A mathematical theory of stochastic microlensing. II. Random images, shear, and the Kac-Rice formula

Continuing our development of a mathematical theory of stochastic microlensing, we study the random shear and expected number of random lensed images of different types. In particular, we characterize the first three leading terms in the asymptotic expression of the joint probability density function (pdf) of the random shear tensor due to point masses in the limit of an infinite number of stars. Up to this order, the pdf depends on the magnitude of the shear tensor, the optical depth, and the mean number of stars through a combination of radial position and the star's mass. As a consequence, the pdf's of the shear components are seen to converge, in the limit of an infinite number of stars, to shifted Cauchy distributions, which shows that the shear components have heavy tails in that limit. The asymptotic pdf of the shear magnitude in the limit of an infinite number of stars is also presented. All the results on the random microlensing shear are given for a general point in the lens plane. Extending to the general random distributions (not necessarily uniform) of the lenses, we employ the Kac-Rice formula and Morse theory to deduce general formulas for the expected total number of images and the expected number of saddle images. We further generalize these results by considering random sources defined on a countable compact covering of the light source plane. This is done to introduce the notion of global expected number of positive parity images due to a general lensing map. Applying the result to microlensing, we calculate the asymptotic global expected number of minimum images in the limit of an infinite number of stars, where the stars are uniformly distributed. This global expectation is bounded, while the global expected number of images and the global expected number of saddle images diverge as the order of the number of stars. © 2009 American Institute of Physics.

Detecting separate time scales in genetic expression data.

BACKGROUND: Biological processes occur on a vast range of time scales, and many of them occur concurrently. As a result, system-wide measurements of gene expression have the potential to capture many of these processes simultaneously. The challenge however, is to separate these processes and time scales in the data. In many cases the number of processes and their time scales is unknown. This issue is particularly relevant to developmental biologists, who are interested in processes such as growth, segmentation and differentiation, which can all take place simultaneously, but on different time scales. RESULTS: We introduce a flexible and statistically rigorous method for detecting different time scales in time-series gene expression data, by identifying expression patterns that are temporally shifted between replicate datasets. We apply our approach to a Saccharomyces cerevisiae cell-cycle dataset and an Arabidopsis thaliana root developmental dataset. In both datasets our method successfully detects processes operating on several different time scales. Furthermore we show that many of these time scales can be associated with particular biological functions. CONCLUSIONS: The spatiotemporal modules identified by our method suggest the presence of multiple biological processes, acting at distinct time scales in both the Arabidopsis root and yeast. Using similar large-scale expression datasets, the identification of biological processes acting at multiple time scales in many organisms is now possible.

A dimensionless number for understanding the evolutionary dynamics of antigenically variable RNA viruses.

Antigenically variable RNA viruses are significant contributors to the burden of infectious disease worldwide. One reason for their ubiquity is their ability to escape herd immunity through rapid antigenic evolution and thereby to reinfect previously infected hosts. However, the ways in which these viruses evolve antigenically are highly diverse. Some have only limited diversity in the long-run, with every emergence of a new antigenic variant coupled with a replacement of the older variant. Other viruses rapidly accumulate antigenic diversity over time. Others still exhibit dynamics that can be considered evolutionary intermediates between these two extremes. Here, we present a theoretical framework that aims to understand these differences in evolutionary patterns by considering a virus's epidemiological dynamics in a given host population. Our framework, based on a dimensionless number, probabilistically anticipates patterns of viral antigenic diversification and thereby quantifies a virus's evolutionary potential. It is therefore similar in spirit to the basic reproduction number, the well-known dimensionless number which quantifies a pathogen's reproductive potential. We further outline how our theoretical framework can be applied to empirical viral systems, using influenza A/H3N2 as a case study. We end with predictions of our framework and work that remains to be done to further integrate viral evolutionary dynamics with disease ecology.

Radioactive in situ hybridization for detecting diverse gene expression patterns in tissue.

Knowing the timing, level, cellular localization, and cell type that a gene is expressed in contributes to our understanding of the function of the gene. Each of these features can be accomplished with in situ hybridization to mRNAs within cells. Here we present a radioactive in situ hybridization method modified from Clayton et al. (1988)(1) that has been working successfully in our lab for many years, especially for adult vertebrate brains(2-5). The long complementary RNA (cRNA) probes to the target sequence allows for detection of low abundance transcripts(6,7). Incorporation of radioactive nucleotides into the cRNA probes allows for further detection sensitivity of low abundance transcripts and quantitative analyses, either by light sensitive x-ray film or emulsion coated over the tissue. These detection methods provide a long-term record of target gene expression. Compared with non-radioactive probe methods, such as DIG-labeling, the radioactive probe hybridization method does not require multiple amplification steps using HRP-antibodies and/or TSA kit to detect low abundance transcripts. Therefore, this method provides a linear relation between signal intensity and targeted mRNA amounts for quantitative analysis. It allows processing 100-200 slides simultaneously. It works well for different developmental stages of embryos. Most developmental studies of gene expression use whole embryos and non-radioactive approaches(8,9), in part because embryonic tissue is more fragile than adult tissue, with less cohesion between cells, making it difficult to see boundaries between cell populations with tissue sections. In contrast, our radioactive approach, due to the larger range of sensitivity, is able to obtain higher contrast in resolution of gene expression between tissue regions, making it easier to see boundaries between populations. Using this method, researchers could reveal the possible significance of a newly identified gene, and further predict the function of the gene of interest.

Infection of monkeys by simian-human immunodeficiency viruses with transmitted/founder clade C HIV-1 envelopes.

Simian-human immunodeficiency viruses (SHIVs) that mirror natural transmitted/founder (T/F) viruses in man are needed for evaluation of HIV-1 vaccine candidates in nonhuman primates. Currently available SHIVs contain HIV-1 env genes from chronically-infected individuals and do not reflect the characteristics of biologically relevant HIV-1 strains that mediate human transmission. We chose to develop clade C SHIVs, as clade C is the major infecting subtype of HIV-1 in the world. We constructed 10 clade C SHIVs expressing Env proteins from T/F viruses. Three of these ten clade C SHIVs (SHIV KB9 C3, SHIV KB9 C4 and SHIV KB9 C5) replicated in naïve rhesus monkeys. These three SHIVs are mucosally transmissible and are neutralized by sCD4 and several HIV-1 broadly neutralizing antibodies. However, like natural T/F viruses, they exhibit low Env reactivity and a Tier 2 neutralization sensitivity. Of note, none of the clade C T/F SHIVs elicited detectable autologous neutralizing antibodies in the infected monkeys, even though antibodies that neutralized a heterologous Tier 1 HIV-1 were generated. Challenge with these three new clade C SHIVs will provide biologically relevant tests for vaccine protection in rhesus macaques.

Human Non-neutralizing HIV-1 Envelope Monoclonal Antibodies Limit the Number of Founder Viruses during SHIV Mucosal Infection in Rhesus Macaques.

HIV-1 mucosal transmission begins with virus or virus-infected cells moving through mucus across mucosal epithelium to infect CD4+ T cells. Although broadly neutralizing antibodies (bnAbs) are the type of HIV-1 antibodies that are most likely protective, they are not induced with current vaccine candidates. In contrast, antibodies that do not neutralize primary HIV-1 strains in the TZM-bl infection assay are readily induced by current vaccine candidates and have also been implicated as secondary correlates of decreased HIV-1 risk in the RV144 vaccine efficacy trial. Here, we have studied the capacity of anti-Env monoclonal antibodies (mAbs) against either the immunodominant region of gp41 (7B2 IgG1), the first constant region of gp120 (A32 IgG1), or the third variable loop (V3) of gp120 (CH22 IgG1) to modulate in vivo rectal mucosal transmission of a high-dose simian-human immunodeficiency virus (SHIV-BaL) in rhesus macaques. 7B2 IgG1 or A32 IgG1, each containing mutations to enhance Fc function, was administered passively to rhesus macaques but afforded no protection against productive clinical infection while the positive control antibody CH22 IgG1 prevented infection in 4 of 6 animals. Enumeration of transmitted/founder (T/F) viruses revealed that passive infusion of each of the three antibodies significantly reduced the number of T/F genomes. Thus, some antibodies that bind HIV-1 Env but fail to neutralize virus in traditional neutralization assays may limit the number of T/F viruses involved in transmission without leading to enhancement of viral infection. For one of these mAbs, gp41 mAb 7B2, we provide the first co-crystal structure in complex with a common cyclical loop motif demonstrated to be critical for infection by other retroviruses.

Plasma miRNAs as early biomarkers for detecting hepatocellular carcinoma.

The early detection of hepatocellular carcinoma (HCC) presents a challenge because of the lack of specific biomarkers. Serum/plasma microRNAs (miRNAs) can discriminate HCC patients from controls. We aimed to identify and evaluate HCC-associated plasma miRNAs originating from the liver as early biomarkers for detecting HCC. In this multicenter three-phase study, we first performed screening using both plasma (HCC before and after liver transplantation or liver hepatectomy) and tissue samples (HCC, para-carcinoma and cirrhotic tissues). Then, we evaluated the diagnostic potential of the miRNAs in two case-control studies (training and validation sets). Finally, we used two prospective cohorts to test the potential of the identified miRNAs for the early detection of HCC. During the screening phase, we identified ten miRNAs, eight of which (miR-20a-5p, miR-25-3p, miR-30a-5p, miR-92a-3p, miR-132-3p, miR-185-5p, miR-320a and miR-324-3p) were significantly overexpressed in the HBV-positive HCC patients compared with the HBV-positive cancer-free controls in both the training and validation sets, with a sensitivity of 0.866 and specificity of 0.646. Furthermore, we assessed the potential for early HCC detection of these eight newly identified miRNAs and three previously reported miRNAs (miR-192-5p, miR-21-5p and miR-375) in two prospective cohorts. Our meta-analysis revealed that four miRNAs (miR-20a-5p, miR-320a, miR-324-3p and miR-375) could be used as preclinical biomarkers (pmeta  < 0.05) for HCC. The expression profile of the eight-miRNA panel can be used to discriminate HCC patients from cancer-free controls, and the four-miRNA panel (alone or combined with AFP) could be a blood-based early detection biomarker for HCC screening.