A nonlinear model of cell interaction with an acoustic field.

A theoretical and experimental nonlinear analysis of cellular response/displacement to ultrasound excitations is presented. Linear cell models can predict the resonant frequency (fR∼5MHz), but only a nonlinear analysis can reveal the amount of mechanical energy that couples into the cell and the bifurcation behavior of the cell when it is excited near resonance. The cell dynamics is described by the nonlinear viscoelastic constitutive behavior of the cytoplasm, nucleus and their respective membranes, in the presence of a fluid with an oscillating pressure field. The method of multiple scales is used to derive the amplitude of oscillation of the cytoplasm and nucleus as a function of frequency. A major finding is the existence of multiple solutions for a range of sub-resonant frequencies. At positive detuning (f>fR), the mechanical energy that couples into the cell is small, it is higher at resonance but significantly higher at sub-resonant frequencies in the multiplicity range. Experimentally it was shown when 3.5MHz is approached sub- and supra-resonance and 6.5MHz is approached sub-resonance, gene expression was statistically higher than that when stimulated directly. Thus, there exists an optimal range of frequencies for ultrasound treatment - in the region of multiplicity where deformation and thus mechanical energy coupling is maximized. The ultrasound protocol must be designed to operate at the solution associated with the higher mechanical energy - thus the start-up conditions should be in the domain of attraction of the high energy solution.

Modeling nanoparticle delivery of TB drugs to granulomas.

Tuberculosis, which typically presents as a pulmonary disease, has a complex pathology. The primary site of infection, the Ghon focus, recruits immune cells and a granuloma forms. At earlier stages the granuloma is still vascularized, offering the best opportunity for drug treatment. In the more progressive state blood flow is reduced and a distinct caseous structure develops. Effective delivery of drugs to bacilli in the core of the granuloma becomes very difficult. It is perceivable that granuloma cores could create conditions where bacilli persist and develop resistance. In this study we analyze drug delivery to granulomas by means of a nanoparticle delivery system. The model consists of two parts; the overall distribution of the nanoparticles is described by a simple circulatory model and this result is used in the second part, focusing on transport in a capillary lined with macrophages. Nanoparticles enter the macrophages where they are metabolized and the drugs are released. The model reveals significant differences in drug concentrations between the plasma and macrophages. Based on the results of the model, strategies for improved drug delivery are proposed.

A state-time epidemiology model of tuberculosis: importance of re-infection.

An epidemiological model is presented that considers five possible states of a population: susceptible (S), exposed (W), infectious (Y), in treatment (Z) and recovered (R). In certain instances transition rates (from one state to another) depend on the time spent in the state; therefore the states W, Y and Z depend on time and length of stay in that state - similar to age-structured models. The model is particularly amenable to describe delays of exposed persons to become infectious and re-infection of exposed persons. Other transitions that depend on state time include the case finding and diagnosis, increased death rate and treatment interruption. The mathematical model comprises of a set of partial differential and ordinary differential equations. Non-steady state solutions are first presented, followed by a bifurcation study of the stationary states.

A fundamental study of the PCR amplification of GC-rich DNA templates.

A theoretical analysis is presented with experimental confirmation to conclusively demonstrate the critical role that annealing plays in efficient PCR amplification of GC-rich templates. The analysis is focused on the annealing of primers at alternative binding sites (competitive annealing) and the main result is a quantitative expression of the efficiency (eta) of annealing as a function of temperature (T(A)), annealing period (t(A)), and template composition. The optimal efficiency lies in a narrow region of T(A) and t(A) for GC-rich templates and a much broader region for normal GC templates. To confirm the theoretical findings, the following genes have been PCR amplified from human cDNA template: ARX and HBB (with 78.72% and 52.99% GC, respectively). Theoretical results are in excellent agreement with the experimental findings. Optimum annealing times for GC-rich genes lie in the range of 3-6s and depend on annealing temperature. Annealing times greater than 10s yield smeared PCR amplified products. The non-GC-rich gene did not exhibit this sensitivity to annealing times. Theory and experimental results show that shorter annealing times are not only sufficient but can actually aid in more efficient PCR amplification of GC-rich templates.

A quantitative model of error accumulation during PCR amplification.

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 study a quantitative model of error 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 function as well as the reaction conditions; specifically the temperature and the dNTP pool composition. Thermally induced errors stem mostly from three sources: A+G depurination, oxidative damage of guanine to 8-oxoG and cytosine deamination to uracil. The post-PCR modifications of sequences are primarily due to exposure of nucleic acids to elevated temperatures, especially 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 management of the PCR process.