Developing a Minimally Structured Mathematical Mode of Cancer Treatment with Oncolytic Viruses and Dendritic Cell Injections

Mathematical models of biological systems must strike a balance between being sufficiently complex to capture important biological features, while being simple enough that they remain tractable through analysis or simulation. In this work, we rigorously explore how to balance these competing interests when modeling murine melanoma treatment with oncolytic viruses and dendritic cell injections. Previously, we developed a system of six ordinary differential equations containing fourteen parameters that well describes experimental data on the efficacy of these treatments. Here, we explore whether this previously developed model is the minimal model needed to accurately describe the data. Using a variety of techniques, including sensitivity analyses and a parameter sloppiness analysis, we find that our model can be reduced by one variable and three parameters and still give excellent fits to the data. We also argue that our model is not too simple to capture the dynamics of the data, and that the original and minimal models make similar predictions about the efficacy and robustness of protocols not considered in experiments. Reducing the model to its minimal form allows us to increase the tractability of the system in the face of parametric uncertainty

Absolute estimation of initial concentrations of amplicon in a real-time RT-PCR process

<p>Abstract</p> <p>Background</p> <p>Since real time PCR was first developed, several approaches to estimating the initial quantity of template in an RT-PCR reaction have been tried. While initially only the early thermal cycles corresponding to exponential duplication were used, lately there has been an effort to use all of the cycles in a PCR. The efforts have included both fitting empirical sigmoid curves and more elaborate mechanistic models that explore the chemical reactions taking place during each cycle. The more elaborate mechanistic models require many more parameters than can be fit from a single amplification, while the empirical models provide little insight and are difficult to tailor to specific reactants.</p> <p>Results</p> <p>We directly estimate the initial amount of amplicon using a simplified mechanistic model based on chemical reactions in the annealing step of the PCR. The basic model includes the duplication of DNA with the digestion of Taqman probe and the re-annealing between previously synthesized DNA strands of opposite orientation. By modelling the amount of Taqman probe digested and matching that with the observed fluorescence, the conversion factor between the number of fluorescing dye molecules and observed fluorescent emission can be estimated, along with the absolute initial amount of amplicon and the rate parameter for re-annealing. The model is applied to several PCR reactions with known amounts of amplicon and is shown to work reasonably well. An expanded version of the model allows duplication of amplicon without release of fluorescent dye, by adding 1 more parameter to the model. The additional process is helpful in most cases where the initial primer concentration exceeds the initial probe concentration. Software for applying the algorithm to data may be downloaded at <url>http://www.niehs.nih.gov/research/resources/software/pcranalyzer/</url></p> <p>Conclusion</p> <p>We present proof of the principle that a mechanistically based model can be fit to observations from a single PCR amplification. Initial amounts of amplicon are well estimated without using a standard solution. Using the ratio of the predicted initial amounts of amplicon from 2 PCRs is shown to work well even when the absolute amounts of amplicon are underestimated in the individual PCRs.</p

A Mechanistic Model of PCR for Accurate Quantification of Quantitative PCR Data

Background: Quantitative PCR (qPCR) is a workhorse laboratory technique for measuring the concentration of a target DNA sequence with high accuracy over a wide dynamic range. The gold standard method for estimating DNA concentrations via qPCR is quantification cycle (Cq) standard curve quantification, which requires the time- and labor-intensive construction of a Cq standard curve. In theory, the shape of a qPCR data curve can be used to directly quantify DNA concentration by fitting a model to data; however, current empirical model-based quantification methods are not as reliable as Cq standard curve quantification. Principal Findings: We have developed a two-parameter mass action kinetic model of PCR (MAK2) that can be fitted to qPCR data in order to quantify target concentration from a single qPCR assay. To compare the accuracy of MAK2-fitting to other qPCR quantification methods, we have applied quantification methods to qPCR dilution series data generated in three independent laboratories using different target sequences. Quantification accuracy was assessed by analyzing the reliability of concentration predictions for targets at known concentrations. Our results indicate that quantification by MAK2-fitting is as reliable as Cq standard curve quantification for a variety of DNA targets and a wide range of concentrations. Significance: We anticipate that MAK2 quantification will have a profound effect on the way qPCR experiments are designed and analyzed. In particular, MAK2 enables accurate quantification of portable qPCR assays with limited sampl

Toward an Ising Model of Cancer and Beyond

Theoretical and computational tools that can be used in the clinic to predict neoplastic progression and propose individualized optimal treatment strategies to control cancer growth is desired. To develop such a predictive model, one must account for the complex mechanisms involved in tumor growth. Here we review resarch work that we have done toward the development of an "Ising model" of cancer. The review begins with a description of a minimalist four-dimensional (three in space and one in time) cellular automaton (CA) model of cancer in which healthy cells transition between states (proliferative, hypoxic, and necrotic) according to simple local rules and their present states, which can viewed as a stripped-down Ising model of cancer. This model is applied to model the growth of glioblastoma multiforme, the most malignant of brain cancers. This is followed by a discussion of the extension of the model to study the effect on the tumor dynamics and geometry of a mutated subpopulation. A discussion of how tumor growth is affected by chemotherapeutic treatment is then described. How angiogenesis as well as the heterogeneous and confined environment in which a tumor grows is incorporated in the CA model is discussed. The characterization of the level of organization of the invasive network around a solid tumor using spanning trees is subsequently described. Then, we describe open problems and future promising avenues for future research, including the need to develop better molecular-based models that incorporate the true heterogeneous environment over wide range of length and time scales (via imaging data), cell motility, oncogenes, tumor suppressor genes and cell-cell communication. The need to bring to bear the powerful machinery of the theory of heterogeneous media to better understand the behavior of cancer in its microenvironment is presented.Comment: 55 pages, 21 figures and 3 tables. To appear in Physical Biology. Added reference

A new real-time PCR method to overcome significant quantitative inaccuracy due to slight amplification inhibition

<p>Abstract</p> <p>Background</p> <p>Real-time PCR analysis is a sensitive DNA quantification technique that has recently gained considerable attention in biotechnology, microbiology and molecular diagnostics. Although, the cycle-threshold (<it>Ct</it>) method is the present "gold standard", it is far from being a standard assay. Uniform reaction efficiency among samples is the most important assumption of this method. Nevertheless, some authors have reported that it may not be correct and a slight PCR efficiency decrease of about 4% could result in an error of up to 400% using the <it>Ct </it>method. This reaction efficiency decrease may be caused by inhibiting agents used during nucleic acid extraction or copurified from the biological sample.</p> <p>We propose a new method (<it>Cy</it>_<it>0</it>) that does not require the assumption of equal reaction efficiency between unknowns and standard curve.</p> <p>Results</p> <p>The <it>Cy</it>_{<it>0 </it>}method is based on the fit of Richards' equation to real-time PCR data by nonlinear regression in order to obtain the best fit estimators of reaction parameters. Subsequently, these parameters were used to calculate the <it>Cy</it>_{<it>0 </it>}value that minimizes the dependence of its value on PCR kinetic.</p> <p>The <it>Ct</it>, second derivative (<it>Cp</it>), sigmoidal curve fitting method (<it>SCF</it>) and <it>Cy</it>_{<it>0 </it>}methods were compared using two criteria: precision and accuracy. Our results demonstrated that, in optimal amplification conditions, these four methods are equally precise and accurate. However, when PCR efficiency was slightly decreased, diluting amplification mix quantity or adding a biological inhibitor such as IgG, the <it>SCF</it>, <it>Ct </it>and <it>Cp </it>methods were markedly impaired while the <it>Cy</it>_{<it>0 </it>}method gave significantly more accurate and precise results.</p> <p>Conclusion</p> <p>Our results demonstrate that <it>Cy</it>_{<it>0 </it>}represents a significant improvement over the standard methods for obtaining a reliable and precise nucleic acid quantification even in sub-optimal amplification conditions overcoming the underestimation caused by the presence of some PCR inhibitors.</p