Imaging as a (pre)clinical tool in parasitology

Imaging of parasites is central to diagnosis of many parasitic diseases and has thus far played an important role in the development of antiparasitic strategies. The development of novel imaging technologies has revolutionized medicine in fields other than parasitology and has also opened up new avenues for the visualization of parasites. Here we review the role imaging technology has played so far in parasitology and how it may spur further advancement. We point out possibilities to improve current microscopy-based diagnostic methods and how to extend them with radiological imaging modalities. We also highlight in vivo tracking of parasites as a readout for efficacy of new antiparasitic strategies and as a source of fundamental insights for rational design.     

The Galton-Watson process with killing

We investigate general properties of branching processes with killing. These are Galton- Watson processes having the possibility of being terminated with a probability depending on the size of the current generation. A special case has arisen in problems of detecting particular genotypes, where the probability of termination is 1?α^j when the current generation number is j. We show that the analysis of this case can be carried out using known results about the total progeny in branching processes.     

The supercritical p-dimensional Galton-Watson process with immigration

A supercritical multidimensional Galton-Watson process with immigration is investigated. A simpler and more natural proof is given for the standard limit theorem for such processes. The limit random variable is also shown to be absolutely continuous which is a sharpening of the existing result. The assumptions on the immigration distribution are also investigated.     

The dynamics of gene amplification described as a multitype compartmental model and as a branching process.

The present work is aimed at developing the mathematical tools by which the dynamics of gene amplification (GA) can be described in detail. Some discrete compartmental models of GA by disproportionate replication and a general model for other putative GA mechanisms are presented and analyzed. The dynamical distribution of gene copy number in the cell population is calculated with the loss of cells taken either as constant or as copy-number-dependent. Our analysis shows that for a one-copy GA process with constant loss of cells, the relative frequency of single-gene-copy cells (sensitive cells) converges to zero, with the rate of convergence depending on the amplification probability. In contrast, for a one-copy GA process with copy-number-dependent loss of cells, the relative frequency of single-copy cells is bounded, implying a bounded compartment of many-gene-copy cells. Using branching processes theory we calculate the dynamical distribution of the single-gene-copy compartment as well as its extinction probability. Our models are used for estimating treatment prognosis as affected by drug resistance due to GA, showing significant differences in prognosis resulting from small changes in drug dose.     

Real-time quantitative PCR in parasitology

Standard techniques for counting parasites are often time-consuming, difficult and inaccurate, and occasionally unpleasant. Real-time quantitative polymerase chain reaction has recently been applied to parasitology, specifically Plasmodium, Toxoplasma, Leishmania and Neospora. These techniques are truly quantitative, give results over a range of 6-7 orders of magnitude, are quick to perform and require no manipulations post-amplification. They can be used to count genome numbers and to study levels of gene expression. The advantages and limitations of existing thermocyclers and applicable detection systems are discussed here, and promising new developments are highlighted.     

Geographical distribution of a neutral allele considered as a branching process

The limiting spacial correlations are derived for a population of neutral alleles migrating among K colonies. The allelic population is modeled as a subcritical branching process and the limiting correlations are obtained conditional on nonextinction of the population.     

The normalized slope conductance as a tool for quantitative analysis of current-voltage relations

The patch-clamp method, which was awarded the Nobel Prize in 1991, is a well-established and indispensable method to study ion channels in living cells and to biophysically characterize non-voltage-gated ion channels, which comprise about 70% of all ion channels in the human genome. To investigate the biophysical properties of non-voltage-gated ion channels, whole-cell measurements with application of continuous voltage ramps are routinely conducted to obtain current-voltage (IV) relationships. However, adequate tools for detailed and quantitative analysis of IV curves are still missing. We use the example of the transient receptor potential classical (TRPC) channel family to elucidate whether the normalized slope conductance (NSC) is an appropriate tool for reliable discrimination of the IV curves of diverse TRPC channels that differ in their individual curve progression. We provide a robust calculation method for the NSC, and, by applying this method, we find that TRPC channel activators and modulators can evoke different NSC progressions independent from their expression levels, which points to distinguishable active channel states. TRPC6 mutations in patients with focal segmental glomerulosclerosis resulted in distinct NSC progressions, suggesting that the NSC is suitable for investigating structure-function relations and might help unravel the unknown pathomechanisms leading to focal segmental glomerulosclerosis. The NSC is an effective algorithm for extended biophysical characterization of non-voltage-gated ion channels.     

DNase I digestion as a tool for the quantitative evaluation of C-heterochromatic-DNA in situ.

The amount of DNA resisting the C-banding pre-treatments (C-heterochromatic-DNA) was found to account for the interspecific differences of genome size in different Primate groups. The evaluation of this parameter is therefore of great interest in cytotaxonomy. In this work, DNase I digestion was used instead of the pre-treatments C-banding, in an attempt to set up a suitable method for the quantitative evaluation of C-heterochromatic-DNA in both metaphase chromosomes and interphase chromatin. In fact DNase I is known to preferentially digest "active or potentially active" chromatin, and the highly repetitive and inactive DNA in C-heterochromatin should characteristically resist DNase I cleavage. As a model system, differently fixed mouse splenocytes were treated with DNase I for various times, and the digestion was monitored by flow cytometry after propidium iodide staining. In addition, mouse metaphase preparations from lymphocyte cultures were also digested with DNase I, and the amount of residual DNA was evaluated by static microfluorometry. Under controlled conditions of fixation, enzyme concentration, time and temperature, the same limit-digest can be obtained in both interphase nuclei and metaphases, which corresponds to the amount of residual DNA after C-banding and has a C-banding-like pattern in chromosomes.     

On a modified Markov branching process

We modify a Markov branching process such that each particle produces offspring only if its life length is greater than T. We find exact expressions for the mean number of particles at time t.     

Modelling the lineage of a growing population as an age-dependent branching process

A new model for population growth as a branching process is described. It requires knowledge of the population's age-specific survivorship and fecundity curves. The total population size at any time is calculated by summing across all branches of the tree representing the population's lineage and thus the model also allows the lineage of the developing population to be traced. Use of the model is demonstrated by a hypothetical example. The model could be of particular value in tracing the phylogenetic development of populations and/or species.     

First passage time for a supercritical Galton-Watson process restricted to the non-extinction set

In the present paper we obtain the probability distribution and the first two moments, of the number of generations required by a supercritical branching process to cross for the first time a given population size, when it is restricted to the non-extinction set.     

On a stochastic integral of a branching process

This paper is concerned with the properties of a stochastic integral which arises in the study of a modified Markov branching process. Explicit expressions are found for the mean and the limit distribution of the integral.     

A biological and computational model of megakaryocyte development as a stochastic branching process

The purpose of this paper is to describe a model of megakaryocytopoiesis as a branching process with stochastic processes regulating critical control points of differentiation along the stem cell megakaryocyte platelet axis. Progress of cells through these critical control points are regulated by transitional probabilities, which in turn are regulated by influences such as growth factors. The critical control points include transition of resting megakaryocytic stem cells (CFU-meg) into proliferating stem cells, the cessation of cytokinesis, and the cessation of DNA synthesis. A computerized computational method has been developed for directly fitting the stochastic branching model to colony growth data. The computational model has allowed transitional probabilities to be derived from colony size data. The model provides a unifying explanation for much of the heterogeneity of stages of maturation within populations of megakaryocytes and is fully compatible with historical data supporting the stochastic nature of hematopoietic stem cell regulation and with modern molecular concepts about control of the cell cycle.     

The allele distribution in next-generation sequencing data sets is accurately described as the result of a stochastic branching process

With the availability of next-generation sequencing (NGS) technology, it is expected that sequence variants may be called on a genomic scale. Here, we demonstrate that a deeper understanding of the distribution of the variant call frequencies at heterozygous loci in NGS data sets is a prerequisite for sensitive variant detection. We model the crucial steps in an NGS protocol as a stochastic branching process and derive a mathematical framework for the expected distribution of alleles at heterozygous loci before measurement that is sequencing. We confirm our theoretical results by analyzing technical replicates of human exome data and demonstrate that the variance of allele frequencies at heterozygous loci is higher than expected by a simple binomial distribution. Due to this high variance, mutation callers relying on binomial distributed priors are less sensitive for heterozygous variants that deviate strongly from the expected mean frequency. Our results also indicate that error rates can be reduced to a greater degree by technical replicates than by increasing sequencing depth.     

Medical image processing as a necessary tool for a medical diagnostic process

The authors provide a rationale for mathematically processing medical images for the progression of a medical diagnostic process. The tools made by the real-time conveyor 2D processing and visualization technology are proposed for work with medical images. The results of conveyor 2D processing of medical images as graphical presentations are given.