Validation and estimation of parameters for a general probabilistic model of the PCR process.

Earlier work rigorously derived a general probabilistic model for the PCR process that includes as a special case the Velikanov-Kapral model where all nucleotide reaction rates are the same. In this model, the probability of binding of deoxy-nucleoside triphosphate (dNTP) molecules with template strands is derived from the microscopic chemical kinetics. A recursive solution for the probability function of binding of dNTPs is developed for a single cycle and is used to calculate expected yield for a multicycle PCR. The model is able to reproduce important features of the PCR amplification process quantitatively.With a set of favorable reaction conditions, the amplification of the target sequence is fast enough to rapidly outnumber all side products. Furthermore, the final yield of the target sequence in a multicycle PCR run always approaches an asymptotic limit that is less than one. The amplification process itself is highly sensitive to initial concentrations and the reaction rates of addition to the template strand of each type of dNTP in the solution. This paper extends the earlier Saha model with a physics based model of the dependence of the reaction rates on temperature, and estimates parameters in this new model by nonlinear regression. The calibrated model is validated using RT-PCR data.     

Efficient primer design algorithms

MOTIVATION: Primer design involves various parameters such as string-based alignment scores, melting temperature, primer length and GC content. This entails a design approach from multicriteria decision making. Values of some of the criteria are easy to compute while others require intense calculations. RESULTS: The reference point method was found to be tractable for trading-off between deviations from ideal values of all the criteria. Some criteria computations are based on dynamic programs with value iteration whose run time can be bounded by a low-degree polynomial. For designing standard PCR primers, the scheme offers in a relative gain in computing speed of up to 50: 1 over ad-hoc computational methods. Single PCR primer pairs have been used as model systems in order to simplify the quantization of the computational acceleration factors. The program has been structured so as to facilitate the analysis of large numbers of primer pairs with minor modifications. The scheme significantly increases primer design throughput which in turn facilitates the use of oligonucleotides in a wide range of applications including: multiplex PCR and other nucleic acid-based amplification systems, as well as in zip code targeting, oligonucleotide microarrays and nucleic acid-based nanoengineering.     

AN EXTENDED TRANSITION PROBABILITY MODEL OF THE VARIABILITY OF CELL GENERATION TIMES

The transition probability model of variability of cell generation times is extended so that the rate constant for the transition from the A-state to the B-phase of the cell cycle depends on time which a particular cell has already spent in the A-state. A specific time dependence of this rate constant is introduced. It is determined by the value of one constant which is then an additional parameter of the model. The corresponding cell population kinetics are calculated and compared to existing experimental evidence. The model accounts satisfactorily for the generation time distribution function and for the shortening of the G₁ phase of binucleate cells. The time dependence of the transition probability is related to the cell kinetics of an hypothetical cell constituent. A possible relationship is proposed between the chemical parameters within the cell and the parameters of the cell population kinetics.     

In situ reverse transcription-polymerase chain reaction. Applications for light and electron microscopy

Since its discovery in 1986 by Mullis, the polymerase chain reaction (PCR) has been extensively developed by morphologists in order to overcome the main limitation of in situ hybridization, the lack of sensitivity. In situ PCR combines the extreme sensitivity of PCR with the cell-localizing ability of in situ hybridization. The amplification of DNA (PCR) or a cDNA (RT-PCR) in cell or tissue sections has been developed at light and electron microscopic levels. A successful PCR experiment requires the careful optimization of several parameters depending on the tissue (or of cell types), and a compromise must be found between the fixation time, pretreatments and a good preservation of the morphology. Other crucial factors (primer design, concentration in MgCl₂, annealing and elongation temperatures during the amplification steps) and their influence on the specificity and sensitivity of in situ PCR or RT-PCR are discussed. The necessity to run appropriate controls, especially to assess the lack of diffusion of the amplified products, is stressed. Current applications and future trends are also presented.     

PCR detection of nearly any dengue virus strain using a highly sensitive primer 'cocktail'

PCR detection of viral pathogens is extremely useful, but suffers from the challenge of detecting the many variant strains of a given virus that arise over time. Here, we report the computational derivation and initial experimental testing of a combination of 10 PCR primers to be used in a single high-sensitivity mixed PCR reaction for the detection of dengue virus. Primer sequences were computed such that their probability of mispriming with human DNA is extremely low. A 'cocktail' of 10 primers was shown experimentally to be able to detect cDNA clones representing the four serotypes and dengue virus RNA spiked into total human whole blood RNA. Computationally, the primers are predicted to detect 95% of the 1688 dengue strains analyzed (with perfect primer match). Allowing up to one mismatch and one insertion per primer, the primer set detects 99% of strains. Primer sets from three previous studies have been compared with the present set of primers and their relative sensitivity for dengue virus is discussed. These results provide the formulation and demonstration of a mixed primer PCR reagent that may enable the detection of nearly any dengue strain irrespective of serotype, in a single PCR reaction, and illustrate an approach to the broad problem of detecting highly mutable RNA viruses.     

Real time PCR quantification in groundwater of the dehalorespiring Desulfitobacterium dichloroeliminans strain DCA1

Quantifying microorganisms responsible for bioremediation can provide insight in their behavior and can help to obtain a better understanding of the physicochemical parameters monitored during bioremediation. A real time PCR (RTm PCR) assay based on the detection with SYBR Green I was optimized in order to quantify the 1,2-dichloroethane dehalorespiring Desulfitobacterium dichloroeliminans strain DCA1. A primer pair targeting unique regions of the 16 S rRNA gene was designed and tested in silico for its specificity. Selectivity was furthermore evaluated and a Limit of Quantification of 1.5 x 10(4) cells/microL DNA extract was obtained for spiked groundwater. Real time measurements of groundwater samples retrieved from a bioaugmented monitoring well and which had an average concentration lying in the range of the Limit of Quantification were evaluated positively with regards to reproducibility. Validation of the RTm PCR assay on groundwater samples originating from different sites confirmed the specificity of the designed primer pair. This RTm PCR assay can be used to survey the abundance and kinetics of strain DCA1 in in situ bioaugmentation field studies.     

A rapid PCR-based method for the identification of ob mutant mice

With increasing incidence of obesity, there is greater demand for suitable research and therapeutic models. The ob/ob mouse model develops obesity by 5 weeks of age. Previously, a method using DNA purification, PCR, and restriction digestion of products was devised to identify mice bearing the ob allele. Here, we describe a direct PCR method that requires no DNA purification. Wild-type and ob-specific primers are used under the same conditions in two separate and simultaneously run three-primer PCRs. Standard PCR using the wild-type primer mix produces 191 bp and 104 bp bands in +/+ and ob/+ and only the control 191 bp band in ob/ob animals. The ob-specific primer reaction produces 191 bp and 123 bp bands in ob/+ and ob/ob and only the control 191 bp band in +/+ animals. Phenotypic weight gain in offspring of heterozygous intercrosses was used to validate genotypes. This primer-specific PCR method allows simultaneous identification of +/+, ob/+, and ob/ob genotypes prior to breeding age to facilitate breeding and research studies in an important model of clinical obesity.     

Solid phase DNA amplification: a Brownian dynamics study of crowding effects

Solid phase amplification (SPA), a new method to amplify DNA, is characterized by the use of surface-bound primers. This limits the amplification to two-dimensional surfaces and therefore allows the easy parallelization of DNA amplification in a single system. SPA leads to the formation of small but dense DNA brushes, called DNA colonies. For a molecule to successfully duplicate itself, it needs to bend so that its free end can find a matching primer, located on the surface. We used Brownian dynamics simulations (with a united-atom model) to model the basic kinetics of an SPA experiment. The simulations mimic the temperature cycles and the molecule duplication process found in SPA. Our results indicate that the steric interaction between molecules leads to a decreased duplication probability for molecules in the center of a colony and to an outward leaning for the molecules on the perimeter. These effects result in slower amplification (compared to solution PCR) and indicate that steric interaction alone can explain the loss of the exponential growth (characteristic of solution PCR) of the number of molecules in an SPA experiment. Furthermore, the growth of the colony as a function of the number of thermal cycles is found to be similar to the one obtained with a simple Monte Carlo simulation.     

Quasi-elastic light scattering from migrating chemotactic bands of Escherichia coli. III. Studies of band formation propagation and motility in oxygen and serine substrates.

A series of light scattering experiments have been performed to study both macroscopic aspects of band formation and propagation and microscopic motility parameters of Escherichia coli in the combined substrate gradients of oxygen and serine. From the band formation experiment the conclusion is drawn that a minimum threshold gradient of the substrate is required for bacteria to form a band. From the band propagation experiment in the serine substrate the motility coefficient mu and chemotactic coefficient delta are determined. A separate quasi-elastic scattering experiment has been made with a propagating band to obtain three microscopic motility parameters: mean twiddle time tau 1, mean run time tau 2, and mean run speed V2. Finally, a scaling argument is made to connect the macroscopic parameters mu and delta with the microscopic parameters tau 1, tau 2, and V2, thus achieving a unified understanding of macroscopic and microscopic aspect of chemotaxis.     

A microscopic model of enzyme kinetics.

Many in vivo enzymatic processes, such as those of the tissue factor pathway of blood coagulation, occur in environments with facilitated substrate delivery or enzymes bound to cellular or lipid surfaces, which are quite different from the ideal fluid environment for which the Michaelis-Menten equation was derived. To describe the kinetics of such reactions, we propose a microscopic model that focuses on the kinetics of a single-enzyme molecule. This model provides the foundation for macroscopic models of the system kinetics of reactions occurring in both ideal and nonideal environments. For ideal reaction systems, the corresponding macroscopic models thus derived are consistent with the Michaelis-Menten equation. It is shown that the apparent Km is in fact a function of the mechanism of substrate delivery and should be interpreted as the substrate level at which the enzyme vacancy time equals the residence time of ES-complexes; it is suggested that our microscopic model parameters characterize more accurately an enzyme and its catalytic efficiency than does the classical Km. This model can also be incorporated into computer simulations of more complex reactions as an alternative to explicit analytical formulation of a macroscopic model.     

Assessment of the specificity of Burkholderia and Pseudomonas qPCR assays for detection of these genera in soil using 454 pyrosequencing

In this study, two highly specific quantitative PCR assays targeting the bacterial genera Burkholderia and Pseudomonas were developed and evaluated on soil samples. The primers were targeting different multivariate regions of the 16S rRNA gene and designed to be compatible with quantitative PCR and the high throughput 454 pyrosequencing technique. The developed assays were validated using the standard methods. All tests with the new developed assays showed very high specificity. Pyrosequencing was used for direct analysis of the PCR product and applied as a specificity measurement of the primers. The Pseudomonas primers showed a 99% primer specificity, which covered 200 different Pseudomonas sequence clusters in 0.5 g of soil. In contrast to that the same approach using the genus-specific Burkholderia primers showed only 8% primer specificity. This discrepancy in primer specificity between the normal procedures compared with pyrosequencing illustrates that the common validation procedures for quantitative PCR primers may be misleading. Our results exemplify the fact that current 16S RNA gene sequence databases might lack resolution within many taxonomic groups and emphasize the necessity for a standardized and functional primer validation protocol. A possible solution to this could be to supplement the normal verification of quantitative PCR assays with a pyrosequencing approach.     

Specific PCR product primer design using memetic algorithm

To provide feasible primer sets for performing a polymerase chain reaction (PCR) experiment, many primer design methods have been proposed. However, the majority of these methods require a relatively long time to obtain an optimal solution since large quantities of template DNA need to be analyzed. Furthermore, the designed primer sets usually do not provide a specific PCR product size. In recent years, evolutionary computation has been applied to PCR primer design and yielded promising results. In this article, a memetic algorithm (MA) is proposed to solve primer design problems associated with providing a specific product size for PCR experiments. The MA is compared with a genetic algorithm (GA) using an accuracy formula to estimate the quality of the primer design and test the running time. Overall, 50 accession nucleotide sequences were sampled for the comparison of the accuracy of the GA and MA for primer design. Five hundred runs of the GA and MA primer design were performed with PCR product lengths of 150–300 bps and 500–800 bps, and two different methods of calculating T_m for each accession nucleotide sequence were tested. A comparison of the accuracy results for the GA and MA primer design showed that the MA primer design yielded better results than the GA primer design. The results further indicate that the proposed method finds optimal or near‐optimal primer sets and effective PCR products in a dry dock experiment. Related materials are available online at http://bio.kuas.edu.tw/ma‐pd/ . © 2009 American Institute of Chemical Engineers Biotechnol. Prog., 2009     

Incorporating observability thresholds of tumors into the two-stage carcinogenesis model

This paper discusses a general way of incorporating the growth kinetics of malignant tumors with the two-stage carcinogenesis model. The model is presented using time-homogeneous rate parameters. In that case, the differential equations comprising the model are straightforward to solve using standard numerical techniques and software. An extension of the method to time-dependent rate parameters is included in Appendix A. Allowing the rate parameters to be time-dependent does incur computational cost. An expression is given for the expected time without visible tumor, a generalization of the expected time to an observable tumor that includes the possibility of tumor regression. The model is illustrated using incidental liver tumor data in control rats from NTP rodent carcinogenicity studies, using linear birth-death kinetics of tumors combined with a non-absorbing detection limit. The approach is also shown to be potentially useful with tumor observability thresholds having more complicated features.     

A stochastic formulation of the gompertzian growth model for in vitro bactericidal kinetics: parameter estimation and extinction probability

Time-kill curves have frequently been employed to study the antimicrobial effects of antibiotics. The relevance of pharmacodynamic modeling to these investigations has been emphasized in many studies of bactericidal kinetics. Stochastic models are needed that take into account the randomness of the mechanisms of both bacterial growth and bacteria-drug interactions. However, most of the models currently used to describe antibiotic activity against microorganisms are deterministic. In this paper we examine a stochastic differential equation representing a stochastic version of a pharmacodynamic model of bacterial growth undergoing random fluctuations, and derive its solution, mean value and covariance structure. An explicit likelihood function is obtained both when the process is observed continuously over a period of time and when data is sampled at time points, as is the custom in these experimental conditions. Some asymptotic properties of the maximum likelihood estimators for the model parameters are discussed. The model is applied to analyze in vitro time-kill data and to estimate model parameters; the probability of the bacterial population size dropping below some critical threshold is also evaluated. Finally, the relationship between bacterial extinction probability and the pharmacodynamic parameters estimated is discussed.     

In situ amplification using universal energy transfer-labeled primers.

We developed an amplification detection system in which a universal energy transfer-labeled primer (UniPrimer) is used in combination with any target-specific primer pair. The target specific primers each have a 5' tail sequence, which is homologous to the 3' end of the UniPrimer which, in turn, has a hairpin structure on the 5' end. The hairpin structure brings the fluorophore and quencher into close proximity when the primer is free in solution, providing efficient quenching. When the primer is incorporated into the PCR product, the hairpin structure is unfolded and a fluorescent signal can be detected. Using hepatitis C and human papillomavirus as model systems, this study demonstrates several advantages in the hot-start in situ PCR technique with the UniPrimer system, including target specific detection of one DNA copy per cell without a separate in situ hybridization step and detection of an RNA target by RT in situ PCR without overnight DNase digestion. The UniPrimer-based in situ PCR allows rapid and simple detection of any DNA or RNA target without concern for the background from DNA repair invariably evident in paraffin-embedded tissue when a labeled nucleotide is used.     

Set of novel tools for PCR primer design.

We have developed a new package of computer programs and algorithms for different PCR applications, including allele-specific PCR, multiplex PCR, and long PCR. The package is included in the upcoming VectorNTI suite software and attempts to incorporate most of the current knowledge about PCR primer design. A wide range of primer characteristics is available for user manipulation to provide improved efficiency and increased flexibility of primer design. To accelerate the primer calculations, we have optimized algorithms using recent advances in computer science such as dynamic trees and lazy evaluation. Proper structural organization of input parameters provides further program acceleration. New Vector NTI primer design software allows calculations of primer pairs for long PCR amplification of 120-kb genomic DNA in 5 min under most stringent input parameters and clustering 435 primer pairs for multiplex PCR within 30 min on a standard Pentium III PC. Our program allows the user to take advantage of molecule annotation by applying different kinds of filtering features during PCR primer design.     

Indexed PCR Primers Induce Template-Specific Bias in Large-Scale DNA Sequencing Studies

Massively parallel sequencing is rapidly emerging as an efficient way to quantify biodiversity at all levels, from genetic variation and expression to ecological community assemblage. However, the number of reads produced per sequencing run far exceeds the number required per sample for many applications, compelling researchers to sequence multiple samples per run in order to maximize efficiency. For studies that include a PCR step, this can be accomplished using primers that include an index sequence allowing sample origin to be determined after sequencing. The use of indexed primers assumes they behave no differently than standard primers; however, we found that indexed primers cause substantial template sequence-specific bias, resulting in radically different profiles of the same environmental sample. Likely the outcome of differential amplification efficiency due to primer-template mismatch, two indexed primer sets spuriously change the inferred sequence abundance from the same DNA extraction by up to 77.1%. We demonstrate that a double PCR approach alleviates these effects in applications where indexed primers are necessary.     

Bias caused by template annealing in the amplification of mixtures of 16S rRNA genes by PCR.

The PCR is used widely for the study of rRNA genes amplified from mixed microbial populations. These studies resemble quantitative applications of PCR in that the templates are mixtures of homologs and the relative abundance of amplicons is thought to provide some measure of the gene ratios in the starting mixture. Although such studies have established the presence of novel rRNA genes in many natural ecosystems, inferences about gene abundance have been limited by uncertainties about the relative efficiency of gene amplification in the PCR. To address this question, three rRNA gene standards were prepared by PCR, mixed in known proportions, and amplified a second time by using primer pairs in which one primer was labeled with a fluorescent nucleotide derivative. The PCR products were digested with restriction endonucleases, and the frequencies of genes in the products were determined by electrophoresis on an Applied Biosystems 373A automated DNA sequencer in Genescan mode. Mixtures of two templates amplified with the 519F-1406R primer pair yielded products in the predicted proportions. A second primer pair (27F-338R) resulted in strong bias towards 1:1 mixtures of genes in final products, regardless of the initial proportions of the templates. This bias was strongly dependent on the number of cycles of replication. The results fit a kinetic model in which the reannealing of genes progressively inhibits the formation of template-primer hybrids.