Encoding of low-quality DNA profiles as genotype probability matrices for improved profile comparisons, relatedness evaluation and database searches

Many DNA profiles recovered from crime scene samples are of a quality that does not allow them to be searched against, nor entered into, databases. We propose a method for the comparison of profiles arising from two DNA samples, one or both of which can have multiple donors and be affected by low DNA template or degraded DNA. We compute likelihood ratios to evaluate the hypothesis that the two samples have a common DNA donor, and hypotheses specifying the relatedness of two donors. Our method uses a probability distribution for the genotype of the donor of interest in each sample. This distribution can be obtained from a statistical model, or we can exploit the ability of trained human experts to assess genotype probabilities, thus extracting much information that would be discarded by standard interpretation rules. Our method is compatible with established methods in simple settings, but is more widely applicable and can make better use of information than many current methods for the analysis of mixed-source, low-template DNA profiles. It can accommodate uncertainty arising from relatedness instead of or in addition to uncertainty arising from noisy genotyping. We describe a computer program GPMDNA, available under an open source license, to calculate LRs using the method presented in this paper.Comment: 28 pages. Accepted for publication 2-Sep-2016 - Forensic Science International: Genetic

Verifying likelihoods for low template DNA profiles using multiple replicates

AbstractTo date there is no generally accepted method to test the validity of algorithms used to compute likelihood ratios (LR) evaluating forensic DNA profiles from low-template and/or degraded samples. An upper bound on the LR is provided by the inverse of the match probability, which is the usual measure of weight of evidence for standard DNA profiles not subject to the stochastic effects that are the hallmark of low-template profiles. However, even for low-template profiles the LR in favour of a true prosecution hypothesis should approach this bound as the number of profiling replicates increases, provided that the queried contributor is the major contributor. Moreover, for sufficiently many replicates the standard LR for mixtures is often surpassed by the low-template LR. It follows that multiple LTDNA replicates can provide stronger evidence for a contributor to a mixture than a standard analysis of a good-quality profile. Here, we examine the performance of the likeLTD software for up to eight replicate profiling runs. We consider simulated and laboratory-generated replicates as well as resampling replicates from a real crime case. We show that LRs generated by likeLTD usually do exceed the mixture LR given sufficient replicates, are bounded above by the inverse match probability and do approach this bound closely when this is expected. We also show good performance of likeLTD even when a large majority of alleles are designated as uncertain, and suggest that there can be advantages to using different profiling sensitivities for different replicates. Overall, our results support both the validity of the underlying mathematical model and its correct implementation in the likeLTD software

Diffusional Relaxation in Random Sequential Deposition

The effect of diffusional relaxation on the random sequential deposition process is studied in the limit of fast deposition. Expression for the coverage as a function of time are analytically derived for both the short-time and long-time regimes. These results are tested and compared with numerical simulations.Comment: 9 pages + 2 figure

Model of Cluster Growth and Phase Separation: Exact Results in One Dimension

We present exact results for a lattice model of cluster growth in 1D. The growth mechanism involves interface hopping and pairwise annihilation supplemented by spontaneous creation of the stable-phase, +1, regions by overturning the unstable-phase, -1, spins with probability p. For cluster coarsening at phase coexistence, p=0, the conventional structure-factor scaling applies. In this limit our model falls in the class of diffusion-limited reactions A+A->inert. The +1 cluster size grows diffusively, ~t**(1/2), and the two-point correlation function obeys scaling. However, for p>0, i.e., for the dynamics of formation of stable phase from unstable phase, we find that structure-factor scaling breaks down; the length scale associated with the size of the growing +1 clusters reflects only the short-distance properties of the two-point correlations.Comment: 12 page

Tight Clustering of Extracellular BP180 Epitopes Recognized by Bullous Pemphigoid Autoantibodies

Bullous pemphigoid is a blistering skin disease associated with autoantibodies against the BP180 antigen, a transmembrane component of the hemidesmosome. Anti-BP180 antibodies have been demonstrated to be pathogenic in a passive transfer mouse model. One extracellular site on human BP180 (MCW-1) was previously shown to be recognized by 50–60% of bullous pemphigoid sera. To facilitate the identification of additional autoantibody-reactive epitopes, recombinant forms of the BP180 ectodomain were generated using both bacterial and mammalian expression systems. One recombinant protein, sec180e, that was expressed in COS-1 cells and that contained the entire BP180 ectodomain, provided us with a tool to detect conformational epitopes. Bullous pemphigoid sera immuno-adsorbed against the major noncollagenous NC16A domain no longer reacted with sec180e, indicating that autoantibody reactivity to the BP180 ectodomain is restricted to the NC16A region. Immunoblot analysis of bullous pemphigoid sera immunoadsorbed with a series of recombinant NC16A peptides revealed the presence of three novel autoantigenic sites that, along with the MCW-1 epitope, are clustered within the N-terminal 45 amino acid stretch of NC16A. All 15 bullous pemphigoid sera tested reacted with a recombinant protein containing this BP180 segment. No disease-associated epitopes were detectable within the remaining 28 amino acids of NC16A. Thus, bullous pemphigoid patient autoantibodies react with a set of epitopes on the BP180 ectodomain that are highly clustered. This autoantibody-reactive region on human BP180 shows overlap with the corresponding murine BP180 site that is targeted by antibodies that are pathogenic in the mouse model of bullous pemphigoid. These findings suggest new directions for the development of diagnostic and therapeutic tools for this disease

Accurate Liability Estimation Improves Power in Ascertained Case Control Studies

Linear mixed models (LMMs) have emerged as the method of choice for confounded genome-wide association studies. However, the performance of LMMs in non-randomly ascertained case-control studies deteriorates with increasing sample size. We propose a framework called LEAP (Liability Estimator As a Phenotype, https://github.com/omerwe/LEAP) that tests for association with estimated latent values corresponding to severity of phenotype, and demonstrate that this can lead to a substantial power increase

Group testing with Random Pools: Phase Transitions and Optimal Strategy

The problem of Group Testing is to identify defective items out of a set of objects by means of pool queries of the form "Does the pool contain at least a defective?". The aim is of course to perform detection with the fewest possible queries, a problem which has relevant practical applications in different fields including molecular biology and computer science. Here we study GT in the probabilistic setting focusing on the regime of small defective probability and large number of objects, $p \to 0$ and $N \to \infty$. We construct and analyze one-stage algorithms for which we establish the occurrence of a non-detection/detection phase transition resulting in a sharp threshold, $\bar M$, for the number of tests. By optimizing the pool design we construct algorithms whose detection threshold follows the optimal scaling $\bar M\propto Np|\log p|$. Then we consider two-stages algorithms and analyze their performance for different choices of the first stage pools. In particular, via a proper random choice of the pools, we construct algorithms which attain the optimal value (previously determined in Ref. [16]) for the mean number of tests required for complete detection. We finally discuss the optimal pool design in the case of finite $p$

A renormalization group study of a class of reaction-diffusion model, with particles input

We study a class of reaction-diffusion model extrapolating continuously between the pure coagulation-diffusion case ($A+A\to A$) and the pure annihilation-diffusion one ($A+A\to\emptyset$) with particles input ($\emptyset\to A$) at a rate $J$. For dimension $d\leq 2$, the dynamics strongly depends on the fluctuations while, for $d >2$, the behaviour is mean-field like. The models are mapped onto a field theory which properties are studied in a renormalization group approach. Simple relations are found between the time-dependent correlation functions of the different models of the class. For the pure coagulation-diffusion model the time-dependent density is found to be of the form $c(t,J,D) = (J/D)^{1/\delta}{\cal F}[(J/D)^{\Delta} Dt]$, where $D$ is the diffusion constant. The critical exponent $\delta$ and $\Delta$ are computed to all orders in $\epsilon=2-d$, where $d$ is the dimension of the system, while the scaling function $\cal F$ is computed to second order in $\epsilon$. For the one-dimensional case an exact analytical solution is provided which predictions are compared with the results of the renormalization group approach for $\epsilon=1$.Comment: Ten pages, using Latex and IOP macro. Two latex figures. Submitted to Journal of Physics A. Also available at http://mykonos.unige.ch/~rey/publi.htm