Mathematical modeling of pathogen trajectory in a patient care environment.

OBJECTIVE: Minimizing healthcare worker exposure to airborne infectious pathogens is an important infection control practice. This study utilized mathematical modeling to evaluate the trajectories and subsequent concentrations of particles following a simulated release in a patient care room. DESIGN: Observational study. SETTING: Biocontainment unit patient care room at a university-affiliated tertiary care medical center. METHODS: Quantitative mathematical modeling of airflow in a patient care room was achieved using a computational fluid dynamics software package. Models were created on the basis of a release of particles from various locations in the room. Computerized particle trajectories were presented in time-lapse fashion over a blueprint of the room. A series of smoke tests were conducted to visually validate the model. RESULTS: Most particles released from the head of the bed initially rose to the ceiling and then spread across the ceiling and throughout the room. The highest particle concentrations were observed at the head of the bed nearest to the air return vent, and the lowest concentrations were observed at the foot of the bed. CONCLUSIONS: Mathematical modeling provides clinically relevant data on the potential exposure risk in patient care rooms and is applicable in multiple healthcare delivery settings. The information obtained through mathematical modeling could potentially serve as an infection control modality to enhance the protection of healthcare workers.

A new rapid method for Clostridium difficile DNA extraction and detection in stool: toward point-of-care diagnostic testing.

We describe a new method for the rapid diagnosis of Clostridium difficile infection, with stool sample preparation and DNA extraction by heat and physical disruption in a single-use lysis microreactor (LMR), followed by a rapid PCR amplification step. All steps can be accomplished in <20 minutes overall. Gel electrophoresis is currently used to detect the amplification product, pending real-time availability with an ultra-rapid thermocycler. Compared with the dual enzyme immunoassay (EIA) screening test (C. diff Quik Chek Complete; Techlab, Blacksburg, VA), the novel LMR/PCR assay showed complete concordance with all glutamate dehydrogenase (GDH) results (GDH(+)/toxin(+), n = 48; GDH(-)/toxin(-), n = 81). All 69 stool samples with discordant EIA results (GDH(+)/toxin(-)) were tested by both the LMR/PCR assay and the loop-mediated isothermal amplification test (LAMP) (Illumigene C. difficile; Meridian Bioscience, Cincinnati, OH). In 64/69 EIA-discordant samples, LAMP and LMR/PCR results matched (both positive in 29 sample and both negative in 35 samples); in the remaining 5 samples, results were discrepant between the LAMP assay (all five negative) and the LMR/PCR assay (all 5 positive). Overall, LMR/PCR testing matched the current algorithm of EIA and/or LAMP reflex testing in 193/198 (97.5%) samples. The present proof-of-concept study suggests that the novel LMR/PCR technique described here may be developed as an inexpensive, rapid, and reliable point-of-care diagnostic test for C. difficile infection and other infectious diseases.

Experimental Validation of a Fundamental Model for PCR Efficiency.

Recently a theoretical analysis of PCR efficiency has been published by Booth et al., (2010). The PCR yield is the product of three efficiencies: (i) the annealing efficiency is the fraction of templates that form binary complexes with primers during annealing, (ii)the polymerase binding efficiency is the fraction of binary complexes that bind to polymerase to form ternary complexes and (iii)the elongation efficiency is the fraction of ternary complexes that extend fully. Yield is controlled by the smallest of the three efficiencies and control could shift from one type of efficiency to another over the course of a PCR experiment. Experiments have been designed that are specifically controlled by each one of the efficiencies and the results are consistent with the mathematical model. The experimental data has also been used to quantify six key parameters of the theoretical model. An important application of the fully characterized model is to calculate initial template concentration from real-time PCR data. Given the PCR protocol, the midpoint cycle number (where the template concentration is half that of the final concentration) can be theoretically determined and graphed for a variety of initial DNA concentrations. Real-time results can be used to calculate the midpoint cycle number and consequently the initial DNA concentration, using this graph. The application becomes particularly simple if a conservative PCR protocol is followed where only the annealing efficiency is controlling.

A model of tuberculosis transmission and intervention strategies in an urban residential area.

The model herein aims to explore the dynamics of the spread of tuberculosis (TB) in an informal settlement or township. The population is divided into households of various sizes and also based on commuting status. The model dynamics distinguishes between three distinct social patterns: the exposure of commuters during travel, random diurnal interaction and familial exposure at night. Following the general SLIR models, the population is further segmented into susceptible (S), exposed/latently infected (L), active/infectious (I), and recovered (R) individuals. During the daytime, commuters travel on public transport, while non-commuters randomly interact in the community to mimic chance encounters with infectious persons. At night, each family interacts and sleeps together in the home. The risk of exposure to TB is based on the proximity, duration, and frequency of encounters with infectious persons. The model is applied to a hypothetical population to explore the effects of different intervention strategies including vaccination, wearing of masks during the commute, prophylactic treatment of latent infections and more effective case-finding and treatment. The most important findings of the model are: (1) members of larger families are responsible for more disease transmissions than those from smaller families, (2) daily commutes on public transport provide ideal conditions for transmission of the disease, (3) improved diagnosis and treatment has the greatest impact on the spread of the disease, and (4) detecting TB at the first clinic visit, when patients are still smear negative, is key.

Automated two-column purification of iminobiotin and BrdU-labeled PCR products for rapid cloning: application to genes synthesized by polymerase chain assembly.

Polymerase chain assembly (PCA) is a powerful tool for basic biological research and biotechnology applications. During the last several years, major advances have been made in de novo gene synthesis. However, there is still a need for fast and reproducible methods to automatically purify the synthesized genes. Upon completion of PCA, the subsequent PCR-amplified product mixture still contains undesired shorter DNA fragments that hinder cloning efforts. To avoid tedious gel purification, an automated two-column purification has been developed and used in conjunction with rapid PCA. The system enables fast synthesis and isolation of the full-length DNA of interest, important for facile cloning of desired DNA fragments. During the PCR amplification step, forward and reverse primers tagged with iminobiotin and bromodeoxyuridine labels, respectively, were used. The automated purification was then performed on the PCR mixture using two affinity/immunocapture columns in series to isolate only the desired full-length product. The procedure has been applied to the pUC19 beta-lactamase gene (929 bp). Follow-up PCR of the purified product, cloning, and sequencing demonstrated the technique's effectiveness in obtaining the pure full-length gene. The purification has also been performed on other synthesized genes, indicating its utility as a general approach.

Efficiency of the Polymerase Chain Reaction.

The polymerase chain reaction (PCR) has found wide application in biochemistry and molecular biology such as gene expression studies, mutation detection, forensic analysis and pathogen detection. Increasingly quantitative real time PCR is used to assess copy numbers from overall yield. In this study the yield is analyzed as a function of several processes: (1) thermal damage of the template and polymerase occurs during the denaturing step, (2) competition exists between primers and templates to either anneal or form dsDNA, (3) polymerase binding to annealed products (primer/ssDNA) to form ternary complexes and (4) extension of ternary complexes. Explicit expressions are provided for the efficiency of each process, therefore reaction conditions can be directly linked to the overall yield. Examples are provided where different processes play the yield-limiting role. The analysis will give researchers a unique understanding of the factors that control the reaction and will aid in the interpretation of experimental results.

Gene synthesis by integrated polymerase chain assembly and PCR amplification using a high-speed thermocycler.

Polymerase chain assembly (PCA) is a technique used to synthesize genes ranging from a few hundred base pairs to many kilobase pairs in length. In traditional PCA, equimolar concentrations of single stranded DNA oligonucleotides are repeatedly hybridized and extended by a polymerase enzyme into longer dsDNA constructs, with relatively few full-length sequences being assembled. Thus, traditional PCA is followed by a second primer-mediated PCR reaction to amplify the desired full-length sequence to useful, detectable quantities. Integration of assembly and primer-mediated amplification steps into a single reaction using a high-speed thermocycler is shown to produce similar results. For the integrated technique, the effects of oligo concentration, primer concentration, and number of oligonucleotides are explored. The technique is successfully demonstrated for the synthesis of two genes encoding EPCR-1 (653bp) and pUC19 beta-lactamase (929bp) in under 20min. However, rapid integrated PCA-PCR was found to be problematic when attempted with the TM-1 gene (1509bp). Partial oligonucleotide sets of TM-1 could be assembled and amplified simultaneously, indicating that the technique may be limited to a maximum number of oligonucleotides due to competitive annealing and competition for primers.

A model of the complex response of Staphylococcus aureus to methicillin.

It is widely accepted that beta-lactam antimicrobials cause cell death through a mechanism that interferes with cell wall synthesis. Later studies have also revealed that beta-lactams modify the autolysis function (the natural process of self-exfoliation of the cell wall) of cells. The dynamic equilibrium between growth and autolysis is perturbed by the presence of the antimicrobial. Studies with Staphylococcus aureus to determine the minimum inhibitory concentration (MIC) have revealed complex responses to methicillin exposure. The organism exhibits four qualitatively different responses: homogeneous sensitivity, homogeneous resistance, heterogeneous resistance and the so-called 'Eagle-effect'. A mathematical model is presented that links antimicrobial action on the molecular level with the overall response of the cell population to antimicrobial exposure. The cell population is modeled as a probability density function F(x,t) that depends on cell wall thickness x and time t. The function F(x,t) is the solution to a Fokker-Planck equation. The fixed point solutions are perturbed by the antimicrobial load and the advection of F(x,t) depends on the rates of cell wall synthesis, autolysis and the antimicrobial concentration. Solutions of the Fokker-Planck model are presented for all four qualitative responses of S. aureus to methicillin exposure.

Principles of rapid polymerase chain reactions: mathematical modeling and experimental verification.

Polymerase chain reaction (PCR) is an important diagnostic tool for the amplification of DNA. The PCR process can be treated as a problem in biochemical engineering. This study focuses on the development of a mathematical model of the polymerase chain reaction. The PCR process consists of three steps: denaturation of target DNA, annealing of sequence-specific oligonucleotide primers and the enzyme-catalyzed elongation of the annealed complex (primer:DNA:polymerase). The denaturation step separates the double strands of DNA; this model assumes denaturation is complete. The annealing step describes the formation of a primer-fragment complex followed by the attachment of the polymerase to form a ternary complex. This step is complicated by competitive annealing between primers and incomplete fragments including primer-primer reactions. The elongation step is modeled by a stochastic method. Species that compete during the elongation step are deoxynucleotide triphosphates dCTP, dATP, dTTP, dGTP, dUTP, and pyrophosphate. Thermal deamination of dCTP to form dUTP is included in the model. The probability for a species to arrive at the active site is based on its molar fraction. The number of random insertion events depends on the average processing speed of the polymerase and the elongation time of the simulation. The numerical stochastic experiment is repeated a sufficient number of times to construct a probability density distribution (PDF). The moment of the PDF and the annealing step products provide the product distribution at the end of the elongation step. The overall yield is compared to six experimental values of the yield. In all cases the comparisons are very good.