Harmonic moments of non homogeneous branching processes

We study the harmonic moments of Galton-Watson processes, possibly non homogeneous, with positive values. Good estimates of these are needed to compute unbiased estimators for non canonical branching Markov processes, which occur, for instance, in the modeling of the polymerase chain reaction. By convexity, the ratio of the harmonic mean to the mean is at most 1. We prove that, for every square integrable branching mechanisms, this ratio lies between 1-A/k and 1-B/k for every initial population of size k greater than A. The positive constants A and B, such that B is at most A, are explicit and depend only on the generation-by-generation branching mechanisms. In particular, we do not use the distribution of the limit of the classical martingale associated to the Galton-Watson process. Thus, emphasis is put on non asymptotic bounds and on the dependence of the harmonic mean upon the size of the initial population. In the Bernoulli case, which is relevant for the modeling of the polymerase chain reaction, we prove essentially optimal bounds that are valid for every initial population. Finally, in the general case and for large enough initial populations, similar techniques yield sharp estimates of the harmonic moments of higher degrees

Design of an innovative polymerase chain reaction device based on buoyancy driven flow

This paper was presented at the 2nd Micro and Nano Flows Conference (MNF2009), which was held at Brunel University, West London, UK. The conference was organised by Brunel University and supported by the Institution of Mechanical Engineers, IPEM, the Italian Union of Thermofluid dynamics, the Process Intensification Network, HEXAG - the Heat Exchange Action Group and the Institute of Mathematics and its Applications.Polymerase Chain Reaction (PCR) plays a central role in the field of molecular biology. The miniaturization of PCR systems is promising as it potentially minimizes costly reagent consumption and time required for analysis. In PCR microdevices a sample solution is usually handled by external pumps. An alternative solution relies on temperature-induced density difference in the presence of a body force to induce buoyancy driven flow. This alternative method is easy to be used and does not require expensive setup, but, to date, the thermo-fluid-dynamic field in the micro-channels still needs to be optimized. The present study focuses on the design of micro-channels, having innovative and optimized shapes to obtain proper fluid actuation and DNA sample amplification within buoyancy driven flow PCR devices. A parametric study is carried out by means of computational thermal fluid dynamic modeling: several channel geometry configurations were compared in terms of time required for analysis, temperature distribution and priming volume. The advantages and disadvantages of such configurations are discussed

Computational Investigations on Polymerase Actions in Gene Transcription and Replication Combining Physical Modeling and Atomistic Simulations

Polymerases are protein enzymes that move along nucleic acid chains and catalyze template-based polymerization reactions during gene transcription and replication. The polymerases also substantially improve transcription or replication fidelity through the non-equilibrium enzymatic cycles. We briefly review computational efforts that have been made toward understanding mechano-chemical coupling and fidelity control mechanisms of the polymerase elongation. The polymerases are regarded as molecular information motors during the elongation process. It requires a full spectrum of computational approaches from multiple time and length scales to understand the full polymerase functional cycle. We keep away from quantum mechanics based approaches to the polymerase catalysis due to abundant former surveys, while address only statistical physics modeling approach and all-atom molecular dynamics simulation approach. We organize this review around our own modeling and simulation practices on a single-subunit T7 RNA polymerase, and summarize commensurate studies on structurally similar DNA polymerases. For multi-subunit RNA polymerases that have been intensively studied in recent years, we leave detailed discussions on the simulation achievements to other computational chemical surveys, while only introduce very recently published representative studies, including our own preliminary work on structure-based modeling on yeast RNA polymerase II. In the end, we quickly go through kinetic modeling on elongation pauses and backtracking activities. We emphasize the fluctuation and control mechanisms of the polymerase actions, highlight the non-equilibrium physical nature of the system, and try to bring some perspectives toward understanding replication and transcription regulation from single molecular details to a genome-wide scale

Simulation of between repeat variability in real time PCR reactions

While many decisions rely on real time quantitative PCR (qPCR) analysis few attempts have hitherto been made to quantify bounds of precision accounting for the various sources of variation involved in the measurement process. Besides influences of more obvious factors such as camera noise and pipetting variation, changing efficiencies within and between reactions affect PCR results to a degree which is not fully recognized. Here, we develop a statistical framework that models measurement error and other sources of variation as they contribute to fluorescence observations during the amplification process and to derived parameter estimates. Evaluation of reproducibility is then based on simulations capable of generating realistic variation patterns. To this end, we start from a relatively simple statistical model for the evolution of efficiency in a single PCR reaction and introduce additional error components, one at a time, to arrive at stochastic data generation capable of simulating the variation patterns witnessed in repeated reactions (technical repeats). Most of the variation in C-q values was adequately captured by the statistical model in terms of foreseen components. To recreate the dispersion of the repeats' plateau levels while keeping the other aspects of the PCR curves within realistic bounds, additional sources of reagent consumption (side reactions) enter into the model. Once an adequate data generating model is available, simulations can serve to evaluate various aspects of PCR under the assumptions of the model and beyond

Infectiousness in a Cohort of Brazilian Dogs: Why Culling Fails to Control Visceral Leishmaniasis in Areas of High Transmission

The elimination of seropositive dogs in Brazil has been used to control zoonotic visceral leishmaniasis but with little success. To elucidate the reasons for this, the infectiousness of 50 sentinel dogs exposed to natural Leishmania chagasi infection was assessed through time by xenodiagnosis with the sandfly vector, Lutzomyia longipalpis. Eighteen (43%) of 42 infected dogs became infectious after a median of 333 days in the field (105 days after seroconversion). Seven highly infectious dogs (17%) accounted for >80% of sandfly infections. There were positive correlations between infectiousness and anti-Leishmania immunoglobulin G, parasite detection by polymerase chain reaction, and clinical disease (logistic regression, r2 = 0.080.18). The sensitivity of enzyme-linked immunosorbent assay to detect currently infectious dogs was high (96%) but lower in the latent period (<63%), and specificity was low (24%). Mathematical modeling suggests that culling programs fail because of high incidence of infection and infectiousness, the insensitivity of the diagnostic test to detect infectious dogs, and time delays between diagnosis and culling

A combined computational-experimental approach to define the structural origin of antibody recognition of sialyl-Tn, a tumor-associated carbohydrate antigen.

Anti-carbohydrate monoclonal antibodies (mAbs) hold great promise as cancer therapeutics and diagnostics. However, their specificity can be mixed, and detailed characterization is problematic, because antibody-glycan complexes are challenging to crystallize. Here, we developed a generalizable approach employing high-throughput techniques for characterizing the structure and specificity of such mAbs, and applied it to the mAb TKH2 developed against the tumor-associated carbohydrate antigen sialyl-Tn (STn). The mAb specificity was defined by apparent KD values determined by quantitative glycan microarray screening. Key residues in the antibody combining site were identified by site-directed mutagenesis, and the glycan-antigen contact surface was defined using saturation transfer difference NMR (STD-NMR). These features were then employed as metrics for selecting the optimal 3D-model of the antibody-glycan complex, out of thousands plausible options generated by automated docking and molecular dynamics simulation. STn-specificity was further validated by computationally screening of the selected&nbsp;antibody 3D-model against the human sialyl-Tn-glycome. This computational-experimental approach would allow rational design of potent antibodies targeting carbohydrates

Enhanced analysis of real-time PCR data by using a variable efficiency model : FPK-PCR

Current methodology in real-time Polymerase chain reaction (PCR) analysis performs well provided PCR efficiency remains constant over reactions. Yet, small changes in efficiency can lead to large quantification errors. Particularly in biological samples, the possible presence of inhibitors forms a challenge. We present a new approach to single reaction efficiency calculation, called Full Process Kinetics-PCR (FPK-PCR). It combines a kinetically more realistic model with flexible adaptation to the full range of data. By reconstructing the entire chain of cycle efficiencies, rather than restricting the focus on a 'window of application', one extracts additional information and loses a level of arbitrariness. The maximal efficiency estimates returned by the model are comparable in accuracy and precision to both the golden standard of serial dilution and other single reaction efficiency methods. The cycle-to-cycle changes in efficiency, as described by the FPK-PCR procedure, stay considerably closer to the data than those from other S-shaped models. The assessment of individual cycle efficiencies returns more information than other single efficiency methods. It allows in-depth interpretation of real-time PCR data and reconstruction of the fluorescence data, providing quality control. Finally, by implementing a global efficiency model, reproducibility is improved as the selection of a window of application is avoided

Continuous Flow vs. Static Chamber μPCR Devices on Flexible Polymeric Substrates

This paper was presented at the 4th Micro and Nano Flows Conference (MNF2014), which was held at University College, London, UK. The conference was organised by Brunel University and supported by the Italian Union of Thermofluiddynamics, IPEM, the Process Intensification Network, the Institution of Mechanical Engineers, the Heat Transfer Society, HEXAG - the Heat Exchange Action Group, and the Energy Institute, ASME Press, LCN London Centre for Nanotechnology, UCL University College London, UCL Engineering, the International NanoScience Community, www.nanopaprika.eu.Two types of μPCR devices, a continuous flow and a static chamber device, fabricated on flexible polymeric substrates are compared in the current computational study. Laminar flow, heat transfer in both solid and fluid, mass conservation of species, and reaction kinetics of PCR are coupled using COMSOL. The comparison is performed under same conditions; same material stack (based on flexible polymeric films with integrated microheaters), same species initial concentrations, amplification of the same volume of fluid sample, and implementation of the same PCR protocol. Performance is quantified in terms of DNA amplification, energy consumption, and total operating time. The calculations show that the efficiency of DNA amplification is higher in the continuous flow device. However, the continuous flow device requires (~6 times) greater energy consumption which is justified by the smaller thermal mass of the static chamber device. As regards the speed, the total time required for the static chamber μPCR is comparable to the time for the continuous flow μPCR

Functional interplay between NTP leaving group and base pair recognition during RNA polymerase II nucleotide incorporation revealed by methylene substitution.

RNA polymerase II (pol II) utilizes a complex interaction network to select and incorporate correct nucleoside triphosphate (NTP) substrates with high efficiency and fidelity. Our previous 'synthetic nucleic acid substitution' strategy has been successfully applied in dissecting the function of nucleic acid moieties in pol II transcription. However, how the triphosphate moiety of substrate influences the rate of P-O bond cleavage and formation during nucleotide incorporation is still unclear. Here, by employing β,γ-bridging atom-'substituted' NTPs, we elucidate how the methylene substitution in the pyrophosphate leaving group affects cognate and non-cognate nucleotide incorporation. Intriguingly, the effect of the β,γ-methylene substitution on the non-cognate UTP/dT scaffold (∼3-fold decrease in kpol) is significantly different from that of the cognate ATP/dT scaffold (∼130-fold decrease in kpol). Removal of the wobble hydrogen bonds in U:dT recovers a strong response to methylene substitution of UTP. Our kinetic and modeling studies are consistent with a unique altered transition state for bond formation and cleavage for UTP/dT incorporation compared with ATP/dT incorporation. Collectively, our data reveals the functional interplay between NTP triphosphate moiety and base pair hydrogen bonding recognition during nucleotide incorporation