What Molecules Increase In Number During Pcr

• Journal List
• HHS Author Manuscripts
• PMC1544370

Comput Biol Chem. Author manuscript; bachelor in PMC 2007 Apr 1.

Published in terminal edited form every bit:

PMCID: PMC1544370

NIHMSID: NIHMS10078

A QUANTITATIVE MODEL OF ERROR ACCUMULATION DURING PCR Distension

E Pienaar

^aDepartment of Chemical Engineering, University of Nebraska, Lincoln, NE 68588

M Theron

^bDepartment of Human Genetics, University of the Costless State, Bloemfontein 9330, South Africa

M Nelson

^cMegabase Research Products, Lincoln, NE 68504

HJ Viljoen

^aDepartment of Chemical Engineering science, University of Nebraska, Lincoln, NE 68588

Abstract

The amplification of target Dna by the polymerase chain reaction (PCR) produces copies which may contain errors. Two sources of errors are associated with the PCR process: (1) editing errors that occur during Dna polymerase-catalyzed enzymatic copying and (2) errors due to Dna thermal damage. In this written report a quantitative model of fault frequencies is proposed and the role of reaction conditions is investigated. The errors which are ascribed to the polymerase depend on the efficiency of its editing office as well equally the reaction atmospheric condition; specifically the temperature and the dNTP pool limerick. Thermally induced errors stem generally from 3 sources: A+G depurination, oxidative damage of guanine to eight-oxoG and cytosine deamination to uracil. The post-PCR modifications of sequences are primarily due to exposure of nucleic acids to elevated temperatures, specially if the Dna is in a single-stranded form. The proposed quantitative model predicts the accumulation of errors over the course of a PCR cycle. Thermal damage contributes significantly to the total errors; therefore consideration must be given to thermal direction of the PCR process.

Keywords: Polymerase chain reaction, thermal harm, depurination, cytosine deamination

1. Introduction

The use of PCR to amplify a Dna target and cloning of unmarried re-create genes has become an important process in molecular biology. In about applications the objective is to identify the presence or absenteeism of a specific DNA fragment and the mistake frequency is not of utmost importance. However, errors play a office in polymerase stability and in some instances the presence of an error could terminate the extension process. As the involvement in constructed Dna grows, techniques like PCA (polymerase chain assembly, Stemmer et al. 1995) are used to synthesize DNA molecules. Ane attribute of DNA synthesis that is critical is the command of errors. Therefore a quantitative model of the error frequencies of DNA products from PCR may be helpful to adjust reaction conditions, reaction compositions, and the choice of polymerase.

One source of mistake stems from editing mistakes of the enzyme when the annealed oligomers are enzymatically extended. Extension errors tin can be reduced with a high fidelity polymerase enzyme and optimization of the biochemical reaction conditions during DNA extension. Pfu polymerase (Pyrococcus furiosus) has outstanding fidelity, but its extension rate is very slow (∼20 nt/sec at 72°C). Thermus aquaticus polymerase (Taq Pol) has an elongation rate of approximately lxxx nt/sec at 72°C (Innis et al., 1988; Gelfand and White, 1990; Whitney et al., 2004), but has no 3′ editing action. Faster thermostable β-type Deoxyribonucleic acid polymerases such every bit Pyrococcus kodakaraensis (KOD Pol; Toyobo Co. Ltd., Osaka; Mizuguchi et al., 1999) or KlenTaq22(Cline et al., 1996) are preferred for loftier-speed distension of Deoxyribonucleic acid. In practice, the error rate of KOD Political leader is extremely low during conditions of loftier-speed PCR. Mizuguchi et al., (1999) reported an error rate of ∼1.1 errors/10⁶ bp for KOD Pol.

A major contributor to the errors in synthetic Dna molecules is thermally induced harm. Errors due to thermal harm stalk by and large from three sources: A+G depurination (Lindahl and Nyberg, 1972), oxidative damage of guanine to 8-oxoG (Cadet et al., 2002, Hsu et al., 2004) and cytosine deamination to uracil (Lindahl and Nyberg, 1974). Depurination involves the removal of a purine (adenine or guanine) from the DNA molecule, leaving only the carbohydrate and phosphate backbone (attached to the DNA molecule). Cytosine deamination is illustrated in Fig. one. These modifications of sequences are primarily due to exposure of nucleic acids to elevated temperatures, specially if the Deoxyribonucleic acid is in a single-stranded class. Thermal damage results in either incorrect nucleotides being inserted into the complementary strand or the polymerase stalling at the abasic site. Thus consideration must be given to reduce impairment to DNA in the rational design of the procedure. For instance, oxidative damage tin exist reduced in PCR experiments by purging mixtures with argon to remove dissolved oxygen.

Schematic representation of Cytosine deamination to Uracil. Hither the alphabetic character X represents the ribose phosphate office of the nucleotide.

The effects of thermal damage are also reflected in the product yield. Degradation of the template DNA (especially during pre-amplification denaturation) has been correlated with a significant subtract in production yield (Gustafson et al., 1993, Sikorsky et al. 2004). Yap et al., (1991) suggested lowering the denaturing temperatures after the beginning few cycles in order to amend product yield.

Few precautions are taken to minimize DNA thermal damage during PCR experiments and gene associates experiments. For example, Smith et al., (2003) utilized a xvi hr Taq ligase reaction at 65°C. Based on the published charge per unit constants for A+Yard depurination and C deamination, 1 expects very high levels of errors when such overnight heating of Dna is carried out. In particular, the rate constants published by Fryxell and Zuckerandl (2000) and Lindahl and Nyberg (1972, 1974) predict that A+G depurination and C deamination volition reach levels of 0.2 to 0.iii% afterward i 60 minutes at 72°C; i.due east., one in every 300 to 500 bases will be thermally damaged.

Furthermore, the thermocyclers used in these experiments are slow and accept been used in combination with conservatively long thermocycling protocols. For example, in the widely used PCR protocol of Saiki et al.,(1985), one minute temperature holds at each of three temperatures 94°C, 55°C, and 72°C are employed. Therefore DNA unnecessarily spends 2 minutes per bicycle at temperatures greater than 70°C, during which fourth dimension A+G depurination and C deamination occur.

It is concluded from the discussion that loftier-fidelity synthesis of DNA molecules requires an awareness of biosynthetic errors and a practical strategy to minimize these errors. Mistake control requires a cardinal understanding of (1) the human relationship between the kinetics of the polymerase chain reaction and errors which occur during DNA replication and (2) thermal management of the process to minimize loftier temperature exposure. In summary, the combination of a fast thermocycler, in which Dna spends very little time at elevated temperature and kinetically optimized DNA biochemistry, is the optimum strategy.

ii. Mathematical model of error formation

The ii sources of errors which occur during PCR amplification of DNA are (one) mistakes made by the polymerase and (2) thermal harm of the DNA in double-and single-stranded form. If mistakes occur early in the PCR process, the erroneous templates could lead to a big number of DNA copies with mistakes in their sequence. On the other manus, if mistakes occur later in the PCR process and/or incorrect templates course a modest fraction of the total template population, then the full error concentration will be low. Furthermore, if a Deoxyribonucleic acid polymerase is used that does not process certain errors (such as uracil insertion or C deamination), then these erroneous templates are not amplified. We demand to distinguish between (i) how errors originate and (2) how errors proliferate. In this study the focus is on the origin of errors, therefore the mathematical model only describes the errors which occur when an authentic template is copied during one PCR bike.

Modeling Strategy

The modeling strategy is summarized as follows.

1. A template is selected and the PCR conditions are specified.

2. The PCR cycle is divided into Due north segments of xms each; south₁,s₂,..s_N. The segment numbering starts at the beginning of the annealing footstep. A temperature is assigned to each segment; T(south_i),T(s_ii),..T(s_N.).

3. The number of nucleotides which are added to the template over the interval s_j is calculated from the polymerase kinetic model, described in section 2.one.

4. For temperature T(s_j), the degree of melting is calculated for the double stranded part of the template by the Monte Carlo method described in department two.3.

5. The number of ds[A+1000], ss[A+Thousand], ds[C] and ss[C] are calculated.

6. The rates of double(single) stranded depurination and C deamination are calculated at T(s_j). The rate expressions are described in department ii.2. Later the respective rates are multiplied by the time interval southward_j , the contributions are added to the respective cumulative errors.

7. The time is advanced to due south_j+1 and steps (three) to (6) are repeated.

8. At the end of segment s_N the errors produced by the polymerase catalyzed extension (cf. department 2.one) are added to the cumulative thermal errors.

Remark: We distinguish between the rates for the template and the complementary strand. A iv letter note is used to identify rates: the kickoff two letters indicate single or double stranded kinetics ( ss or ds ), the third letter identifies the blazon of reaction- d is depurination, c is C deamination. The concluding letter identifies the strand, t is the template and c is the complementary strand.

2.i Kinetics and Mistake product by polymerase

A better understanding of the fidelity of the polymerase chain reaction is obtained from a perspective of the polymerase kinetics. For that reason, a brief discussion on the kinetics of the polymerase chain reaction is given. The kinetic mechanisms and structure/function relationships of T7 DNA polymerase, KlenTaq Dna polymerase, and a Bacillus Dna polymerase which have been worked out in some detail (Johnson, 1993; Kiefer et al., 1998; Li and Waksman, 2001; Patel et al., 1991), suggested that all Deoxyribonucleic acid polymerases have the same broadly conserved molecular properties and mechanisms, but that each polymerase also has unique features (Jager and Pata, 1999). Viljoen et al., (2005) and Griep et al., (2005) developed a macroscopic model of PCR kinetics which is based on the probabilistic kinetic approach described past Ninio (1987). The principle idea of Ninio′s approach is to track a single enzyme/template complex over time and to make up one's mind its boilerplate behavior. The main results of the analysis macrokinetics model are expressions for the average extension rate v_ave (or its inverse t_ave -the average insertion time per nucleotide) and the error frequency.

The extension charge per unit depends explicitly on template composition N_i (i = A,C,T,G), the dNTP puddle limerick, expressed as molar fractions, east.g. x_A =[dATP]/[dNTP]) and it depends implicitly on the temperature via the model parameters.

Average extension rate:

The average time to insert a nucleotide is:

t ave = 1 ν ave = 1 N ∑ i = A , C , T , Yard Due north i [ x i τ ∕ P Due south + ( 1 − 10 i ) τ I ∕ P Due south ] x i + ( 1 − 10 i ) P S I ∕ P S ( seconds ∕ nucleotide )

(one)

The reaction pathway, as discussed past Patel et al., 1991, involves several steps. Forward and opposite rate constants are associated with each pace. The parameters τ, P_Southward ,τ _I and P_SI in eq. (one) are functions of these charge per unit constants (meet Viljoen et al. 2005 for details). The parameters τ, P_Southward ,τ _I and P_SI can be viewed equally functions of the kinetic rate constants of the reaction pathway, but a more tangible interpretation of the parameters is as follows. The probability to insert a right nucleotide is P_S and the probability to insert an wrong nucleotide is P_SI ≪ i (because polymerases are efficient). The parametersτ and τ _I are the boilerplate passage times for a correct (τ) or an wrong nucleotide (τ _I ). The right hand side of eq. (1) contains just 3 parameters; Γ = τ P S, Γ I = τ I P South I and Φ =P _{S I}  ∕P _{Due south} . The parameters (Γ, Γ _I , Φ) are functions of the type of polymerase and temperature. (Since the parameters are derived from kinetic constants, we posit Arrhenius forms of temperature dependence.) Other factors such as the (G+C) contents of the template and its size will also play a role.

The brief discussion on the kinetics helps to show the connection between the kinetics and errors. Eq.(1) is as well used to calculate the progression of the Deoxyribonucleic acid extension during a PCR cycle. This data is needed to determine the fraction of total template length that is single stranded.

Mistake frequency of polymerase extension

The kinetic model (i) provides an guess of the number of errors which are made afterward extension of a DNA template of length Due north:

Eastward = { ∑ i = A , C , T , Thousand Due north i ( 1 − x i ) P S I ten i P S + ( ane − x i ) P S I } ∕ Northward ≈ { ∑ i = A , C , T , G Due north i ( 1 − x i ) Φ x i } .

(2)

The parameter Φ =P _{South I}  ∕P _{Due south} in eq. (2) is characteristic for a specific type of DNA polymerase and can exist estimated from published information. For example, Mizuguchi, et al., (1999) reported the mistake frequency of Pyrococcus kodakaraensis (KOD Pol) under equimolar dNTP puddle weather as φ = 1.1×10^-half-dozen159 (i.due east. 1.ane errors per million base of operations pairs). Till date the authors are non aware of published information on the temperature dependence of Φ, but such a relation certainly exists. Therefore the fault frequency model in eq. (two) will be used in the overall error model without accounting for changes in temperature during a PCR cycle.

Information technology follows from eq. (2) that the dNTP pool composition influences the mistake frequency. If the template consists of approximately equal amounts of A, C, T and G, the optimum dNTP pool composition is 10_A = 10_C = ten_G = x_T = 0.25. If the dNTP puddle is skew, the polymerase has to process an increased number of incorrect nucleotides and the extension rate slows down. If the template has a high G+C content, the optimum dNTP puddle limerick shifts towards higher tooth fractions of C and G. Thus an optimum dNTP puddle composition is associated with a template. The contrapuntal results are that an imbalanced dNTP pool increases t_ave and increases the fault frequency. The post-obit important conclusion came from the report past Griep et al., (2005a): The error frequency is a minimum at the optimum dNTP pool composition.

Kinetic parameter values

The parameters (Γ, Γ _I , Φ) which are used in this study pertain to the β type polymerase Pyrococcus kodakaraensis (KOD). Mizuguchi, et al., (1999) reported the error frequency of Pyrococcus kodakaraensis (KOD Pol) under equimolar dNTP pool conditions every bit Φ=1.1×10^-half-dozen. The parameters Γ and Γ _I are assumed to accept Arrhenius forms of temperature dependence (since they are functions of rate constants). For a selected amplicon, the minimum elongation times have been measured at different elongation temperatures and dNTP puddle compositions. The amplicon that has been used in the report is a 52% GC-rich, 2517-base pair fragment of pUC19 (Griep et al. (2005b)). The minimum elongation times have been measured at dissimilar elongation temperatures and unlike dNTP pool compositions using a PCRJet® thermocycler (Megabase Inquiry Products, Lincoln, NE). The results are every bit follow:

Γ = three.5 × ten⁻¹² e ^{xviii.v∕R T} (1000 s)

(3)

Γ _I = iv × 10¹³ e ^{−22∕R T} (thousand s).

(4)

(R = 0.00198kcal/molK)

Notation that Γ and Γ _I have opposing temperature dependence. The parameter Γ describes the characteristic time to insert a right nucleotide and it becomes shorter if the temperature is increased. In contrast, the parameter Γ _I increases with temperature due to lower processivity. The parameters Γ and Γ _I are calculated at a given temperature T(s_j) and used in eq.(1) to determine the number of nucleotides which are added during interval s_j .

2.ii Thermal impairment

The mathematical model of thermal damage focuses on two reactions; (i) cytosine deamination and (2) depurination. Cytosine deamination is slowest at pH=8-8.5, the rate increases sharply at higher pH and more gradually at lower pH and it exhibits a small positive salt effect. The deamination rates are dissimilar for ssDNA and dsDNA. Fryxell and Zuckerkandl (2000) used information from iii different sources to obtain the post-obit rate expression for dsDNA:

C deamination of double stranded Deoxyribonucleic acid

k _{C d southward} = 2.66 × 10¹⁰ eastward ^{−32∕R T} s ⁻¹,  (R = 0.00198 kcal ∕ mole K),

(5)

Lindahl and Nyberg (1974) measured deamination rates of cytosine in denatured Due east. coli DNA. At 95°C and 80°C the rates are 2.two ×10^-vii south^-1 and 1.iii ×10^-viii s^-one respectively. If an Arrhenius plot is fitted between the two points, the rate constant is;

C deamination of single stranded Dna

grand _{C s due south} = ane.8 × ten²² e ^{−48.6∕R T} s ⁻ⁱ.

(6)

Cytosine deamination of ssDNA does non just have a much larger activation energy than the deamination rate of dsDNA, only the reaction is much faster over the temperature ranges 60-95°C.

Depurination reactions are strongly catalyzed at depression pH. Based on the experimental data of Lindahl and Nyberg (1972), the charge per unit constant for depurination of dsDNA at pH=7.four is;

A+G depurination of double stranded Dna

k _{D P d due south} = 2.3 × ten¹¹ east ^{−31∕R T} southward ⁻¹.

(seven)

The depurination charge per unit abiding of ssDNA is nominally 3.3 times higher than for dsDNA (cf. Fig. 8 in Lindahl and Nyberg, 1972);

Cumulative depurination damage over one cycle of protocol P2. The double stranded depurination values for the template and the complementary strand are very close and the plots overlap.

A+1000 depurination of single stranded Dna

r _{D P s southward} = 7.6 × 10^eleven eastward ^{−31∕R T} s ⁻¹.

(8)

The total aggregating of errors during PCA consists of the sum of thermal damage and PCR-based errors (cf. eq. (ii)). To apply eqns. (5-eight) to a target template, it is necessary to know the degree of melting. At the starting time of a PCR cycle, defined as the completion of primer/template annealing, the bulk of the template is in single stranded form. As extension progresses, the fraction of the template that is double stranded increases. Even so, it is not correct to assume that the polymerase/template complex marks the transition betwixt dsDNA and ssDNA. Double stranded Dna may form bubbles and localized melting may occur even at moderate temperatures. As the temperature increases to the denaturing temperature, the fraction of ssDNA template increases. Thus a model that describes the helix/curlicue transitions is needed to assess the thermal damage.

2.3 A Model of dsDNA/ssDNA transition

The model that is proposed in this study is based on the assumption that the energy of the DNA molecule depends on nearest neighbors (NN) and the salt concentration of the solution. The nearest neighbor concept was pioneered by Crothers and Zimm (1964), Gray and Tinoco (1970) and Uhlenbeck et al. (1973). Several experimental studies measured nearest neighbor interactions, specifically free energies and entropies. Santalucia (1998) provided a unified view of seven different studies and showed that half-dozen of the studies are in good agreement. The results are listed in Table i. There has also been some controversy nearly the office of the length of the Dna molecule on nearest neighbor thermodynamics. Santalucia (1998) addressed the controversy and showed that in that location is a length dependence on the salt concentration, just no dependence exists for nearest neighbor energies. The values in Tabular array ane are complimentary energy, measured in kcal/mole at 37°C. When a pair is presented every bit AT/TA it means the 5′ -iii′ AT is paired with the 3′-5′ TA.

Table i

Free Energy Values of NN (kcal/mole)

AA/TT	AT/TA	TA/AT	CA/GT	GT/CA	CT/GA	GA/CT	CG/GC	GC/CG	GG/CC	Init. with GC	Init. with AT
-1.00	-0.88	-0.58	-1.45	-1.44	-1.28	-ane.thirty	-ii.17	-two.24	-one.84	0.98	1.03

The concluding 2 columns list the values if the dsDNA molecule begins/ends with a GC or AT pair. For example, the oligomer AATGCC (5′ -3′) has free energy

ΔThousand ₃₇ = (-i.00) +(-0.88) +(-i.45) +(-2.24) +(-1.84) +(1.03) + (0.98) = -5.twoscore kcal/mole.

The values in Table 1 are denoted equally ΔG ^IK ₃₇ (I,One thousand=A,C,T,G). Usually the enthalpy is constant, but the costless energy changes with temperature as follows:

Δ G T I Yard = Δ H I G − T Δ Due south I K = Δ M 37 I K − ( T − 310.fifteen ) Δ Due south I Chiliad

(9)

In Tabular array ii the entropy is listed for all x dissimilar nearest neighbour combinations.

Table 2

Entropy Values of NN (cal/mole Thou)

AA/TT	AT/TA	TA/AT	CA/GT	GT/CA	CT/GA	GA/CT	CG/GC	GC/CG	GG/CC	Init. with GC	Init. with AT
-22.2	-20.4	-21.3	-22.7	-22.4	-21.0	-22.2	-27.two	-24.4	-19.9	-2.8	4.ane

Santalucia (1998) proposed a salt correction for ΔSouth ^IK and ΔG ^IK ₃₇, just these corrections are length dependent and results for oligomers shorter than 26 bp have been reported. The gratuitous energy of nucleation is corrected in similar manner, using the terminal 2 columns in Tables ​ 1 and ​ 2 in the right hand side of eq. (10):

Δ G T Init : A T , G C = Δ One thousand 37 Init : A T , M C − ( T − 310.xv ) Δ Due south Init : A T , G C

(10)

The free free energy due to nucleation depends on the type of base pair at position 1 and position Northward (first and last positions). After the temperature correction has been made equally shown in eq. (10), nosotros denote this contribution to the complimentary energy equally ΔK ^Nucl _T .

2 sources contribute directly to the complimentary energy of a base pair; the hydrogen bail of the base pair and the stacking interaction. If the two contributions are combined, the doublet format is used. The singlet format refers to the separation of the 2 contributions. The data presented in Table 1 is in doublet format. Frank-Kamenetskii (1971) investigated the strength of the hydrogen bonds as a function of the table salt concentration (tooth) and expressed his findings in terms of temperature every bit follows:

T A T = 355.55 + 7.95 ln [ Na + ] T One thousand C = 391.55 + 4.89 ln [ Na + ]

(11a,b)

The complimentary energy associated with the hydrogen bond is

Δ G T H : A T = ( T A T − T ) Δ S H A T Δ G T H : G C = ( T G C − T ) Δ S H G C

(12a,b)

The entropy values are Δ Southward H A T = Δ S H G C = − 0.0224 ( cal ∕ mol . K ) (cf. Santalucia, 1998).

Monte Carlo Method

A Monte Carlo method is used to decide the degree of melting. First the gratis energy associated with each base pair is determined. Next the free free energy associated with the alternative country (helical to ringlet or vice versa) is calculated. A metroplis determination-making alogorithm is applied to each base pair based on the deviation in energy. The Monte Carlo process is repeated until steady state is reached. Consider the j th base pair in a template of length Due north. Define a state part S _j for each base of operations pair, S _j = 0 if the j th base pair has a hydrogen bond, otherwise S_j =1.Suppose the 5′-3′ composition at positions j-1, j, j+1 are ACG. The nearest neighbor contributions to the gratuitous energy of the j th base pair is:

Δ Thou j N North = 1 2 [ Δ G T G T − S j − 1 Δ Grand T H : A T − South j Δ M T H : G C ] + 1 2 [ Δ G T C G − S j + 1 Δ G T H : G C − Due south j Δ K T H : G C ]

(13)

The free energy due to nucleation ΔGrand ^Nucl _T is distributed amidst all base pairs with hydrogen bonds and the contribution to the j th base pair is:

Δ G j Nucl . = Δ G T Nucl . ∕ ∑ thou = i ( 1 − Southward k )

(14)

The free energy of the j th base pair in its current state is therefore:

The gratis energy of the j th base pair is calculated one time again for the opposite state of base of operations pair j. The state functions of all other base of operations pairs are kept equally before. Denote the costless energy of the j th base pair in its opposite state as ΔThou^O _j . Thus the contribution due to nucleation appears in only one of the two cases. Too notation that for the end base pairs simply one of the 2 terms in eq. (10) is used.

Later on the free energy departure( Δ E j = Δ K j o − Δ K j ) has been determined for all N base pairs, the probability for transition is calculated. The Urban center algorithm defines the following transition probabilities:

P ( S j → one − S j ) = i Δ East j ≤ 0 e − Δ East j ∕ R T Δ E j > 0

(xvi)

To demonstrate the Monte Carlo method, it is applied to a sequence of 100 base pairs at 0.2M Na⁺ with varying M+C concentration. The melting curve is shown in Fig. 2 in comparison to the Marmur-Doty relation (cf. Grisham and Garrett, p.371-372 (1998)) that correlates melting temperature and G+C fraction: T_M=69.three+41f_GC. The maximum difference at the low Thousand+C fraction is ii.5°C and it is ii.seven°C at the high 1000+C fraction.

In the following section the results of the model are reported.

3. Results

The theoretical error productions of 2 PCR protocols are compared in this study. The first protocol (P1) is typical for a conventional estrus block thermocycler and the 2nd protocol (P2) is typical for a rapid thermocycler, the PCRJet® (Quintanar and Nelson, 2002). For the purpose of the model a sequence of 416 nucleotides has been generated that serves as the 3′-v′ strand of the template and it is shown in Fig. iii. The G+C content is 40%. The primer lengths are 16 bp each.

Computer generated sequence of the 3′-five′strand of target.

The commencement protocol (P1), proposed by Saiki et al., (1985), has the following holding times per cycle; 1 min at 94°C, i min at 55°C, 1 min at 72°C. A PCR bike consists of the holding times and the ramp times. The temperature-time history of a single bike is shown in Fig. four.

Thermal cycle of Saiki et al. protocol (P1). The annealing time is t1, the ramp fourth dimension to the elongation temperature is t2, the elongation fourth dimension is t3, the ramp time to denature temperature is t4, the denature time is t5 and the ramp fourth dimension to the annealing temperature is t6.

The second protocol (P2) is for the fast PCRJet® thermocycler (cf. review in Nature-Moore, 2005). Fast thermocycling with the PCRJet® is accomplished by the flow of high velocity air through a reaction chamber that houses an assortment of cuvettes. Ii inlet air streams (one hot, i common cold) are pre-conditioned and mixed to achieve the required temperature and menstruum rate in the reaction chamber. The response time of the PCRJet® is less than 100 ms, thus users are able to do "thermal management", which is the concept that Deoxyribonucleic acid impairment can be minimized with fast and precise thermal control.

In Fig. 5 a PCRJet® temperature-time profile is shown. The contour is typical for the PCR protocols which are used in PCRJet® experiments to amplify templates of like length as the 1 shown in Fig. 3. The maximum heating/cooling rate which can exist achieved with the PCRJet® depends on the dimensions of the cuvettes. If Lightcycler capillaries (www.roche-applied-science.com)) with a twenty μl chapters are used, a rate of 47°C/sec has been measured. In Table 3 the time intervals for both protocols are listed. Time is measured in milliseconds. The total fourth dimension for P1 is 206.000s and for P2 the full time is iv.660s.

Temperature (°C) vs. Fourth dimension (seconds) bike for the PCRJet® protocol (P2).

Table iii

Time Intervals of Protocols P1 and P2 (in milliseconds)

	t1	t2	t3	t4	t5	t6	Full
P1	60,000	5,600	60,000	seven,400	sixty,000	thirteen,000	206,000
P2	i,000	360	ii,000	470	0	830	iv,660

Thermal Damage for Protocol P1.

In Fig. six the cumulative errors due to A+G thermal depurination are shown for the P1 protocol. The nigh damage occurs when the DNA is in unmarried-stranded class. If the progression of the error accumulation is overlayed on the temperature-time history of Fig. 4, it is noted that the error rate increases dramatically when the temperature rises from 72°C to 94°C. The extensive denaturation agree largely contributes to the total error count. The linear slopes of the depurination graphs betoken a constant charge per unit of depurination and thus a constant temperature (denaturation value). The complementary strand has fewer depurination errors. The template and its complementary strand have approximately the same number of purine sites (A+1000), hence the dsdc and dsdt curves are nearly identical.

Cumulative depurination impairment over 1 bicycle of protocol P1. The double stranded depurination values for the template and the complementary strand are very close and the plots overlap.

In Fig. 7, cytosine deamination in ssDNA and dsDNA is shown over 1 thermal cycle. Similar to the depurination example, the single-stranded cytosines deaminate the almost, followed by the single-stranded complementary strand. If the cytosines are in double-stranded form, the deamination of the ii strands is the same since they accept equal cytosine content. However, the contribution of the double-stranded deamination to the total deamination is almost negligible. In club to control the C deamination damage, the exposure time of unmarried stranded DNA to high temperature must exist minimized.

Cumulative cytosine deamination over one cycle of protocol P1. The double stranded values for the template (dsct) and the complementary strand (dscc) are very close and the plots overlap.

A comparison of Fig. 6 and Fig. 7 confirms that depurination is the ascendant source of thermal Dna damage. In add-on, the most harm is incurred when the DNA is in single-stranded form. The total error accumulation in the template after ane wheel is 0.003. This number tin can exist interpreted in diverse means. When a template of 416 bp is copied, at that place is a 0.3% hazard to have either a depurination (most probable) or C deamination event. On the average, 1 in every 333 copies will have a thermal fault. The thermal error frequency for P1 is expressed as errors/10⁶ bp:

Φ _T = 7.2 errors/10⁶ base pairs.

The error frequency for the KOD polymerase is in the social club of one.one errors/x⁶ nucleotides. The thermal damage contributes far more to the total error count than the polymerase. The model predicts a total error frequency of:

ΦTotal= 8.3errors/ten⁶ base pairs

Thermal damage to DNA is minimized when nucleic acids spend equally little time as possible at elevated temperatures (> l°C). Therefore, thermal harm to Deoxyribonucleic acid is reduced when fast thermocycling protocols are used. In the following section a typical protocol of the PCRJet® is analyzed.

Thermal Impairment for Protocol P2.

In Fig. 5 the temperature-time contour is shown for protocol P2. The sample is annealed for 1 2d, the temperature is raised at a rate of 47°C/sec to 72°C, where it remains for 2 seconds before it is raised to 94°C.

No time is spent at the denaturation temperature and the sample is immediately cooled to 55°C. The total time for ane bicycle is four.66 seconds.

In Fig. viii the cumulative depurination damage is shown for the template DNA and its complementary strand. The rates increase when the temperature is raised subsequently the annealing pace. A closer look at the ssdt bend reveals that, towards the end of the elongation step, the rate slows down a little. The caption is equally follows. The template can exist divided into two parts: behind the polymerase circuitous site it is double stranded and partially melted, ahead of the insertion site it is only single stranded. The (A+1000) concentration in the office of the template that has not been copied becomes progressively less with extension. The corporeality of single stranded (A+Thou) in the office of the template that has been extended depends on the melting behavior of the dsDNA. Over the first ii.5 seconds the total unmarried stranded (A+Thousand) concentration declines, considering the gain in unmarried stranded (A+G) due to melting of dsDNA is more offset past the reduction in the (A+G) concentration in the unmarried stranded part of the template. The point is illustrated in Fig. 9. The single stranded depurination of the template (denoted as d D d t), is plotted equally a function of time over one bike. The rate of depurination is the production of the rate abiding (eq. (8)) and the number of single stranded purines:

The single stranded depurination (dp) rate, scaled past the maximum and the number of single stranded [A+G] scaled by its maximum.

d D d t = r D P s south × [ A + 1000 ] s s = 7.6 × 10 11 e − 31 ∕ R T × [ A + M ] s s .

The rate in Fig.nine.is scaled with its maximum value at the denaturation temperature. The number of [A+G] sites on the template strand that are unmarried stranded are shown also, scaled by their maximum. The maximum {A+G} single stranded sites of 202 are at the start of the cycle. The rate has a skew bimodal shape which indicates two local maxima. Over the starting time two.5 seconds the ss [A+G] number decreases, primarily due to a conversion into ds [A+G] as the extension proceeds and not due to depurination-note the low depurination rate over this catamenia. The first maximum of the depurination charge per unit is a result of the relatively high number of ss [A+Grand] at the time when the temperature increases to the elongation value. The second maximum is due to the maximum (denaturation) temperature. When the temperature increases to the denaturation value, ds [A+One thousand] is converted into ss [A+Chiliad]-this increase in ss [A+G] compounds the college reaction charge per unit abiding and the depurination rate shows the sharp spike. If the denaturation time would be prolonged, the rate would decline afterwards ss [A+G] has been depleted.

Fig. 10 shows the C deamination harm for the fast protocol P2. The qualititative forms of the curves are like to the depurination case, but the values are lower by gene x. The single stranded C deamination is much larger than double stranded C deamination. Information technology is farther noted that the template strand and complementary strand acquire almost the same amount of C deamination at the end of the cycle. The huge increase in C deamination, when the temperature increases to the denaturation value, is a issue of the Arrhenius effect.

Cumulative cytosine deamination over 1 bike of protocol P2. The double-stranded DNA values (dsct) and the complementary strand (dscc) are very shut and the plots overlap.

The full error frequency for P2 is:

Φ _Total = Φ _T + Φ _PCR =(0.026 +1.1) errors/10^{half dozen} base of operations pairs

Conspicuously the PCR fidelity plays the about of import function in the mistake product of protocol P2.

The target Deoxyribonucleic acid that has been used in all the examples contains 40% (G+C) and this limerick holds for the template and complementary strands. An interesting situation arises when the template strand contains forty%K and the complementary strand contains 40% C. The (G+C) content of the target is now 60%, only the purines and pyrimidines are non evenly distributed between the two strands. The total errors (expressed in errors per million base of operations pairs) are shown in Fig. 11.

Cumulative thermal damage for a template that contains 60% M+C. The complementary strand contains 40% C and the template strand contains 40%One thousand.

The template strand acquires significantly more errors than the complementary strand. The reason is that depurination rates are higher than C deamination rates. If the thermal cycle involves long holds at elevated temperatures the disparity in error content betwixt the strands volition go more pronounced.

iv. Other implications of thermal damage

The effect of thermal harm in DNA reaches across classical PCR applications. Nucleotides in the presence of h2o are bailiwick to hydrolytic attack and higher temperatures accelerate the reaction rates. We want to mention a few situations where thermal harm is of particular concern.

Structure of Dna molecules from synthetic oligonucleotides

Although damage does not bear on diagnostic PCR too adversely, at that place are applications of PCR where error minimization becomes important. One example is the construction of large Dna molecules from oligonucleotides. It is crucial that DNA molecules which are assembled from shorter oligonucleotides are error-free or nearly error-gratis to maintain their functionality. In the PCA strategies originally described by Barnett and Erfle (1990) and Ciccarelli et al., (1991), several overlapping non-phosphorylated 3′OH oligonucleotides are annealed in a unmarried reaction at concentrations of less than 0.ane μM. After 20-30 cycles of PCR amplification, the concentrations of the ii outer primers are increased to ∼one μM and another xxx-35 cycles of PCR are carried out (Stemmer et al., 1995). Although only a few full-length DNA molecules gather during the offset PCR stage, they are selectively amplified during the second stage. Using this technique, Stemmer et al., (1995) constructed a ∼2,700 bp long synthetic plasmid from 134 different overlapping 3′OH oligonucleotides. Refinements on the Stemmer et al., (1995) protocol have been described by Mehta et al., (1997), Gao et al., (2004), Shevchuk et al., (2004), and Young and Dong (2004), whereby double-stranded Dna molecules of 1.2 to twenty kb have been assembled by PCA.

In the classic method of gene assembly used past Khorana (1979), synthetic DNA oligonucleotides are 5′ phosphorylated using T4 kinase, annealed to form overlapping duplexes, and and so enzymatically joined together using T4 Deoxyribonucleic acid ligase. A variation of this method was recently used by Smith et al., (2003) to synthesize a 5,386 bp φX174 RFI Deoxyribonucleic acid molecule in ii weeks. Over 250 oligonucleotides of 42 bp each were 5′ phosphorylated, gel-purified, annealed, and ligated. After overnight high temperature ligation (65°C), the DNA ligated production was and then amplified using the PCA strategy of Stemmer et al., (1995). Therefore, enzymatic steps such as a 65°C overnight ligase reaction (Smith et al., 2003) are expected to upshot in substantial thermal depurination and C deamination in Dna; on the lodge of 2-iii errors/one,000 bp.

PCR Distension of Long DNA Fragments

Typical amplification atmospheric condition for DNA fragments > 20kb would involve an initial denaturing footstep at 92°C for 2 minutes, followed by a ii-step PCR government of 10 cycles at 92°C for 10 sec, 55°C-65°C for 30 sec, and 68-72°C for 18 min: twenty cycles at 92°C for 10 sec, 55-65°C for thirty sec and 68-72°C for 18 min with an boosted x sec per cycle elongation for each successive bicycle, concluded past a last elongation at 68-72°C for vii min (www.roche-applied-science.com). A three-footstep cycling is proposed if the T_chiliad of the primers is beneath 68°C: pre-amplification denaturation at 94°C for 30 seconds, followed past either thirty to 35 cycles of 94°C for 30 sec, 55°C-65°C for 30 sec and 68-72°C for 45-60 sec per kb of target. If the T_grand of the primers is equal or greater 68°C, a 2-step cycling of xxx to 35 cycles at 94°C for 30 sec, 68°C for 45-threescore sec per kb of target (world wide web.invitrogen.com). If the target molecule has a length of 20kb, it is recommended to use an annealing or annealing/extension period of fifteen-20 min per bike at temperatures between 68°C and 72°C. Amplification of longer templates require college dNTP concentrations (∼500μM) and common salt concentrations (∼2.75 mM) besides as longer oligonucleotides (22-34 nucleotides) with balancing melting temperatures above 60°C to enhance reaction specificity (www.roche-applied-science.com).

The typical conditions which accept been described here will make the DNA fragments specially vulnerable to thermal damage. The model that has been presented can be used to determine the thermal impairment for such long protocols. Besides no mention has been fabricated until now of the consequence of thermal harm on the primers. These short DNA fragments are bailiwick to the same hydrolytic assail every bit the Deoxyribonucleic acid templates. Therefore similar modifications of their construction are expected and in fourth dimension-consuming protocols with prolonged exposure at loftier temperatures the primer/template annealing volition exist compromised.

5. Conclusions

The PCR procedure typically consists of three distinct thermal steps: denaturation at temperatures > 90°C, primer annealing at fifty-65°C, followed by enzymatic elongation at 68-75°C. At annealing temperatures the Dna molecules are more often than not in the double stranded form, hence the hydrolytic assault on the DNA bases are sterically hindered. Two hydrolytic damage reactions are prominent at elevated temperatures; C deamination and A+G depurination. The rate constants of these thermal damage reactions follow Arrhenius kinetics, hence the rates increase rapidly with temperature. The following conclusions are drawn from this study:

1. Depurination plays a more important role than C deamination in thermal damage to Dna during PCR amplification.

2. If the standard PCR thermocycling protocols (cf. Saiki et al., 1986) are followed, and then thermal damage may be the largest contributor to the overall error frequency in amplified Dna.

3. Thermal harm to Dna is minimized if high-speed PCR protocols are employed.

4. In detail, the denaturation property time must exist kept to a minimum.

5. The periods (fourth dimension/cycle) for the protocols P1 and P2 are 206 sec. and 4.7 sec. respectively. The full errors (depurination and C deamination) are 7.2/10⁶ bp and 0.026/x⁶ bp respectively. Thus a fifty-fold reduction in the PCR period leads to a 270-fold reduction in errors.

6. Thermal damage can assist to explain the reduction in yields at high cycle numbers.

7. Long PCR is subject to significant thermal harm. Quantitative models of thermal damage are the ideal tools to investigate the role that thermal impairment may play in long PCR and information technology may lead to a ameliorate agreement of the process.

8. New PCR applications, such as assembly PCR, require college standards of replication allegiance. To attain these higher standards, current protocols volition accept to include thermal direction.

6. Acknowledgement

EP and HJV gratefully admit the financial support of the National Institutes of Wellness through grant R21RR20219.

seven. Literature cited

• Barnett RW, Erfle H. Rapid Generation of DNA Fragments by PCR Amplification of Crude, Constructed Oligonucleotides. Nucleic Acids Res. 1990;18:3094. [PMC free commodity] [PubMed] [Google Scholar]
• Buck J, Bellon S, Berger K, Bourdat A-Grand, Douki T, Duarte V, Frelon Due south, Gasparutto D, Muller Eastward, Ravanat J-50, Sauvaigo Due south. "Contempo Aspects of Oxidative Dna Harm: Guanine Lesions, Measurement and Substrate Specificity of Deoxyribonucleic acid Repair Glycosylases." Biol. Chem. 2002;383:933–943. [PubMed] [Google Scholar]
• Ciccarelli RB, Bunyuzlu P, Huan J, Scott C, Oakes F. "Structure of constructed genes using PCR after automatic DNA synthesis of their entire top and bottom strands." Nucleic Acids Res. 1991;19:6007–6013. [PMC free article] [PubMed] [Google Scholar]
• Cline J, Braman JC, Hogrefe HH. "PCR fidelity of Pfu Deoxyribonucleic acid polymerase and other thermostable polymerases" Nucleic Acids Res. 1996;24:3546–3551. [PMC gratuitous article] [PubMed] [Google Scholar]
• Crothers DM, Zimm BH. #x201C;Theory of the Melting Transition of Constructed Polynucleotides: Evaluation of the Stacking Gratis Energy." J. Mol. Biol. 1964;9:1–nine. [PubMed] [Google Scholar]
• Eadie JS, Davidson DS. "Guanine modification during chemical DNA synthesis." Nucleic Acids Res. 1987;15:8333–8349. [PMC costless article] [PubMed] [Google Scholar]
• Frank-Kamenetskii Medico. "Simplification of the empirical relationship between melting temperature of DNA, its GC content and concentration of sodium ions in solution" Biopolymer. 1971;10:2623–2624. [PubMed] [Google Scholar]
• Fryxell KJ, Zuckerkandl E. "Cytosine deamination plays a primary role in the evolution of mammalian isochors" Mol. Biol. Evol. 2000;17:1371–83. [PubMed] [Google Scholar]
• Gao Ten, Yo P, Keith A, Ragan T, Harris T. Thermodynamically Balanced Inside-Out TBIO PCR-Based Gene Synthesis: A Novel Method of Primer Design for Loftier-Fidelity Associates of Longer Gene Sequences. Nucleic Acids Res. 2004;31:e143–e164. [PMC gratuitous commodity] [PubMed] [Google Scholar]
• Gelfand DH, White TJ. "Thermostable DNA Polymerases." In: Innis MA, Gelfand DH, Sninsky JJ, White TJ, editors. PCR Protocols: a Guide to Methods & Applications. Academic Press, Inc.; San Diego: 1990. [Google Scholar]
• Gray DM, Tinoco I., jr. 1970"A new arroyo to the study of sequence-dependent properties of polynucleotides." Biopolymers. 9:223–244. [Google Scholar]
• Griep Thou, Whitney SE, Nelson RM, Viljoen HJ. "Deoxyribonucleic acid polymerase chain reaction: prediction of mistake frequencies and extension rates" AIChE J. 2005a (in impress) [Google Scholar]
• Griep M, Kotera CA, Nelson RM, Viljoen HJ. "Kinetics of the Deoxyribonucleic acid Polymerase Pyrococcus Kodakaraensis." Chem. Eng. Sci. 2005b (in review) [Google Scholar]
• Grisham CM, Garrett RH. Biochemistry. 1998 Thomson Learning. [Google Scholar]
• Hsu GW, Ober M, Carell T, Beese LS. "Mistake-decumbent replication of oxidatively damaged Dna past a loftier-fidelity polymerase" Nature. 2004;431:217–21. [PubMed] [Google Scholar]
• Innis MA, Myambo KB, Gelfand DH, Brow MAD. "Dna sequencing with Thermus aquaticus Dna polymerase and direct sequencing of polymerase chain-reaction amplified Dna." Proc. Nat. Acad. Sciences USA. 1988;85:9436–9440. [PMC complimentary article] [PubMed] [Google Scholar]
• Khorana HG. "Total Synthesis of a Gene." Science. 1979;203:614–625. [PubMed] [Google Scholar]
• Jager J, Pata JD. "Getting a grip: polymerases and their substrates." Current Opinion Struct. Biology. 1999;9:21–28. [PubMed] [Google Scholar]
• Johnson KA. "Conformational coupling in Dna polymerase fidelity." Annu Rev Biochem. 1993;62:685–713. [PubMed] [Google Scholar]
• Kiefer JR, Mao C, Braman JC, Beese LS. "Visualizing Deoxyribonucleic acid replication in a catalytically active Bacillus Dna polymerase crystal" Nature. 1998;391:304–7. [PubMed] [Google Scholar]
• Li Y, Waksman G. "Structural studies of the Klentaq1 DNA polymerase" Current Organic Chemistry. 2001;v:871–883. [Google Scholar]
• Lindahl T, Nyberg B. "Rate of depurination of native Dna." Biochemistry. 1972;11:3610–3618. [PubMed] [Google Scholar]
• Lindahl T, Nyberg B. "Heat-induced deamination of cytosine residues in deoxyribonucleic acrid." Biochemistry. 1974;13:3405–3410. [PubMed] [Google Scholar]
• Mehta DV, DiGate RJ, Banville DL, Guiles RD. "Optimized Gene Synthesis, Loftier Level Expression, Isotopic Enrichment, and Refolding of Human Interleukin-five." Protein Expression & Purification. 1997;11:86–94. [PubMed] [Google Scholar]
• Mizuguchi H, Nakatsuji M, Fujiwara S, Takagi M, Imanaka T. "Characterization and awarding to hot start PCR of neutralizing monoclonal antibodies against KOD Dna polymerase" J. Biochem. 1999;126:762–768. [PubMed] [Google Scholar]
• Moore P. "PCR: Replicating Success." Nature. 2005;435:235–238. [PubMed] [Google Scholar]
• Ninio J. "Culling to the steady-land method: derivation of reaction rates from outset-passage times and pathway probabilities." Proc Natl Acad Sci U Southward A. 1987;84:663–7. [PMC gratis article] [PubMed] [Google Scholar]
• Quintanar A, Nelson RM. "A procedure and appliance for high-speed amplification of Deoxyribonucleic acid." U.S. Patent No. 6,472,186 2002.
• Saiki RK, Scharf S, Faloona F, Mullis KB, Horn GT, Erlich HA, Arnheim N. "Enzymatic amplification of beta-globin genomic sequences and brake site analysis for diagnosis of sickle cell anemia." Science. 1985;230:1350–1354. [PubMed] [Google Scholar]
• SantaLucia J. "A unified view of polymer, dumbbell, and oligonucleotide DNA nearest-neighbor thermodynamics." Proc. Natl. Acad. Sci. Usa. 1998;95:1460–1465. [PMC gratis article] [PubMed] [Google Scholar]
• Shevchuk NA, Bryksin AV, Nusinovich YA, Cabello FC, Sutherland 1000, Ladisch S. "Construction of long Deoxyribonucleic acid molecules using long PCR-based fusion of several fragments simultaneously." Nucleic Acids Res. 2004;32:e19–e47. [PMC free article] [PubMed] [Google Scholar]
• Sikorsky JA, Primerano DA, Fenger TW, Denvir J. "Outcome of Dna damage on PCR amplification efficiency with the relative threshold bicycle method." Biochem. Biophys. Res. Comm. 2004;323:823–830. [PubMed] [Google Scholar]
• Smith HO, Hutchison CA, Pfannkock C, Venter JC. "Generating a synthetic genome by whole genome associates: φX174 bacteriophage from synthetic oligonucleotides." Proc. Nat. Acad. Sciences Us. 2003;100:15,440–fifteen,445. [PMC free article] [PubMed] [Google Scholar]
• Stemmer WPC, Crameri A, Ha KD, Brennan TM, Heyneker HL. "Single-pace assembly of a gene and entire plasmid from large numbers of oligodeoxyribonucleotides." Factor. 1995;164:49–53. [PubMed] [Google Scholar]
• Uhlenbeck OC, Tapping PN, Dengler B, Tinoco I., jr. "Stability of RNA hairpin loops: A 6-C g-U half-dozen." J. Mol. Biol. 1973;73:483–496. [PubMed] [Google Scholar]
• Viljoen SV, Griep Yard, Nelson RM, Viljoen HJ. "A Macroscopic Kinetic Model for DNA Polymerase Elongation and High Fidelity Nucleotide Selection." Comp. Biol & Chem. 2005;29:101–110. [PubMed] [Google Scholar]
• Whitney SE, Sudhir A, Nelson RM, Viljoen HJ. "Principles of rapid polymerase chain reactions: mathematical modeling and experimental verification." Computational Biology and Chemistry. 2004;28:195–209. [PubMed] [Google Scholar]
• Wittwer CT, Filmore GC, Garling DJ. "Minimizing the time required for DNA amplification by efficient estrus transfer to small samples." Anal. Biochem. 1990;186:328–331. [PubMed] [Google Scholar]
• Young Fifty, Dong Q. "Two-step total gene synthesis method." Nucleic Acids Res. 2004;32:e59–e71. [PMC free article] [PubMed] [Google Scholar]

What Molecules Increase In Number During Pcr,

Source: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1544370/

Posted by: blackstockwhippyraton62.blogspot.com

Share this post