On random polynomials over finite fields

We consider random monic polynomials of degree n over a finite field of q elements, chosen with all qn possibilities equally likely, factored into monic irreducible factors. More generally, relaxing the restriction that q be a prime power, we consider that multiset construction in which the total number of possibilities of weight n is qn. We establish various approximations for the joint distribution of factors, by giving upper bounds on the total variation distance to simpler discrete distributions. For example, the counts for particular factors are approximately independent and geometrically distributed, and the counts for all factors of sizes 1, 2, ..., b, where b = O(n/log n), are approximated by independent negative binomial random variables. As another example, the joint distribution of the large factors is close to the joint distribution of the large cycles in a random permutation. We show how these discrete approximations imply a Brownian motion functional central limit theorem and a Poisson-Dirichiet limit theorem, together with appropriate error estimates. We also give Poisson approximations, with error bounds, for the distribution of the total number of factor

Simulating the component counts of combinatorial structures.

This article describes and compares methods for simulating the component counts of random logarithmic combinatorial structures such as permutations and mappings. We exploit the Feller coupling for simulating permutations to provide a very fast method for simulating logarithmic assemblies more generally. For logarithmic multisets and selections, this approach is replaced by an acceptance/rejection method based on a particular conditioning relationship that represents the distribution of the combinatorial structure as that of independent random variables conditioned on a weighted sum. We show how to improve its acceptance rate. We illustrate the method by estimating the probability that a random mapping has no repeated component sizes, and establish the asymptotic distribution of the difference between the number of components and the number of distinct component sizes for a very general class of logarithmic structures.ADB acknowledges support from ARC grants DP150101459 and DP150103588

Effects of tyrosine kinase inhibitors on protein kinase-independent systems

AbstractTyrosine kinase inhibitors have been widely used to probe the role of tyrosine phosphorylation in cellular signalling. These inhibitors exhibit an apparent specificity for tyrosine kinases over the serine/threonine kinases but little is known about their effects on other enzymes or biological systems. We demonstrate that genistein, erbstatin and α-cyanoeinnamamides (tyrphostins) have inhibitory effects on fatty acid synthesis, lactate transport, mitochondrial oxidative phosphorylation and aldehyde dehydrogenase. We propose, therefore, that results obtained using tyrosine kinase inhibitors should be interpreted with caution, particularly if used at concentrations sufficient to inhibit these non-protein kinase-dependent events

Monitoring of In Vivo Function of Superparamagnetic Iron Oxide Labelled Murine Dendritic Cells during Anti-Tumour Vaccination

Dendritic cells (DCs) generated in vitro to present tumour antigens have been injected in cancer patients to boost in vivo anti-tumour immune responses. This approach to cancer immunotherapy has had limited success. For anti-tumour therapy, delivery and subsequent migration of DCs to lymph nodes leading to effective stimulation of effector T cells is thought to be essential. The ability to non-invasively monitor the fate of adoptively transferred DCs in vivo using magnetic resonance imaging (MRI) is an important clinical tool to correlate their in vivo behavior with response to treatment. Previous reports of superparamagnetic iron oxides (SPIOs) labelling of different cell types, including DCs, have indicated varying detrimental effects on cell viability, migration, differentiation and immune function. Here we describe an optimised labelling procedure using a short incubation time and low concentration of clinically used SPIO Endorem to successfully track murine DC migration in vivo using MRI in a mouse tumour model. First, intracellular labelling of bone marrow derived DCs was monitored in vitro using electron microscopy and MRI relaxometry. Second, the in vitro characterisation of SPIO labelled DCs demonstrated that viability, phenotype and functions were comparable to unlabelled DCs. Third, ex vivo SPIO labelled DCs, when injected subcutaneously, allowed for the longitudinal monitoring by MR imaging of their migration in vivo. Fourth, the SPIO DCs induced the proliferation of adoptively transferred CD4+ T cells but, most importantly, they primed cytotoxic CD8+ T cell responses to protect against a B16-Ova tumour challenge. Finally, using anatomical information from the MR images, the immigration of DCs was confirmed by the increase in lymph node size post-DC injection. These results demonstrate that the SPIO labelling protocol developed in this study is not detrimental for DC function in vitro and in vivo has potential clinical application in monitoring therapeutic DCs in patients with cancer

In Vivo SPECT Reporter Gene Imaging of Regulatory T Cells

Regulatory T cells (Tregs) were identified several years ago and are key in controlling autoimmune diseases and limiting immune responses to foreign antigens, including alloantigens. In vivo imaging techniques including intravital microscopy as well as whole body imaging using bioluminescence probes have contributed to the understanding of in vivo Treg function, their mechanisms of action and target cells. Imaging of the human sodium/iodide symporter via Single Photon Emission Computed Tomography (SPECT) has been used to image various cell types in vivo. It has several advantages over the aforementioned imaging techniques including high sensitivity, it allows non-invasive whole body studies of viable cell migration and localisation of cells over time and lastly it may offer the possibility to be translated to the clinic. This study addresses whether SPECT/CT imaging can be used to visualise the migratory pattern of Tregs in vivo. Treg lines derived from CD4+CD25+FoxP3+ cells were retrovirally transduced with a construct encoding for the human Sodium Iodide Symporter (NIS) and the fluorescent protein mCherry and stimulated with autologous DCs. NIS expressing self-specific Tregs were specifically radiolabelled in vitro with Technetium-99m pertechnetate (99mTcO4−) and exposure of these cells to radioactivity did not affect cell viability, phenotype or function. In addition adoptively transferred Treg-NIS cells were imaged in vivo in C57BL/6 (BL/6) mice by SPECT/CT using 99mTcO4−. After 24 hours NIS expressing Tregs were observed in the spleen and their localisation was further confirmed by organ biodistribution studies and flow cytometry analysis. The data presented here suggests that SPECT/CT imaging can be utilised in preclinical imaging studies of adoptively transferred Tregs without affecting Treg function and viability thereby allowing longitudinal studies within disease models

Breaking the waves: improved detection of copy number variation from microarray-based comparative genomic hybridization.

BACKGROUND: Large-scale high throughput studies using microarray technology have established that copy number variation (CNV) throughout the genome is more frequent than previously thought. Such variation is known to play an important role in the presence and development of phenotypes such as HIV-1 infection and Alzheimer's disease. However, methods for analyzing the complex data produced and identifying regions of CNV are still being refined. RESULTS: We describe the presence of a genome-wide technical artifact, spatial autocorrelation or 'wave', which occurs in a large dataset used to determine the location of CNV across the genome. By removing this artifact we are able to obtain both a more biologically meaningful clustering of the data and an increase in the number of CNVs identified by current calling methods without a major increase in the number of false positives detected. Moreover, removing this artifact is critical for the development of a novel model-based CNV calling algorithm - CNVmix - that uses cross-sample information to identify regions of the genome where CNVs occur. For regions of CNV that are identified by both CNVmix and current methods, we demonstrate that CNVmix is better able to categorize samples into groups that represent copy number gains or losses. CONCLUSION: Removing artifactual 'waves' (which appear to be a general feature of array comparative genomic hybridization (aCGH) datasets) and using cross-sample information when identifying CNVs enables more biological information to be extracted from aCGH experiments designed to investigate copy number variation in normal individuals.RIGHTS : This article is licensed under the BioMed Central licence at http://www.biomedcentral.com/about/license which is similar to the 'Creative Commons Attribution Licence'. In brief you may : copy, distribute, and display the work; make derivative works; or make commercial use of the work - under the following conditions: the original author must be given credit; for any reuse or distribution, it must be made clear to others what the license terms of this work are

Fixation and Spread of Somatic Mutations in Adult Human Colonic Epithelium.

We investigated the means and timing by which mutations become fixed in the human colonic epithelium by visualizing somatic clones and mathematical inference. Fixation requires two sequential steps. First, one of approximately seven active stem cells residing within each colonic crypt has to be mutated. Second, the mutated stem cell has to replace neighbors to populate the entire crypt in a process that takes several years. Subsequent clonal expansion due to crypt fission is infrequent for neutral mutations (around 0.7% of all crypts undergo fission in a single year). Pro-oncogenic mutations subvert both stem cell replacement to accelerate fixation and clonal expansion by crypt fission to achieve high mutant allele frequencies with age. The benchmarking of these behaviors allows the advantage associated with different gene-specific mutations to be compared irrespective of the cellular mechanisms by which they are conferred

Bayesian model comparison with un-normalised likelihoods

Models for which the likelihood function can be evaluated only up to a parameter-dependent unknown normalizing constant, such as Markov random field models, are used widely in computer science, statistical physics, spatial statistics, and network analysis. However, Bayesian analysis of these models using standard Monte Carlo methods is not possible due to the intractability of their likelihood functions. Several methods that permit exact, or close to exact, simulation from the posterior distribution have recently been developed. However, estimating the evidence and Bayes’ factors for these models remains challenging in general. This paper describes new random weight importance sampling and sequential Monte Carlo methods for estimating BFs that use simulation to circumvent the evaluation of the intractable likelihood, and compares them to existing methods. In some cases we observe an advantage in the use of biased weight estimates. An initial investigation into the theoretical and empirical properties of this class of methods is presented. Some support for the use of biased estimates is presented, but we advocate caution in the use of such estimates

Contributions to Drug Resistance in Glioblastoma Derived from Malignant Cells in the Sub-Ependymal Zone

Glioblastoma (GB), the most common and aggressive adult brain tumor, is characterized by extreme phenotypic diversity and treatment failure. Through fluorescence-guided resection, we identified fluorescent tissue in the sub-ependymal zone (SEZ) of GB patients. Histological analysis and genomic characterization revealed that the SEZ harbors malignant cells with tumor-initiating capacity, analogous to cells isolated from the fluorescent tumor mass (T). We observed resistance to supra-maximal chemotherapy doses along with differential patterns of drug response between T and SEZ in the same tumor. Our results reveal novel insights into GB growth dynamics, with implications for understanding and limiting treatment resistance

Predicting how many animals will be where: how to build, calibrate and evaluate individual-based models

Individual-based models (IBMs) can simulate the actions of individual animals as they interact with one another and the landscape in which they live. When used in spatially-explicit landscapes IBMs can show how populations change over time in response to management actions. For instance, IBMs are being used to design strategies of conservation and of the exploitation of fisheries, and for assessing the effects on populations of major construction projects and of novel agricultural chemicals. In such real world contexts, it becomes especially important to build IBMs in a principled fashion, and to approach calibration and evaluation systematically. We argue that insights from physiological and behavioural ecology offer a recipe for building realistic models, and that Approximate Bayesian Computation (ABC) is a promising technique for the calibration and evaluation of IBMs. IBMs are constructed primarily from knowledge about individuals. In ecological applications the relevant knowledge is found in physiological and behavioural ecology, and we approach these from an evolutionary perspective by taking into account how physiological and behavioural processes contribute to life histories, and how those life histories evolve. Evolutionary life history theory shows that, other things being equal, organisms should grow to sexual maturity as fast as possible, and then reproduce as fast as possible, while minimising per capita death rate. Physiological and behavioural ecology are largely built on these principles together with the laws of conservation of matter and energy. To complete construction of an IBM information is also needed on the effects of competitors, conspecifics and food scarcity; the maximum rates of ingestion, growth and reproduction, and life-history parameters. Using this knowledge about physiological and behavioural processes provides a principled way to build IBMs, but model parameters vary between species and are often difficult to measure. A common solution is to manually compare model outputs with observations from real landscapes and so to obtain parameters which produce acceptable fits of model to data. However, this procedure can be convoluted and lead to over-calibrated and thus inflexible models. Many formal statistical techniques are unsuitable for use with IBMs, but we argue that ABC offers a potential way forward. It can be used to calibrate and compare complex stochastic models and to assess the uncertainty in their predictions. We describe methods used to implement ABC in an accessible way and illustrate them with examples and discussion of recent studies. Although much progress has been made, theoretical issues remain, and some of these are outlined and discussed