PCR Analyzer Software

Developed by:

Dr. Chris Portier
National Institute of Environmental Health Sciences
National Institute of Health
portier@niehs.nih.gov

Dr. Marjo Smith
Constella Group, LLC
msmith@constellagroup.com

Programmed by:

Shawn Harris
Constella Group, LLC
sharris@constellagroup.com

© Copyright 2007

PCR Analyzer Software Version 1.0 Release Description

The algorithm provides an estimate for the initial amount of amplicon present in a PCR. Only a single amplification is used for the estimate. If a fold change is required between 2 PCRs, find estimates of both initial amounts of amplicon, then take the ratio.

The algorithm is described in detail in the following journal article: Smith, MV, CR Miller, M Kohn, NJ Walker and CJ Portier (2007) Absolute estimation of initial concentrations of amplicon n a real-time RT-PCR process, BMC Bioinformatics, 8:409. (http://www.biomedcentral.com/1471-2105/8/409)

This help file is arranged according to the questions in the menu. The questions are written in bold letters.

First menu page

Input File Name: and Output File Name:

The input file is assumed to be a text file with the results of PCR amplifications arranged in columns. The input file may contain data in more than 1 column (corresponding to different PCR amplifications), but only 1 column can be used at a time. The output file will likewise be a text file named by the user. The paths and file names of both should be entered in the first 2 spaces.

Data column index:

If the input file contains the observations of more than 1 PCR, enter the column containing the observations of interest in the appropriate space. If the input file contains only a single column, enter ‘1’.

Primer Concentration (nM/l): and Probe Concentration (nM/l):

The initial concentrations of the probe and both primers are assumed to be given in nM/l. The primer concentration is assumed to be the same for both forward and reverse primers. Enter the concentrations of both primers and probe.

First cycle to double number of amplicon molecules (Enter 1 or 2):

If the data came from a transcription experiment, it is likely that the initial solution contain a number amplicon molecules, but none of the opposite orientation. In that case, the first thermal cycle will produce an equal number of molecules with orientation opposite to that of the amplicon, but it will not increase or double the number of amplicon molecules. That will happen only in the 2^nd cycle, when primers extend along the molecules of opposite orientation. In that case, the first doubling cycle for amplicon will be the 2^nd cycle. If the data came from a genomics experiment, it’s possible the initial solution contains equal numbers of both the amplicon and its reverse. In that case the first doubling cycle for amplicon will be the 1^st cycle.

Tubule volume (ul):

This specifies the volume (in microliters) of the amplification tubule.

Second menu page

The algorithm estimates the initial amount of amplicon by modeling key chemical reactions taking place in the extension/annealing phases of the thermal cycles of a PCR, then optimizing the output via a cost function over 2 or 3 estimated parameters. An additional parameter (the conversion factor between fluorescent units and the number of probe molecules digested, releasing fluorescence) is computed within the program. As is usually the case with optimization of nonlinear models, it is recommended that you run the algorithm several times with different initial values and pick the solution with the lowest final cost function. The expression below is the cost function used in the algorithm

The squared difference is between the observation in the kth cycle (obs(k) ), which is cumulative, and the cumulative prediction multiplied by the conversion factor between number of digested probe molecules and fluorescent units. The weights are the increments in observed fluorescence, ensuring that the cycles with the largest signal are weighted most heavily.

The user may choose between 2 models:

Initial values (Basic model):

The ‘basic’ model includes only duplication of target sequence with the release of fluorescence and the re-annealing between previously formed single strands of DNA of opposite orientation. This model estimates a total of 3 parameters: the initial amount of amplicon, the competition coefficient of the re-annealing process and the conversion factor between fluorescent emission and number of digested probe molecules. The model equations for the extension/anneal phase of the i^th thermal cycle are

where the solution to the first equation, w_iq(t), refers to the number of triplexes of single DNA strands with probe and primer molecules attached, w_ir(t) is the number of re-annealed duplexes, and Ai, Pi and Qi denote the initial number of single strands of amplicon, primer and probe molecules respectively at the beginning of the i^th anneal/extension step; M_q and M_r represent the rate of formation of triplexes and the rate of re-annealing respectively. These equations are assumed to go to steady state for each thermal phase, so that only the relative sizes of M_q and M_r are important. Hence, M_q may be assumed equal to 1, and M_r is specified with respect to that. The steady state solution to the first equation, w_iq(steady state), is used as pred(i) in the cost function.

Re-annealing constant (M_r):

This requires an initial guess for the coefficient in the 2^nd equation, M_r. Generally values of M_r range from about 1000 to 10000. The default value listed is 3000, but some widely spaced alternatives should be tried, such as 1000 and 8000.

Initial amount of amplicon (number of molecules):

This is the initial guess for the initial amount of amplicon. If you are fairly certain of the region for the initial amount of amplicon, try several values from that region. If you have no idea how much amplicon you might have initially, try several widely spaced guesses. Eg, 10², 10⁴, 10⁶, 10⁸. The final estimate should correspond to the solution with the lowest cost function.

Initial values (Expanded model):

The ‘expanded’ model includes the duplication of target sequence with the release of fluorescence and the re-annealing between previously formed single strands of DNA of opposite orientation, just as the basic model. It also however includes duplication of target sequence without the release of fluorescence. This model estimates a total of 4 parameters: the initial amount of amplicon, the competition coefficient of the re-annealing process, the competition coefficient of the unmarked duplication process, and the conversion factor between fluorescent emission and number of digested probe molecules. The model equations for the extension/anneal phase of the i^th thermal cycle are

Where all parameters have the same meaning as in the basic model, but the 2^nd equation is added. The solution to the 2^nd equation, w_is(t), refers to the number of single strands of DNA with an attached primer but without an attached probe molecule. Thus the 2^nd equation models duplication of DNA ‘unmarked’ by the release of fluorescence. M_s is the coefficient of unmarked duplication, again relative to M_q. The steady state solution to the first equation, w_iq(steady state), is used as pred(i) in the cost function.

Re-annealing constant (M_r):

This requires an initial guess for the coefficient in the 3rd equation, M_r. Generally values of M_r range from about 1000 to 10000. The default value listed is 3000, but some widely spaced alternatives should be tried, such as 1000 and 8000.

Initial amount of amplicon (number of molecules):

This is the initial guess for the initial amount of amplicon. If you are fairly certain of the region for the initial amount of amplicon, try several values from that region. If you have no idea how much amplicon you might have initially, try several widely spaced guesses. Eg, 10², 10⁴, 10⁶, 10⁸. The final estimate should correspond to the solution with the lowest cost function.

Unmarked duplication constant (Ms):

This requires an initial guess for the coefficient in the 2^nd equation, M_s. Generally values of M_s range from about 10 to 200. The default listed is 50, but some alternatives should be tried, such as 20 and 70.

Assumptions used by the models are:

1. The synthesis of DNA strands of both orientations is assumed to proceed at the same pace, so that only the hybridization of the orientation complementary to the probe molecule needs to be modeled explicitly.
2. All DNA synthesis and re-annealing is assumed to go to completion allowing no single stranded DNA left by the end of each anneal/extension step. Thus the differential equations do not contain dissociation terms and the attachments they describe are assumed irreversible. While the experimental duration of the anneal/extension steps for the data in this paper was fixed at 60 seconds, when PCR runs with anneal/extension steps varying from 30 seconds to 90 seconds were compared, no discernible differences were observed (not shown).
3. All double strands are assumed to separate by the end of the denaturation step.
4. The duplication of target sequence is modeled as a single 3-way reaction rather than modeling the attachment of probe and primer molecules to the DNA strands separately.
5. Although unplanned chemical reactions, such as primer-dimerization may take place in a PCR, none are modeled here. In fact there is no other source of inefficiency in the basic model than the re-annealing of previously formed DNA strands.