymerase than a mismatch. The relative specificity of mismatches varied according to each arrangement, but in general, purine : purine mispairs were harder to extend than other combinations. The results obtained using the method of the invention demonstrate that for Taq DNA polymerase during rapid cycle PCR, the matched base configuration would be the preferred substrate in the presence of all other mismatches.

Finally, values for the inhibition constant K, have been calculated for each pair of primers and the results are shown in Table 1. K, provides a quantitative measure of inhibitor potency [27]. Values for K, are usually derived from an inhibition study of the effects of a substance on kinetics or binding of a substrate or effectors. Such studies are usually performed in the presence of the true substrate (for kinetics) or ligand (for binding) AND the inhibitor.

Therefore the K, value in this model represents a substrate inhibition constant since the substrate only is present. The constant can be interpreted as the ability of the mismatched primer to form a dead-end complex by binding to the active site of the enzyme without efficient extension. In

addition, it may represent the ability of the primers to bind dystopically to a particular template, such that replication rate is depressed. In both cases, one might expect KA1 for a mismatched primer to be higher than that of the true primer. This is supported by data in which the three transversion mispairs, G: A, A: A, and T: T, exhibited a significantly highel Kl value than all other mispairs. Consistently, K, was lower for a match. By considering the other parameter values associated with each configuration, we propose that these particular mispairs bind to the enzyme with low affinity and extend with low efficiency, forming a stable dead-end complex that inhibits progression of the reaction.

High substrate inhibition Factors that have been attributed to attenuation of PCR include depletion of substrate (dNTPs or primers), thermal inactivation or limiting concentration of DNA polymerase, inhibition of enzyme activity by increasing pyrophosphate production, reannealing of amplicon at concentrations above l o 8 M, reduction in the denaturation efficiency per cycle, destruction of product due to enzyme 5'-3'exonuclease activity [32], product to product reannealing [4] or the chelation of critical metal ions by the substrate depriving the enzyme of a cofactor [27]. For each theory, the characteristics of high substrate inhibition would be apparent.

Other investigations have shown that by including increasing amounts of"random"DNA into the PCR test from the beginning amplification could be inhibited [32,33]. It was suggested that the accumulation of product during later cycles is more likely to inhibit the enzyme before the more trivial factors such as exhausting primers, metal ions or dNTPs, which are added in huge molar excess. In conjunction with the excellent fit of our model to real data (Figure 7A-D), evidence is provided that high substrate inhibition does indeed play a predominant role in curtailing amplification during the final cycles of a PCR.

However, one might have expected the Kl for a match to be greater than or equal to a mismatch if it were proposed that high substrate inhibition were the sole cause of the PCR plateau phase. Our data show that, in the case of a mismatch, other factors come into play, which further add to the magnitude of the K, value. This is supported by Figure 8A-D/Figure 9 in which the model's prediction of substrate accumulation was more accurate for a match-than mismatch- primed PCR test. So although high substrate inhibition is the likely cause of the plateau phase in conventional PCR, we demonstrate that the actual presence of a mismatch has an effect on the

intrinsic ability of the enzyme to function effectively, displaying a direct inhibitory effect on the PCR.

In summary, we demonstrate for the first time kinetic parameters that may be estimated in a real-time rapid PCR system in order to provide a method that is directly applicable to the design of SNP genotyping assays. An appreciation of kinetic parameters may be used in order to predict the likely success of a SNP or other genotyping assay thereby increasing the chances of success of the assay and reducing the amount of empirical optimisation that may be required.

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